Research ArticleDesign of Joint Spatial and Power Domain Multiplexing Schemefor Massive MIMO Systems
Zheng Jiang Bin Han Peng Chen Fengyi Yang and Qi Bi
Technology Innovation Center China Telecom Corporation Limited China Telecom Beijing Information Science andTechnology Innovation Park Southern Zone of Future Science and Technology City Beiqijia Changping Beijing 102209 China
Correspondence should be addressed to Zheng Jiang jiangzhctbricomcn
Received 14 August 2015 Accepted 15 October 2015
Academic Editor Wei Xiang
Copyright copy 2015 Zheng Jiang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Massive Multiple-Input Multiple-Output (MIMO) is one of the key techniques in 5th generation wireless systems (5G) due toits potential ability to improve spectral efficiency Most of the existing works on massive MIMO only consider Time DivisionDuplex (TDD) operation that relies on channel reciprocity between uplink and downlink channels For Frequency Division Duplex(FDD) systems with continued efforts some downlinkmultiuserMIMO schemewas recently proposed in order to enable ldquomassiveMIMOrdquo gains and simplified system operations with limited number of radio frequency (RF) chains in FDD system However theseschemes such as Joint Spatial Division and Multiplexing (JSDM) scheme and hybrid precoding scheme only focus on multiusertransmission in spatial domain Different frommost of the existing works this paper proposes Joint Spatial and PowerMultiplexing(JSPM) scheme in FDD systems It extends existing FDD schemes from spatial division andmultiplexing to joint spatial and powerdomain to achieve more multiplexing gain The user grouping and scheduling scheme of JSPM is studied and the asymptoticexpression for the sum capacity is derived as well Finally simulations are conducted to illustrate the effectiveness of the proposedscheme
1 Introduction
With increasing popularity of smart phones pads andtablet computers mobile data traffic is experiencing unprece-dented growth Mobile broadband networks need to supportexplosively growing consumer data rate demands and needto tackle the exponential increase in the predicted trafficvolumes An efficient radio access technology combined withhigher spectrum efficiency is essential to achieve the growingdemands faced by wireless carriers Massive MIMO is oneof the core technologies expected to be adopted by thenext generations of wireless communication systems WithmassiveMIMO plenty of user equipment (UE) can be servedsimultaneously by the system with the antenna array of a fewhundred antennas on the same time-frequency resource [1 2]
Massive MIMO relies on spatial multiplexing to makeadvantages over conventional passive antenna system whichneeds the base station (BS) to have accurate channel knowl-edge on both the uplink and the downlink On the uplink it iseasy to accomplish this by letting theUE send pilots based on
which BS estimates the channel responses to the UE On thedownlink in conventionalMIMOsystems such as LongTermEvolution (LTE) system BS sends cell reference signals (CRS)orand Channel State Information Reference Signals (CSI-RS) based on which UE estimates the channel responsesquantizes the obtained channel estimates and feeds themback to the BS Since the amount of time-frequency resourcesneeded for downlink reference signals is proportional to thenumber of antennas and the amount of uplink channel stateinformation (CSI) feedback resources is proportional to thenumber of active users a massive MIMO systemmay requireup to tens of times more resources than a conventionalsystem Due to this the massive MIMO is more likely to beapplied in TDD systems which rely on reciprocity betweenthe uplink and downlink channels [3ndash5]
On the other hand considerable effort has been ded-icated to study the implementation of massive MIMO inFDD systems with various practical constraints includingnonideal CSI at the transmitter [6] the overhead incurredby downlink channel probing and CSI feedback [7 8] Joint
Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2015 Article ID 368463 10 pageshttpdxdoiorg1011552015368463
2 International Journal of Antennas and Propagation
Spatial Division and Multiplexing (JSDM) was proposed in[9ndash11] to enable massive MIMO gains for FDD systemsMeanwhile as large bandwidth is available atmillimeter wave(mmWave) frequencies to provide gigabit-per-second datarates the hybrid analogdigital processing strategies wereproposed in [12ndash15] for mmWave systems with large antennaarrays
The downlink beamforming of both JSDM and hybridprecoding scheme includes two stages that is a prebeam-forming stage that depends on UErsquos channel covariance and aMU-MIMO precoding stage for the effective channel formedby the first stage The prebeamforming matrix is chosen inorder to minimize the interference across different spatialgroups and the MU-MIMO precoding matrix takes care ofthe multiuser interference within each group
Both of these beamforming stages achieve multiplexinggain in spatial domain It is well-known that the maximumspatial multiplexing gain is limited by the number of trans-mitting and receiving antennas in massive MIMO systems[16] Thus more multiplexing gain is achieved in the firstprebeamforming stage the less multiplexing gain is achievedin the second MU-MIMO stage In order to achieve moremultiplexing gain in theMU-MIMOstage the power domainis introduced in spatial multiplexing transmission schemeand the joint spatial and power multiplexing (JSPM) schemefor massive MIMO system is proposed in this paper Theproposed scheme not only relaxes the full channel knowledgeto achieve the spatial multiplexing gain by using the channelsecond order statistics but also applies multiuser powerallocation transmission at BS side and successive interferencecanceller (SIC) on UE side to achieve the power-domainuser multiplexing gain The performance of the proposedJSPM scheme is illustrated by simulations and comparedwith that of JSDM The results show that even with the fixedspatial quantization and simplified transmit power allocationgrouping scheme the proposed scheme outperforms JSDMbecause of the additional power-domain multiplexing gain
The remainder of this paper is organized as followsSection 2 describes the overall system model and the keyfunctionalities utilized to introduce JSPM The asymptoticexpression of JSPM is derived Section 3 discusses the schemeof the user spatial grouping and multiuser power-domainparing Furthermore the computational complexity of JSPMscheme is discussed In Section 4 the system-level simulationconfiguration is described and the results of the system-levelperformance of JSPM in comparison to JSDM are providedFinally Section 5 concludes the paper
2 System Model
In this section we consider the downlink communication ofa massiveMIMO system as shown in Figure 1 where the basestation (BS) is equipped with 119873
119905transmit antennas under
the total transmit power constraint of 119875 and serving119880 signalantenna UE
We assume that H = [h1 h
119906 h
119880] is the 119873
119905times 119880
dimensional matrix that represents the channel between theBS and UE h
119906is the119873t times 1 dimensional channel realization
between the BS and user 119906
BS
BG 3UE 1
UE 2
UE 4
UE 3UE 5
BG 1
BG 2BG 4
BG 5
UE 4
PG 1
PG 2
Figure 1 A massive MIMO BS to serve randomly located UE
The system received signal is denoted as
y = H119867x + n (1)
where y denotes the collection of received symbols for all the119880 users x = Td is the transmitted signal vector of dimensions119873119905times 1 T = BVP is the downlink beamforming matrix
consisting of three parts B is the prebeamforming matrixof dimensions 119873
119905times 119873119861 which is generated based on the
channel covariance statistics V is the 119873119861times 119873119872
multiuserMIMO precoding matrix which is a function of the reduceddimensional effective channel H = B119867H P is the power-domain multiplexing matrix of dimensions 119873
119872times 119873119878 d
denotes the 119878 times 1 vector of transmitted user data symbolsn sim 119862119873(0 I
119880119896) denotes additive spatially and temporally
white Gaussian noise with zero mean and unit variance As aresult the received signal in (1) can bewritten in the followingmanner
y = H119867BVPd + n = H119867VPd + n (2)
where prebeamforming matrix B makes the channel Hbecome different approximately mutually orthogonal sub-spaces H based on channel statistical characteristic UE canbe partitioned into these subspaces to form several disjointuser groups
If we define119880 users can be partitioned into 119866 groups theoverall119873
Based on [11] H119892 = U119892(Λ119892)12w119892 Then we can makethe effective channel matrixH become an approximate blockdiagonal matrix by designing B119892 = U119892 then (H119892)119867B119894 asymp 0where 119892 1198921015840 isin 1 119866 and 119892 = 119892
1015840 Furthermore the y119892 in(4) can be expressed as
where V119892 and P119892 are the multiuser MIMO precoding matrixand the power-domain multiplexing matrix of user cluster119892 respectively d119892 is the transmitted signal of cluster 119892 andn119892 sim 119862119873(0 I119892) From (5) we can derive that V is the blockdiagonal matrix V = diag(V1 V119866)
The number of downlink data streams of group 119892 isdenoted as 119903119892 which is the effective rank of R119892 and MU-MIMO precoding matrix in group 119892 is simply the identitymatrix that is V119892 = I119903
119892
In order to allocate the downlinkdata streams to the users we select 119903119892 out of users in 119880119892which is the number of users in group 119892 according to a maxSINR criterion as follows
where 119898 = 1 119903119892 119887119892119898119887119892119899is the 119898th and 119899th column of B119892
ℎ119892
119906is the channel response vector of user 119906 in spatial group 119892
and 120588 = 119875sum119866119892=1119903119892
Each user feeds its SINR values and 119898th beam indexcorresponding to this SINR back BS can then identify eachtype of UE by a set of indices 119906 119892119898where indices 119906 119892119898are the user index spatial groupnumberwhich user119906 belongsto and beam index corresponding to SINR119892
119906119898 respectively
In addition to these indices a new index introduced inJSPM to identify UEs is the power-domain group indexwhich can be decided based on RSRP value of UE feedbackand the predefined thresholds For example we can predefineseveral intervals of RSRP as different power groups if a UEfeedback RSRP value is in 119889th RSRP interval the UE isconsidered to belong to power group 119889
For UE with a different power group index 119889 and thesame beam index119898 UE can be paired to use power-domainmultiplexing the presentation is
s119892 = P119892d119892 (7)
where s119892 = [s1198921 s119892
119903119892] is 119903119892 transmission data streams
P119892 with dimensions 119903119892 times 119880119892 is power-domain multiplexingmatrix to multiplex 119880119892 user data into 119903119892 data stream d119892 =[d1198921 d119892
119880119892] is the data vector of 119880119892 users in group 119892
There are two criteria of power-domain multiuser sched-uler as follows
The first is the fact that multiplexing candidate users willbe selected from UE set with the same spatial group index 119892and beam index 119898 but with different power-domain groupindex For example if user 1199061015840 and user 119906 are two selectedusers tomultiuser transmission in power domain theywill beallocated in different power groups such as user 1199061015840 isin 119880119892
1198981198891015840
and user 119906 isin 119880119892119898119889119894
variables 1198891015840 and 119889 are different powergroup indices 119880119892
119898is the user set of spatial group 119892 and beam
119898The second is the multiplexing candidate user that will
maximize the PF scheduling metric as follows
119876119880119892
119898= sum
119906isin119880119892
119898
(119877 (119906)
119877 (119906)
) (8)
where 119876119880119892
119898denotes the PF scheduling metric for power-
domain multiplexing candidate user set 119880119892119898 119877(119906) is the
instantaneous throughput of user 119906 119877(119906) is the averagethroughput of user 119906
We assume that the SIC receiver of user 119906 is able to cancelperfectly and successively the interference from other user119908 with channel gain 119875119892
1199061015840 |(ℎ119892
1199061015840)119867(119887119892
119898)|2gt 119875119892
119906|(ℎ119892
119906)119867(119887119892
119898)|2 119906 isin
119880119892
119898119889 and 1199061015840 isin 119880119892
1198981199061015840 Then SINR of user 119906 can be estimated
where 120583119892119898119895(119909) 119895 = 1 119903
119892are the eigenvalues of 119860119892
119898(119909)
119860119892
119898(119909) = (Λ
119892)12
(119880119892)119867
119887119892
119898(119887119892
119898)119867
119880119892(Λ119892)12
minus 119909(sum
119899 =119898
(Λ119892)12
(119880119892)119867
119887119892
119899(119887119892
119899)119867
119880119892(Λ
g)12
+ sum
1198921015840=119892
(Λ119892)12
(119880119892)119867
1198611198921015840
(1198611198921015840
)
119867
119880119892(Λ119892)12
)
(16)
Without loss of generality we assume the ordering
120583119892
1198981(119909) ge sdot sdot sdot ge 120583
119892
119898119903119892(119909)
120575119889=
119875119892
119906
1 + 119868119892
11990610158401198981198891015840
(17)
The growth function of CDF 119865(119909) with corresponding PDF119891(119909) is
119892 (119909) =1 minus 119865 (119909)
119891 (119909)
119892infin= lim119909rarrinfin
119892 (119909) = 120575119889(120583119892
119898)infin
(18)
where (1205831198921198981)infin
= lim119909rarrinfin
120583119892
1198981(119909) is a bound positive
constant [11]Considering the ideal channel estimation and the fixed
power assignments to users 119868119892119908119898119889
rarr 0 120575119889rarr 119875119892
119889
Then we have119897119892
119898
sum
119889=1
119875119892
119889= 119875119892 (19)
With extreme value theory [11] we have thatmax1le119906le119880
119892SINR119892119906119898119889
which behaves as 120575119889(120583119892
1198981)infin log119880119892 +
119874(log log119880119892) for 119880119892 rarr infin
The sum rate asymptotic formula for a group 119892 is
119877119892=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (120575119889(120583119892
1198981)infin
log (119880119892)) + 119900 (1)
=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (120575119889) +
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
(120583119892
1198981)infin
+
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log log (119880119892) + 119900 (1)
=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (119875119892119889) +
119903119892
sum
119898=1
119897119892
119898log log (119880119892)
+
119903119892
sum
119898=1
119897119892
119898log (120583119892
1198981)infin
+ 119900 (1)
(20)
as 119880119892 rarr infinSumming over 119892 the sum rate asymptotic formula can be
written as
119877sum =119866
sum
119892=1
119897119892
119898
sum
119889=1
119903119892 log (119875
119889) +
119866
sum
119892=1
119871119892 log log (119880119892)
+ 119874 (1)
(21)
With finite 119873119905antennas total transmit power constraint
of 119875 119880119892 users and 119871119892 data streams per group with the equaltransmission power and common covariance R119892 where usershave mutually statistically independent channel vectors for119880119892rarr infin the sum capacity of a MU-MIMO downlink
system is given by
119877sum =119866
sum
119892=1
119871119892 [
[
log log (119880119892) + log( 119875
sum119866
119892=1119871119892)]
]
+ 119874 (1)
(22)
where 119874(1) denotes a constant independent of 119880119892
3 Designs for JSPM in FDD
In the proposed JSPM scheme the downlink transmissionstrategy is designed in the following three parts
(1) Based on cell environment and channel covariancemeasurement BS can split whole channel space intoseveral disjoint subspaces by using prebeamformingmatrix Therefore based on CSI SINR and RSRPvalues feedback from UE that estimates these valuesbased on the subspaces BS can partition its servingUE into several subspace groups with approximatelysimilar channel covariance eigenvectors and channelpath lossThe spatial and power-domain characters ofeach type of UE can be identified by a set of indicesthat is UE index119906 spatial group index119892 beam index119898 power group index 119889
International Journal of Antennas and Propagation 5
(2) For UE marked with different spatial group indicesor the same spatial group index but different beamindices MU-MIMO downlink transmission on thesame time-frequency resource is performed
(3) For UE marked with the same spatial group indexthe same beam index and different power groupindices multiuser power pairing is performed If userpairing succeeds the multiuser power allocation andthe power-domain usermultiplexing transmission areperformed
Among the above the user grouping and multiuserselection in power-domain are two key issues for the systemperformance the following discussion will focus more on thestrategies of these two issues
31 User Grouping As mentioned before in order to exploiteffectively the JSPM approach the usersrsquo population will bepartitioned into groups according to the following qualitativeprinciples (1) users in the same group have channel covari-ance eigenspace spanning (approximately) a given commonsubspace which characterizes the spatial group BS can getthis information by UE CSI SINR and RSRP measurementfeedback (2) the subspaces of spatial groups served on thesame time-frequency slot by JSDM must be (approximately)mutually orthogonal or at least have empty intersection
The fixed quantization algorithm of user grouping in [11]is an effective and low complexity scheme for applicationin practical network In this algorithm the group subspacesare fixed a priori based on the geometry of cell coverageand their channel scattering In our proposed scheme thefixed quantization algorithm in [11] is extended to frequencydomain When we increase the number of fixed quantizationspatial group to reduce coverage holes the overlappingbetween different spatial groups will also increase and causethe strong interference of intergroups In this case we canallocate transmission resource in different frequency bandsdynamically for UE that belongs to adjacent groups in orderto reduce the interference of intergroups
By choosing 119866 AoAs 120579119892 and fixed ASΔ we can definethe 119866 disjoint intervals [120579119892 minus Δ 120579119892 + Δ] This methodconsists essentially to form predefined ldquonarrow sectorsrdquo andassociate users to sectors according to minimum chordaldistance quantization For example suppose 119866 = 3 choosing1205791= minus45
∘ 1205792 = 0∘ and 1205793 = 45
∘ Δ = 15∘ such as
BG1 BG2 and BG3 shown in Figure 1 we note that thethree subspaces are disjoint However as UE is distributeduniformly and these three subspaces are discontinuous someUE cannot be associated with these subspaces exactly suchas UE4 shown in Figure 1 If we define more dense subspacesuch as 119866 = 5 there are five spatial groups such as BG1BG2 BG5 shown in Figure 1 and different subspace willbe overlapping the interference of inter-group will increaseIn this case we can allocate UE that is in the adjacentsubspace to different frequency resources in order to reducethe intergroup interference
In Figure 1 there are five spatial groups in order to avoidintergroup interference BS can separate BG1 BG2 and BG3
groups and BG4 and BG5 groups into different frequencybands
This scheme makes sense especially for mmWave mobilesystems which have huge frequency broadband to be used
32 Multiuser Transmit Power Allocation and Candidate UserSelection Due to power-domain multiuser multiplexing thetransmit power allocation to one user affects the achievablethroughput of not only that user but also the throughput ofother pairing users The best performance of power-domainmultiuser multiplexing is achieved by exhaustive full searchof user pairs and transmission power allocations [18]
In order to reduce further the computational complexitythe scheme of predefined user grouping and pergroup fixedpower allocation can be used With this approach UE isdivided into different user groups according to their channelpath loss and the predefined thresholds In this predefinedpower-domain grouping the users can be paired togetheronly if they belong to different power groups With thepredefined power grouping the power allocation could alsobe simplified by applying fixed power assignments to theusers belonging to the same group For example for theuser group with good channel gain small power (eg 03P)is allocated and for the user group with bad channel gainlarge power (eg 07P) is allocated where the total powerassigned to different user groups is kept equal to P Predefineduser grouping and fixed power allocation can effectivelydecrease the amount of downlink signaling related toUE datadetection For example the order of successive interferencecancellation (SIC) and information on power assignment donot need to be transmitted in every subframe but rather on alarger time scale
For example as shown in Figure 2 there are two spatialgroups BG1 and BG2 and two power groups PG1 and PG2UE1 belongs to BG1 and PG1 and UE2 and UE3 belong toBG1 and BG2 respectively but both belong to PG2 As forthe aforementioned spatial and power-domain multiplexingstrategies UE3 can be paired with UE1 and UE2 in the spatialdomain and be applied to MU-MIMO transmission UE1can be paired with UE2 in power domain as it belongs tosame spatial group but different power groups and it can beapplied to multiuser power multiplexing transmission UE1can perform SIC operation to cancel the interference fromUE2
33 Computational Complexity Discussion As multiusertransmission of power domain introduced in JSPM will leadto additional algorithm implementation complexity we willdiscuss the computational complexity of JSPM in comparisonwith the exiting JSDM scheme in this section The additionalimplementation complexity of JSDM is composed of threeparts the first part is multiuser selection and pairing inpower domain in BS side the second part is multiplexingtransmission processing in power domain in BS side and thethird part is SIC processing in UE side The first two partsincrease the implementation complexity of BS side and thelast part increases the complexity of UE side
In order to simplify complexity analysis we assume thatUE in power domain is separated into two groups that is cell
6 International Journal of Antennas and Propagation
Numbers of complex numberaddition and multiplication JSDM JSPM with fix power
user paring algorithmJSPM with power domain
greedy algorithmPrebeamforming 119866 times 119874 (119873
119905
3) + 119866 times 119880
119892times119872119892
119861times 119873119905
Multiuser precoding 119866 times 119874((119880119892)3
) + 119866 times 119880119892times 119903119892times119872119892
119861
Power domain user paring 119880119892
119898119889times 119880119892
1198981198891015840times 119866 times 119874 ((119903
119892)2
) 1198622
(119880119892
119898119889+119880119892
1198981198891015840)times 119866 times 119874((119903
119892)2
)
Power domain multiplexing 119880119892times 119903119892times 119866 119880
119892times 119903119892times 119866
center user group and cell edge user group numbers of thetwo groups of UE are noted as 119880119892
119898119889and 119880119892
1198981198891015840 respectively
The computational complexity of JSPM and JSDM in BS sideis presented in Table 1
FromTable 1 we can see that although the power-domainmultiplexing transmission of JSPM leads to computationalcomplexity increase the added complexity accounts fora small part of the overall JSPM complexity The maincomputational complexity comes from the singular valuedecomposition (SVD) processing of channel matrix H =
[H1 sdot sdot sdot H119866] with 119874(119873119905
3) computational complexity in
multiuser beamforming procedure Therefore the extra com-plexity introduced by adopting JSPM has very limited impacton the overall system implementation
From computational complexity listed in Table 1 we cansee that the approach of predefined user grouping and per-group fixed power allocation has more less computationalcomplexity compared with greedy algorithm with the costof little performance degradation which we will discuss inSection 4
For UE side the detection complexity of cell center UEwill not change the detection complexity of cell edge UE willbe double because for cell edge UE they will firstly detectthe information of cell center pairing UE and subtract itfrom receiving signals and then detect its own informationHowever 3GPPRAN4has finished SIC performance require-ment in 3GPP TS36101 [19] which means that Rel12 UE
has enough capability to fulfill the detection performancerequirement of JSPM
4 Performance Evaluation and Analysis
41 Validation of the Asymptotic Analysis In this section wecompare the results obtained via the method of deterministicequivalents withMonte Carlo simulations in order to validatethe asymptotic analysis in Section 2
In our discussion BS is equipped with a uniform circulararray with 100 isotropic antenna elements the distancebetween antenna elements equals 1205822 where 120582 is the carrierwavelength As the user mutual statistical independent chan-nel is important for analytical results the one-ring channelmodel [11] is adopted Users form 119866 = 6 symmetric spatialgroups with the angular spread (AS)Δ = 15
We fixed to serve 119903119892 = 5 data streams per spatial group sothat the total number of active users is 30 119897119892
119898is fixed to equal
2 SNR = P with the noise unit variance normalizationThe comparison of sum spectrum efficiencies of JSPM
obtained by using deterministic equivalent approximationand simulations is illustrated in Figure 3 The green solidline with ldquosquaresrdquo is obtained using the JSPM correspondingdeterministic equivalent approximation the red solid linewith ldquo119909rdquo is obtained through JSPM simulation and the bluesolid line with ldquo119900rdquo is obtained through JSDM simulation
