Opportunistic multiuser MIMO for OFDM networksMounir Esslaoui

Information and Telecom Systems LabAbdelmalek Essaadi University

M’Hannech II 93000, Tetouan, MoroccoEmail: mounir.ess@gmail.com

Felip Riera-Palou and Guillem FemeniasMobile Communications Group

University of the Balearic Islands07122 Mallorca (Illes Balears), Spain

Email: {felip.riera,guillem.femenias}@uib.es

Abstract—This paper considers the application of oppor-tunistic multiuser multiple-input multiple-output (MU-MIMO)techniques to multicarrier wireless networks based on orthogonalfrequency division multiplexing (OFDM). Unlike related workwhere the design of the MU-MIMO component is jointly per-formed with the subcarrier allocation among the users (e.g. someform of OFDMA is present), here it is assumed that the selectedusers will have to share the utilization of all the subcarriers in thesystem. This scenario would be typical of deployments based ontime multiplexing policies (e.g., WLANs) where the proposed MU-MIMO add-on would serve to increase the system capacity. A newalgorithm is introduced to select the users taking into accounttheir channel response over all subcarriers and performing a jointfrequency-space power allocation. Numerical results demonstratevery significant improvements in terms of sum-rate capacity incomparison to a conventional (opportunistic) TDMA scheme.

Index Terms—Multiuser multiple-input multiple-output(MIMO), opportunistic, orthogonal frequency divisionmultiplexing (OFDM), channel state information (CSI).

I. INTRODUCTION

One of the key challenges faced by the forthcoming wire-less communication systems, commonly referred to as fourthgeneration (4G) systems, is to transmit signals at a rate thatis as close as possible to the theoretical channel capacitywhile satisfying quality of service (QoS) constraints. Thedevelopment of these systems must take into account theproblem of limited radio resources and the harshness ofwireless channel conditions. Recent years have witnessed theconvergence of the different proposals to a physical layerarchitecture based on multiantenna multicarrier principles. Onone hand, the use of multiple-input multiple-output (MIMO)wireless systems has become a key technology to increasechannel capacity and thus allowing higher data rates. Telatar[1], showed that in a flat-fading Rayleigh channel, the capacityof MIMO systems can be improved by a factor dependenton the minimum number of transmit and receive antennas,if perfect channel state information (CSI) is available. Onthe other hand, orthogonal frequency-division multiplexing(OFDM) is an effective technique to mitigate the effects ofintersymbol interference (ISI) in frequency-selective channelsby turning a broadband frequency-selective channel into aseries of parallel (non-interfering) narrowband sub-channelsthat allow simple receiver structures to be used [2]. Thecombination of MIMO and OFDM is an attractive solution

for next generation WLANs and 4G mobile cellular wirelesssystems owing to its abilities to provide high data rates whilebeing very robust against channel impairments [3].

Recent research on MIMO-OFDM systems has focused onissues related to the availability of CSI at the transmitter.If this condition is fulfilled, precoding can be designed toexploit the channel conditions, minimizing interference andreducing complexity at the receiver [4]. In practical MIMO-OFDM systems, it is well accepted that multiple antennascan be easily deployed at the base station (BS) since theydo not have tight constraints regarding space, available powerand/or computational complexity. In contrast, mobile stations(MS) are typically limited to have a small number of antennasdue to size and cost restrictions, thus limiting the potentialcapacity benefits of MIMO. Given this asymmetric availabilityof resources, and in order to increase capacity, the multipleantennas at the BS can be employed to simultaneously servevarious users using the so-called multiuser MIMO (MU-MIMO) techniques [5], which aim at maximising system ca-pacity by treating the resulting interference among the differentuser streams. Dirty paper coding (DPC) [6] is the optimalMU-MIMO precoding strategy and is based on interferencepre-cancellation. However, this solution suffers from a highcomputational complexity and it is difficult to implement,especially when the number of users is large.