International Journal of Antennas and Propagation 7
JSPM analyticalJSPM simJSDM sim
0
50
100
150
200
250
Sum
rate
(bps
Hz)
5 10 150SNR (dB)
Figure 3 Comparison of sum spectrum efficiencies
For multiuser spatial transmission simulation the approachof ZF beam-forming (ZFBF) and joint group processing(JGP) is used For multiuser transmission of power-domainsimulation the predefined user grouping and per-group fixedpower allocation scheme in power-domain is applied
As shown in Figure 3 the trend of JSPM simulationresult is coincided with that of JSPM deterministic equivalentapproximation Furthermore simulation results show that theperformance of JSPM outperforms JSDM
42 JSPM Performance Gain In this section we presentsystem-level simulation results of the investigation on theperformance gains of JSPM in LTE system In our simulationa multicell system-level simulation is conducted and a 19-hexagonal macro cell model with 3 cells per cell site isemployedThedetails of the simulation assumptions are listedin Table 2
BS is equippedwith antenna array of 8times8X-pol elementsas shown in Figure 4 For the simulation there are 2 verticalprebeamforming groups by using prebeamforming matrix Bcolumns of which can be 4-element DFT weight the highbeam group is tilted to 80 degrees and the low beam groupis tilted to 100 degrees Therefore UE in serving cell canbe partitioned into two vertical spatial groups by BS basedon UE RSRP measurement and feedback responding to twovertical antenna ports each vertical antenna port is mappedto four vertical rows of antenna elements with one polardirection such as +45∘ polar as shown in Figure 4 Then BScan apply MU-MIMO transmission for UE in each verticalgroup by usingmatrixV MatrixV can be composed with UEfeedback precodingmatrix index for eight horizontal antennaports UE gets the horizontal channel spatial information bymeasuring the horizontal CSI-RS ports In the simulation theone horizontal antenna port is mapped to two columns ofantenna elements of one polar direction for example port 0
12
Verticalport 0
Verticalport 1
Horizontalport 01
Horizontalport 23
Horizontalport 45
Horizontalport 67
78 1516middot middot middot middot middot middot
Figure 4 Antenna array with 8 times 8 X-pol elements
25
3
35
4
45
5
Cel
l ave
rage
SE
(bps
Hz)
8 12 164Number of users
JSDM 8 times 8A 30kmJSDM 8 times 8A 3km
JSPM 8 times 8A 3km greedJSPM 8 times 8A 30km fixedJSPM 8 times 8A 3km fixed
Figure 5 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
is mapped to column 1 and 3 of +45∘ polar antenna elementsas shown in Figure 4 In simulation the fix power-domaingrouping scheme is adopted the threshold for predefineduser grouping is 8 dB and the power ratio is (03P 07P)
Figure 5 shows the cell average spectrum efficiency (inbitssecHz) of JSDM and JSPM versus the number of usersin the systemThe results show that JSPM can achieve highercell average spectrum efficiency (more than 15 gain with16 users per cell and 3 kmh velocity condition) than JSDMas JSPM can achieve additional power-domain multiplexinggain The ratio of UE multiplexing in spatial and powerdomain for different amounts of UE per cell are summarizedin Table 3 From Table 3 it can be seen that as the amountof UE per cell is increased the ratio of UE multiplexingin spatial and power domain is increased and the ratio of
8 International Journal of Antennas and Propagation
Table 2 Major simulation parameters
Parameters ValuesTx power 46 dBm for 3D-UMa 500mDuplex FDDBS antenna configurations Antenna elements config 8 times 8 times 2 (plusmn45) 05120582H08120582VTraffic model Full buffer modelWrapping method Geographical distance basedMetrics 5 50 UPTSystem bandwidth 10MHz (50 PRBs)UE attachment Based on RSRPNumber of UEs per cell 481216Network synchronization SynchronizedUE speed 3 kmhUE distribution According to 36873 [20]
ReceiverNonideal channel estimation and interference modeling detailed guidelinesaccording to Rel-12 assumptionsMMSE-IRC and IC receiver and detailed guidelines according to Rel-12assumptions [21]
UE Rx antenna configuration 1 Rx
Feedback
PUSCH 3-2CQI PMI and RI reporting triggered per 5msFeedback delay is 5msRel-10 8 Tx codebook
Transmission scheme Dynamic SUMU-MIMO with rank adaptationOverhead 3 symbols for DL CCHs 2 CRS ports and DM-RS with 12 REs per PRBCSI-RS 5msecSRS 1 Tx 5ms periodicity wideband
Table 3 Ratio of UE multiplexing comparison for different UEnumbers per cell
Number of UEsper cell
Ratio of UEmultiplexing of JSPM
[]
Ratio of UEmultiplexing of JSDM
[]4 302 2848 439 37212 496 41416 507 437
UE multiplexing is about 30 when the number of UEsper cell is 4 while the ratio of UE multiplexing increases toapproximately 50 when the amount of UE is 16 Thereforethe gain of JSPM is also increased as shown in Figure 5
The performances of JSPM and JSDM with UE speed30 kmh are also provided in Figure 5 These results indicatethat the performances of JSPM and JSDM both decrease withUE speed increasing For JSPM the performance loss is about19 when UE speed increases from 3 kmh to 30 kmh with16 users per cell since UE mobility causes the rapid channelchange and reduces the BS channel estimation accuracyTherefore JSPM scheme is more suitable for a stationary or
semistationary scenario such as to provide coverage and highdata rate for users in office rooms or tall buildings
For the sake of performance comparison of differentpower-domain user pairing strategies we also provide theperformance of JSPM with fixed power user paring selection(denoted as blue solid line with ldquolowastrdquo) and greedy user paringselection (denoted as blue solid line with square) in Figure 5Although the performance loss of fixed power user pairingcompared with greedy user paring is about 15 with 16 usersper cell and 3 kmh velocity condition the fixed power userparing algorithm can provide less computational complexityand easier system implementation than greedy algorithm asdiscussed in Section 33 hence it will be the preferredmethodfor practical user pairing in BS side
43 Different Antenna Type Performances In this subsectionwe perform JSPM performance evaluation for two antennatypes with 8 times 8 and 4 times 16 X-polar antenna elementsrespectively As the typical application scenario of massiveMIMO is providing high-speed data service for users intall buildings the vertical grouping scheme which has beendiscussed in the above section is adopted for both 8 times 8 X-polar and 4 times 16 X-polar antenna types in the simulationFor the antenna array with 4 times 16 X-polar antenna ele-ments there are 2 vertical prebeamforming groups by using
International Journal of Antennas and Propagation 9
Figure 6 Antenna array with 4 times 16 X-pol elements
128 164Number of users
28
3
32
34
36
38
4
42
44
46
48
Cell
aver
age s
pect
rum
effici
ency
(bps
Hz)
JSPM 8 times 8AJSPM 4 times 16A
Figure 7 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
prebeamforming matrix B columns of which can be 2-elementDFTweight two beam groups are tilted to 80 and 100degrees respectively Two vertical antenna ports are mappedto four vertical rows of antenna elements with one polardirection each one is corresponding to two rows For eighthorizontal antenna ports each horizontal antenna port ismapped to four columns of antenna elements of one polardirection for example port 0 is mapped to column 1356 of+45∘ polar antenna elements as shown in Figure 6
In the simulation the other schemes such as user spatialgrouping schemeMU-MIMO scheme andmultiuser power-domain transmission scheme are the same as thatmentionedin previous section
Figure 7 shows the cell average spectrum efficiency com-parison between two types of antenna array Figure 8 givesthe CDF comparison of UE spectrum efficiency between twotypes of antenna array with 481216 UEs per cell Based onthese results it can be seen that the 4 times 16 antenna arrayhas better performance than the 8 times 8 antenna array bothin cell average spectrum efficiency and in 50 CDF of UEspectrum efficiency This is because that BS with 4 times 16antenna array which has more horizontal column antennascan form narrower beams and separates the spatial channelinto more subspace therefore it can achieve more spatialmultiplexing gain
JSPM 4 times 16A 16 UEsJSPM 4 times 16A 12 UEsJSPM 4 times 16A 8 UEsJSPM 4 times 16A 4 UEs
JSPM 8 times 8A 16 UEsJSPM 8 times 8A 12 UEsJSPM 8 times 8A 8 UEsJSPM 8 times 8A 4 UEs
0
01
02
03
04
05
06
07
08
09
1
CDF
51 2 3 4 60User spectrum efficiency (bpsHz)
Figure 8 CDF of UE spectrum efficiency
It can be also seen that the antenna array with morecolumn antennas can achieve higher multiplexing gain forJSPM scheme with number limitation of antenna elements inthe practical network
5 Conclusion
In this paper a joint spatial and power-domain multiusertransmission scheme called JSPM is proposed for FDDmassive MIMO systems In this scheme BS divides theUE into different groups in spatial and power domainsand each type of UE is identified with a set of indicesincluding spatial domain index beam index and power-domain index Based on these UE indices BS can performmultiuser paring and scheduling in both spatial and powerdomain Compared with the traditional spatial multiplexingschemes the proposed JSPM scheme can achieve additionalpower-domain multiplexing gain The system-level simula-tion results validate that with 16 users per cell JSPM canachieve more than 15 spectrum efficiency gain comparedwith JSDM and the JSPM gain increases with the numberof active users per cell The simulation results also show thatthe antenna array with larger number of horizontal columnantennas has the better performance since user distributionin the horizontal plane is more intensive than that in thevertical plane in practical networks
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
10 International Journal of Antennas and Propagation
References
[1] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2014
[2] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010
[3] K Zheng L Zhao J Mei B Shao W Xiang and L HanzoldquoSurvey of large-scale MIMO systemsrdquo IEEE CommunicationsSurveys amp Tutorials vol 17 no 3 pp 1738ndash1760 2015
[4] K Zheng YWangWWangM Dohler and JWang ldquoEnergy-efficient wireless in-home the need for interference-controlledfemtocellsrdquo IEEE Wireless Communications vol 18 no 6 pp36ndash44 2011
[5] J Jose A Ashikhmin T L Marzetta and S Vishwanath ldquoPilotcontamination and precoding inmulti-cell TDD systemsrdquo IEEETransactions on Wireless Communications vol 10 no 8 pp2640ndash2651 2011
[6] H Huh A M Tulino and G Caire ldquoNetwork MIMO with lin-ear zero-forcing beamforming large system analysis impact ofchannel estimation and reduced-complexity schedulingrdquo IEEETransactions on InformationTheory vol 58 no 5 pp 2911ndash29342012
[7] G Caire N JindalM Kobayashi andN Ravindran ldquoMultiuserMIMO achievable rates with downlink training and channelstate feedbackrdquo IEEE Transactions on Information Theory vol56 no 6 pp 2845ndash2866 2010
[8] M Kobayashi N Jindal and G Caire ldquoTraining and feedbackoptimization for multiuser MIMO downlinkrdquo IEEE Transac-tions on Communications vol 59 no 8 pp 2228ndash2240 2011
[9] A Adhikary J Nam J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing the large-scale array regimerdquo IEEETransactions on Information Theory vol 59 no 10 pp 6441ndash6463 2013
[10] J Nam J-Y Ahn A Adhikary and G Caire ldquoJoint spatialdivision and multiplexing realizing massive MIMO gains withlimited channel state informationrdquo in Proceedings of the 46thAnnual Conference on Information Sciences and Systems (CISSrsquo12) Princeton NJ USA March 2012
[11] J Nam A Adhikary J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing opportunistic beamforming usergrouping and simplified downlink schedulingrdquo IEEE Journal onSelected Topics in Signal Processing vol 8 no 5 pp 876ndash8902014
[12] VVenkateswaran andA-J van derVeen ldquoAnalog beamformingin MIMO communications with phase shift networks andonline channel estimationrdquo IEEETransactions on Signal Process-ing vol 58 no 8 pp 4131ndash4143 2010
[13] K Zheng L Zhao J Mei M DohlerW Xiang and Y Peng ldquo10Gbs hetsnets with millimeter-wave communications accessand networking-challenges and protocolsrdquo IEEE Communica-tions Magazine vol 53 no 1 pp 222ndash231 2015
[14] O E Ayach R W Heath Jr S Abu-Surra S Rajagopal and ZPi ldquoLow complexity precoding for largemillimeterwaveMIMOsystemsrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo12) pp 3724ndash3729 Ottawa CanadaJune 2012
[15] A Alkhateeb O El Ayach G Leus and R W Heath ldquoHybridprecoding for millimeter wave cellular systems with partialchannel knowledgerdquo in Proceedings of the Information Theory
and Applications Workshop (ITA rsquo13) pp 1ndash5 IEEE San DiegoCalif USA February 2013
[16] D Tse and P Viswanath Fundamentals ofWireless Communica-tion Cambridge University Press Cambridge UK July 2005
[17] M Sharif and B Hassibi ldquoOn the capacity of MIMO broadcastchannels with partial side informationrdquo IEEE Transactions onInformation Theory vol 51 no 2 pp 506ndash522 2005
[18] A Benjebbovu A Li Y Saito Y Kishiyama A Harada and TNakamura ldquoSystem-level performance of downlink NOMA forfuture LTE enhancementsrdquo in Proceedings of the IEEE GlobecomWorkshops (GC rsquo13) pp 66ndash70 IEEE Atlanta GaUSADecem-ber 2013
[19] 3GPP TS36101 (V1310) ldquoEvolved Universal Terrestrial RadioAccess (E-UTRA) User Equipment (UE) radio transmissionand receptionrdquo October 2015
[20] 3GPP TR36873 (V1220) ldquoStudy on 3D channel model forLTErdquo July 2015
[21] 3GPP ldquoStudy on network-assisted interference cancellation andsuppression (NAIC) for LTErdquo 3GPP TR36866 (V1201) 2014
2 International Journal of Antennas and Propagation
Spatial Division and Multiplexing (JSDM) was proposed in[9ndash11] to enable massive MIMO gains for FDD systemsMeanwhile as large bandwidth is available atmillimeter wave(mmWave) frequencies to provide gigabit-per-second datarates the hybrid analogdigital processing strategies wereproposed in [12ndash15] for mmWave systems with large antennaarrays
The downlink beamforming of both JSDM and hybridprecoding scheme includes two stages that is a prebeam-forming stage that depends on UErsquos channel covariance and aMU-MIMO precoding stage for the effective channel formedby the first stage The prebeamforming matrix is chosen inorder to minimize the interference across different spatialgroups and the MU-MIMO precoding matrix takes care ofthe multiuser interference within each group
Both of these beamforming stages achieve multiplexinggain in spatial domain It is well-known that the maximumspatial multiplexing gain is limited by the number of trans-mitting and receiving antennas in massive MIMO systems[16] Thus more multiplexing gain is achieved in the firstprebeamforming stage the less multiplexing gain is achievedin the second MU-MIMO stage In order to achieve moremultiplexing gain in theMU-MIMOstage the power domainis introduced in spatial multiplexing transmission schemeand the joint spatial and power multiplexing (JSPM) schemefor massive MIMO system is proposed in this paper Theproposed scheme not only relaxes the full channel knowledgeto achieve the spatial multiplexing gain by using the channelsecond order statistics but also applies multiuser powerallocation transmission at BS side and successive interferencecanceller (SIC) on UE side to achieve the power-domainuser multiplexing gain The performance of the proposedJSPM scheme is illustrated by simulations and comparedwith that of JSDM The results show that even with the fixedspatial quantization and simplified transmit power allocationgrouping scheme the proposed scheme outperforms JSDMbecause of the additional power-domain multiplexing gain
The remainder of this paper is organized as followsSection 2 describes the overall system model and the keyfunctionalities utilized to introduce JSPM The asymptoticexpression of JSPM is derived Section 3 discusses the schemeof the user spatial grouping and multiuser power-domainparing Furthermore the computational complexity of JSPMscheme is discussed In Section 4 the system-level simulationconfiguration is described and the results of the system-levelperformance of JSPM in comparison to JSDM are providedFinally Section 5 concludes the paper
2 System Model
In this section we consider the downlink communication ofa massiveMIMO system as shown in Figure 1 where the basestation (BS) is equipped with 119873
119905transmit antennas under
the total transmit power constraint of 119875 and serving119880 signalantenna UE
We assume that H = [h1 h
119906 h
119880] is the 119873
119905times 119880
dimensional matrix that represents the channel between theBS and UE h
119906is the119873t times 1 dimensional channel realization
between the BS and user 119906
BS
BG 3UE 1
UE 2
UE 4
UE 3UE 5
BG 1
BG 2BG 4
BG 5
UE 4
PG 1
PG 2
Figure 1 A massive MIMO BS to serve randomly located UE
The system received signal is denoted as
y = H119867x + n (1)
where y denotes the collection of received symbols for all the119880 users x = Td is the transmitted signal vector of dimensions119873119905times 1 T = BVP is the downlink beamforming matrix
consisting of three parts B is the prebeamforming matrixof dimensions 119873
119905times 119873119861 which is generated based on the
channel covariance statistics V is the 119873119861times 119873119872
multiuserMIMO precoding matrix which is a function of the reduceddimensional effective channel H = B119867H P is the power-domain multiplexing matrix of dimensions 119873
119872times 119873119878 d
denotes the 119878 times 1 vector of transmitted user data symbolsn sim 119862119873(0 I
119880119896) denotes additive spatially and temporally
white Gaussian noise with zero mean and unit variance As aresult the received signal in (1) can bewritten in the followingmanner
y = H119867BVPd + n = H119867VPd + n (2)
where prebeamforming matrix B makes the channel Hbecome different approximately mutually orthogonal sub-spaces H based on channel statistical characteristic UE canbe partitioned into these subspaces to form several disjointuser groups
If we define119880 users can be partitioned into 119866 groups theoverall119873
Based on [11] H119892 = U119892(Λ119892)12w119892 Then we can makethe effective channel matrixH become an approximate blockdiagonal matrix by designing B119892 = U119892 then (H119892)119867B119894 asymp 0where 119892 1198921015840 isin 1 119866 and 119892 = 119892
1015840 Furthermore the y119892 in(4) can be expressed as
where V119892 and P119892 are the multiuser MIMO precoding matrixand the power-domain multiplexing matrix of user cluster119892 respectively d119892 is the transmitted signal of cluster 119892 andn119892 sim 119862119873(0 I119892) From (5) we can derive that V is the blockdiagonal matrix V = diag(V1 V119866)
The number of downlink data streams of group 119892 isdenoted as 119903119892 which is the effective rank of R119892 and MU-MIMO precoding matrix in group 119892 is simply the identitymatrix that is V119892 = I119903
119892
In order to allocate the downlinkdata streams to the users we select 119903119892 out of users in 119880119892which is the number of users in group 119892 according to a maxSINR criterion as follows
where 119898 = 1 119903119892 119887119892119898119887119892119899is the 119898th and 119899th column of B119892
ℎ119892
119906is the channel response vector of user 119906 in spatial group 119892
and 120588 = 119875sum119866119892=1119903119892
Each user feeds its SINR values and 119898th beam indexcorresponding to this SINR back BS can then identify eachtype of UE by a set of indices 119906 119892119898where indices 119906 119892119898are the user index spatial groupnumberwhich user119906 belongsto and beam index corresponding to SINR119892
119906119898 respectively
In addition to these indices a new index introduced inJSPM to identify UEs is the power-domain group indexwhich can be decided based on RSRP value of UE feedbackand the predefined thresholds For example we can predefineseveral intervals of RSRP as different power groups if a UEfeedback RSRP value is in 119889th RSRP interval the UE isconsidered to belong to power group 119889
For UE with a different power group index 119889 and thesame beam index119898 UE can be paired to use power-domainmultiplexing the presentation is
s119892 = P119892d119892 (7)
where s119892 = [s1198921 s119892
119903119892] is 119903119892 transmission data streams
P119892 with dimensions 119903119892 times 119880119892 is power-domain multiplexingmatrix to multiplex 119880119892 user data into 119903119892 data stream d119892 =[d1198921 d119892
119880119892] is the data vector of 119880119892 users in group 119892
There are two criteria of power-domain multiuser sched-uler as follows
The first is the fact that multiplexing candidate users willbe selected from UE set with the same spatial group index 119892and beam index 119898 but with different power-domain groupindex For example if user 1199061015840 and user 119906 are two selectedusers tomultiuser transmission in power domain theywill beallocated in different power groups such as user 1199061015840 isin 119880119892
1198981198891015840
and user 119906 isin 119880119892119898119889119894
variables 1198891015840 and 119889 are different powergroup indices 119880119892
119898is the user set of spatial group 119892 and beam
119898The second is the multiplexing candidate user that will
maximize the PF scheduling metric as follows
119876119880119892
119898= sum
119906isin119880119892
119898
(119877 (119906)
119877 (119906)
) (8)
where 119876119880119892
119898denotes the PF scheduling metric for power-
domain multiplexing candidate user set 119880119892119898 119877(119906) is the
instantaneous throughput of user 119906 119877(119906) is the averagethroughput of user 119906
We assume that the SIC receiver of user 119906 is able to cancelperfectly and successively the interference from other user119908 with channel gain 119875119892
1199061015840 |(ℎ119892
1199061015840)119867(119887119892
119898)|2gt 119875119892
119906|(ℎ119892
119906)119867(119887119892
119898)|2 119906 isin
119880119892
119898119889 and 1199061015840 isin 119880119892
1198981199061015840 Then SINR of user 119906 can be estimated
where 120583119892119898119895(119909) 119895 = 1 119903
119892are the eigenvalues of 119860119892
119898(119909)
119860119892
119898(119909) = (Λ
119892)12
(119880119892)119867
119887119892
119898(119887119892
119898)119867
119880119892(Λ119892)12
minus 119909(sum
119899 =119898
(Λ119892)12
(119880119892)119867
119887119892
119899(119887119892
119899)119867
119880119892(Λ
g)12
+ sum
1198921015840=119892
(Λ119892)12
(119880119892)119867
1198611198921015840
(1198611198921015840
)
119867
119880119892(Λ119892)12
)
(16)
Without loss of generality we assume the ordering
120583119892
1198981(119909) ge sdot sdot sdot ge 120583
119892
119898119903119892(119909)
120575119889=
119875119892
119906
1 + 119868119892
11990610158401198981198891015840
(17)
The growth function of CDF 119865(119909) with corresponding PDF119891(119909) is
119892 (119909) =1 minus 119865 (119909)
119891 (119909)
119892infin= lim119909rarrinfin
119892 (119909) = 120575119889(120583119892
119898)infin
(18)
where (1205831198921198981)infin
= lim119909rarrinfin
120583119892
1198981(119909) is a bound positive
constant [11]Considering the ideal channel estimation and the fixed
power assignments to users 119868119892119908119898119889
rarr 0 120575119889rarr 119875119892
119889
Then we have119897119892
119898
sum
119889=1
119875119892
119889= 119875119892 (19)
With extreme value theory [11] we have thatmax1le119906le119880
119892SINR119892119906119898119889
which behaves as 120575119889(120583119892
1198981)infin log119880119892 +
119874(log log119880119892) for 119880119892 rarr infin
The sum rate asymptotic formula for a group 119892 is
119877119892=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (120575119889(120583119892
1198981)infin
log (119880119892)) + 119900 (1)
=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (120575119889) +
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
(120583119892
1198981)infin
+
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log log (119880119892) + 119900 (1)
=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (119875119892119889) +
119903119892
sum
119898=1
119897119892
119898log log (119880119892)
+
119903119892
sum
119898=1
119897119892
119898log (120583119892
1198981)infin
+ 119900 (1)
(20)
as 119880119892 rarr infinSumming over 119892 the sum rate asymptotic formula can be
written as
119877sum =119866
sum
119892=1
119897119892
119898
sum
119889=1
119903119892 log (119875
119889) +
119866
sum
119892=1
119871119892 log log (119880119892)
+ 119874 (1)
(21)
With finite 119873119905antennas total transmit power constraint
of 119875 119880119892 users and 119871119892 data streams per group with the equaltransmission power and common covariance R119892 where usershave mutually statistically independent channel vectors for119880119892rarr infin the sum capacity of a MU-MIMO downlink
system is given by
119877sum =119866
sum
119892=1
119871119892 [
[
log log (119880119892) + log( 119875
sum119866
119892=1119871119892)]
]
+ 119874 (1)
(22)
where 119874(1) denotes a constant independent of 119880119892
3 Designs for JSPM in FDD
In the proposed JSPM scheme the downlink transmissionstrategy is designed in the following three parts
(1) Based on cell environment and channel covariancemeasurement BS can split whole channel space intoseveral disjoint subspaces by using prebeamformingmatrix Therefore based on CSI SINR and RSRPvalues feedback from UE that estimates these valuesbased on the subspaces BS can partition its servingUE into several subspace groups with approximatelysimilar channel covariance eigenvectors and channelpath lossThe spatial and power-domain characters ofeach type of UE can be identified by a set of indicesthat is UE index119906 spatial group index119892 beam index119898 power group index 119889
International Journal of Antennas and Propagation 5
(2) For UE marked with different spatial group indicesor the same spatial group index but different beamindices MU-MIMO downlink transmission on thesame time-frequency resource is performed