Opportunistic beamforming/transmission [7] refers to ascheme where the transmitter, in light of the available CSI,chooses the destination user with the most favorable channelcondition, obtaining in this way multiuser diversity. In thissuboptimal strategy, the BS selects a set of random beam-forming weights, and users send back information regardingthe measured signal-to-noise ratio (SNR) to the transmitterin order to report which beam gives the best performance andwhat rate they can support using it. A different way of utilizingthe available CSI consists of allowing a multiantenna equippedtransmitter to exploit the spatial dimension (via beamforming)to transmit to various users at the same time while minimizingtheir cross-interference. The landmark work of [8] combinedboth ideas, opportunistic transmission and MU-MIMO, intro-ducing the idea of simultaneously transmitting to various usersselected from the total user pool by virtue of their separability,i.e., those users which can be more easily orthogonalised bymeans of linear beamforming are selected for transmission.Remarkably, aside from simple linear filtering for the beam-

978-1-61284-887-7/11/$26.00 ©2011 IEEE

UserSelectionusingMUS

Coding&

Modulation

Coding&

ModulationLinear

Precoding&

waterfilling

IFFT

IFFT

FFT

FFT

Demodulation&

decoding

Demodulation&

decodingDetection

Detection

Mobile terminalsBase station

User 1data

Userdata

Channel state information

… … …

User 1data

Userdata

Fig. 1. Block diagram of generic CSIT-aided downlink MIMO-OFDM system with 𝑁𝑇 transmit antennas and 𝑁𝑢 users, each with one receive antenna.

forming part, the authors in [8] proposed a low-complexityscheme for the user selection that was shown to be almostoptimal, thus resulting in important sum-rate gains. Recently,there have been extensions of this work to scenarios where usermultiplexing takes place by means of orthogonal frequencydivision multiple access (OFDMA) [9]. In this case the ideais to jointly perform the beamformer design, user selectionand subcarrier allocation with the objective of maximisingthe overall sum-rate. While this is a powerful approach inOFDMA-based setups, in those cases where user multiplexingtakes place by some other means, most notably, time division,some new mechanism is required in order to extract multiuserdiversity gain. In order to fill this gap, this paper addressesthe design of a low complexity multiuser selection algorithmfor opportunistic MU-MIMO networks, where users transmitstrictly using OFDM (i.e., frequency is not used for multipleaccess). Starting from the results in [8], the scheme proposedin this paper makes a user selection based on an orthogonalitymeasure that takes into account the channel response ofthe different users over all subcarriers and the design of asubcarrier specific precoder. Numerical results serve to confirmthe effectiveness of the proposed method.

The rest of the paper is organized as follows: Section IIpresents the system model. The proposed multicarrier userselection algorithm is described in Section III and the resultingnumerical results are shown in Section IV. Finally, Section Vsummarises the main outcomes of the paper and provides hintsfor further research work. This introduction concludes with abrief notational remark: vectors and matrices are denoted bylower- and upper-case bold letters, respectively, while non-bold letters are used for scalars, 𝒟(𝑿) is a (block) diagonalmatrix with 𝑿 at its main diagonal, #𝒰 is the cardinalityof set 𝒰 , 𝑇 and 𝐻 serve to denote transpose and complextranspose respectively, [𝑨]𝑖,𝑗 is the (𝑖, 𝑗)-element of matrix 𝑨,𝑰𝑃 is the 𝑃 × 𝑃 identity matrix, ∥𝒂∥ denotes the Euclideannorm of a vector 𝒂 and (𝒛)+ = max(𝒛, 0).

II. SYSTEM MODEL

The downlink of a single-cell multicarrier system operat-ing through 𝑁𝑐 subcarriers over a bandwidth of 𝑊 Hz is

considered. The base station is equipped with 𝑁𝑇 transmitantennas whereas each mobile station is equipped with a singleantenna1. There are 𝑁𝑢 (≥ 𝑁𝑇 ) active users in the cell out ofwhich 𝑈 ≤ 𝑁𝑇 are selected, forming the set 𝒰 (𝑈 = #𝒰 ), ata given time slot for simultaneous transmission. The systemblock diagram is depicted in Fig. 1.

The 𝑁𝑐 × 𝑁𝑇 matrix 𝑯𝑢 = [𝒉𝑢,1 . . . 𝒉𝑢,𝑁𝑇], with

1 ≤ 𝑢 ≤ 𝑁𝑢, represents the user-specific channel matrix,where 𝒉𝑢,𝑘 = [ℎ𝑢,𝑘[1] ⋅ ⋅ ⋅ ℎ𝑢,𝑘[𝑁𝑐]]

𝑇 denotes the frequencyresponse over the 𝑁𝑐 subcarriers of the link between the 𝑘thtransmit antenna and MS 𝑢.