(3) For UE marked with the same spatial group indexthe same beam index and different power groupindices multiuser power pairing is performed If userpairing succeeds the multiuser power allocation andthe power-domain usermultiplexing transmission areperformed
Among the above the user grouping and multiuserselection in power-domain are two key issues for the systemperformance the following discussion will focus more on thestrategies of these two issues
31 User Grouping As mentioned before in order to exploiteffectively the JSPM approach the usersrsquo population will bepartitioned into groups according to the following qualitativeprinciples (1) users in the same group have channel covari-ance eigenspace spanning (approximately) a given commonsubspace which characterizes the spatial group BS can getthis information by UE CSI SINR and RSRP measurementfeedback (2) the subspaces of spatial groups served on thesame time-frequency slot by JSDM must be (approximately)mutually orthogonal or at least have empty intersection
The fixed quantization algorithm of user grouping in [11]is an effective and low complexity scheme for applicationin practical network In this algorithm the group subspacesare fixed a priori based on the geometry of cell coverageand their channel scattering In our proposed scheme thefixed quantization algorithm in [11] is extended to frequencydomain When we increase the number of fixed quantizationspatial group to reduce coverage holes the overlappingbetween different spatial groups will also increase and causethe strong interference of intergroups In this case we canallocate transmission resource in different frequency bandsdynamically for UE that belongs to adjacent groups in orderto reduce the interference of intergroups
By choosing 119866 AoAs 120579119892 and fixed ASΔ we can definethe 119866 disjoint intervals [120579119892 minus Δ 120579119892 + Δ] This methodconsists essentially to form predefined ldquonarrow sectorsrdquo andassociate users to sectors according to minimum chordaldistance quantization For example suppose 119866 = 3 choosing1205791= minus45
∘ 1205792 = 0∘ and 1205793 = 45
∘ Δ = 15∘ such as
BG1 BG2 and BG3 shown in Figure 1 we note that thethree subspaces are disjoint However as UE is distributeduniformly and these three subspaces are discontinuous someUE cannot be associated with these subspaces exactly suchas UE4 shown in Figure 1 If we define more dense subspacesuch as 119866 = 5 there are five spatial groups such as BG1BG2 BG5 shown in Figure 1 and different subspace willbe overlapping the interference of inter-group will increaseIn this case we can allocate UE that is in the adjacentsubspace to different frequency resources in order to reducethe intergroup interference
In Figure 1 there are five spatial groups in order to avoidintergroup interference BS can separate BG1 BG2 and BG3
groups and BG4 and BG5 groups into different frequencybands
This scheme makes sense especially for mmWave mobilesystems which have huge frequency broadband to be used
32 Multiuser Transmit Power Allocation and Candidate UserSelection Due to power-domain multiuser multiplexing thetransmit power allocation to one user affects the achievablethroughput of not only that user but also the throughput ofother pairing users The best performance of power-domainmultiuser multiplexing is achieved by exhaustive full searchof user pairs and transmission power allocations [18]
In order to reduce further the computational complexitythe scheme of predefined user grouping and pergroup fixedpower allocation can be used With this approach UE isdivided into different user groups according to their channelpath loss and the predefined thresholds In this predefinedpower-domain grouping the users can be paired togetheronly if they belong to different power groups With thepredefined power grouping the power allocation could alsobe simplified by applying fixed power assignments to theusers belonging to the same group For example for theuser group with good channel gain small power (eg 03P)is allocated and for the user group with bad channel gainlarge power (eg 07P) is allocated where the total powerassigned to different user groups is kept equal to P Predefineduser grouping and fixed power allocation can effectivelydecrease the amount of downlink signaling related toUE datadetection For example the order of successive interferencecancellation (SIC) and information on power assignment donot need to be transmitted in every subframe but rather on alarger time scale
For example as shown in Figure 2 there are two spatialgroups BG1 and BG2 and two power groups PG1 and PG2UE1 belongs to BG1 and PG1 and UE2 and UE3 belong toBG1 and BG2 respectively but both belong to PG2 As forthe aforementioned spatial and power-domain multiplexingstrategies UE3 can be paired with UE1 and UE2 in the spatialdomain and be applied to MU-MIMO transmission UE1can be paired with UE2 in power domain as it belongs tosame spatial group but different power groups and it can beapplied to multiuser power multiplexing transmission UE1can perform SIC operation to cancel the interference fromUE2
33 Computational Complexity Discussion As multiusertransmission of power domain introduced in JSPM will leadto additional algorithm implementation complexity we willdiscuss the computational complexity of JSPM in comparisonwith the exiting JSDM scheme in this section The additionalimplementation complexity of JSDM is composed of threeparts the first part is multiuser selection and pairing inpower domain in BS side the second part is multiplexingtransmission processing in power domain in BS side and thethird part is SIC processing in UE side The first two partsincrease the implementation complexity of BS side and thelast part increases the complexity of UE side
In order to simplify complexity analysis we assume thatUE in power domain is separated into two groups that is cell
6 International Journal of Antennas and Propagation
Numbers of complex numberaddition and multiplication JSDM JSPM with fix power
user paring algorithmJSPM with power domain
greedy algorithmPrebeamforming 119866 times 119874 (119873
119905
3) + 119866 times 119880
119892times119872119892
119861times 119873119905
Multiuser precoding 119866 times 119874((119880119892)3
) + 119866 times 119880119892times 119903119892times119872119892
119861
Power domain user paring 119880119892
119898119889times 119880119892
1198981198891015840times 119866 times 119874 ((119903
119892)2
) 1198622
(119880119892
119898119889+119880119892
1198981198891015840)times 119866 times 119874((119903
119892)2
)
Power domain multiplexing 119880119892times 119903119892times 119866 119880
119892times 119903119892times 119866
center user group and cell edge user group numbers of thetwo groups of UE are noted as 119880119892
119898119889and 119880119892
1198981198891015840 respectively
The computational complexity of JSPM and JSDM in BS sideis presented in Table 1
FromTable 1 we can see that although the power-domainmultiplexing transmission of JSPM leads to computationalcomplexity increase the added complexity accounts fora small part of the overall JSPM complexity The maincomputational complexity comes from the singular valuedecomposition (SVD) processing of channel matrix H =
[H1 sdot sdot sdot H119866] with 119874(119873119905
3) computational complexity in
multiuser beamforming procedure Therefore the extra com-plexity introduced by adopting JSPM has very limited impacton the overall system implementation
From computational complexity listed in Table 1 we cansee that the approach of predefined user grouping and per-group fixed power allocation has more less computationalcomplexity compared with greedy algorithm with the costof little performance degradation which we will discuss inSection 4
For UE side the detection complexity of cell center UEwill not change the detection complexity of cell edge UE willbe double because for cell edge UE they will firstly detectthe information of cell center pairing UE and subtract itfrom receiving signals and then detect its own informationHowever 3GPPRAN4has finished SIC performance require-ment in 3GPP TS36101 [19] which means that Rel12 UE
has enough capability to fulfill the detection performancerequirement of JSPM
4 Performance Evaluation and Analysis
41 Validation of the Asymptotic Analysis In this section wecompare the results obtained via the method of deterministicequivalents withMonte Carlo simulations in order to validatethe asymptotic analysis in Section 2
In our discussion BS is equipped with a uniform circulararray with 100 isotropic antenna elements the distancebetween antenna elements equals 1205822 where 120582 is the carrierwavelength As the user mutual statistical independent chan-nel is important for analytical results the one-ring channelmodel [11] is adopted Users form 119866 = 6 symmetric spatialgroups with the angular spread (AS)Δ = 15
We fixed to serve 119903119892 = 5 data streams per spatial group sothat the total number of active users is 30 119897119892
119898is fixed to equal
2 SNR = P with the noise unit variance normalizationThe comparison of sum spectrum efficiencies of JSPM
obtained by using deterministic equivalent approximationand simulations is illustrated in Figure 3 The green solidline with ldquosquaresrdquo is obtained using the JSPM correspondingdeterministic equivalent approximation the red solid linewith ldquo119909rdquo is obtained through JSPM simulation and the bluesolid line with ldquo119900rdquo is obtained through JSDM simulation
International Journal of Antennas and Propagation 7
JSPM analyticalJSPM simJSDM sim
0
50
100
150
200
250
Sum
rate
(bps
Hz)
5 10 150SNR (dB)
Figure 3 Comparison of sum spectrum efficiencies
For multiuser spatial transmission simulation the approachof ZF beam-forming (ZFBF) and joint group processing(JGP) is used For multiuser transmission of power-domainsimulation the predefined user grouping and per-group fixedpower allocation scheme in power-domain is applied
As shown in Figure 3 the trend of JSPM simulationresult is coincided with that of JSPM deterministic equivalentapproximation Furthermore simulation results show that theperformance of JSPM outperforms JSDM
42 JSPM Performance Gain In this section we presentsystem-level simulation results of the investigation on theperformance gains of JSPM in LTE system In our simulationa multicell system-level simulation is conducted and a 19-hexagonal macro cell model with 3 cells per cell site isemployedThedetails of the simulation assumptions are listedin Table 2
BS is equippedwith antenna array of 8times8X-pol elementsas shown in Figure 4 For the simulation there are 2 verticalprebeamforming groups by using prebeamforming matrix Bcolumns of which can be 4-element DFT weight the highbeam group is tilted to 80 degrees and the low beam groupis tilted to 100 degrees Therefore UE in serving cell canbe partitioned into two vertical spatial groups by BS basedon UE RSRP measurement and feedback responding to twovertical antenna ports each vertical antenna port is mappedto four vertical rows of antenna elements with one polardirection such as +45∘ polar as shown in Figure 4 Then BScan apply MU-MIMO transmission for UE in each verticalgroup by usingmatrixV MatrixV can be composed with UEfeedback precodingmatrix index for eight horizontal antennaports UE gets the horizontal channel spatial information bymeasuring the horizontal CSI-RS ports In the simulation theone horizontal antenna port is mapped to two columns ofantenna elements of one polar direction for example port 0
12
Verticalport 0
Verticalport 1
Horizontalport 01
Horizontalport 23
Horizontalport 45
Horizontalport 67
78 1516middot middot middot middot middot middot
Figure 4 Antenna array with 8 times 8 X-pol elements
25
3
35
4
45
5
Cel
l ave
rage
SE
(bps
Hz)
8 12 164Number of users
JSDM 8 times 8A 30kmJSDM 8 times 8A 3km
JSPM 8 times 8A 3km greedJSPM 8 times 8A 30km fixedJSPM 8 times 8A 3km fixed
Figure 5 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
is mapped to column 1 and 3 of +45∘ polar antenna elementsas shown in Figure 4 In simulation the fix power-domaingrouping scheme is adopted the threshold for predefineduser grouping is 8 dB and the power ratio is (03P 07P)
Figure 5 shows the cell average spectrum efficiency (inbitssecHz) of JSDM and JSPM versus the number of usersin the systemThe results show that JSPM can achieve highercell average spectrum efficiency (more than 15 gain with16 users per cell and 3 kmh velocity condition) than JSDMas JSPM can achieve additional power-domain multiplexinggain The ratio of UE multiplexing in spatial and powerdomain for different amounts of UE per cell are summarizedin Table 3 From Table 3 it can be seen that as the amountof UE per cell is increased the ratio of UE multiplexingin spatial and power domain is increased and the ratio of
8 International Journal of Antennas and Propagation
Table 2 Major simulation parameters
Parameters ValuesTx power 46 dBm for 3D-UMa 500mDuplex FDDBS antenna configurations Antenna elements config 8 times 8 times 2 (plusmn45) 05120582H08120582VTraffic model Full buffer modelWrapping method Geographical distance basedMetrics 5 50 UPTSystem bandwidth 10MHz (50 PRBs)UE attachment Based on RSRPNumber of UEs per cell 481216Network synchronization SynchronizedUE speed 3 kmhUE distribution According to 36873 [20]
ReceiverNonideal channel estimation and interference modeling detailed guidelinesaccording to Rel-12 assumptionsMMSE-IRC and IC receiver and detailed guidelines according to Rel-12assumptions [21]
UE Rx antenna configuration 1 Rx
Feedback
PUSCH 3-2CQI PMI and RI reporting triggered per 5msFeedback delay is 5msRel-10 8 Tx codebook
Transmission scheme Dynamic SUMU-MIMO with rank adaptationOverhead 3 symbols for DL CCHs 2 CRS ports and DM-RS with 12 REs per PRBCSI-RS 5msecSRS 1 Tx 5ms periodicity wideband
Table 3 Ratio of UE multiplexing comparison for different UEnumbers per cell
Number of UEsper cell
Ratio of UEmultiplexing of JSPM
[]
Ratio of UEmultiplexing of JSDM
[]4 302 2848 439 37212 496 41416 507 437
UE multiplexing is about 30 when the number of UEsper cell is 4 while the ratio of UE multiplexing increases toapproximately 50 when the amount of UE is 16 Thereforethe gain of JSPM is also increased as shown in Figure 5
The performances of JSPM and JSDM with UE speed30 kmh are also provided in Figure 5 These results indicatethat the performances of JSPM and JSDM both decrease withUE speed increasing For JSPM the performance loss is about19 when UE speed increases from 3 kmh to 30 kmh with16 users per cell since UE mobility causes the rapid channelchange and reduces the BS channel estimation accuracyTherefore JSPM scheme is more suitable for a stationary or
semistationary scenario such as to provide coverage and highdata rate for users in office rooms or tall buildings
For the sake of performance comparison of differentpower-domain user pairing strategies we also provide theperformance of JSPM with fixed power user paring selection(denoted as blue solid line with ldquolowastrdquo) and greedy user paringselection (denoted as blue solid line with square) in Figure 5Although the performance loss of fixed power user pairingcompared with greedy user paring is about 15 with 16 usersper cell and 3 kmh velocity condition the fixed power userparing algorithm can provide less computational complexityand easier system implementation than greedy algorithm asdiscussed in Section 33 hence it will be the preferredmethodfor practical user pairing in BS side
43 Different Antenna Type Performances In this subsectionwe perform JSPM performance evaluation for two antennatypes with 8 times 8 and 4 times 16 X-polar antenna elementsrespectively As the typical application scenario of massiveMIMO is providing high-speed data service for users intall buildings the vertical grouping scheme which has beendiscussed in the above section is adopted for both 8 times 8 X-polar and 4 times 16 X-polar antenna types in the simulationFor the antenna array with 4 times 16 X-polar antenna ele-ments there are 2 vertical prebeamforming groups by using
International Journal of Antennas and Propagation 9
Figure 6 Antenna array with 4 times 16 X-pol elements
128 164Number of users
28
3
32
34
36
38
4
42
44
46
48
Cell
aver
age s
pect
rum
effici
ency
(bps
Hz)
JSPM 8 times 8AJSPM 4 times 16A
Figure 7 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
prebeamforming matrix B columns of which can be 2-elementDFTweight two beam groups are tilted to 80 and 100degrees respectively Two vertical antenna ports are mappedto four vertical rows of antenna elements with one polardirection each one is corresponding to two rows For eighthorizontal antenna ports each horizontal antenna port ismapped to four columns of antenna elements of one polardirection for example port 0 is mapped to column 1356 of+45∘ polar antenna elements as shown in Figure 6
In the simulation the other schemes such as user spatialgrouping schemeMU-MIMO scheme andmultiuser power-domain transmission scheme are the same as thatmentionedin previous section
Figure 7 shows the cell average spectrum efficiency com-parison between two types of antenna array Figure 8 givesthe CDF comparison of UE spectrum efficiency between twotypes of antenna array with 481216 UEs per cell Based onthese results it can be seen that the 4 times 16 antenna arrayhas better performance than the 8 times 8 antenna array bothin cell average spectrum efficiency and in 50 CDF of UEspectrum efficiency This is because that BS with 4 times 16antenna array which has more horizontal column antennascan form narrower beams and separates the spatial channelinto more subspace therefore it can achieve more spatialmultiplexing gain
JSPM 4 times 16A 16 UEsJSPM 4 times 16A 12 UEsJSPM 4 times 16A 8 UEsJSPM 4 times 16A 4 UEs
JSPM 8 times 8A 16 UEsJSPM 8 times 8A 12 UEsJSPM 8 times 8A 8 UEsJSPM 8 times 8A 4 UEs
0
01
02
03
04
05
06
07
08
09
1
CDF
51 2 3 4 60User spectrum efficiency (bpsHz)
Figure 8 CDF of UE spectrum efficiency
It can be also seen that the antenna array with morecolumn antennas can achieve higher multiplexing gain forJSPM scheme with number limitation of antenna elements inthe practical network
5 Conclusion
In this paper a joint spatial and power-domain multiusertransmission scheme called JSPM is proposed for FDDmassive MIMO systems In this scheme BS divides theUE into different groups in spatial and power domainsand each type of UE is identified with a set of indicesincluding spatial domain index beam index and power-domain index Based on these UE indices BS can performmultiuser paring and scheduling in both spatial and powerdomain Compared with the traditional spatial multiplexingschemes the proposed JSPM scheme can achieve additionalpower-domain multiplexing gain The system-level simula-tion results validate that with 16 users per cell JSPM canachieve more than 15 spectrum efficiency gain comparedwith JSDM and the JSPM gain increases with the numberof active users per cell The simulation results also show thatthe antenna array with larger number of horizontal columnantennas has the better performance since user distributionin the horizontal plane is more intensive than that in thevertical plane in practical networks
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
10 International Journal of Antennas and Propagation
References
[1] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2014
[2] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010
[3] K Zheng L Zhao J Mei B Shao W Xiang and L HanzoldquoSurvey of large-scale MIMO systemsrdquo IEEE CommunicationsSurveys amp Tutorials vol 17 no 3 pp 1738ndash1760 2015
[4] K Zheng YWangWWangM Dohler and JWang ldquoEnergy-efficient wireless in-home the need for interference-controlledfemtocellsrdquo IEEE Wireless Communications vol 18 no 6 pp36ndash44 2011
[5] J Jose A Ashikhmin T L Marzetta and S Vishwanath ldquoPilotcontamination and precoding inmulti-cell TDD systemsrdquo IEEETransactions on Wireless Communications vol 10 no 8 pp2640ndash2651 2011
[6] H Huh A M Tulino and G Caire ldquoNetwork MIMO with lin-ear zero-forcing beamforming large system analysis impact ofchannel estimation and reduced-complexity schedulingrdquo IEEETransactions on InformationTheory vol 58 no 5 pp 2911ndash29342012
[7] G Caire N JindalM Kobayashi andN Ravindran ldquoMultiuserMIMO achievable rates with downlink training and channelstate feedbackrdquo IEEE Transactions on Information Theory vol56 no 6 pp 2845ndash2866 2010
[8] M Kobayashi N Jindal and G Caire ldquoTraining and feedbackoptimization for multiuser MIMO downlinkrdquo IEEE Transac-tions on Communications vol 59 no 8 pp 2228ndash2240 2011
[9] A Adhikary J Nam J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing the large-scale array regimerdquo IEEETransactions on Information Theory vol 59 no 10 pp 6441ndash6463 2013
[10] J Nam J-Y Ahn A Adhikary and G Caire ldquoJoint spatialdivision and multiplexing realizing massive MIMO gains withlimited channel state informationrdquo in Proceedings of the 46thAnnual Conference on Information Sciences and Systems (CISSrsquo12) Princeton NJ USA March 2012
[11] J Nam A Adhikary J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing opportunistic beamforming usergrouping and simplified downlink schedulingrdquo IEEE Journal onSelected Topics in Signal Processing vol 8 no 5 pp 876ndash8902014
[12] VVenkateswaran andA-J van derVeen ldquoAnalog beamformingin MIMO communications with phase shift networks andonline channel estimationrdquo IEEETransactions on Signal Process-ing vol 58 no 8 pp 4131ndash4143 2010
[13] K Zheng L Zhao J Mei M DohlerW Xiang and Y Peng ldquo10Gbs hetsnets with millimeter-wave communications accessand networking-challenges and protocolsrdquo IEEE Communica-tions Magazine vol 53 no 1 pp 222ndash231 2015
[14] O E Ayach R W Heath Jr S Abu-Surra S Rajagopal and ZPi ldquoLow complexity precoding for largemillimeterwaveMIMOsystemsrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo12) pp 3724ndash3729 Ottawa CanadaJune 2012
[15] A Alkhateeb O El Ayach G Leus and R W Heath ldquoHybridprecoding for millimeter wave cellular systems with partialchannel knowledgerdquo in Proceedings of the Information Theory
and Applications Workshop (ITA rsquo13) pp 1ndash5 IEEE San DiegoCalif USA February 2013
[16] D Tse and P Viswanath Fundamentals ofWireless Communica-tion Cambridge University Press Cambridge UK July 2005
[17] M Sharif and B Hassibi ldquoOn the capacity of MIMO broadcastchannels with partial side informationrdquo IEEE Transactions onInformation Theory vol 51 no 2 pp 506ndash522 2005
[18] A Benjebbovu A Li Y Saito Y Kishiyama A Harada and TNakamura ldquoSystem-level performance of downlink NOMA forfuture LTE enhancementsrdquo in Proceedings of the IEEE GlobecomWorkshops (GC rsquo13) pp 66ndash70 IEEE Atlanta GaUSADecem-ber 2013
[19] 3GPP TS36101 (V1310) ldquoEvolved Universal Terrestrial RadioAccess (E-UTRA) User Equipment (UE) radio transmissionand receptionrdquo October 2015
[20] 3GPP TR36873 (V1220) ldquoStudy on 3D channel model forLTErdquo July 2015
[21] 3GPP ldquoStudy on network-assisted interference cancellation andsuppression (NAIC) for LTErdquo 3GPP TR36866 (V1201) 2014
Based on [11] H119892 = U119892(Λ119892)12w119892 Then we can makethe effective channel matrixH become an approximate blockdiagonal matrix by designing B119892 = U119892 then (H119892)119867B119894 asymp 0where 119892 1198921015840 isin 1 119866 and 119892 = 119892
1015840 Furthermore the y119892 in(4) can be expressed as
where V119892 and P119892 are the multiuser MIMO precoding matrixand the power-domain multiplexing matrix of user cluster119892 respectively d119892 is the transmitted signal of cluster 119892 andn119892 sim 119862119873(0 I119892) From (5) we can derive that V is the blockdiagonal matrix V = diag(V1 V119866)
The number of downlink data streams of group 119892 isdenoted as 119903119892 which is the effective rank of R119892 and MU-MIMO precoding matrix in group 119892 is simply the identitymatrix that is V119892 = I119903
119892
In order to allocate the downlinkdata streams to the users we select 119903119892 out of users in 119880119892which is the number of users in group 119892 according to a maxSINR criterion as follows
where 119898 = 1 119903119892 119887119892119898119887119892119899is the 119898th and 119899th column of B119892
ℎ119892
119906is the channel response vector of user 119906 in spatial group 119892
and 120588 = 119875sum119866119892=1119903119892
Each user feeds its SINR values and 119898th beam indexcorresponding to this SINR back BS can then identify eachtype of UE by a set of indices 119906 119892119898where indices 119906 119892119898are the user index spatial groupnumberwhich user119906 belongsto and beam index corresponding to SINR119892
119906119898 respectively
In addition to these indices a new index introduced inJSPM to identify UEs is the power-domain group indexwhich can be decided based on RSRP value of UE feedbackand the predefined thresholds For example we can predefineseveral intervals of RSRP as different power groups if a UEfeedback RSRP value is in 119889th RSRP interval the UE isconsidered to belong to power group 119889
For UE with a different power group index 119889 and thesame beam index119898 UE can be paired to use power-domainmultiplexing the presentation is
s119892 = P119892d119892 (7)
where s119892 = [s1198921 s119892
119903119892] is 119903119892 transmission data streams
P119892 with dimensions 119903119892 times 119880119892 is power-domain multiplexingmatrix to multiplex 119880119892 user data into 119903119892 data stream d119892 =[d1198921 d119892
119880119892] is the data vector of 119880119892 users in group 119892
There are two criteria of power-domain multiuser sched-uler as follows
The first is the fact that multiplexing candidate users willbe selected from UE set with the same spatial group index 119892and beam index 119898 but with different power-domain groupindex For example if user 1199061015840 and user 119906 are two selectedusers tomultiuser transmission in power domain theywill beallocated in different power groups such as user 1199061015840 isin 119880119892
1198981198891015840