Assuming perfect frequency synchronization between thetransmitter and receiver and cyclic prefix duration exceedingthe channel delay spread, the received signal for user 𝑢 onsubcarrier 𝑞 for an arbitrary OFDM symbol is given by

𝑦𝑢[𝑞] = 𝒉𝑢[𝑞]𝒙[𝑞] + 𝜂𝑢[𝑞] (1)

where 𝒉𝑢[𝑞] = [ℎ𝑢,1[𝑞] ⋅ ⋅ ⋅ ℎ𝑢,𝑁𝑇[𝑞]] represents the fre-

quency response of the 𝑢th user over the 𝑞th subcarrier,𝒙[𝑞] = [𝑥1[𝑞] ⋅ ⋅ ⋅ 𝑥𝑁𝑇

[𝑞]]𝑇 is the 𝑁𝑇 ×1 transmitted symbol

from the BS on subcarrier 𝑞 and 𝜂𝑢[𝑞] is a zero-mean whiteGaussian noise sample with variance 𝜎2

𝜂 . The BS has totalpower 𝑃𝑇 available for transmission and, as in [8], it isassumed that all users experiment the same SNR.

Given the general reception equation in (1), the challengeis now how to select the user(s) to which to transmit andhow to perform the precoding operation, that is, how tocompute the transmitted symbol vector 𝒙[𝑞] as a function ofthe user information symbols 𝑠𝑢[𝑞], typically drawn from afinite complex constellation (e.g., QPSK, 16-QAM). Note that,under the assumption of a pure OFDM scheme, for each timeslot there will be 𝑈 ×𝑁𝑐 symbols to be transmitted.

III. MULTIUSER TRANSMIT STRATEGIES

A. Opportunistic multicarrier TDMA

In MU-MIMO networks purely based on OFDM, whereuser multiplexing takes place using (opportunistic) TDMA

1The generalization to multiantenna receivers, and based on the results of[8], [10], should be relatively straightforward.

techniques, the base station selects a single user at a time(e.g. 𝑈 = 1) who will be allocated all the spectrum andpower resources. In this scenario it is easy to show that, oncea user has been selected, the precoding operation is simplyimplemented by means of maximum ratio transmission (MRT)[11], that is,

𝒙[𝑞] = 𝒘𝑢[𝑞]𝑠𝑢[𝑞], (2)

where 𝒘𝑢[𝑞] = 𝒉𝐻𝑢 [𝑞], thus resulting in received symbol

estimates given by

𝑠TDMA𝑢 [𝑞] = 𝑦𝑢[𝑞] = ∥𝒉𝑢[𝑞]∥2𝑠𝑢[𝑞] + 𝜂𝑢[𝑞]. (3)

User selection is conducted by choosing the MS that exper-iments the best channel realisation, which when maximisingthe sum-rate amounts to select the ones maximising,

𝐶TDMA = max𝑢∈{1,⋅⋅⋅ ,𝑁𝑢}

1

𝑁𝑐

𝑁𝑐∑𝑞=1

log2

(1 +

𝑃𝑡[𝑞]

𝜎2𝜂

∥𝒉𝑢[𝑞]∥2)

(4)where 𝑃𝑡[𝑞] is the power allocated to the 𝑞th subcarrier givenby the waterfilling solution and satisfying the total powerconstraint

∑𝑁𝑐

𝑞=1 𝑃𝑡[𝑞] = 𝑃𝑇 .

B. Opportunistic multicarrier MU-MIMO

The objective of the multicarrier user selection (MUS)algorithm presented in this section is to maximize the overallsum-rate of the system by transmitting simultaneously tovarious users on all subcarriers while relying only on linearprocessing.

For a particular user selection set 𝒰 , let us define 𝑯𝒰 [𝑞] asthe #𝒰×𝑁𝑇 matrix collecting the channel coefficients for theselected users on subcarrier 𝑞. The transmitted symbol vector𝒙[𝑞] is then obtained from the information symbols belongingto the selected users 𝒔𝑢[𝑞] by means of linear precoding as

𝒙[𝑞] =𝑈∑

𝑢=1

√𝑃𝑢[𝑞]𝑾 𝒰 [𝑞]𝒔𝑢[𝑞], (5)

where 𝑾 𝒰 [𝑞] = [𝒘1[𝑞] ⋅ ⋅ ⋅𝒘𝑈 [𝑞]] is the precoding matrixwhich for the case of zero forcing beamforming (ZFBF) isgiven by

𝑾 𝒰 [𝑞] = 𝑯𝐻𝒰 [𝑞]

(𝑯𝒰 [𝑞]𝑯𝐻

𝒰 [𝑞])−1

. (6)

Plugging (5) into the reception equation (1), it is found thatthe information symbol estimate for an arbitrary user 𝑢 ∈ 𝒰is given by

𝑠MU-MIMO𝑢 [𝑞] = 𝑦𝑢[𝑞] =

𝑈∑𝑢=1

√𝑃𝑢[𝑞]𝒉𝑢[𝑞]𝒘𝑢[𝑞]𝒔𝑢[𝑞] + 𝜂𝑢[𝑞].

(7)After some straightforward calculations it can be seen thatthe combined precoder-channel gain for user 𝑢 on the 𝑞thsubcarrier can be expressed as

𝛾𝑢[𝑞] =1[(

𝑯𝒰 [𝑞]𝑯𝐻𝒰 [𝑞]

)−1]𝑢,𝑢

, (8)

which allows the sum-rate capacity over all subcarriers to beexpressed as,

𝐶MU-MIMO =1

𝑁𝑐

𝑁𝑐∑𝑞=1

𝑈∑𝑢=1

log2

(1 +

𝑃𝑢[𝑞]

𝜎2𝜂

𝛾𝑢[𝑞]

), (9)

where 𝑃𝑢[𝑞] denotes the power allocated to the 𝑢th user onthe 𝑞th subcarrier. The optimal power allocation that achievesthe maximum sum-rate is given by the waterfilling solution

𝑃𝑢[𝑞] =

(𝜇− 𝜎2

𝜂

𝛾𝑢[𝑞]

)+

, (10)

where 𝜇 is the water level chosen to satisfy the powerallocation constraint

𝑁𝑐∑𝑞=1

𝑈∑𝑢=1

𝑃𝑢[𝑞] = 𝑃𝑇 . (11)

Note that the waterfilling should be jointly conducted in thespatial (e.g., user) and frequency domains. Based on the userselection algorithm introduced in [8], a multicarrier extensionis now presented that aims at the same objective, namely, toselect users who are as orthogonal as possible among themand that lead to the maximisation of (9). Notice that now thechannel responses over all subcarriers play a role.

The multicarrier user selection (MUS) algorithm, sum-marised below, takes care of selecting the sum-rate maximisinguser group 𝒰 from an initial pool 𝒯1 = {1, ⋅ ⋅ ⋅ , 𝑁𝑢} for agiven time slot. The BS will then simultaneously transmit toall users in 𝒰 . The selection procedure works as follows: instep (a), 𝒯1 is initialised with the 𝑁𝑢 users in the cell. In step(b), and for each successive iteration (indexed by 𝑖), the vector𝒈𝑢[𝑞] is found as the component of 𝒉𝑢[𝑞] most orthogonal to

the subspace spanned by{𝒈𝜋(1)[𝑞] ⋅ ⋅ ⋅ 𝒈𝜋(𝑖−1)[𝑞]

}averaged

Algorithm 1 : Multicarrier user selection (MUS).(a)Initialisation: 𝑖 = 1, 𝒯1 = {1, ⋅ ⋅ ⋅ , 𝑁𝑢},𝒰 = ∅.while (#𝒯𝑖 ∕= 0)&(𝑈 < 𝑁𝑇 ) do(b)Orthogonality measure computation:for Each user 𝑢 ∈ 𝒯𝑖 do

for Each subcarrier 𝑞 do

𝒈𝑢[𝑞] = 𝒉𝑢[𝑞]

(𝑰𝑁𝑇

−∑𝑖−1𝑗=1

𝒈𝐻𝜋(𝑗)[𝑞]𝒈𝜋(𝑗)[𝑞]

∥𝒈𝜋(𝑗)[𝑞]∥2

)end for

end for(c)Choose most orthogonal user:𝜋(𝑖) = argmax

𝑢∈𝒯𝑖

∑𝑁𝑐

𝑞=1 ∥𝒈𝑢[𝑞]∥𝒰 = 𝒰 ∪𝜋(𝑖)(d)Discard poorly orthogonal users:

𝒯𝑖+1 =

{𝑢 ∈ 𝒯𝑖, 𝑢 ∕= 𝜋(𝑖) : 1

𝑁𝑐

∑𝑁𝑐

𝑞=1

∣𝒉𝑢[𝑞]𝒈𝐻𝜋(𝑖)[𝑞]∣

∥𝒉𝑢[𝑞]∥∥𝒈𝐻𝜋(𝑖)

[𝑞]∥ < 𝜃

}𝑖 = 𝑖+ 1

end while

over all subcarriers, that is,

𝒈𝑢[𝑞] = 𝒉𝑢[𝑞]