and user 119906 isin 119880119892119898119889119894
variables 1198891015840 and 119889 are different powergroup indices 119880119892
119898is the user set of spatial group 119892 and beam
119898The second is the multiplexing candidate user that will
maximize the PF scheduling metric as follows
119876119880119892
119898= sum
119906isin119880119892
119898
(119877 (119906)
119877 (119906)
) (8)
where 119876119880119892
119898denotes the PF scheduling metric for power-
domain multiplexing candidate user set 119880119892119898 119877(119906) is the
instantaneous throughput of user 119906 119877(119906) is the averagethroughput of user 119906
We assume that the SIC receiver of user 119906 is able to cancelperfectly and successively the interference from other user119908 with channel gain 119875119892
1199061015840 |(ℎ119892
1199061015840)119867(119887119892
119898)|2gt 119875119892
119906|(ℎ119892
119906)119867(119887119892
119898)|2 119906 isin
119880119892
119898119889 and 1199061015840 isin 119880119892
1198981199061015840 Then SINR of user 119906 can be estimated
where 120583119892119898119895(119909) 119895 = 1 119903
119892are the eigenvalues of 119860119892
119898(119909)
119860119892
119898(119909) = (Λ
119892)12
(119880119892)119867
119887119892
119898(119887119892
119898)119867
119880119892(Λ119892)12
minus 119909(sum
119899 =119898
(Λ119892)12
(119880119892)119867
119887119892
119899(119887119892
119899)119867
119880119892(Λ
g)12
+ sum
1198921015840=119892
(Λ119892)12
(119880119892)119867
1198611198921015840
(1198611198921015840
)
119867
119880119892(Λ119892)12
)
(16)
Without loss of generality we assume the ordering
120583119892
1198981(119909) ge sdot sdot sdot ge 120583
119892
119898119903119892(119909)
120575119889=
119875119892
119906
1 + 119868119892
11990610158401198981198891015840
(17)
The growth function of CDF 119865(119909) with corresponding PDF119891(119909) is
119892 (119909) =1 minus 119865 (119909)
119891 (119909)
119892infin= lim119909rarrinfin
119892 (119909) = 120575119889(120583119892
119898)infin
(18)
where (1205831198921198981)infin
= lim119909rarrinfin
120583119892
1198981(119909) is a bound positive
constant [11]Considering the ideal channel estimation and the fixed
power assignments to users 119868119892119908119898119889
rarr 0 120575119889rarr 119875119892
119889
Then we have119897119892
119898
sum
119889=1
119875119892
119889= 119875119892 (19)
With extreme value theory [11] we have thatmax1le119906le119880
119892SINR119892119906119898119889
which behaves as 120575119889(120583119892
1198981)infin log119880119892 +
119874(log log119880119892) for 119880119892 rarr infin
The sum rate asymptotic formula for a group 119892 is
119877119892=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (120575119889(120583119892
1198981)infin
log (119880119892)) + 119900 (1)
=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (120575119889) +
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
(120583119892
1198981)infin
+
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log log (119880119892) + 119900 (1)
=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (119875119892119889) +
119903119892
sum
119898=1
119897119892
119898log log (119880119892)
+
119903119892
sum
119898=1
119897119892
119898log (120583119892
1198981)infin
+ 119900 (1)
(20)
as 119880119892 rarr infinSumming over 119892 the sum rate asymptotic formula can be
written as
119877sum =119866
sum
119892=1
119897119892
119898
sum
119889=1
119903119892 log (119875
119889) +
119866
sum
119892=1
119871119892 log log (119880119892)
+ 119874 (1)
(21)
With finite 119873119905antennas total transmit power constraint
of 119875 119880119892 users and 119871119892 data streams per group with the equaltransmission power and common covariance R119892 where usershave mutually statistically independent channel vectors for119880119892rarr infin the sum capacity of a MU-MIMO downlink
system is given by
119877sum =119866
sum
119892=1
119871119892 [
[
log log (119880119892) + log( 119875
sum119866
119892=1119871119892)]
]
+ 119874 (1)
(22)
where 119874(1) denotes a constant independent of 119880119892
3 Designs for JSPM in FDD
In the proposed JSPM scheme the downlink transmissionstrategy is designed in the following three parts
(1) Based on cell environment and channel covariancemeasurement BS can split whole channel space intoseveral disjoint subspaces by using prebeamformingmatrix Therefore based on CSI SINR and RSRPvalues feedback from UE that estimates these valuesbased on the subspaces BS can partition its servingUE into several subspace groups with approximatelysimilar channel covariance eigenvectors and channelpath lossThe spatial and power-domain characters ofeach type of UE can be identified by a set of indicesthat is UE index119906 spatial group index119892 beam index119898 power group index 119889
International Journal of Antennas and Propagation 5
(2) For UE marked with different spatial group indicesor the same spatial group index but different beamindices MU-MIMO downlink transmission on thesame time-frequency resource is performed
(3) For UE marked with the same spatial group indexthe same beam index and different power groupindices multiuser power pairing is performed If userpairing succeeds the multiuser power allocation andthe power-domain usermultiplexing transmission areperformed
Among the above the user grouping and multiuserselection in power-domain are two key issues for the systemperformance the following discussion will focus more on thestrategies of these two issues
31 User Grouping As mentioned before in order to exploiteffectively the JSPM approach the usersrsquo population will bepartitioned into groups according to the following qualitativeprinciples (1) users in the same group have channel covari-ance eigenspace spanning (approximately) a given commonsubspace which characterizes the spatial group BS can getthis information by UE CSI SINR and RSRP measurementfeedback (2) the subspaces of spatial groups served on thesame time-frequency slot by JSDM must be (approximately)mutually orthogonal or at least have empty intersection
The fixed quantization algorithm of user grouping in [11]is an effective and low complexity scheme for applicationin practical network In this algorithm the group subspacesare fixed a priori based on the geometry of cell coverageand their channel scattering In our proposed scheme thefixed quantization algorithm in [11] is extended to frequencydomain When we increase the number of fixed quantizationspatial group to reduce coverage holes the overlappingbetween different spatial groups will also increase and causethe strong interference of intergroups In this case we canallocate transmission resource in different frequency bandsdynamically for UE that belongs to adjacent groups in orderto reduce the interference of intergroups
By choosing 119866 AoAs 120579119892 and fixed ASΔ we can definethe 119866 disjoint intervals [120579119892 minus Δ 120579119892 + Δ] This methodconsists essentially to form predefined ldquonarrow sectorsrdquo andassociate users to sectors according to minimum chordaldistance quantization For example suppose 119866 = 3 choosing1205791= minus45
∘ 1205792 = 0∘ and 1205793 = 45
∘ Δ = 15∘ such as
BG1 BG2 and BG3 shown in Figure 1 we note that thethree subspaces are disjoint However as UE is distributeduniformly and these three subspaces are discontinuous someUE cannot be associated with these subspaces exactly suchas UE4 shown in Figure 1 If we define more dense subspacesuch as 119866 = 5 there are five spatial groups such as BG1BG2 BG5 shown in Figure 1 and different subspace willbe overlapping the interference of inter-group will increaseIn this case we can allocate UE that is in the adjacentsubspace to different frequency resources in order to reducethe intergroup interference
In Figure 1 there are five spatial groups in order to avoidintergroup interference BS can separate BG1 BG2 and BG3
groups and BG4 and BG5 groups into different frequencybands
This scheme makes sense especially for mmWave mobilesystems which have huge frequency broadband to be used
32 Multiuser Transmit Power Allocation and Candidate UserSelection Due to power-domain multiuser multiplexing thetransmit power allocation to one user affects the achievablethroughput of not only that user but also the throughput ofother pairing users The best performance of power-domainmultiuser multiplexing is achieved by exhaustive full searchof user pairs and transmission power allocations [18]
In order to reduce further the computational complexitythe scheme of predefined user grouping and pergroup fixedpower allocation can be used With this approach UE isdivided into different user groups according to their channelpath loss and the predefined thresholds In this predefinedpower-domain grouping the users can be paired togetheronly if they belong to different power groups With thepredefined power grouping the power allocation could alsobe simplified by applying fixed power assignments to theusers belonging to the same group For example for theuser group with good channel gain small power (eg 03P)is allocated and for the user group with bad channel gainlarge power (eg 07P) is allocated where the total powerassigned to different user groups is kept equal to P Predefineduser grouping and fixed power allocation can effectivelydecrease the amount of downlink signaling related toUE datadetection For example the order of successive interferencecancellation (SIC) and information on power assignment donot need to be transmitted in every subframe but rather on alarger time scale
For example as shown in Figure 2 there are two spatialgroups BG1 and BG2 and two power groups PG1 and PG2UE1 belongs to BG1 and PG1 and UE2 and UE3 belong toBG1 and BG2 respectively but both belong to PG2 As forthe aforementioned spatial and power-domain multiplexingstrategies UE3 can be paired with UE1 and UE2 in the spatialdomain and be applied to MU-MIMO transmission UE1can be paired with UE2 in power domain as it belongs tosame spatial group but different power groups and it can beapplied to multiuser power multiplexing transmission UE1can perform SIC operation to cancel the interference fromUE2
33 Computational Complexity Discussion As multiusertransmission of power domain introduced in JSPM will leadto additional algorithm implementation complexity we willdiscuss the computational complexity of JSPM in comparisonwith the exiting JSDM scheme in this section The additionalimplementation complexity of JSDM is composed of threeparts the first part is multiuser selection and pairing inpower domain in BS side the second part is multiplexingtransmission processing in power domain in BS side and thethird part is SIC processing in UE side The first two partsincrease the implementation complexity of BS side and thelast part increases the complexity of UE side
In order to simplify complexity analysis we assume thatUE in power domain is separated into two groups that is cell
6 International Journal of Antennas and Propagation
Numbers of complex numberaddition and multiplication JSDM JSPM with fix power
user paring algorithmJSPM with power domain
greedy algorithmPrebeamforming 119866 times 119874 (119873
119905
3) + 119866 times 119880
119892times119872119892
119861times 119873119905
Multiuser precoding 119866 times 119874((119880119892)3
) + 119866 times 119880119892times 119903119892times119872119892
119861
Power domain user paring 119880119892
119898119889times 119880119892
1198981198891015840times 119866 times 119874 ((119903
119892)2
) 1198622
(119880119892
119898119889+119880119892
1198981198891015840)times 119866 times 119874((119903
119892)2
)
Power domain multiplexing 119880119892times 119903119892times 119866 119880
119892times 119903119892times 119866
center user group and cell edge user group numbers of thetwo groups of UE are noted as 119880119892
119898119889and 119880119892
1198981198891015840 respectively
The computational complexity of JSPM and JSDM in BS sideis presented in Table 1
FromTable 1 we can see that although the power-domainmultiplexing transmission of JSPM leads to computationalcomplexity increase the added complexity accounts fora small part of the overall JSPM complexity The maincomputational complexity comes from the singular valuedecomposition (SVD) processing of channel matrix H =
[H1 sdot sdot sdot H119866] with 119874(119873119905
3) computational complexity in
multiuser beamforming procedure Therefore the extra com-plexity introduced by adopting JSPM has very limited impacton the overall system implementation
From computational complexity listed in Table 1 we cansee that the approach of predefined user grouping and per-group fixed power allocation has more less computationalcomplexity compared with greedy algorithm with the costof little performance degradation which we will discuss inSection 4
For UE side the detection complexity of cell center UEwill not change the detection complexity of cell edge UE willbe double because for cell edge UE they will firstly detectthe information of cell center pairing UE and subtract itfrom receiving signals and then detect its own informationHowever 3GPPRAN4has finished SIC performance require-ment in 3GPP TS36101 [19] which means that Rel12 UE
has enough capability to fulfill the detection performancerequirement of JSPM
4 Performance Evaluation and Analysis
41 Validation of the Asymptotic Analysis In this section wecompare the results obtained via the method of deterministicequivalents withMonte Carlo simulations in order to validatethe asymptotic analysis in Section 2
In our discussion BS is equipped with a uniform circulararray with 100 isotropic antenna elements the distancebetween antenna elements equals 1205822 where 120582 is the carrierwavelength As the user mutual statistical independent chan-nel is important for analytical results the one-ring channelmodel [11] is adopted Users form 119866 = 6 symmetric spatialgroups with the angular spread (AS)Δ = 15
We fixed to serve 119903119892 = 5 data streams per spatial group sothat the total number of active users is 30 119897119892
119898is fixed to equal
2 SNR = P with the noise unit variance normalizationThe comparison of sum spectrum efficiencies of JSPM
obtained by using deterministic equivalent approximationand simulations is illustrated in Figure 3 The green solidline with ldquosquaresrdquo is obtained using the JSPM correspondingdeterministic equivalent approximation the red solid linewith ldquo119909rdquo is obtained through JSPM simulation and the bluesolid line with ldquo119900rdquo is obtained through JSDM simulation
International Journal of Antennas and Propagation 7
JSPM analyticalJSPM simJSDM sim
0
50
100
150
200
250
Sum
rate
(bps
Hz)
5 10 150SNR (dB)
Figure 3 Comparison of sum spectrum efficiencies
For multiuser spatial transmission simulation the approachof ZF beam-forming (ZFBF) and joint group processing(JGP) is used For multiuser transmission of power-domainsimulation the predefined user grouping and per-group fixedpower allocation scheme in power-domain is applied
As shown in Figure 3 the trend of JSPM simulationresult is coincided with that of JSPM deterministic equivalentapproximation Furthermore simulation results show that theperformance of JSPM outperforms JSDM
42 JSPM Performance Gain In this section we presentsystem-level simulation results of the investigation on theperformance gains of JSPM in LTE system In our simulationa multicell system-level simulation is conducted and a 19-hexagonal macro cell model with 3 cells per cell site isemployedThedetails of the simulation assumptions are listedin Table 2
BS is equippedwith antenna array of 8times8X-pol elementsas shown in Figure 4 For the simulation there are 2 verticalprebeamforming groups by using prebeamforming matrix Bcolumns of which can be 4-element DFT weight the highbeam group is tilted to 80 degrees and the low beam groupis tilted to 100 degrees Therefore UE in serving cell canbe partitioned into two vertical spatial groups by BS basedon UE RSRP measurement and feedback responding to twovertical antenna ports each vertical antenna port is mappedto four vertical rows of antenna elements with one polardirection such as +45∘ polar as shown in Figure 4 Then BScan apply MU-MIMO transmission for UE in each verticalgroup by usingmatrixV MatrixV can be composed with UEfeedback precodingmatrix index for eight horizontal antennaports UE gets the horizontal channel spatial information bymeasuring the horizontal CSI-RS ports In the simulation theone horizontal antenna port is mapped to two columns ofantenna elements of one polar direction for example port 0
12
Verticalport 0
Verticalport 1
Horizontalport 01
Horizontalport 23
Horizontalport 45
Horizontalport 67
78 1516middot middot middot middot middot middot
Figure 4 Antenna array with 8 times 8 X-pol elements
25
3
35
4
45
5
Cel
l ave
rage
SE
(bps
Hz)
8 12 164Number of users
JSDM 8 times 8A 30kmJSDM 8 times 8A 3km
JSPM 8 times 8A 3km greedJSPM 8 times 8A 30km fixedJSPM 8 times 8A 3km fixed
Figure 5 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
is mapped to column 1 and 3 of +45∘ polar antenna elementsas shown in Figure 4 In simulation the fix power-domaingrouping scheme is adopted the threshold for predefineduser grouping is 8 dB and the power ratio is (03P 07P)
Figure 5 shows the cell average spectrum efficiency (inbitssecHz) of JSDM and JSPM versus the number of usersin the systemThe results show that JSPM can achieve highercell average spectrum efficiency (more than 15 gain with16 users per cell and 3 kmh velocity condition) than JSDMas JSPM can achieve additional power-domain multiplexinggain The ratio of UE multiplexing in spatial and powerdomain for different amounts of UE per cell are summarizedin Table 3 From Table 3 it can be seen that as the amountof UE per cell is increased the ratio of UE multiplexingin spatial and power domain is increased and the ratio of
8 International Journal of Antennas and Propagation
Table 2 Major simulation parameters
Parameters ValuesTx power 46 dBm for 3D-UMa 500mDuplex FDDBS antenna configurations Antenna elements config 8 times 8 times 2 (plusmn45) 05120582H08120582VTraffic model Full buffer modelWrapping method Geographical distance basedMetrics 5 50 UPTSystem bandwidth 10MHz (50 PRBs)UE attachment Based on RSRPNumber of UEs per cell 481216Network synchronization SynchronizedUE speed 3 kmhUE distribution According to 36873 [20]
ReceiverNonideal channel estimation and interference modeling detailed guidelinesaccording to Rel-12 assumptionsMMSE-IRC and IC receiver and detailed guidelines according to Rel-12assumptions [21]
UE Rx antenna configuration 1 Rx
Feedback
PUSCH 3-2CQI PMI and RI reporting triggered per 5msFeedback delay is 5msRel-10 8 Tx codebook
Transmission scheme Dynamic SUMU-MIMO with rank adaptationOverhead 3 symbols for DL CCHs 2 CRS ports and DM-RS with 12 REs per PRBCSI-RS 5msecSRS 1 Tx 5ms periodicity wideband
Table 3 Ratio of UE multiplexing comparison for different UEnumbers per cell
Number of UEsper cell
Ratio of UEmultiplexing of JSPM
[]
Ratio of UEmultiplexing of JSDM
[]4 302 2848 439 37212 496 41416 507 437
UE multiplexing is about 30 when the number of UEsper cell is 4 while the ratio of UE multiplexing increases toapproximately 50 when the amount of UE is 16 Thereforethe gain of JSPM is also increased as shown in Figure 5
The performances of JSPM and JSDM with UE speed30 kmh are also provided in Figure 5 These results indicatethat the performances of JSPM and JSDM both decrease withUE speed increasing For JSPM the performance loss is about19 when UE speed increases from 3 kmh to 30 kmh with16 users per cell since UE mobility causes the rapid channelchange and reduces the BS channel estimation accuracyTherefore JSPM scheme is more suitable for a stationary or
semistationary scenario such as to provide coverage and highdata rate for users in office rooms or tall buildings
For the sake of performance comparison of differentpower-domain user pairing strategies we also provide theperformance of JSPM with fixed power user paring selection(denoted as blue solid line with ldquolowastrdquo) and greedy user paringselection (denoted as blue solid line with square) in Figure 5Although the performance loss of fixed power user pairingcompared with greedy user paring is about 15 with 16 usersper cell and 3 kmh velocity condition the fixed power userparing algorithm can provide less computational complexityand easier system implementation than greedy algorithm asdiscussed in Section 33 hence it will be the preferredmethodfor practical user pairing in BS side
43 Different Antenna Type Performances In this subsectionwe perform JSPM performance evaluation for two antennatypes with 8 times 8 and 4 times 16 X-polar antenna elementsrespectively As the typical application scenario of massiveMIMO is providing high-speed data service for users intall buildings the vertical grouping scheme which has beendiscussed in the above section is adopted for both 8 times 8 X-polar and 4 times 16 X-polar antenna types in the simulationFor the antenna array with 4 times 16 X-polar antenna ele-ments there are 2 vertical prebeamforming groups by using
International Journal of Antennas and Propagation 9
Figure 6 Antenna array with 4 times 16 X-pol elements
128 164Number of users
28
3
32
34
36
38
4
42
44
46
48
Cell
aver
age s
pect
rum
effici
ency
(bps
Hz)
JSPM 8 times 8AJSPM 4 times 16A
Figure 7 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
prebeamforming matrix B columns of which can be 2-elementDFTweight two beam groups are tilted to 80 and 100degrees respectively Two vertical antenna ports are mappedto four vertical rows of antenna elements with one polardirection each one is corresponding to two rows For eighthorizontal antenna ports each horizontal antenna port ismapped to four columns of antenna elements of one polardirection for example port 0 is mapped to column 1356 of+45∘ polar antenna elements as shown in Figure 6
In the simulation the other schemes such as user spatialgrouping schemeMU-MIMO scheme andmultiuser power-domain transmission scheme are the same as thatmentionedin previous section
Figure 7 shows the cell average spectrum efficiency com-parison between two types of antenna array Figure 8 givesthe CDF comparison of UE spectrum efficiency between twotypes of antenna array with 481216 UEs per cell Based onthese results it can be seen that the 4 times 16 antenna arrayhas better performance than the 8 times 8 antenna array bothin cell average spectrum efficiency and in 50 CDF of UEspectrum efficiency This is because that BS with 4 times 16antenna array which has more horizontal column antennascan form narrower beams and separates the spatial channelinto more subspace therefore it can achieve more spatialmultiplexing gain
JSPM 4 times 16A 16 UEsJSPM 4 times 16A 12 UEsJSPM 4 times 16A 8 UEsJSPM 4 times 16A 4 UEs
JSPM 8 times 8A 16 UEsJSPM 8 times 8A 12 UEsJSPM 8 times 8A 8 UEsJSPM 8 times 8A 4 UEs
0
01
02
03
04
05
06
07
08
09
1
CDF
51 2 3 4 60User spectrum efficiency (bpsHz)
Figure 8 CDF of UE spectrum efficiency
It can be also seen that the antenna array with morecolumn antennas can achieve higher multiplexing gain forJSPM scheme with number limitation of antenna elements inthe practical network
5 Conclusion
In this paper a joint spatial and power-domain multiusertransmission scheme called JSPM is proposed for FDDmassive MIMO systems In this scheme BS divides theUE into different groups in spatial and power domainsand each type of UE is identified with a set of indicesincluding spatial domain index beam index and power-domain index Based on these UE indices BS can performmultiuser paring and scheduling in both spatial and powerdomain Compared with the traditional spatial multiplexingschemes the proposed JSPM scheme can achieve additionalpower-domain multiplexing gain The system-level simula-tion results validate that with 16 users per cell JSPM canachieve more than 15 spectrum efficiency gain comparedwith JSDM and the JSPM gain increases with the numberof active users per cell The simulation results also show thatthe antenna array with larger number of horizontal columnantennas has the better performance since user distributionin the horizontal plane is more intensive than that in thevertical plane in practical networks
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
10 International Journal of Antennas and Propagation
References
[1] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2014
[2] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010
[3] K Zheng L Zhao J Mei B Shao W Xiang and L HanzoldquoSurvey of large-scale MIMO systemsrdquo IEEE CommunicationsSurveys amp Tutorials vol 17 no 3 pp 1738ndash1760 2015
[4] K Zheng YWangWWangM Dohler and JWang ldquoEnergy-efficient wireless in-home the need for interference-controlledfemtocellsrdquo IEEE Wireless Communications vol 18 no 6 pp36ndash44 2011
[5] J Jose A Ashikhmin T L Marzetta and S Vishwanath ldquoPilotcontamination and precoding inmulti-cell TDD systemsrdquo IEEETransactions on Wireless Communications vol 10 no 8 pp2640ndash2651 2011
[6] H Huh A M Tulino and G Caire ldquoNetwork MIMO with lin-ear zero-forcing beamforming large system analysis impact ofchannel estimation and reduced-complexity schedulingrdquo IEEETransactions on InformationTheory vol 58 no 5 pp 2911ndash29342012
[7] G Caire N JindalM Kobayashi andN Ravindran ldquoMultiuserMIMO achievable rates with downlink training and channelstate feedbackrdquo IEEE Transactions on Information Theory vol56 no 6 pp 2845ndash2866 2010
[8] M Kobayashi N Jindal and G Caire ldquoTraining and feedbackoptimization for multiuser MIMO downlinkrdquo IEEE Transac-tions on Communications vol 59 no 8 pp 2228ndash2240 2011
[9] A Adhikary J Nam J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing the large-scale array regimerdquo IEEETransactions on Information Theory vol 59 no 10 pp 6441ndash6463 2013
[10] J Nam J-Y Ahn A Adhikary and G Caire ldquoJoint spatialdivision and multiplexing realizing massive MIMO gains withlimited channel state informationrdquo in Proceedings of the 46thAnnual Conference on Information Sciences and Systems (CISSrsquo12) Princeton NJ USA March 2012
[11] J Nam A Adhikary J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing opportunistic beamforming usergrouping and simplified downlink schedulingrdquo IEEE Journal onSelected Topics in Signal Processing vol 8 no 5 pp 876ndash8902014
[12] VVenkateswaran andA-J van derVeen ldquoAnalog beamformingin MIMO communications with phase shift networks andonline channel estimationrdquo IEEETransactions on Signal Process-ing vol 58 no 8 pp 4131ndash4143 2010
[13] K Zheng L Zhao J Mei M DohlerW Xiang and Y Peng ldquo10Gbs hetsnets with millimeter-wave communications accessand networking-challenges and protocolsrdquo IEEE Communica-tions Magazine vol 53 no 1 pp 222ndash231 2015
[14] O E Ayach R W Heath Jr S Abu-Surra S Rajagopal and ZPi ldquoLow complexity precoding for largemillimeterwaveMIMOsystemsrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo12) pp 3724ndash3729 Ottawa CanadaJune 2012
[15] A Alkhateeb O El Ayach G Leus and R W Heath ldquoHybridprecoding for millimeter wave cellular systems with partialchannel knowledgerdquo in Proceedings of the Information Theory
and Applications Workshop (ITA rsquo13) pp 1ndash5 IEEE San DiegoCalif USA February 2013
[16] D Tse and P Viswanath Fundamentals ofWireless Communica-tion Cambridge University Press Cambridge UK July 2005
[17] M Sharif and B Hassibi ldquoOn the capacity of MIMO broadcastchannels with partial side informationrdquo IEEE Transactions onInformation Theory vol 51 no 2 pp 506ndash522 2005
[18] A Benjebbovu A Li Y Saito Y Kishiyama A Harada and TNakamura ldquoSystem-level performance of downlink NOMA forfuture LTE enhancementsrdquo in Proceedings of the IEEE GlobecomWorkshops (GC rsquo13) pp 66ndash70 IEEE Atlanta GaUSADecem-ber 2013
[19] 3GPP TS36101 (V1310) ldquoEvolved Universal Terrestrial RadioAccess (E-UTRA) User Equipment (UE) radio transmissionand receptionrdquo October 2015
[20] 3GPP TR36873 (V1220) ldquoStudy on 3D channel model forLTErdquo July 2015
[21] 3GPP ldquoStudy on network-assisted interference cancellation andsuppression (NAIC) for LTErdquo 3GPP TR36866 (V1201) 2014
where 120583119892119898119895(119909) 119895 = 1 119903
119892are the eigenvalues of 119860119892
119898(119909)
119860119892
119898(119909) = (Λ
119892)12
(119880119892)119867
119887119892
119898(119887119892
119898)119867
119880119892(Λ119892)12
minus 119909(sum
119899 =119898
(Λ119892)12
(119880119892)119867
119887119892
119899(119887119892
119899)119867
119880119892(Λ
g)12
+ sum
1198921015840=119892
(Λ119892)12
(119880119892)119867
1198611198921015840
(1198611198921015840
)
119867
119880119892(Λ119892)12
)
(16)
Without loss of generality we assume the ordering
120583119892
1198981(119909) ge sdot sdot sdot ge 120583
119892
119898119903119892(119909)
120575119889=
119875119892
119906
1 + 119868119892
11990610158401198981198891015840
(17)
The growth function of CDF 119865(119909) with corresponding PDF119891(119909) is
119892 (119909) =1 minus 119865 (119909)
119891 (119909)
119892infin= lim119909rarrinfin
119892 (119909) = 120575119889(120583119892
119898)infin
(18)
where (1205831198921198981)infin
= lim119909rarrinfin
120583119892
1198981(119909) is a bound positive
constant [11]Considering the ideal channel estimation and the fixed
power assignments to users 119868119892119908119898119889
rarr 0 120575119889rarr 119875119892
119889
Then we have119897119892
119898
sum
119889=1
119875119892
119889= 119875119892 (19)
With extreme value theory [11] we have thatmax1le119906le119880
119892SINR119892119906119898119889
which behaves as 120575119889(120583119892
1198981)infin log119880119892 +
119874(log log119880119892) for 119880119892 rarr infin
The sum rate asymptotic formula for a group 119892 is
119877119892=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (120575119889(120583119892
1198981)infin
log (119880119892)) + 119900 (1)
=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (120575119889) +
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
(120583119892
1198981)infin
+
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log log (119880119892) + 119900 (1)
=
119903119892
sum
119898=1
119897119892
119898
sum
119889=1
log (119875119892119889) +
119903119892
sum
119898=1
119897119892
119898log log (119880119892)
+
119903119892
sum
119898=1
119897119892
119898log (120583119892
1198981)infin
+ 119900 (1)
(20)
as 119880119892 rarr infinSumming over 119892 the sum rate asymptotic formula can be
written as
119877sum =119866
sum
119892=1
119897119892
119898
sum
119889=1
119903119892 log (119875
119889) +
119866
sum
119892=1
119871119892 log log (119880119892)
+ 119874 (1)
(21)
With finite 119873119905antennas total transmit power constraint
of 119875 119880119892 users and 119871119892 data streams per group with the equaltransmission power and common covariance R119892 where usershave mutually statistically independent channel vectors for119880119892rarr infin the sum capacity of a MU-MIMO downlink
system is given by
119877sum =119866
sum
119892=1
119871119892 [
[
log log (119880119892) + log( 119875
sum119866
119892=1119871119892)]
]
+ 119874 (1)
(22)
where 119874(1) denotes a constant independent of 119880119892
3 Designs for JSPM in FDD
In the proposed JSPM scheme the downlink transmissionstrategy is designed in the following three parts
(1) Based on cell environment and channel covariancemeasurement BS can split whole channel space intoseveral disjoint subspaces by using prebeamformingmatrix Therefore based on CSI SINR and RSRPvalues feedback from UE that estimates these valuesbased on the subspaces BS can partition its servingUE into several subspace groups with approximatelysimilar channel covariance eigenvectors and channelpath lossThe spatial and power-domain characters ofeach type of UE can be identified by a set of indicesthat is UE index119906 spatial group index119892 beam index119898 power group index 119889
International Journal of Antennas and Propagation 5
(2) For UE marked with different spatial group indicesor the same spatial group index but different beamindices MU-MIMO downlink transmission on thesame time-frequency resource is performed
(3) For UE marked with the same spatial group indexthe same beam index and different power groupindices multiuser power pairing is performed If userpairing succeeds the multiuser power allocation andthe power-domain usermultiplexing transmission areperformed
Among the above the user grouping and multiuserselection in power-domain are two key issues for the systemperformance the following discussion will focus more on thestrategies of these two issues
31 User Grouping As mentioned before in order to exploiteffectively the JSPM approach the usersrsquo population will bepartitioned into groups according to the following qualitativeprinciples (1) users in the same group have channel covari-ance eigenspace spanning (approximately) a given commonsubspace which characterizes the spatial group BS can getthis information by UE CSI SINR and RSRP measurementfeedback (2) the subspaces of spatial groups served on thesame time-frequency slot by JSDM must be (approximately)mutually orthogonal or at least have empty intersection
The fixed quantization algorithm of user grouping in [11]is an effective and low complexity scheme for applicationin practical network In this algorithm the group subspacesare fixed a priori based on the geometry of cell coverageand their channel scattering In our proposed scheme thefixed quantization algorithm in [11] is extended to frequencydomain When we increase the number of fixed quantizationspatial group to reduce coverage holes the overlappingbetween different spatial groups will also increase and causethe strong interference of intergroups In this case we canallocate transmission resource in different frequency bandsdynamically for UE that belongs to adjacent groups in orderto reduce the interference of intergroups
By choosing 119866 AoAs 120579119892 and fixed ASΔ we can definethe 119866 disjoint intervals [120579119892 minus Δ 120579119892 + Δ] This methodconsists essentially to form predefined ldquonarrow sectorsrdquo andassociate users to sectors according to minimum chordaldistance quantization For example suppose 119866 = 3 choosing1205791= minus45
∘ 1205792 = 0∘ and 1205793 = 45
∘ Δ = 15∘ such as
BG1 BG2 and BG3 shown in Figure 1 we note that thethree subspaces are disjoint However as UE is distributeduniformly and these three subspaces are discontinuous someUE cannot be associated with these subspaces exactly suchas UE4 shown in Figure 1 If we define more dense subspacesuch as 119866 = 5 there are five spatial groups such as BG1BG2 BG5 shown in Figure 1 and different subspace willbe overlapping the interference of inter-group will increaseIn this case we can allocate UE that is in the adjacentsubspace to different frequency resources in order to reducethe intergroup interference
In Figure 1 there are five spatial groups in order to avoidintergroup interference BS can separate BG1 BG2 and BG3
groups and BG4 and BG5 groups into different frequencybands
This scheme makes sense especially for mmWave mobilesystems which have huge frequency broadband to be used
32 Multiuser Transmit Power Allocation and Candidate UserSelection Due to power-domain multiuser multiplexing thetransmit power allocation to one user affects the achievablethroughput of not only that user but also the throughput ofother pairing users The best performance of power-domainmultiuser multiplexing is achieved by exhaustive full searchof user pairs and transmission power allocations [18]
In order to reduce further the computational complexitythe scheme of predefined user grouping and pergroup fixedpower allocation can be used With this approach UE isdivided into different user groups according to their channelpath loss and the predefined thresholds In this predefinedpower-domain grouping the users can be paired togetheronly if they belong to different power groups With thepredefined power grouping the power allocation could alsobe simplified by applying fixed power assignments to theusers belonging to the same group For example for theuser group with good channel gain small power (eg 03P)is allocated and for the user group with bad channel gainlarge power (eg 07P) is allocated where the total powerassigned to different user groups is kept equal to P Predefineduser grouping and fixed power allocation can effectivelydecrease the amount of downlink signaling related toUE datadetection For example the order of successive interferencecancellation (SIC) and information on power assignment donot need to be transmitted in every subframe but rather on alarger time scale
For example as shown in Figure 2 there are two spatialgroups BG1 and BG2 and two power groups PG1 and PG2UE1 belongs to BG1 and PG1 and UE2 and UE3 belong toBG1 and BG2 respectively but both belong to PG2 As forthe aforementioned spatial and power-domain multiplexingstrategies UE3 can be paired with UE1 and UE2 in the spatialdomain and be applied to MU-MIMO transmission UE1can be paired with UE2 in power domain as it belongs tosame spatial group but different power groups and it can beapplied to multiuser power multiplexing transmission UE1can perform SIC operation to cancel the interference fromUE2
33 Computational Complexity Discussion As multiusertransmission of power domain introduced in JSPM will leadto additional algorithm implementation complexity we willdiscuss the computational complexity of JSPM in comparisonwith the exiting JSDM scheme in this section The additionalimplementation complexity of JSDM is composed of threeparts the first part is multiuser selection and pairing inpower domain in BS side the second part is multiplexingtransmission processing in power domain in BS side and thethird part is SIC processing in UE side The first two partsincrease the implementation complexity of BS side and thelast part increases the complexity of UE side
In order to simplify complexity analysis we assume thatUE in power domain is separated into two groups that is cell
6 International Journal of Antennas and Propagation
Numbers of complex numberaddition and multiplication JSDM JSPM with fix power
user paring algorithmJSPM with power domain
greedy algorithmPrebeamforming 119866 times 119874 (119873
119905
3) + 119866 times 119880
119892times119872119892
119861times 119873119905
Multiuser precoding 119866 times 119874((119880119892)3
) + 119866 times 119880119892times 119903119892times119872119892
119861
Power domain user paring 119880119892
119898119889times 119880119892
1198981198891015840times 119866 times 119874 ((119903
119892)2
) 1198622
(119880119892
119898119889+119880119892
1198981198891015840)times 119866 times 119874((119903
119892)2
)
Power domain multiplexing 119880119892times 119903119892times 119866 119880
119892times 119903119892times 119866
center user group and cell edge user group numbers of thetwo groups of UE are noted as 119880119892
119898119889and 119880119892
1198981198891015840 respectively
The computational complexity of JSPM and JSDM in BS sideis presented in Table 1
FromTable 1 we can see that although the power-domainmultiplexing transmission of JSPM leads to computationalcomplexity increase the added complexity accounts fora small part of the overall JSPM complexity The maincomputational complexity comes from the singular valuedecomposition (SVD) processing of channel matrix H =
[H1 sdot sdot sdot H119866] with 119874(119873119905
3) computational complexity in
multiuser beamforming procedure Therefore the extra com-plexity introduced by adopting JSPM has very limited impacton the overall system implementation
From computational complexity listed in Table 1 we cansee that the approach of predefined user grouping and per-group fixed power allocation has more less computationalcomplexity compared with greedy algorithm with the costof little performance degradation which we will discuss inSection 4
For UE side the detection complexity of cell center UEwill not change the detection complexity of cell edge UE willbe double because for cell edge UE they will firstly detectthe information of cell center pairing UE and subtract itfrom receiving signals and then detect its own informationHowever 3GPPRAN4has finished SIC performance require-ment in 3GPP TS36101 [19] which means that Rel12 UE
has enough capability to fulfill the detection performancerequirement of JSPM
4 Performance Evaluation and Analysis
41 Validation of the Asymptotic Analysis In this section wecompare the results obtained via the method of deterministicequivalents withMonte Carlo simulations in order to validatethe asymptotic analysis in Section 2
In our discussion BS is equipped with a uniform circulararray with 100 isotropic antenna elements the distancebetween antenna elements equals 1205822 where 120582 is the carrierwavelength As the user mutual statistical independent chan-nel is important for analytical results the one-ring channelmodel [11] is adopted Users form 119866 = 6 symmetric spatialgroups with the angular spread (AS)Δ = 15
We fixed to serve 119903119892 = 5 data streams per spatial group sothat the total number of active users is 30 119897119892
119898is fixed to equal
2 SNR = P with the noise unit variance normalizationThe comparison of sum spectrum efficiencies of JSPM
obtained by using deterministic equivalent approximationand simulations is illustrated in Figure 3 The green solidline with ldquosquaresrdquo is obtained using the JSPM correspondingdeterministic equivalent approximation the red solid linewith ldquo119909rdquo is obtained through JSPM simulation and the bluesolid line with ldquo119900rdquo is obtained through JSDM simulation
International Journal of Antennas and Propagation 7
JSPM analyticalJSPM simJSDM sim
0
50
100
150
200
250
Sum
rate
(bps
Hz)
5 10 150SNR (dB)
Figure 3 Comparison of sum spectrum efficiencies
For multiuser spatial transmission simulation the approachof ZF beam-forming (ZFBF) and joint group processing(JGP) is used For multiuser transmission of power-domainsimulation the predefined user grouping and per-group fixedpower allocation scheme in power-domain is applied
As shown in Figure 3 the trend of JSPM simulationresult is coincided with that of JSPM deterministic equivalentapproximation Furthermore simulation results show that theperformance of JSPM outperforms JSDM
42 JSPM Performance Gain In this section we presentsystem-level simulation results of the investigation on theperformance gains of JSPM in LTE system In our simulationa multicell system-level simulation is conducted and a 19-hexagonal macro cell model with 3 cells per cell site isemployedThedetails of the simulation assumptions are listedin Table 2
BS is equippedwith antenna array of 8times8X-pol elementsas shown in Figure 4 For the simulation there are 2 verticalprebeamforming groups by using prebeamforming matrix Bcolumns of which can be 4-element DFT weight the highbeam group is tilted to 80 degrees and the low beam groupis tilted to 100 degrees Therefore UE in serving cell canbe partitioned into two vertical spatial groups by BS basedon UE RSRP measurement and feedback responding to twovertical antenna ports each vertical antenna port is mappedto four vertical rows of antenna elements with one polardirection such as +45∘ polar as shown in Figure 4 Then BScan apply MU-MIMO transmission for UE in each verticalgroup by usingmatrixV MatrixV can be composed with UEfeedback precodingmatrix index for eight horizontal antennaports UE gets the horizontal channel spatial information bymeasuring the horizontal CSI-RS ports In the simulation theone horizontal antenna port is mapped to two columns ofantenna elements of one polar direction for example port 0
12
Verticalport 0
Verticalport 1
Horizontalport 01
Horizontalport 23
Horizontalport 45
Horizontalport 67
78 1516middot middot middot middot middot middot
Figure 4 Antenna array with 8 times 8 X-pol elements
25
3
35
4
45
5
Cel
l ave
rage
SE
(bps
Hz)
8 12 164Number of users
JSDM 8 times 8A 30kmJSDM 8 times 8A 3km
JSPM 8 times 8A 3km greedJSPM 8 times 8A 30km fixedJSPM 8 times 8A 3km fixed
Figure 5 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
is mapped to column 1 and 3 of +45∘ polar antenna elementsas shown in Figure 4 In simulation the fix power-domaingrouping scheme is adopted the threshold for predefineduser grouping is 8 dB and the power ratio is (03P 07P)
Figure 5 shows the cell average spectrum efficiency (inbitssecHz) of JSDM and JSPM versus the number of usersin the systemThe results show that JSPM can achieve highercell average spectrum efficiency (more than 15 gain with16 users per cell and 3 kmh velocity condition) than JSDMas JSPM can achieve additional power-domain multiplexinggain The ratio of UE multiplexing in spatial and powerdomain for different amounts of UE per cell are summarizedin Table 3 From Table 3 it can be seen that as the amountof UE per cell is increased the ratio of UE multiplexingin spatial and power domain is increased and the ratio of
8 International Journal of Antennas and Propagation
Table 2 Major simulation parameters
Parameters ValuesTx power 46 dBm for 3D-UMa 500mDuplex FDDBS antenna configurations Antenna elements config 8 times 8 times 2 (plusmn45) 05120582H08120582VTraffic model Full buffer modelWrapping method Geographical distance basedMetrics 5 50 UPTSystem bandwidth 10MHz (50 PRBs)UE attachment Based on RSRPNumber of UEs per cell 481216Network synchronization SynchronizedUE speed 3 kmhUE distribution According to 36873 [20]
ReceiverNonideal channel estimation and interference modeling detailed guidelinesaccording to Rel-12 assumptionsMMSE-IRC and IC receiver and detailed guidelines according to Rel-12assumptions [21]
UE Rx antenna configuration 1 Rx
Feedback
PUSCH 3-2CQI PMI and RI reporting triggered per 5msFeedback delay is 5msRel-10 8 Tx codebook
Transmission scheme Dynamic SUMU-MIMO with rank adaptationOverhead 3 symbols for DL CCHs 2 CRS ports and DM-RS with 12 REs per PRBCSI-RS 5msecSRS 1 Tx 5ms periodicity wideband
Table 3 Ratio of UE multiplexing comparison for different UEnumbers per cell
Number of UEsper cell
Ratio of UEmultiplexing of JSPM
[]
Ratio of UEmultiplexing of JSDM
[]4 302 2848 439 37212 496 41416 507 437
UE multiplexing is about 30 when the number of UEsper cell is 4 while the ratio of UE multiplexing increases toapproximately 50 when the amount of UE is 16 Thereforethe gain of JSPM is also increased as shown in Figure 5
The performances of JSPM and JSDM with UE speed30 kmh are also provided in Figure 5 These results indicatethat the performances of JSPM and JSDM both decrease withUE speed increasing For JSPM the performance loss is about19 when UE speed increases from 3 kmh to 30 kmh with16 users per cell since UE mobility causes the rapid channelchange and reduces the BS channel estimation accuracyTherefore JSPM scheme is more suitable for a stationary or
semistationary scenario such as to provide coverage and highdata rate for users in office rooms or tall buildings
For the sake of performance comparison of differentpower-domain user pairing strategies we also provide theperformance of JSPM with fixed power user paring selection(denoted as blue solid line with ldquolowastrdquo) and greedy user paringselection (denoted as blue solid line with square) in Figure 5Although the performance loss of fixed power user pairingcompared with greedy user paring is about 15 with 16 usersper cell and 3 kmh velocity condition the fixed power userparing algorithm can provide less computational complexityand easier system implementation than greedy algorithm asdiscussed in Section 33 hence it will be the preferredmethodfor practical user pairing in BS side
43 Different Antenna Type Performances In this subsectionwe perform JSPM performance evaluation for two antennatypes with 8 times 8 and 4 times 16 X-polar antenna elementsrespectively As the typical application scenario of massiveMIMO is providing high-speed data service for users intall buildings the vertical grouping scheme which has beendiscussed in the above section is adopted for both 8 times 8 X-polar and 4 times 16 X-polar antenna types in the simulationFor the antenna array with 4 times 16 X-polar antenna ele-ments there are 2 vertical prebeamforming groups by using
International Journal of Antennas and Propagation 9
Figure 6 Antenna array with 4 times 16 X-pol elements
128 164Number of users
28
3
32
34
36
38
4
42
44
46
48
Cell
aver
age s
pect
rum
effici
ency
(bps
Hz)
JSPM 8 times 8AJSPM 4 times 16A
Figure 7 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
prebeamforming matrix B columns of which can be 2-elementDFTweight two beam groups are tilted to 80 and 100degrees respectively Two vertical antenna ports are mappedto four vertical rows of antenna elements with one polardirection each one is corresponding to two rows For eighthorizontal antenna ports each horizontal antenna port ismapped to four columns of antenna elements of one polardirection for example port 0 is mapped to column 1356 of+45∘ polar antenna elements as shown in Figure 6
In the simulation the other schemes such as user spatialgrouping schemeMU-MIMO scheme andmultiuser power-domain transmission scheme are the same as thatmentionedin previous section
Figure 7 shows the cell average spectrum efficiency com-parison between two types of antenna array Figure 8 givesthe CDF comparison of UE spectrum efficiency between twotypes of antenna array with 481216 UEs per cell Based onthese results it can be seen that the 4 times 16 antenna arrayhas better performance than the 8 times 8 antenna array bothin cell average spectrum efficiency and in 50 CDF of UEspectrum efficiency This is because that BS with 4 times 16antenna array which has more horizontal column antennascan form narrower beams and separates the spatial channelinto more subspace therefore it can achieve more spatialmultiplexing gain
JSPM 4 times 16A 16 UEsJSPM 4 times 16A 12 UEsJSPM 4 times 16A 8 UEsJSPM 4 times 16A 4 UEs
JSPM 8 times 8A 16 UEsJSPM 8 times 8A 12 UEsJSPM 8 times 8A 8 UEsJSPM 8 times 8A 4 UEs
0
01
02
03
04
05
06
07
08
09
1
CDF
51 2 3 4 60User spectrum efficiency (bpsHz)
Figure 8 CDF of UE spectrum efficiency
It can be also seen that the antenna array with morecolumn antennas can achieve higher multiplexing gain forJSPM scheme with number limitation of antenna elements inthe practical network
5 Conclusion
In this paper a joint spatial and power-domain multiusertransmission scheme called JSPM is proposed for FDDmassive MIMO systems In this scheme BS divides theUE into different groups in spatial and power domainsand each type of UE is identified with a set of indicesincluding spatial domain index beam index and power-domain index Based on these UE indices BS can performmultiuser paring and scheduling in both spatial and powerdomain Compared with the traditional spatial multiplexingschemes the proposed JSPM scheme can achieve additionalpower-domain multiplexing gain The system-level simula-tion results validate that with 16 users per cell JSPM canachieve more than 15 spectrum efficiency gain comparedwith JSDM and the JSPM gain increases with the numberof active users per cell The simulation results also show thatthe antenna array with larger number of horizontal columnantennas has the better performance since user distributionin the horizontal plane is more intensive than that in thevertical plane in practical networks
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
10 International Journal of Antennas and Propagation
References
[1] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2014
[2] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010
[3] K Zheng L Zhao J Mei B Shao W Xiang and L HanzoldquoSurvey of large-scale MIMO systemsrdquo IEEE CommunicationsSurveys amp Tutorials vol 17 no 3 pp 1738ndash1760 2015
[4] K Zheng YWangWWangM Dohler and JWang ldquoEnergy-efficient wireless in-home the need for interference-controlledfemtocellsrdquo IEEE Wireless Communications vol 18 no 6 pp36ndash44 2011
[5] J Jose A Ashikhmin T L Marzetta and S Vishwanath ldquoPilotcontamination and precoding inmulti-cell TDD systemsrdquo IEEETransactions on Wireless Communications vol 10 no 8 pp2640ndash2651 2011
[6] H Huh A M Tulino and G Caire ldquoNetwork MIMO with lin-ear zero-forcing beamforming large system analysis impact ofchannel estimation and reduced-complexity schedulingrdquo IEEETransactions on InformationTheory vol 58 no 5 pp 2911ndash29342012