⎛⎝𝑰𝑁𝑇

−𝑖−1∑𝑗=1

𝒈𝐻𝜋(𝑗)[𝑞]𝒈𝜋(𝑗)[𝑞]

∥𝒈𝜋(𝑗)[𝑞]∥2

⎞⎠ . (12)

Step (c) selects the best user 𝜋(𝑖) corresponding to the largestprojected norm ∥𝒈𝑢∥ averaged accross subcarriers,

𝜋(𝑖) = argmax𝑢∈𝒯𝑖

𝑁𝑐∑𝑞=1

∥𝒈𝑢[𝑞]∥, (13)

and includes this user in the selected user set 𝒰 . Finally, instep (d), poorly orthogonal users are discarded from the userpool in order to simplify the computational requirements ofthe MUS algorithm. To this end only those users in 𝒯𝑖 whoseorthogonality coefficient 𝜃𝑢 given by

𝜃𝑢 =1

𝑁𝑐

𝑁𝑐∑𝑞=1

∣𝒉𝑢[𝑞]𝒈𝐻𝜋(𝑖)[𝑞]∣

∥𝒉𝑢[𝑞]∥∥𝒈𝐻𝜋(𝑖)[𝑞]∥

(14)

is below a certain threshold 𝜃 (small positive number) arekept. Note that, effectively, 𝜃 controls the minimum degreeof orthogonality between the already selected user(s) 𝜋(𝑖) andthose users that still remain in the pool of potentially selectableusers. Finally, the process stops when the number of users inthe active subset equals the number of transmit antennas 𝑁𝑇

or the list of remaining users is empty.

IV. NUMERICAL RESULTS

Numerical results have been obtained using physical-layerparameters typical of current WLANs (𝑊 = 20 MHz,𝑁𝑐 ≤ 64) and assuming the base station is equipped with𝑁𝑇 = 4 transmit antennas and the different MS have all singleantenna architctures. The channel profiles used to generate thefrequency-selective channel responses correspond to profilesB (residential), D (typical office) and E (large office) fromchannel models developed within the IEEE 802.11n standard[12]. Unless otherwise specified, the BS is assumed to transmitwith total power 𝑃𝑇 to ensure that every subcarrier, onaverage, operates with an 𝑆𝑁𝑅[𝑞] = 10 dB. In Fig. 2the sum-rate capacity, obtained using (9), is shown for theproposed beamforming scheme with multicarrier user selection(MC-MU-MIMO-MUS) as a function of the orthogonalityparameter 𝜃. The number of users has been fixed respectivelyto 10, 100 and 1000 and the number of subcarriers to 𝑁𝑐 = 64.Note that it is important to find the optimal value of 𝜃 becauseif it is too large, non-orthogonal users are selected in theuser grouping algorithm and the channel gains are reduceddue to zero forcing channel inversion while if it is too small,multiuser diversity gain is reduced. From the figure we can seethat optimal values of 𝜃 which maximize the sum-rate capacityare in the range [0.4− 0.6]. These optimal values decrease asthe number of users grows, however, and as a compromisevalue, for the rest of this study a value of 𝜃 = 0.45 has beenused for the rest of simulations. Figure 3 compares the sum-rate capacity as a function of the number of users for MC-MU-MIMO-MUS, MC-MU-MIMO with optimal user selection

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

12

14

16

18

θ

Sum

−ra

te (

bits

/s/H

z)

Nu = 10

Nu = 100

Nu = 1000

Fig. 2. Sum-rate capacity of MC-MU-MIMO-MUS vs. 𝜃. 𝑆𝑁𝑅[𝑞] = 10dB. 𝑁𝑐 = 64. Channel profile B.

0 20 40 60 80 1000

2

4

6

8

10

12

14

Number of users

Sum

−ra

te (

bits

/s/H

z)

Channel B − MC−MU−MIMO−MUSChannel B − Optimum MC−MU−MIMOChannel B − Opportunistic MC−TDMAChannel D − MC−MU−MIMO−MUSChannel D − Optimum MC−MU−MIMOChannel D − Opportunistic MC−TDMAChannel E − MC−MU−MIMO−MUSChannel E − Optimum MC−MU−MIMOChannel E − Opportunistic MC−TDMA

Fig. 3. Sum-rate capacity vs. number of users. 𝑆𝑁𝑅[𝑞] = 10 dB. 𝑁𝑐 = 64.𝜃 = 0.45. Channel profiles B, D and E.