[7] G Caire N JindalM Kobayashi andN Ravindran ldquoMultiuserMIMO achievable rates with downlink training and channelstate feedbackrdquo IEEE Transactions on Information Theory vol56 no 6 pp 2845ndash2866 2010
[8] M Kobayashi N Jindal and G Caire ldquoTraining and feedbackoptimization for multiuser MIMO downlinkrdquo IEEE Transac-tions on Communications vol 59 no 8 pp 2228ndash2240 2011
[9] A Adhikary J Nam J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing the large-scale array regimerdquo IEEETransactions on Information Theory vol 59 no 10 pp 6441ndash6463 2013
[10] J Nam J-Y Ahn A Adhikary and G Caire ldquoJoint spatialdivision and multiplexing realizing massive MIMO gains withlimited channel state informationrdquo in Proceedings of the 46thAnnual Conference on Information Sciences and Systems (CISSrsquo12) Princeton NJ USA March 2012
[11] J Nam A Adhikary J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing opportunistic beamforming usergrouping and simplified downlink schedulingrdquo IEEE Journal onSelected Topics in Signal Processing vol 8 no 5 pp 876ndash8902014
[12] VVenkateswaran andA-J van derVeen ldquoAnalog beamformingin MIMO communications with phase shift networks andonline channel estimationrdquo IEEETransactions on Signal Process-ing vol 58 no 8 pp 4131ndash4143 2010
[13] K Zheng L Zhao J Mei M DohlerW Xiang and Y Peng ldquo10Gbs hetsnets with millimeter-wave communications accessand networking-challenges and protocolsrdquo IEEE Communica-tions Magazine vol 53 no 1 pp 222ndash231 2015
[14] O E Ayach R W Heath Jr S Abu-Surra S Rajagopal and ZPi ldquoLow complexity precoding for largemillimeterwaveMIMOsystemsrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo12) pp 3724ndash3729 Ottawa CanadaJune 2012
[15] A Alkhateeb O El Ayach G Leus and R W Heath ldquoHybridprecoding for millimeter wave cellular systems with partialchannel knowledgerdquo in Proceedings of the Information Theory
and Applications Workshop (ITA rsquo13) pp 1ndash5 IEEE San DiegoCalif USA February 2013
[16] D Tse and P Viswanath Fundamentals ofWireless Communica-tion Cambridge University Press Cambridge UK July 2005
[17] M Sharif and B Hassibi ldquoOn the capacity of MIMO broadcastchannels with partial side informationrdquo IEEE Transactions onInformation Theory vol 51 no 2 pp 506ndash522 2005
[18] A Benjebbovu A Li Y Saito Y Kishiyama A Harada and TNakamura ldquoSystem-level performance of downlink NOMA forfuture LTE enhancementsrdquo in Proceedings of the IEEE GlobecomWorkshops (GC rsquo13) pp 66ndash70 IEEE Atlanta GaUSADecem-ber 2013
[19] 3GPP TS36101 (V1310) ldquoEvolved Universal Terrestrial RadioAccess (E-UTRA) User Equipment (UE) radio transmissionand receptionrdquo October 2015
[20] 3GPP TR36873 (V1220) ldquoStudy on 3D channel model forLTErdquo July 2015
[21] 3GPP ldquoStudy on network-assisted interference cancellation andsuppression (NAIC) for LTErdquo 3GPP TR36866 (V1201) 2014
International Journal of Antennas and Propagation 5
(2) For UE marked with different spatial group indicesor the same spatial group index but different beamindices MU-MIMO downlink transmission on thesame time-frequency resource is performed
(3) For UE marked with the same spatial group indexthe same beam index and different power groupindices multiuser power pairing is performed If userpairing succeeds the multiuser power allocation andthe power-domain usermultiplexing transmission areperformed
Among the above the user grouping and multiuserselection in power-domain are two key issues for the systemperformance the following discussion will focus more on thestrategies of these two issues
31 User Grouping As mentioned before in order to exploiteffectively the JSPM approach the usersrsquo population will bepartitioned into groups according to the following qualitativeprinciples (1) users in the same group have channel covari-ance eigenspace spanning (approximately) a given commonsubspace which characterizes the spatial group BS can getthis information by UE CSI SINR and RSRP measurementfeedback (2) the subspaces of spatial groups served on thesame time-frequency slot by JSDM must be (approximately)mutually orthogonal or at least have empty intersection
The fixed quantization algorithm of user grouping in [11]is an effective and low complexity scheme for applicationin practical network In this algorithm the group subspacesare fixed a priori based on the geometry of cell coverageand their channel scattering In our proposed scheme thefixed quantization algorithm in [11] is extended to frequencydomain When we increase the number of fixed quantizationspatial group to reduce coverage holes the overlappingbetween different spatial groups will also increase and causethe strong interference of intergroups In this case we canallocate transmission resource in different frequency bandsdynamically for UE that belongs to adjacent groups in orderto reduce the interference of intergroups
By choosing 119866 AoAs 120579119892 and fixed ASΔ we can definethe 119866 disjoint intervals [120579119892 minus Δ 120579119892 + Δ] This methodconsists essentially to form predefined ldquonarrow sectorsrdquo andassociate users to sectors according to minimum chordaldistance quantization For example suppose 119866 = 3 choosing1205791= minus45
∘ 1205792 = 0∘ and 1205793 = 45
∘ Δ = 15∘ such as
BG1 BG2 and BG3 shown in Figure 1 we note that thethree subspaces are disjoint However as UE is distributeduniformly and these three subspaces are discontinuous someUE cannot be associated with these subspaces exactly suchas UE4 shown in Figure 1 If we define more dense subspacesuch as 119866 = 5 there are five spatial groups such as BG1BG2 BG5 shown in Figure 1 and different subspace willbe overlapping the interference of inter-group will increaseIn this case we can allocate UE that is in the adjacentsubspace to different frequency resources in order to reducethe intergroup interference
In Figure 1 there are five spatial groups in order to avoidintergroup interference BS can separate BG1 BG2 and BG3
groups and BG4 and BG5 groups into different frequencybands
This scheme makes sense especially for mmWave mobilesystems which have huge frequency broadband to be used
32 Multiuser Transmit Power Allocation and Candidate UserSelection Due to power-domain multiuser multiplexing thetransmit power allocation to one user affects the achievablethroughput of not only that user but also the throughput ofother pairing users The best performance of power-domainmultiuser multiplexing is achieved by exhaustive full searchof user pairs and transmission power allocations [18]
In order to reduce further the computational complexitythe scheme of predefined user grouping and pergroup fixedpower allocation can be used With this approach UE isdivided into different user groups according to their channelpath loss and the predefined thresholds In this predefinedpower-domain grouping the users can be paired togetheronly if they belong to different power groups With thepredefined power grouping the power allocation could alsobe simplified by applying fixed power assignments to theusers belonging to the same group For example for theuser group with good channel gain small power (eg 03P)is allocated and for the user group with bad channel gainlarge power (eg 07P) is allocated where the total powerassigned to different user groups is kept equal to P Predefineduser grouping and fixed power allocation can effectivelydecrease the amount of downlink signaling related toUE datadetection For example the order of successive interferencecancellation (SIC) and information on power assignment donot need to be transmitted in every subframe but rather on alarger time scale
For example as shown in Figure 2 there are two spatialgroups BG1 and BG2 and two power groups PG1 and PG2UE1 belongs to BG1 and PG1 and UE2 and UE3 belong toBG1 and BG2 respectively but both belong to PG2 As forthe aforementioned spatial and power-domain multiplexingstrategies UE3 can be paired with UE1 and UE2 in the spatialdomain and be applied to MU-MIMO transmission UE1can be paired with UE2 in power domain as it belongs tosame spatial group but different power groups and it can beapplied to multiuser power multiplexing transmission UE1can perform SIC operation to cancel the interference fromUE2
33 Computational Complexity Discussion As multiusertransmission of power domain introduced in JSPM will leadto additional algorithm implementation complexity we willdiscuss the computational complexity of JSPM in comparisonwith the exiting JSDM scheme in this section The additionalimplementation complexity of JSDM is composed of threeparts the first part is multiuser selection and pairing inpower domain in BS side the second part is multiplexingtransmission processing in power domain in BS side and thethird part is SIC processing in UE side The first two partsincrease the implementation complexity of BS side and thelast part increases the complexity of UE side
In order to simplify complexity analysis we assume thatUE in power domain is separated into two groups that is cell
6 International Journal of Antennas and Propagation
Numbers of complex numberaddition and multiplication JSDM JSPM with fix power
user paring algorithmJSPM with power domain
greedy algorithmPrebeamforming 119866 times 119874 (119873
119905
3) + 119866 times 119880
119892times119872119892
119861times 119873119905
Multiuser precoding 119866 times 119874((119880119892)3
) + 119866 times 119880119892times 119903119892times119872119892
119861
Power domain user paring 119880119892
119898119889times 119880119892
1198981198891015840times 119866 times 119874 ((119903
119892)2
) 1198622
(119880119892
119898119889+119880119892
1198981198891015840)times 119866 times 119874((119903
119892)2
)
Power domain multiplexing 119880119892times 119903119892times 119866 119880
119892times 119903119892times 119866
center user group and cell edge user group numbers of thetwo groups of UE are noted as 119880119892
119898119889and 119880119892
1198981198891015840 respectively
The computational complexity of JSPM and JSDM in BS sideis presented in Table 1
FromTable 1 we can see that although the power-domainmultiplexing transmission of JSPM leads to computationalcomplexity increase the added complexity accounts fora small part of the overall JSPM complexity The maincomputational complexity comes from the singular valuedecomposition (SVD) processing of channel matrix H =
[H1 sdot sdot sdot H119866] with 119874(119873119905
3) computational complexity in
multiuser beamforming procedure Therefore the extra com-plexity introduced by adopting JSPM has very limited impacton the overall system implementation
From computational complexity listed in Table 1 we cansee that the approach of predefined user grouping and per-group fixed power allocation has more less computationalcomplexity compared with greedy algorithm with the costof little performance degradation which we will discuss inSection 4
For UE side the detection complexity of cell center UEwill not change the detection complexity of cell edge UE willbe double because for cell edge UE they will firstly detectthe information of cell center pairing UE and subtract itfrom receiving signals and then detect its own informationHowever 3GPPRAN4has finished SIC performance require-ment in 3GPP TS36101 [19] which means that Rel12 UE
has enough capability to fulfill the detection performancerequirement of JSPM
4 Performance Evaluation and Analysis
41 Validation of the Asymptotic Analysis In this section wecompare the results obtained via the method of deterministicequivalents withMonte Carlo simulations in order to validatethe asymptotic analysis in Section 2
In our discussion BS is equipped with a uniform circulararray with 100 isotropic antenna elements the distancebetween antenna elements equals 1205822 where 120582 is the carrierwavelength As the user mutual statistical independent chan-nel is important for analytical results the one-ring channelmodel [11] is adopted Users form 119866 = 6 symmetric spatialgroups with the angular spread (AS)Δ = 15
We fixed to serve 119903119892 = 5 data streams per spatial group sothat the total number of active users is 30 119897119892
119898is fixed to equal
2 SNR = P with the noise unit variance normalizationThe comparison of sum spectrum efficiencies of JSPM
obtained by using deterministic equivalent approximationand simulations is illustrated in Figure 3 The green solidline with ldquosquaresrdquo is obtained using the JSPM correspondingdeterministic equivalent approximation the red solid linewith ldquo119909rdquo is obtained through JSPM simulation and the bluesolid line with ldquo119900rdquo is obtained through JSDM simulation
International Journal of Antennas and Propagation 7
JSPM analyticalJSPM simJSDM sim
0
50
100
150
200
250
Sum
rate
(bps
Hz)
5 10 150SNR (dB)
Figure 3 Comparison of sum spectrum efficiencies
For multiuser spatial transmission simulation the approachof ZF beam-forming (ZFBF) and joint group processing(JGP) is used For multiuser transmission of power-domainsimulation the predefined user grouping and per-group fixedpower allocation scheme in power-domain is applied
As shown in Figure 3 the trend of JSPM simulationresult is coincided with that of JSPM deterministic equivalentapproximation Furthermore simulation results show that theperformance of JSPM outperforms JSDM
42 JSPM Performance Gain In this section we presentsystem-level simulation results of the investigation on theperformance gains of JSPM in LTE system In our simulationa multicell system-level simulation is conducted and a 19-hexagonal macro cell model with 3 cells per cell site isemployedThedetails of the simulation assumptions are listedin Table 2
BS is equippedwith antenna array of 8times8X-pol elementsas shown in Figure 4 For the simulation there are 2 verticalprebeamforming groups by using prebeamforming matrix Bcolumns of which can be 4-element DFT weight the highbeam group is tilted to 80 degrees and the low beam groupis tilted to 100 degrees Therefore UE in serving cell canbe partitioned into two vertical spatial groups by BS basedon UE RSRP measurement and feedback responding to twovertical antenna ports each vertical antenna port is mappedto four vertical rows of antenna elements with one polardirection such as +45∘ polar as shown in Figure 4 Then BScan apply MU-MIMO transmission for UE in each verticalgroup by usingmatrixV MatrixV can be composed with UEfeedback precodingmatrix index for eight horizontal antennaports UE gets the horizontal channel spatial information bymeasuring the horizontal CSI-RS ports In the simulation theone horizontal antenna port is mapped to two columns ofantenna elements of one polar direction for example port 0
12
Verticalport 0
Verticalport 1
Horizontalport 01
Horizontalport 23
Horizontalport 45
Horizontalport 67
78 1516middot middot middot middot middot middot
Figure 4 Antenna array with 8 times 8 X-pol elements
25
3
35
4
45
5
Cel
l ave
rage
SE
(bps
Hz)
8 12 164Number of users
JSDM 8 times 8A 30kmJSDM 8 times 8A 3km
JSPM 8 times 8A 3km greedJSPM 8 times 8A 30km fixedJSPM 8 times 8A 3km fixed
Figure 5 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
is mapped to column 1 and 3 of +45∘ polar antenna elementsas shown in Figure 4 In simulation the fix power-domaingrouping scheme is adopted the threshold for predefineduser grouping is 8 dB and the power ratio is (03P 07P)
Figure 5 shows the cell average spectrum efficiency (inbitssecHz) of JSDM and JSPM versus the number of usersin the systemThe results show that JSPM can achieve highercell average spectrum efficiency (more than 15 gain with16 users per cell and 3 kmh velocity condition) than JSDMas JSPM can achieve additional power-domain multiplexinggain The ratio of UE multiplexing in spatial and powerdomain for different amounts of UE per cell are summarizedin Table 3 From Table 3 it can be seen that as the amountof UE per cell is increased the ratio of UE multiplexingin spatial and power domain is increased and the ratio of
8 International Journal of Antennas and Propagation
Table 2 Major simulation parameters
Parameters ValuesTx power 46 dBm for 3D-UMa 500mDuplex FDDBS antenna configurations Antenna elements config 8 times 8 times 2 (plusmn45) 05120582H08120582VTraffic model Full buffer modelWrapping method Geographical distance basedMetrics 5 50 UPTSystem bandwidth 10MHz (50 PRBs)UE attachment Based on RSRPNumber of UEs per cell 481216Network synchronization SynchronizedUE speed 3 kmhUE distribution According to 36873 [20]
ReceiverNonideal channel estimation and interference modeling detailed guidelinesaccording to Rel-12 assumptionsMMSE-IRC and IC receiver and detailed guidelines according to Rel-12assumptions [21]
UE Rx antenna configuration 1 Rx
Feedback
PUSCH 3-2CQI PMI and RI reporting triggered per 5msFeedback delay is 5msRel-10 8 Tx codebook
Transmission scheme Dynamic SUMU-MIMO with rank adaptationOverhead 3 symbols for DL CCHs 2 CRS ports and DM-RS with 12 REs per PRBCSI-RS 5msecSRS 1 Tx 5ms periodicity wideband
Table 3 Ratio of UE multiplexing comparison for different UEnumbers per cell
Number of UEsper cell
Ratio of UEmultiplexing of JSPM
[]
Ratio of UEmultiplexing of JSDM
[]4 302 2848 439 37212 496 41416 507 437
UE multiplexing is about 30 when the number of UEsper cell is 4 while the ratio of UE multiplexing increases toapproximately 50 when the amount of UE is 16 Thereforethe gain of JSPM is also increased as shown in Figure 5
The performances of JSPM and JSDM with UE speed30 kmh are also provided in Figure 5 These results indicatethat the performances of JSPM and JSDM both decrease withUE speed increasing For JSPM the performance loss is about19 when UE speed increases from 3 kmh to 30 kmh with16 users per cell since UE mobility causes the rapid channelchange and reduces the BS channel estimation accuracyTherefore JSPM scheme is more suitable for a stationary or
semistationary scenario such as to provide coverage and highdata rate for users in office rooms or tall buildings
For the sake of performance comparison of differentpower-domain user pairing strategies we also provide theperformance of JSPM with fixed power user paring selection(denoted as blue solid line with ldquolowastrdquo) and greedy user paringselection (denoted as blue solid line with square) in Figure 5Although the performance loss of fixed power user pairingcompared with greedy user paring is about 15 with 16 usersper cell and 3 kmh velocity condition the fixed power userparing algorithm can provide less computational complexityand easier system implementation than greedy algorithm asdiscussed in Section 33 hence it will be the preferredmethodfor practical user pairing in BS side
43 Different Antenna Type Performances In this subsectionwe perform JSPM performance evaluation for two antennatypes with 8 times 8 and 4 times 16 X-polar antenna elementsrespectively As the typical application scenario of massiveMIMO is providing high-speed data service for users intall buildings the vertical grouping scheme which has beendiscussed in the above section is adopted for both 8 times 8 X-polar and 4 times 16 X-polar antenna types in the simulationFor the antenna array with 4 times 16 X-polar antenna ele-ments there are 2 vertical prebeamforming groups by using
International Journal of Antennas and Propagation 9
Figure 6 Antenna array with 4 times 16 X-pol elements
128 164Number of users
28
3
32
34
36
38
4
42
44
46
48
Cell
aver
age s
pect
rum
effici
ency
(bps
Hz)
JSPM 8 times 8AJSPM 4 times 16A
Figure 7 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
prebeamforming matrix B columns of which can be 2-elementDFTweight two beam groups are tilted to 80 and 100degrees respectively Two vertical antenna ports are mappedto four vertical rows of antenna elements with one polardirection each one is corresponding to two rows For eighthorizontal antenna ports each horizontal antenna port ismapped to four columns of antenna elements of one polardirection for example port 0 is mapped to column 1356 of+45∘ polar antenna elements as shown in Figure 6
In the simulation the other schemes such as user spatialgrouping schemeMU-MIMO scheme andmultiuser power-domain transmission scheme are the same as thatmentionedin previous section
Figure 7 shows the cell average spectrum efficiency com-parison between two types of antenna array Figure 8 givesthe CDF comparison of UE spectrum efficiency between twotypes of antenna array with 481216 UEs per cell Based onthese results it can be seen that the 4 times 16 antenna arrayhas better performance than the 8 times 8 antenna array bothin cell average spectrum efficiency and in 50 CDF of UEspectrum efficiency This is because that BS with 4 times 16antenna array which has more horizontal column antennascan form narrower beams and separates the spatial channelinto more subspace therefore it can achieve more spatialmultiplexing gain
JSPM 4 times 16A 16 UEsJSPM 4 times 16A 12 UEsJSPM 4 times 16A 8 UEsJSPM 4 times 16A 4 UEs
JSPM 8 times 8A 16 UEsJSPM 8 times 8A 12 UEsJSPM 8 times 8A 8 UEsJSPM 8 times 8A 4 UEs
0
01
02
03
04
05
06
07
08
09
1
CDF
51 2 3 4 60User spectrum efficiency (bpsHz)
Figure 8 CDF of UE spectrum efficiency
It can be also seen that the antenna array with morecolumn antennas can achieve higher multiplexing gain forJSPM scheme with number limitation of antenna elements inthe practical network
5 Conclusion
In this paper a joint spatial and power-domain multiusertransmission scheme called JSPM is proposed for FDDmassive MIMO systems In this scheme BS divides theUE into different groups in spatial and power domainsand each type of UE is identified with a set of indicesincluding spatial domain index beam index and power-domain index Based on these UE indices BS can performmultiuser paring and scheduling in both spatial and powerdomain Compared with the traditional spatial multiplexingschemes the proposed JSPM scheme can achieve additionalpower-domain multiplexing gain The system-level simula-tion results validate that with 16 users per cell JSPM canachieve more than 15 spectrum efficiency gain comparedwith JSDM and the JSPM gain increases with the numberof active users per cell The simulation results also show thatthe antenna array with larger number of horizontal columnantennas has the better performance since user distributionin the horizontal plane is more intensive than that in thevertical plane in practical networks
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
10 International Journal of Antennas and Propagation
References
[1] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2014
[2] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010
[3] K Zheng L Zhao J Mei B Shao W Xiang and L HanzoldquoSurvey of large-scale MIMO systemsrdquo IEEE CommunicationsSurveys amp Tutorials vol 17 no 3 pp 1738ndash1760 2015
[4] K Zheng YWangWWangM Dohler and JWang ldquoEnergy-efficient wireless in-home the need for interference-controlledfemtocellsrdquo IEEE Wireless Communications vol 18 no 6 pp36ndash44 2011
[5] J Jose A Ashikhmin T L Marzetta and S Vishwanath ldquoPilotcontamination and precoding inmulti-cell TDD systemsrdquo IEEETransactions on Wireless Communications vol 10 no 8 pp2640ndash2651 2011
[6] H Huh A M Tulino and G Caire ldquoNetwork MIMO with lin-ear zero-forcing beamforming large system analysis impact ofchannel estimation and reduced-complexity schedulingrdquo IEEETransactions on InformationTheory vol 58 no 5 pp 2911ndash29342012
[7] G Caire N JindalM Kobayashi andN Ravindran ldquoMultiuserMIMO achievable rates with downlink training and channelstate feedbackrdquo IEEE Transactions on Information Theory vol56 no 6 pp 2845ndash2866 2010
[8] M Kobayashi N Jindal and G Caire ldquoTraining and feedbackoptimization for multiuser MIMO downlinkrdquo IEEE Transac-tions on Communications vol 59 no 8 pp 2228ndash2240 2011
[9] A Adhikary J Nam J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing the large-scale array regimerdquo IEEETransactions on Information Theory vol 59 no 10 pp 6441ndash6463 2013
[10] J Nam J-Y Ahn A Adhikary and G Caire ldquoJoint spatialdivision and multiplexing realizing massive MIMO gains withlimited channel state informationrdquo in Proceedings of the 46thAnnual Conference on Information Sciences and Systems (CISSrsquo12) Princeton NJ USA March 2012
[11] J Nam A Adhikary J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing opportunistic beamforming usergrouping and simplified downlink schedulingrdquo IEEE Journal onSelected Topics in Signal Processing vol 8 no 5 pp 876ndash8902014
[12] VVenkateswaran andA-J van derVeen ldquoAnalog beamformingin MIMO communications with phase shift networks andonline channel estimationrdquo IEEETransactions on Signal Process-ing vol 58 no 8 pp 4131ndash4143 2010
[13] K Zheng L Zhao J Mei M DohlerW Xiang and Y Peng ldquo10Gbs hetsnets with millimeter-wave communications accessand networking-challenges and protocolsrdquo IEEE Communica-tions Magazine vol 53 no 1 pp 222ndash231 2015
[14] O E Ayach R W Heath Jr S Abu-Surra S Rajagopal and ZPi ldquoLow complexity precoding for largemillimeterwaveMIMOsystemsrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo12) pp 3724ndash3729 Ottawa CanadaJune 2012
[15] A Alkhateeb O El Ayach G Leus and R W Heath ldquoHybridprecoding for millimeter wave cellular systems with partialchannel knowledgerdquo in Proceedings of the Information Theory
and Applications Workshop (ITA rsquo13) pp 1ndash5 IEEE San DiegoCalif USA February 2013
[16] D Tse and P Viswanath Fundamentals ofWireless Communica-tion Cambridge University Press Cambridge UK July 2005
[17] M Sharif and B Hassibi ldquoOn the capacity of MIMO broadcastchannels with partial side informationrdquo IEEE Transactions onInformation Theory vol 51 no 2 pp 506ndash522 2005
[18] A Benjebbovu A Li Y Saito Y Kishiyama A Harada and TNakamura ldquoSystem-level performance of downlink NOMA forfuture LTE enhancementsrdquo in Proceedings of the IEEE GlobecomWorkshops (GC rsquo13) pp 66ndash70 IEEE Atlanta GaUSADecem-ber 2013
[19] 3GPP TS36101 (V1310) ldquoEvolved Universal Terrestrial RadioAccess (E-UTRA) User Equipment (UE) radio transmissionand receptionrdquo October 2015
[20] 3GPP TR36873 (V1220) ldquoStudy on 3D channel model forLTErdquo July 2015
[21] 3GPP ldquoStudy on network-assisted interference cancellation andsuppression (NAIC) for LTErdquo 3GPP TR36866 (V1201) 2014
Numbers of complex numberaddition and multiplication JSDM JSPM with fix power
user paring algorithmJSPM with power domain
greedy algorithmPrebeamforming 119866 times 119874 (119873
119905
3) + 119866 times 119880
119892times119872119892
119861times 119873119905
Multiuser precoding 119866 times 119874((119880119892)3
) + 119866 times 119880119892times 119903119892times119872119892
119861
Power domain user paring 119880119892
119898119889times 119880119892
1198981198891015840times 119866 times 119874 ((119903
119892)2
) 1198622
(119880119892
119898119889+119880119892
1198981198891015840)times 119866 times 119874((119903
119892)2
)
Power domain multiplexing 119880119892times 119903119892times 119866 119880
119892times 119903119892times 119866
center user group and cell edge user group numbers of thetwo groups of UE are noted as 119880119892
119898119889and 119880119892
1198981198891015840 respectively
The computational complexity of JSPM and JSDM in BS sideis presented in Table 1
FromTable 1 we can see that although the power-domainmultiplexing transmission of JSPM leads to computationalcomplexity increase the added complexity accounts fora small part of the overall JSPM complexity The maincomputational complexity comes from the singular valuedecomposition (SVD) processing of channel matrix H =
[H1 sdot sdot sdot H119866] with 119874(119873119905
3) computational complexity in
multiuser beamforming procedure Therefore the extra com-plexity introduced by adopting JSPM has very limited impacton the overall system implementation
From computational complexity listed in Table 1 we cansee that the approach of predefined user grouping and per-group fixed power allocation has more less computationalcomplexity compared with greedy algorithm with the costof little performance degradation which we will discuss inSection 4
For UE side the detection complexity of cell center UEwill not change the detection complexity of cell edge UE willbe double because for cell edge UE they will firstly detectthe information of cell center pairing UE and subtract itfrom receiving signals and then detect its own informationHowever 3GPPRAN4has finished SIC performance require-ment in 3GPP TS36101 [19] which means that Rel12 UE
has enough capability to fulfill the detection performancerequirement of JSPM
4 Performance Evaluation and Analysis
41 Validation of the Asymptotic Analysis In this section wecompare the results obtained via the method of deterministicequivalents withMonte Carlo simulations in order to validatethe asymptotic analysis in Section 2
In our discussion BS is equipped with a uniform circulararray with 100 isotropic antenna elements the distancebetween antenna elements equals 1205822 where 120582 is the carrierwavelength As the user mutual statistical independent chan-nel is important for analytical results the one-ring channelmodel [11] is adopted Users form 119866 = 6 symmetric spatialgroups with the angular spread (AS)Δ = 15
We fixed to serve 119903119892 = 5 data streams per spatial group sothat the total number of active users is 30 119897119892
119898is fixed to equal
2 SNR = P with the noise unit variance normalizationThe comparison of sum spectrum efficiencies of JSPM
obtained by using deterministic equivalent approximationand simulations is illustrated in Figure 3 The green solidline with ldquosquaresrdquo is obtained using the JSPM correspondingdeterministic equivalent approximation the red solid linewith ldquo119909rdquo is obtained through JSPM simulation and the bluesolid line with ldquo119900rdquo is obtained through JSDM simulation
International Journal of Antennas and Propagation 7
JSPM analyticalJSPM simJSDM sim
0
50
100
150
200
250
Sum
rate
(bps
Hz)
5 10 150SNR (dB)
Figure 3 Comparison of sum spectrum efficiencies
For multiuser spatial transmission simulation the approachof ZF beam-forming (ZFBF) and joint group processing(JGP) is used For multiuser transmission of power-domainsimulation the predefined user grouping and per-group fixedpower allocation scheme in power-domain is applied
As shown in Figure 3 the trend of JSPM simulationresult is coincided with that of JSPM deterministic equivalentapproximation Furthermore simulation results show that theperformance of JSPM outperforms JSDM
42 JSPM Performance Gain In this section we presentsystem-level simulation results of the investigation on theperformance gains of JSPM in LTE system In our simulationa multicell system-level simulation is conducted and a 19-hexagonal macro cell model with 3 cells per cell site isemployedThedetails of the simulation assumptions are listedin Table 2
BS is equippedwith antenna array of 8times8X-pol elementsas shown in Figure 4 For the simulation there are 2 verticalprebeamforming groups by using prebeamforming matrix Bcolumns of which can be 4-element DFT weight the highbeam group is tilted to 80 degrees and the low beam groupis tilted to 100 degrees Therefore UE in serving cell canbe partitioned into two vertical spatial groups by BS basedon UE RSRP measurement and feedback responding to twovertical antenna ports each vertical antenna port is mappedto four vertical rows of antenna elements with one polardirection such as +45∘ polar as shown in Figure 4 Then BScan apply MU-MIMO transmission for UE in each verticalgroup by usingmatrixV MatrixV can be composed with UEfeedback precodingmatrix index for eight horizontal antennaports UE gets the horizontal channel spatial information bymeasuring the horizontal CSI-RS ports In the simulation theone horizontal antenna port is mapped to two columns ofantenna elements of one polar direction for example port 0
12
Verticalport 0
Verticalport 1
Horizontalport 01
Horizontalport 23
Horizontalport 45
Horizontalport 67
78 1516middot middot middot middot middot middot
Figure 4 Antenna array with 8 times 8 X-pol elements
25
3
35
4
45
5
Cel
l ave
rage
SE
(bps
Hz)
8 12 164Number of users
JSDM 8 times 8A 30kmJSDM 8 times 8A 3km
JSPM 8 times 8A 3km greedJSPM 8 times 8A 30km fixedJSPM 8 times 8A 3km fixed
Figure 5 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
is mapped to column 1 and 3 of +45∘ polar antenna elementsas shown in Figure 4 In simulation the fix power-domaingrouping scheme is adopted the threshold for predefineduser grouping is 8 dB and the power ratio is (03P 07P)
Figure 5 shows the cell average spectrum efficiency (inbitssecHz) of JSDM and JSPM versus the number of usersin the systemThe results show that JSPM can achieve highercell average spectrum efficiency (more than 15 gain with16 users per cell and 3 kmh velocity condition) than JSDMas JSPM can achieve additional power-domain multiplexinggain The ratio of UE multiplexing in spatial and powerdomain for different amounts of UE per cell are summarizedin Table 3 From Table 3 it can be seen that as the amountof UE per cell is increased the ratio of UE multiplexingin spatial and power domain is increased and the ratio of
8 International Journal of Antennas and Propagation
Table 2 Major simulation parameters
Parameters ValuesTx power 46 dBm for 3D-UMa 500mDuplex FDDBS antenna configurations Antenna elements config 8 times 8 times 2 (plusmn45) 05120582H08120582VTraffic model Full buffer modelWrapping method Geographical distance basedMetrics 5 50 UPTSystem bandwidth 10MHz (50 PRBs)UE attachment Based on RSRPNumber of UEs per cell 481216Network synchronization SynchronizedUE speed 3 kmhUE distribution According to 36873 [20]
ReceiverNonideal channel estimation and interference modeling detailed guidelinesaccording to Rel-12 assumptionsMMSE-IRC and IC receiver and detailed guidelines according to Rel-12assumptions [21]
UE Rx antenna configuration 1 Rx
Feedback
PUSCH 3-2CQI PMI and RI reporting triggered per 5msFeedback delay is 5msRel-10 8 Tx codebook
Transmission scheme Dynamic SUMU-MIMO with rank adaptationOverhead 3 symbols for DL CCHs 2 CRS ports and DM-RS with 12 REs per PRBCSI-RS 5msecSRS 1 Tx 5ms periodicity wideband
Table 3 Ratio of UE multiplexing comparison for different UEnumbers per cell
Number of UEsper cell
Ratio of UEmultiplexing of JSPM
[]
Ratio of UEmultiplexing of JSDM
[]4 302 2848 439 37212 496 41416 507 437
UE multiplexing is about 30 when the number of UEsper cell is 4 while the ratio of UE multiplexing increases toapproximately 50 when the amount of UE is 16 Thereforethe gain of JSPM is also increased as shown in Figure 5
The performances of JSPM and JSDM with UE speed30 kmh are also provided in Figure 5 These results indicatethat the performances of JSPM and JSDM both decrease withUE speed increasing For JSPM the performance loss is about19 when UE speed increases from 3 kmh to 30 kmh with16 users per cell since UE mobility causes the rapid channelchange and reduces the BS channel estimation accuracyTherefore JSPM scheme is more suitable for a stationary or
semistationary scenario such as to provide coverage and highdata rate for users in office rooms or tall buildings
For the sake of performance comparison of differentpower-domain user pairing strategies we also provide theperformance of JSPM with fixed power user paring selection(denoted as blue solid line with ldquolowastrdquo) and greedy user paringselection (denoted as blue solid line with square) in Figure 5Although the performance loss of fixed power user pairingcompared with greedy user paring is about 15 with 16 usersper cell and 3 kmh velocity condition the fixed power userparing algorithm can provide less computational complexityand easier system implementation than greedy algorithm asdiscussed in Section 33 hence it will be the preferredmethodfor practical user pairing in BS side
43 Different Antenna Type Performances In this subsectionwe perform JSPM performance evaluation for two antennatypes with 8 times 8 and 4 times 16 X-polar antenna elementsrespectively As the typical application scenario of massiveMIMO is providing high-speed data service for users intall buildings the vertical grouping scheme which has beendiscussed in the above section is adopted for both 8 times 8 X-polar and 4 times 16 X-polar antenna types in the simulationFor the antenna array with 4 times 16 X-polar antenna ele-ments there are 2 vertical prebeamforming groups by using
International Journal of Antennas and Propagation 9
Figure 6 Antenna array with 4 times 16 X-pol elements
128 164Number of users
28
3
32
34
36
38
4
42
44
46
48
Cell
aver
age s
pect
rum
effici
ency
(bps
Hz)
JSPM 8 times 8AJSPM 4 times 16A
Figure 7 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
prebeamforming matrix B columns of which can be 2-elementDFTweight two beam groups are tilted to 80 and 100degrees respectively Two vertical antenna ports are mappedto four vertical rows of antenna elements with one polardirection each one is corresponding to two rows For eighthorizontal antenna ports each horizontal antenna port ismapped to four columns of antenna elements of one polardirection for example port 0 is mapped to column 1356 of+45∘ polar antenna elements as shown in Figure 6
In the simulation the other schemes such as user spatialgrouping schemeMU-MIMO scheme andmultiuser power-domain transmission scheme are the same as thatmentionedin previous section
Figure 7 shows the cell average spectrum efficiency com-parison between two types of antenna array Figure 8 givesthe CDF comparison of UE spectrum efficiency between twotypes of antenna array with 481216 UEs per cell Based onthese results it can be seen that the 4 times 16 antenna arrayhas better performance than the 8 times 8 antenna array bothin cell average spectrum efficiency and in 50 CDF of UEspectrum efficiency This is because that BS with 4 times 16antenna array which has more horizontal column antennascan form narrower beams and separates the spatial channelinto more subspace therefore it can achieve more spatialmultiplexing gain
JSPM 4 times 16A 16 UEsJSPM 4 times 16A 12 UEsJSPM 4 times 16A 8 UEsJSPM 4 times 16A 4 UEs
JSPM 8 times 8A 16 UEsJSPM 8 times 8A 12 UEsJSPM 8 times 8A 8 UEsJSPM 8 times 8A 4 UEs
0
01
02
03
04
05
06
07
08
09
1
CDF
51 2 3 4 60User spectrum efficiency (bpsHz)
Figure 8 CDF of UE spectrum efficiency
It can be also seen that the antenna array with morecolumn antennas can achieve higher multiplexing gain forJSPM scheme with number limitation of antenna elements inthe practical network
5 Conclusion
In this paper a joint spatial and power-domain multiusertransmission scheme called JSPM is proposed for FDDmassive MIMO systems In this scheme BS divides theUE into different groups in spatial and power domainsand each type of UE is identified with a set of indicesincluding spatial domain index beam index and power-domain index Based on these UE indices BS can performmultiuser paring and scheduling in both spatial and powerdomain Compared with the traditional spatial multiplexingschemes the proposed JSPM scheme can achieve additionalpower-domain multiplexing gain The system-level simula-tion results validate that with 16 users per cell JSPM canachieve more than 15 spectrum efficiency gain comparedwith JSDM and the JSPM gain increases with the numberof active users per cell The simulation results also show thatthe antenna array with larger number of horizontal columnantennas has the better performance since user distributionin the horizontal plane is more intensive than that in thevertical plane in practical networks
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
10 International Journal of Antennas and Propagation
References
[1] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2014
[2] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010
[3] K Zheng L Zhao J Mei B Shao W Xiang and L HanzoldquoSurvey of large-scale MIMO systemsrdquo IEEE CommunicationsSurveys amp Tutorials vol 17 no 3 pp 1738ndash1760 2015
[4] K Zheng YWangWWangM Dohler and JWang ldquoEnergy-efficient wireless in-home the need for interference-controlledfemtocellsrdquo IEEE Wireless Communications vol 18 no 6 pp36ndash44 2011
[5] J Jose A Ashikhmin T L Marzetta and S Vishwanath ldquoPilotcontamination and precoding inmulti-cell TDD systemsrdquo IEEETransactions on Wireless Communications vol 10 no 8 pp2640ndash2651 2011
[6] H Huh A M Tulino and G Caire ldquoNetwork MIMO with lin-ear zero-forcing beamforming large system analysis impact ofchannel estimation and reduced-complexity schedulingrdquo IEEETransactions on InformationTheory vol 58 no 5 pp 2911ndash29342012
[7] G Caire N JindalM Kobayashi andN Ravindran ldquoMultiuserMIMO achievable rates with downlink training and channelstate feedbackrdquo IEEE Transactions on Information Theory vol56 no 6 pp 2845ndash2866 2010
[8] M Kobayashi N Jindal and G Caire ldquoTraining and feedbackoptimization for multiuser MIMO downlinkrdquo IEEE Transac-tions on Communications vol 59 no 8 pp 2228ndash2240 2011
[9] A Adhikary J Nam J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing the large-scale array regimerdquo IEEETransactions on Information Theory vol 59 no 10 pp 6441ndash6463 2013
[10] J Nam J-Y Ahn A Adhikary and G Caire ldquoJoint spatialdivision and multiplexing realizing massive MIMO gains withlimited channel state informationrdquo in Proceedings of the 46thAnnual Conference on Information Sciences and Systems (CISSrsquo12) Princeton NJ USA March 2012
[11] J Nam A Adhikary J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing opportunistic beamforming usergrouping and simplified downlink schedulingrdquo IEEE Journal onSelected Topics in Signal Processing vol 8 no 5 pp 876ndash8902014
[12] VVenkateswaran andA-J van derVeen ldquoAnalog beamformingin MIMO communications with phase shift networks andonline channel estimationrdquo IEEETransactions on Signal Process-ing vol 58 no 8 pp 4131ndash4143 2010
[13] K Zheng L Zhao J Mei M DohlerW Xiang and Y Peng ldquo10Gbs hetsnets with millimeter-wave communications accessand networking-challenges and protocolsrdquo IEEE Communica-tions Magazine vol 53 no 1 pp 222ndash231 2015
[14] O E Ayach R W Heath Jr S Abu-Surra S Rajagopal and ZPi ldquoLow complexity precoding for largemillimeterwaveMIMOsystemsrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo12) pp 3724ndash3729 Ottawa CanadaJune 2012
[15] A Alkhateeb O El Ayach G Leus and R W Heath ldquoHybridprecoding for millimeter wave cellular systems with partialchannel knowledgerdquo in Proceedings of the Information Theory
and Applications Workshop (ITA rsquo13) pp 1ndash5 IEEE San DiegoCalif USA February 2013
[16] D Tse and P Viswanath Fundamentals ofWireless Communica-tion Cambridge University Press Cambridge UK July 2005
[17] M Sharif and B Hassibi ldquoOn the capacity of MIMO broadcastchannels with partial side informationrdquo IEEE Transactions onInformation Theory vol 51 no 2 pp 506ndash522 2005
[18] A Benjebbovu A Li Y Saito Y Kishiyama A Harada and TNakamura ldquoSystem-level performance of downlink NOMA forfuture LTE enhancementsrdquo in Proceedings of the IEEE GlobecomWorkshops (GC rsquo13) pp 66ndash70 IEEE Atlanta GaUSADecem-ber 2013
[19] 3GPP TS36101 (V1310) ldquoEvolved Universal Terrestrial RadioAccess (E-UTRA) User Equipment (UE) radio transmissionand receptionrdquo October 2015
[20] 3GPP TR36873 (V1220) ldquoStudy on 3D channel model forLTErdquo July 2015
[21] 3GPP ldquoStudy on network-assisted interference cancellation andsuppression (NAIC) for LTErdquo 3GPP TR36866 (V1201) 2014
International Journal of Antennas and Propagation 7
JSPM analyticalJSPM simJSDM sim
0
50
100
150
200
250
Sum
rate
(bps
Hz)
5 10 150SNR (dB)
Figure 3 Comparison of sum spectrum efficiencies
For multiuser spatial transmission simulation the approachof ZF beam-forming (ZFBF) and joint group processing(JGP) is used For multiuser transmission of power-domainsimulation the predefined user grouping and per-group fixedpower allocation scheme in power-domain is applied
As shown in Figure 3 the trend of JSPM simulationresult is coincided with that of JSPM deterministic equivalentapproximation Furthermore simulation results show that theperformance of JSPM outperforms JSDM
42 JSPM Performance Gain In this section we presentsystem-level simulation results of the investigation on theperformance gains of JSPM in LTE system In our simulationa multicell system-level simulation is conducted and a 19-hexagonal macro cell model with 3 cells per cell site isemployedThedetails of the simulation assumptions are listedin Table 2
BS is equippedwith antenna array of 8times8X-pol elementsas shown in Figure 4 For the simulation there are 2 verticalprebeamforming groups by using prebeamforming matrix Bcolumns of which can be 4-element DFT weight the highbeam group is tilted to 80 degrees and the low beam groupis tilted to 100 degrees Therefore UE in serving cell canbe partitioned into two vertical spatial groups by BS basedon UE RSRP measurement and feedback responding to twovertical antenna ports each vertical antenna port is mappedto four vertical rows of antenna elements with one polardirection such as +45∘ polar as shown in Figure 4 Then BScan apply MU-MIMO transmission for UE in each verticalgroup by usingmatrixV MatrixV can be composed with UEfeedback precodingmatrix index for eight horizontal antennaports UE gets the horizontal channel spatial information bymeasuring the horizontal CSI-RS ports In the simulation theone horizontal antenna port is mapped to two columns ofantenna elements of one polar direction for example port 0
12
Verticalport 0
Verticalport 1
Horizontalport 01
Horizontalport 23
Horizontalport 45
Horizontalport 67
78 1516middot middot middot middot middot middot
Figure 4 Antenna array with 8 times 8 X-pol elements
25
3
35
4
45
5
Cel
l ave
rage
SE
(bps
Hz)
8 12 164Number of users
JSDM 8 times 8A 30kmJSDM 8 times 8A 3km
JSPM 8 times 8A 3km greedJSPM 8 times 8A 30km fixedJSPM 8 times 8A 3km fixed
Figure 5 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
is mapped to column 1 and 3 of +45∘ polar antenna elementsas shown in Figure 4 In simulation the fix power-domaingrouping scheme is adopted the threshold for predefineduser grouping is 8 dB and the power ratio is (03P 07P)
Figure 5 shows the cell average spectrum efficiency (inbitssecHz) of JSDM and JSPM versus the number of usersin the systemThe results show that JSPM can achieve highercell average spectrum efficiency (more than 15 gain with16 users per cell and 3 kmh velocity condition) than JSDMas JSPM can achieve additional power-domain multiplexinggain The ratio of UE multiplexing in spatial and powerdomain for different amounts of UE per cell are summarizedin Table 3 From Table 3 it can be seen that as the amountof UE per cell is increased the ratio of UE multiplexingin spatial and power domain is increased and the ratio of
8 International Journal of Antennas and Propagation
Table 2 Major simulation parameters
Parameters ValuesTx power 46 dBm for 3D-UMa 500mDuplex FDDBS antenna configurations Antenna elements config 8 times 8 times 2 (plusmn45) 05120582H08120582VTraffic model Full buffer modelWrapping method Geographical distance basedMetrics 5 50 UPTSystem bandwidth 10MHz (50 PRBs)UE attachment Based on RSRPNumber of UEs per cell 481216Network synchronization SynchronizedUE speed 3 kmhUE distribution According to 36873 [20]
ReceiverNonideal channel estimation and interference modeling detailed guidelinesaccording to Rel-12 assumptionsMMSE-IRC and IC receiver and detailed guidelines according to Rel-12assumptions [21]
UE Rx antenna configuration 1 Rx
Feedback
PUSCH 3-2CQI PMI and RI reporting triggered per 5msFeedback delay is 5msRel-10 8 Tx codebook
Transmission scheme Dynamic SUMU-MIMO with rank adaptationOverhead 3 symbols for DL CCHs 2 CRS ports and DM-RS with 12 REs per PRBCSI-RS 5msecSRS 1 Tx 5ms periodicity wideband
Table 3 Ratio of UE multiplexing comparison for different UEnumbers per cell
Number of UEsper cell
Ratio of UEmultiplexing of JSPM
[]
Ratio of UEmultiplexing of JSDM
[]4 302 2848 439 37212 496 41416 507 437
UE multiplexing is about 30 when the number of UEsper cell is 4 while the ratio of UE multiplexing increases toapproximately 50 when the amount of UE is 16 Thereforethe gain of JSPM is also increased as shown in Figure 5
The performances of JSPM and JSDM with UE speed30 kmh are also provided in Figure 5 These results indicatethat the performances of JSPM and JSDM both decrease withUE speed increasing For JSPM the performance loss is about19 when UE speed increases from 3 kmh to 30 kmh with16 users per cell since UE mobility causes the rapid channelchange and reduces the BS channel estimation accuracyTherefore JSPM scheme is more suitable for a stationary or
semistationary scenario such as to provide coverage and highdata rate for users in office rooms or tall buildings
For the sake of performance comparison of differentpower-domain user pairing strategies we also provide theperformance of JSPM with fixed power user paring selection(denoted as blue solid line with ldquolowastrdquo) and greedy user paringselection (denoted as blue solid line with square) in Figure 5Although the performance loss of fixed power user pairingcompared with greedy user paring is about 15 with 16 usersper cell and 3 kmh velocity condition the fixed power userparing algorithm can provide less computational complexityand easier system implementation than greedy algorithm asdiscussed in Section 33 hence it will be the preferredmethodfor practical user pairing in BS side
43 Different Antenna Type Performances In this subsectionwe perform JSPM performance evaluation for two antennatypes with 8 times 8 and 4 times 16 X-polar antenna elementsrespectively As the typical application scenario of massiveMIMO is providing high-speed data service for users intall buildings the vertical grouping scheme which has beendiscussed in the above section is adopted for both 8 times 8 X-polar and 4 times 16 X-polar antenna types in the simulationFor the antenna array with 4 times 16 X-polar antenna ele-ments there are 2 vertical prebeamforming groups by using
International Journal of Antennas and Propagation 9
Figure 6 Antenna array with 4 times 16 X-pol elements
128 164Number of users
28
3
32
34
36
38
4
42
44
46
48
Cell
aver
age s
pect
rum
effici
ency
(bps
Hz)
JSPM 8 times 8AJSPM 4 times 16A
Figure 7 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
prebeamforming matrix B columns of which can be 2-elementDFTweight two beam groups are tilted to 80 and 100degrees respectively Two vertical antenna ports are mappedto four vertical rows of antenna elements with one polardirection each one is corresponding to two rows For eighthorizontal antenna ports each horizontal antenna port ismapped to four columns of antenna elements of one polardirection for example port 0 is mapped to column 1356 of+45∘ polar antenna elements as shown in Figure 6
In the simulation the other schemes such as user spatialgrouping schemeMU-MIMO scheme andmultiuser power-domain transmission scheme are the same as thatmentionedin previous section
Figure 7 shows the cell average spectrum efficiency com-parison between two types of antenna array Figure 8 givesthe CDF comparison of UE spectrum efficiency between twotypes of antenna array with 481216 UEs per cell Based onthese results it can be seen that the 4 times 16 antenna arrayhas better performance than the 8 times 8 antenna array bothin cell average spectrum efficiency and in 50 CDF of UEspectrum efficiency This is because that BS with 4 times 16antenna array which has more horizontal column antennascan form narrower beams and separates the spatial channelinto more subspace therefore it can achieve more spatialmultiplexing gain
JSPM 4 times 16A 16 UEsJSPM 4 times 16A 12 UEsJSPM 4 times 16A 8 UEsJSPM 4 times 16A 4 UEs
JSPM 8 times 8A 16 UEsJSPM 8 times 8A 12 UEsJSPM 8 times 8A 8 UEsJSPM 8 times 8A 4 UEs
0
01
02
03
04
05
06
07
08
09
1
CDF
51 2 3 4 60User spectrum efficiency (bpsHz)
Figure 8 CDF of UE spectrum efficiency
It can be also seen that the antenna array with morecolumn antennas can achieve higher multiplexing gain forJSPM scheme with number limitation of antenna elements inthe practical network
5 Conclusion