(optimum MC-MU-MIMO) which relies on an exhaustivesearch of all possible user combinations, and the TDMA-based opportunistic transmission (opportunistic MC-TDMA)provided by (4). Results have been obtained by averaging500 channel realizations for each channel profile. In light ofthe results in this figure three interesting conclusions can bedrawn. First and foremost, as the number of users grows, bothMC-MU-MIMO techniques offer more than a 70%, 65% and50% increase in sum-rate respectively for channels B, D andE when compared to MC-TDMA opportunistic transmission.Second, the suboptimal user selection technique manages toachieve most of the MU-MIMO gain offered by the optimaluser selection at a very low computational cost. Note that, dueto its computational complexity, for the optimal user selectionscheme it was only feasible to compute values for up to𝑁𝑢 = 25 users in the system. As a third and final considerationit is interesting to note that the lesser the frequency selectivity

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

Number of users

Sum

−ra

te (

bits

/s/H

z)

Uniform power allocationWaterfiling in space + Uniform power in frequencyWaterfilling in space and frequencyWaterfilling in frequencyUniform power allocation

Opportunistic MC−TDMA

MC−MU−MIMO−MUS

Fig. 4. Sum-rate capacity vs. number of users. 𝑆𝑁𝑅[𝑞] = 0 dB. 𝑁𝑐 = 64.𝜃 = 0.45. Channel profile B.

is, the larger the multiuser diversity gain becomes, as a modestfrequency selectivity in combination with a large number ofusers increases the chance of having users with strong gainsover most of the subcarriers owing to the large subcarriercorrelation. Figure 4 shows the results when using differentpower allocation strategies for both, MC-MU-MIMO-MUSand opportunistic MC-TDMA. Notice that, as the number ofusers grows, the sum-rate capacity for MC-MU-MIMO-MUSattains higher values when using waterfilling in space andfrequency rather than uniform power allocation. Noticeably,when waterfilling is performed in the spatial domain only(e.g. uniform power distribution in frequency), only a marginaldegradation is observed. This suggests that assigning an equalamount of power per frequency bin and then performing thewaterfilling over the different users (space) results in the mostattractive option in terms of performance and complexity.Note also that for opportunistic MC-TDMA transmission, thewaterfilling solution does not bring any benefits in term ofsum-rate capacity. Finally, Fig. 5 compares the sum-rate ca-pacity of MC-MU-MIMO-MUS and opportunistic MC-TDMAtransmission as a function of the number of active usersin the cell for different number of subcarriers. This graphshows that the proposed method effectively translates the sum-rate capacity gains of the single-carrier system (top plot) tomulticarrier setups (mid and bottom plots).

V. CONCLUSION

This paper has derived an extension of single-carrier mul-tiuser MIMO to a multicarrier architecture based on OFDM.The proposed scheme is composed of a user selection stepthat takes care of selecting those users experimenting the bestchannel realisations taking into account all subcarriers, anda subcarrier-specific precoder designed to minimise inter-userinterference. Simulation results in a wide variety of scenarioshave shown that, when the number of users increases, theproposed MUS algorithm achieves a very significant increasein sum-rate capacity compared to opportunistic MC-TDMA.Systems within the IEEE 802.11 family of standards, which

0 20 40 60 80 1000

5

10

15

Number of users

Sum

−ra

te (

bits

/s/H

z)

0 20 40 60 80 1000

5

10

15

Number of users

Sum

−ra

te(B

its/s

/Hz)

0 20 40 60 80 1000

5

10

15

Number of Users

Sum

−ra

te(b

its/s

/Hz)

MC−MU−MIMO−MUSOpportunistic MC−TDMA

MC−MU−MIMO−MUSOpportunistic MC−TDMA

MS−MU−MIMO−MUSOpportunistic MC−TDMA

Nc=1

Nc=8

Nc=64

Fig. 5. Sum-rate capacity vs. number of users. 𝑆𝑁𝑅[𝑞] = 10 dB. 𝜃 = 0.45.𝑁𝑐 = {1, 8, 64}. Channel profile B.

are based on OFDM and where users share the medium bytime division, rather than OFDMA, would be an immediatetarget for the technique introduced in this study in orderto increase the overall system capacity. Future research willseek to incorporate user fairness in the user selection stepand also in the combination of MC-MU-MIMO with adaptivemodulation and coding.

ACKNOWLEDGMENTS

Work supported in part by MEC and FEDER under project COS-MOS (TEC2008-02422) and an AVERROES mobility scholarship,Spain.

REFERENCES

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