In this paper a joint spatial and power-domain multiusertransmission scheme called JSPM is proposed for FDDmassive MIMO systems In this scheme BS divides theUE into different groups in spatial and power domainsand each type of UE is identified with a set of indicesincluding spatial domain index beam index and power-domain index Based on these UE indices BS can performmultiuser paring and scheduling in both spatial and powerdomain Compared with the traditional spatial multiplexingschemes the proposed JSPM scheme can achieve additionalpower-domain multiplexing gain The system-level simula-tion results validate that with 16 users per cell JSPM canachieve more than 15 spectrum efficiency gain comparedwith JSDM and the JSPM gain increases with the numberof active users per cell The simulation results also show thatthe antenna array with larger number of horizontal columnantennas has the better performance since user distributionin the horizontal plane is more intensive than that in thevertical plane in practical networks
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
10 International Journal of Antennas and Propagation
References
[1] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2014
[2] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010
[3] K Zheng L Zhao J Mei B Shao W Xiang and L HanzoldquoSurvey of large-scale MIMO systemsrdquo IEEE CommunicationsSurveys amp Tutorials vol 17 no 3 pp 1738ndash1760 2015
[4] K Zheng YWangWWangM Dohler and JWang ldquoEnergy-efficient wireless in-home the need for interference-controlledfemtocellsrdquo IEEE Wireless Communications vol 18 no 6 pp36ndash44 2011
[5] J Jose A Ashikhmin T L Marzetta and S Vishwanath ldquoPilotcontamination and precoding inmulti-cell TDD systemsrdquo IEEETransactions on Wireless Communications vol 10 no 8 pp2640ndash2651 2011
[6] H Huh A M Tulino and G Caire ldquoNetwork MIMO with lin-ear zero-forcing beamforming large system analysis impact ofchannel estimation and reduced-complexity schedulingrdquo IEEETransactions on InformationTheory vol 58 no 5 pp 2911ndash29342012
[7] G Caire N JindalM Kobayashi andN Ravindran ldquoMultiuserMIMO achievable rates with downlink training and channelstate feedbackrdquo IEEE Transactions on Information Theory vol56 no 6 pp 2845ndash2866 2010
[8] M Kobayashi N Jindal and G Caire ldquoTraining and feedbackoptimization for multiuser MIMO downlinkrdquo IEEE Transac-tions on Communications vol 59 no 8 pp 2228ndash2240 2011
[9] A Adhikary J Nam J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing the large-scale array regimerdquo IEEETransactions on Information Theory vol 59 no 10 pp 6441ndash6463 2013
[10] J Nam J-Y Ahn A Adhikary and G Caire ldquoJoint spatialdivision and multiplexing realizing massive MIMO gains withlimited channel state informationrdquo in Proceedings of the 46thAnnual Conference on Information Sciences and Systems (CISSrsquo12) Princeton NJ USA March 2012
[11] J Nam A Adhikary J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing opportunistic beamforming usergrouping and simplified downlink schedulingrdquo IEEE Journal onSelected Topics in Signal Processing vol 8 no 5 pp 876ndash8902014
[12] VVenkateswaran andA-J van derVeen ldquoAnalog beamformingin MIMO communications with phase shift networks andonline channel estimationrdquo IEEETransactions on Signal Process-ing vol 58 no 8 pp 4131ndash4143 2010
[13] K Zheng L Zhao J Mei M DohlerW Xiang and Y Peng ldquo10Gbs hetsnets with millimeter-wave communications accessand networking-challenges and protocolsrdquo IEEE Communica-tions Magazine vol 53 no 1 pp 222ndash231 2015
[14] O E Ayach R W Heath Jr S Abu-Surra S Rajagopal and ZPi ldquoLow complexity precoding for largemillimeterwaveMIMOsystemsrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo12) pp 3724ndash3729 Ottawa CanadaJune 2012
[15] A Alkhateeb O El Ayach G Leus and R W Heath ldquoHybridprecoding for millimeter wave cellular systems with partialchannel knowledgerdquo in Proceedings of the Information Theory
and Applications Workshop (ITA rsquo13) pp 1ndash5 IEEE San DiegoCalif USA February 2013
[16] D Tse and P Viswanath Fundamentals ofWireless Communica-tion Cambridge University Press Cambridge UK July 2005
[17] M Sharif and B Hassibi ldquoOn the capacity of MIMO broadcastchannels with partial side informationrdquo IEEE Transactions onInformation Theory vol 51 no 2 pp 506ndash522 2005
[18] A Benjebbovu A Li Y Saito Y Kishiyama A Harada and TNakamura ldquoSystem-level performance of downlink NOMA forfuture LTE enhancementsrdquo in Proceedings of the IEEE GlobecomWorkshops (GC rsquo13) pp 66ndash70 IEEE Atlanta GaUSADecem-ber 2013
[19] 3GPP TS36101 (V1310) ldquoEvolved Universal Terrestrial RadioAccess (E-UTRA) User Equipment (UE) radio transmissionand receptionrdquo October 2015
[20] 3GPP TR36873 (V1220) ldquoStudy on 3D channel model forLTErdquo July 2015
[21] 3GPP ldquoStudy on network-assisted interference cancellation andsuppression (NAIC) for LTErdquo 3GPP TR36866 (V1201) 2014
8 International Journal of Antennas and Propagation
Table 2 Major simulation parameters
Parameters ValuesTx power 46 dBm for 3D-UMa 500mDuplex FDDBS antenna configurations Antenna elements config 8 times 8 times 2 (plusmn45) 05120582H08120582VTraffic model Full buffer modelWrapping method Geographical distance basedMetrics 5 50 UPTSystem bandwidth 10MHz (50 PRBs)UE attachment Based on RSRPNumber of UEs per cell 481216Network synchronization SynchronizedUE speed 3 kmhUE distribution According to 36873 [20]
ReceiverNonideal channel estimation and interference modeling detailed guidelinesaccording to Rel-12 assumptionsMMSE-IRC and IC receiver and detailed guidelines according to Rel-12assumptions [21]
UE Rx antenna configuration 1 Rx
Feedback
PUSCH 3-2CQI PMI and RI reporting triggered per 5msFeedback delay is 5msRel-10 8 Tx codebook
Transmission scheme Dynamic SUMU-MIMO with rank adaptationOverhead 3 symbols for DL CCHs 2 CRS ports and DM-RS with 12 REs per PRBCSI-RS 5msecSRS 1 Tx 5ms periodicity wideband
Table 3 Ratio of UE multiplexing comparison for different UEnumbers per cell
Number of UEsper cell
Ratio of UEmultiplexing of JSPM
[]
Ratio of UEmultiplexing of JSDM
[]4 302 2848 439 37212 496 41416 507 437
UE multiplexing is about 30 when the number of UEsper cell is 4 while the ratio of UE multiplexing increases toapproximately 50 when the amount of UE is 16 Thereforethe gain of JSPM is also increased as shown in Figure 5
The performances of JSPM and JSDM with UE speed30 kmh are also provided in Figure 5 These results indicatethat the performances of JSPM and JSDM both decrease withUE speed increasing For JSPM the performance loss is about19 when UE speed increases from 3 kmh to 30 kmh with16 users per cell since UE mobility causes the rapid channelchange and reduces the BS channel estimation accuracyTherefore JSPM scheme is more suitable for a stationary or
semistationary scenario such as to provide coverage and highdata rate for users in office rooms or tall buildings
For the sake of performance comparison of differentpower-domain user pairing strategies we also provide theperformance of JSPM with fixed power user paring selection(denoted as blue solid line with ldquolowastrdquo) and greedy user paringselection (denoted as blue solid line with square) in Figure 5Although the performance loss of fixed power user pairingcompared with greedy user paring is about 15 with 16 usersper cell and 3 kmh velocity condition the fixed power userparing algorithm can provide less computational complexityand easier system implementation than greedy algorithm asdiscussed in Section 33 hence it will be the preferredmethodfor practical user pairing in BS side
43 Different Antenna Type Performances In this subsectionwe perform JSPM performance evaluation for two antennatypes with 8 times 8 and 4 times 16 X-polar antenna elementsrespectively As the typical application scenario of massiveMIMO is providing high-speed data service for users intall buildings the vertical grouping scheme which has beendiscussed in the above section is adopted for both 8 times 8 X-polar and 4 times 16 X-polar antenna types in the simulationFor the antenna array with 4 times 16 X-polar antenna ele-ments there are 2 vertical prebeamforming groups by using
International Journal of Antennas and Propagation 9
Figure 6 Antenna array with 4 times 16 X-pol elements
128 164Number of users
28
3
32
34
36
38
4
42
44
46
48
Cell
aver
age s
pect
rum
effici
ency
(bps
Hz)
JSPM 8 times 8AJSPM 4 times 16A
Figure 7 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
prebeamforming matrix B columns of which can be 2-elementDFTweight two beam groups are tilted to 80 and 100degrees respectively Two vertical antenna ports are mappedto four vertical rows of antenna elements with one polardirection each one is corresponding to two rows For eighthorizontal antenna ports each horizontal antenna port ismapped to four columns of antenna elements of one polardirection for example port 0 is mapped to column 1356 of+45∘ polar antenna elements as shown in Figure 6
In the simulation the other schemes such as user spatialgrouping schemeMU-MIMO scheme andmultiuser power-domain transmission scheme are the same as thatmentionedin previous section
Figure 7 shows the cell average spectrum efficiency com-parison between two types of antenna array Figure 8 givesthe CDF comparison of UE spectrum efficiency between twotypes of antenna array with 481216 UEs per cell Based onthese results it can be seen that the 4 times 16 antenna arrayhas better performance than the 8 times 8 antenna array bothin cell average spectrum efficiency and in 50 CDF of UEspectrum efficiency This is because that BS with 4 times 16antenna array which has more horizontal column antennascan form narrower beams and separates the spatial channelinto more subspace therefore it can achieve more spatialmultiplexing gain
JSPM 4 times 16A 16 UEsJSPM 4 times 16A 12 UEsJSPM 4 times 16A 8 UEsJSPM 4 times 16A 4 UEs
JSPM 8 times 8A 16 UEsJSPM 8 times 8A 12 UEsJSPM 8 times 8A 8 UEsJSPM 8 times 8A 4 UEs
0
01
02
03
04
05
06
07
08
09
1
CDF
51 2 3 4 60User spectrum efficiency (bpsHz)
Figure 8 CDF of UE spectrum efficiency
It can be also seen that the antenna array with morecolumn antennas can achieve higher multiplexing gain forJSPM scheme with number limitation of antenna elements inthe practical network
5 Conclusion
In this paper a joint spatial and power-domain multiusertransmission scheme called JSPM is proposed for FDDmassive MIMO systems In this scheme BS divides theUE into different groups in spatial and power domainsand each type of UE is identified with a set of indicesincluding spatial domain index beam index and power-domain index Based on these UE indices BS can performmultiuser paring and scheduling in both spatial and powerdomain Compared with the traditional spatial multiplexingschemes the proposed JSPM scheme can achieve additionalpower-domain multiplexing gain The system-level simula-tion results validate that with 16 users per cell JSPM canachieve more than 15 spectrum efficiency gain comparedwith JSDM and the JSPM gain increases with the numberof active users per cell The simulation results also show thatthe antenna array with larger number of horizontal columnantennas has the better performance since user distributionin the horizontal plane is more intensive than that in thevertical plane in practical networks
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
10 International Journal of Antennas and Propagation
References
[1] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2014
[2] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010
[3] K Zheng L Zhao J Mei B Shao W Xiang and L HanzoldquoSurvey of large-scale MIMO systemsrdquo IEEE CommunicationsSurveys amp Tutorials vol 17 no 3 pp 1738ndash1760 2015
[4] K Zheng YWangWWangM Dohler and JWang ldquoEnergy-efficient wireless in-home the need for interference-controlledfemtocellsrdquo IEEE Wireless Communications vol 18 no 6 pp36ndash44 2011
[5] J Jose A Ashikhmin T L Marzetta and S Vishwanath ldquoPilotcontamination and precoding inmulti-cell TDD systemsrdquo IEEETransactions on Wireless Communications vol 10 no 8 pp2640ndash2651 2011
[6] H Huh A M Tulino and G Caire ldquoNetwork MIMO with lin-ear zero-forcing beamforming large system analysis impact ofchannel estimation and reduced-complexity schedulingrdquo IEEETransactions on InformationTheory vol 58 no 5 pp 2911ndash29342012
[7] G Caire N JindalM Kobayashi andN Ravindran ldquoMultiuserMIMO achievable rates with downlink training and channelstate feedbackrdquo IEEE Transactions on Information Theory vol56 no 6 pp 2845ndash2866 2010
[8] M Kobayashi N Jindal and G Caire ldquoTraining and feedbackoptimization for multiuser MIMO downlinkrdquo IEEE Transac-tions on Communications vol 59 no 8 pp 2228ndash2240 2011
[9] A Adhikary J Nam J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing the large-scale array regimerdquo IEEETransactions on Information Theory vol 59 no 10 pp 6441ndash6463 2013
[10] J Nam J-Y Ahn A Adhikary and G Caire ldquoJoint spatialdivision and multiplexing realizing massive MIMO gains withlimited channel state informationrdquo in Proceedings of the 46thAnnual Conference on Information Sciences and Systems (CISSrsquo12) Princeton NJ USA March 2012
[11] J Nam A Adhikary J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing opportunistic beamforming usergrouping and simplified downlink schedulingrdquo IEEE Journal onSelected Topics in Signal Processing vol 8 no 5 pp 876ndash8902014
[12] VVenkateswaran andA-J van derVeen ldquoAnalog beamformingin MIMO communications with phase shift networks andonline channel estimationrdquo IEEETransactions on Signal Process-ing vol 58 no 8 pp 4131ndash4143 2010
[13] K Zheng L Zhao J Mei M DohlerW Xiang and Y Peng ldquo10Gbs hetsnets with millimeter-wave communications accessand networking-challenges and protocolsrdquo IEEE Communica-tions Magazine vol 53 no 1 pp 222ndash231 2015
[14] O E Ayach R W Heath Jr S Abu-Surra S Rajagopal and ZPi ldquoLow complexity precoding for largemillimeterwaveMIMOsystemsrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo12) pp 3724ndash3729 Ottawa CanadaJune 2012
[15] A Alkhateeb O El Ayach G Leus and R W Heath ldquoHybridprecoding for millimeter wave cellular systems with partialchannel knowledgerdquo in Proceedings of the Information Theory
and Applications Workshop (ITA rsquo13) pp 1ndash5 IEEE San DiegoCalif USA February 2013
[16] D Tse and P Viswanath Fundamentals ofWireless Communica-tion Cambridge University Press Cambridge UK July 2005
[17] M Sharif and B Hassibi ldquoOn the capacity of MIMO broadcastchannels with partial side informationrdquo IEEE Transactions onInformation Theory vol 51 no 2 pp 506ndash522 2005
[18] A Benjebbovu A Li Y Saito Y Kishiyama A Harada and TNakamura ldquoSystem-level performance of downlink NOMA forfuture LTE enhancementsrdquo in Proceedings of the IEEE GlobecomWorkshops (GC rsquo13) pp 66ndash70 IEEE Atlanta GaUSADecem-ber 2013
[19] 3GPP TS36101 (V1310) ldquoEvolved Universal Terrestrial RadioAccess (E-UTRA) User Equipment (UE) radio transmissionand receptionrdquo October 2015
[20] 3GPP TR36873 (V1220) ldquoStudy on 3D channel model forLTErdquo July 2015
[21] 3GPP ldquoStudy on network-assisted interference cancellation andsuppression (NAIC) for LTErdquo 3GPP TR36866 (V1201) 2014
Figure 6 Antenna array with 4 times 16 X-pol elements
128 164Number of users
28
3
32
34
36
38
4
42
44
46
48
Cell
aver
age s
pect
rum
effici
ency
(bps
Hz)
JSPM 8 times 8AJSPM 4 times 16A
Figure 7 Cell average spectrum efficiency (SE) comparison withdifferent user numbers per cell
prebeamforming matrix B columns of which can be 2-elementDFTweight two beam groups are tilted to 80 and 100degrees respectively Two vertical antenna ports are mappedto four vertical rows of antenna elements with one polardirection each one is corresponding to two rows For eighthorizontal antenna ports each horizontal antenna port ismapped to four columns of antenna elements of one polardirection for example port 0 is mapped to column 1356 of+45∘ polar antenna elements as shown in Figure 6
In the simulation the other schemes such as user spatialgrouping schemeMU-MIMO scheme andmultiuser power-domain transmission scheme are the same as thatmentionedin previous section
Figure 7 shows the cell average spectrum efficiency com-parison between two types of antenna array Figure 8 givesthe CDF comparison of UE spectrum efficiency between twotypes of antenna array with 481216 UEs per cell Based onthese results it can be seen that the 4 times 16 antenna arrayhas better performance than the 8 times 8 antenna array bothin cell average spectrum efficiency and in 50 CDF of UEspectrum efficiency This is because that BS with 4 times 16antenna array which has more horizontal column antennascan form narrower beams and separates the spatial channelinto more subspace therefore it can achieve more spatialmultiplexing gain
JSPM 4 times 16A 16 UEsJSPM 4 times 16A 12 UEsJSPM 4 times 16A 8 UEsJSPM 4 times 16A 4 UEs
JSPM 8 times 8A 16 UEsJSPM 8 times 8A 12 UEsJSPM 8 times 8A 8 UEsJSPM 8 times 8A 4 UEs
0
01
02
03
04
05
06
07
08
09
1
CDF
51 2 3 4 60User spectrum efficiency (bpsHz)
Figure 8 CDF of UE spectrum efficiency
It can be also seen that the antenna array with morecolumn antennas can achieve higher multiplexing gain forJSPM scheme with number limitation of antenna elements inthe practical network
5 Conclusion
In this paper a joint spatial and power-domain multiusertransmission scheme called JSPM is proposed for FDDmassive MIMO systems In this scheme BS divides theUE into different groups in spatial and power domainsand each type of UE is identified with a set of indicesincluding spatial domain index beam index and power-domain index Based on these UE indices BS can performmultiuser paring and scheduling in both spatial and powerdomain Compared with the traditional spatial multiplexingschemes the proposed JSPM scheme can achieve additionalpower-domain multiplexing gain The system-level simula-tion results validate that with 16 users per cell JSPM canachieve more than 15 spectrum efficiency gain comparedwith JSDM and the JSPM gain increases with the numberof active users per cell The simulation results also show thatthe antenna array with larger number of horizontal columnantennas has the better performance since user distributionin the horizontal plane is more intensive than that in thevertical plane in practical networks
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
10 International Journal of Antennas and Propagation
References
[1] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2014
[2] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010
[3] K Zheng L Zhao J Mei B Shao W Xiang and L HanzoldquoSurvey of large-scale MIMO systemsrdquo IEEE CommunicationsSurveys amp Tutorials vol 17 no 3 pp 1738ndash1760 2015
[4] K Zheng YWangWWangM Dohler and JWang ldquoEnergy-efficient wireless in-home the need for interference-controlledfemtocellsrdquo IEEE Wireless Communications vol 18 no 6 pp36ndash44 2011
[5] J Jose A Ashikhmin T L Marzetta and S Vishwanath ldquoPilotcontamination and precoding inmulti-cell TDD systemsrdquo IEEETransactions on Wireless Communications vol 10 no 8 pp2640ndash2651 2011
[6] H Huh A M Tulino and G Caire ldquoNetwork MIMO with lin-ear zero-forcing beamforming large system analysis impact ofchannel estimation and reduced-complexity schedulingrdquo IEEETransactions on InformationTheory vol 58 no 5 pp 2911ndash29342012
[7] G Caire N JindalM Kobayashi andN Ravindran ldquoMultiuserMIMO achievable rates with downlink training and channelstate feedbackrdquo IEEE Transactions on Information Theory vol56 no 6 pp 2845ndash2866 2010
[8] M Kobayashi N Jindal and G Caire ldquoTraining and feedbackoptimization for multiuser MIMO downlinkrdquo IEEE Transac-tions on Communications vol 59 no 8 pp 2228ndash2240 2011
[9] A Adhikary J Nam J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing the large-scale array regimerdquo IEEETransactions on Information Theory vol 59 no 10 pp 6441ndash6463 2013
[10] J Nam J-Y Ahn A Adhikary and G Caire ldquoJoint spatialdivision and multiplexing realizing massive MIMO gains withlimited channel state informationrdquo in Proceedings of the 46thAnnual Conference on Information Sciences and Systems (CISSrsquo12) Princeton NJ USA March 2012
[11] J Nam A Adhikary J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing opportunistic beamforming usergrouping and simplified downlink schedulingrdquo IEEE Journal onSelected Topics in Signal Processing vol 8 no 5 pp 876ndash8902014
[12] VVenkateswaran andA-J van derVeen ldquoAnalog beamformingin MIMO communications with phase shift networks andonline channel estimationrdquo IEEETransactions on Signal Process-ing vol 58 no 8 pp 4131ndash4143 2010
[13] K Zheng L Zhao J Mei M DohlerW Xiang and Y Peng ldquo10Gbs hetsnets with millimeter-wave communications accessand networking-challenges and protocolsrdquo IEEE Communica-tions Magazine vol 53 no 1 pp 222ndash231 2015
[14] O E Ayach R W Heath Jr S Abu-Surra S Rajagopal and ZPi ldquoLow complexity precoding for largemillimeterwaveMIMOsystemsrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo12) pp 3724ndash3729 Ottawa CanadaJune 2012
[15] A Alkhateeb O El Ayach G Leus and R W Heath ldquoHybridprecoding for millimeter wave cellular systems with partialchannel knowledgerdquo in Proceedings of the Information Theory
and Applications Workshop (ITA rsquo13) pp 1ndash5 IEEE San DiegoCalif USA February 2013
[16] D Tse and P Viswanath Fundamentals ofWireless Communica-tion Cambridge University Press Cambridge UK July 2005
[17] M Sharif and B Hassibi ldquoOn the capacity of MIMO broadcastchannels with partial side informationrdquo IEEE Transactions onInformation Theory vol 51 no 2 pp 506ndash522 2005
[18] A Benjebbovu A Li Y Saito Y Kishiyama A Harada and TNakamura ldquoSystem-level performance of downlink NOMA forfuture LTE enhancementsrdquo in Proceedings of the IEEE GlobecomWorkshops (GC rsquo13) pp 66ndash70 IEEE Atlanta GaUSADecem-ber 2013
[19] 3GPP TS36101 (V1310) ldquoEvolved Universal Terrestrial RadioAccess (E-UTRA) User Equipment (UE) radio transmissionand receptionrdquo October 2015
[20] 3GPP TR36873 (V1220) ldquoStudy on 3D channel model forLTErdquo July 2015
[21] 3GPP ldquoStudy on network-assisted interference cancellation andsuppression (NAIC) for LTErdquo 3GPP TR36866 (V1201) 2014
10 International Journal of Antennas and Propagation
References
[1] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2014
[2] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010
[3] K Zheng L Zhao J Mei B Shao W Xiang and L HanzoldquoSurvey of large-scale MIMO systemsrdquo IEEE CommunicationsSurveys amp Tutorials vol 17 no 3 pp 1738ndash1760 2015
[4] K Zheng YWangWWangM Dohler and JWang ldquoEnergy-efficient wireless in-home the need for interference-controlledfemtocellsrdquo IEEE Wireless Communications vol 18 no 6 pp36ndash44 2011
[5] J Jose A Ashikhmin T L Marzetta and S Vishwanath ldquoPilotcontamination and precoding inmulti-cell TDD systemsrdquo IEEETransactions on Wireless Communications vol 10 no 8 pp2640ndash2651 2011
[6] H Huh A M Tulino and G Caire ldquoNetwork MIMO with lin-ear zero-forcing beamforming large system analysis impact ofchannel estimation and reduced-complexity schedulingrdquo IEEETransactions on InformationTheory vol 58 no 5 pp 2911ndash29342012
[7] G Caire N JindalM Kobayashi andN Ravindran ldquoMultiuserMIMO achievable rates with downlink training and channelstate feedbackrdquo IEEE Transactions on Information Theory vol56 no 6 pp 2845ndash2866 2010
[8] M Kobayashi N Jindal and G Caire ldquoTraining and feedbackoptimization for multiuser MIMO downlinkrdquo IEEE Transac-tions on Communications vol 59 no 8 pp 2228ndash2240 2011
[9] A Adhikary J Nam J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing the large-scale array regimerdquo IEEETransactions on Information Theory vol 59 no 10 pp 6441ndash6463 2013
[10] J Nam J-Y Ahn A Adhikary and G Caire ldquoJoint spatialdivision and multiplexing realizing massive MIMO gains withlimited channel state informationrdquo in Proceedings of the 46thAnnual Conference on Information Sciences and Systems (CISSrsquo12) Princeton NJ USA March 2012
[11] J Nam A Adhikary J-Y Ahn and G Caire ldquoJoint spatialdivision and multiplexing opportunistic beamforming usergrouping and simplified downlink schedulingrdquo IEEE Journal onSelected Topics in Signal Processing vol 8 no 5 pp 876ndash8902014
[12] VVenkateswaran andA-J van derVeen ldquoAnalog beamformingin MIMO communications with phase shift networks andonline channel estimationrdquo IEEETransactions on Signal Process-ing vol 58 no 8 pp 4131ndash4143 2010
[13] K Zheng L Zhao J Mei M DohlerW Xiang and Y Peng ldquo10Gbs hetsnets with millimeter-wave communications accessand networking-challenges and protocolsrdquo IEEE Communica-tions Magazine vol 53 no 1 pp 222ndash231 2015
[14] O E Ayach R W Heath Jr S Abu-Surra S Rajagopal and ZPi ldquoLow complexity precoding for largemillimeterwaveMIMOsystemsrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo12) pp 3724ndash3729 Ottawa CanadaJune 2012
[15] A Alkhateeb O El Ayach G Leus and R W Heath ldquoHybridprecoding for millimeter wave cellular systems with partialchannel knowledgerdquo in Proceedings of the Information Theory
and Applications Workshop (ITA rsquo13) pp 1ndash5 IEEE San DiegoCalif USA February 2013
[16] D Tse and P Viswanath Fundamentals ofWireless Communica-tion Cambridge University Press Cambridge UK July 2005
[17] M Sharif and B Hassibi ldquoOn the capacity of MIMO broadcastchannels with partial side informationrdquo IEEE Transactions onInformation Theory vol 51 no 2 pp 506ndash522 2005
[18] A Benjebbovu A Li Y Saito Y Kishiyama A Harada and TNakamura ldquoSystem-level performance of downlink NOMA forfuture LTE enhancementsrdquo in Proceedings of the IEEE GlobecomWorkshops (GC rsquo13) pp 66ndash70 IEEE Atlanta GaUSADecem-ber 2013
[19] 3GPP TS36101 (V1310) ldquoEvolved Universal Terrestrial RadioAccess (E-UTRA) User Equipment (UE) radio transmissionand receptionrdquo October 2015
[20] 3GPP TR36873 (V1220) ldquoStudy on 3D channel model forLTErdquo July 2015
[21] 3GPP ldquoStudy on network-assisted interference cancellation andsuppression (NAIC) for LTErdquo 3GPP TR36866 (V1201) 2014
