Energy Efficiency Analysis of MISO-OFDM CommunicationSystems Considering Power and Capacity Constraints

Xiaohu Ge & Jinzhong Hu & Cheng-Xiang Wang &

Chan-Hyun Youn & Jing Zhang & Xi Yang

Published online: 25 February 2011# Springer Science+Business Media, LLC 2011

Abstract In this paper, the energy efficiency of multi-inputsingle-output and orthogonal frequency division multiplex-ing (MISO-OFDM) communication systems with powerand capacity constraints is investigated. By formulating thepower allocation problem of MISO-OFDM communicationsystems, the minimum subchannel transmission power isanalyzed with power and capacity constraints. Simulationresults indicate that there exists a specific minimumsubchannel capacity threshold. Moreover, the energyefficiency of MISO-OFDM communication systems startsto increase only when the minimum subchannel capacityexceeds the specific threshold.

Keywords multi-input single-output (MISO) . orthogonalfrequency division multiplexing (OFDM) . energyefficiency . capacity analysis

1 Introduction

Multi-antenna [1] and orthogonal frequency division multi-plexing (OFDM) technologies are widely accepted toimprove the transmission rate in next generation broadbandmobile communication systems, such as Long-Term Evo-lution (LTE)-Advanced and International Mobile Telecom-munications (IMT)-Advanced system [2]. In addition to thetransmission rate improvement, energy efficiency is be-coming increasingly important for next generation broad-band mobile communication systems because of greenhouse effect on the earth [3]. In this case, evaluation ofenergy efficiency of communication systems with multi-antenna and OFDM technologies is an important researchproblem.

In traditional wireless networks, e.g., wireless ad hocnetworks, the energy saving of wireless networks wasimplemented by costing Quality of Service (QoS) ofwireless networks, such as delay and throughput [4].Compared with energy efficiency issues of traditionalwireless networks, the energy efficiency problem of cellularnetworks, especially in the next generation cellular networkor 4th generation (4G) mobile communication system isexpected to save energy without reducing QoS of cellularnetworks. Considering the limitation of spectrum resourcein mobile communication systems [5], in the most case, theenergy efficiency of cellular networks is implemented withthe spectrum efficiency constraint. Kolding and Wigardproposed a discontinuous reception framework in the LTEcommunication system to reduce the energy consumption,

This research was supported by the National Natural ScienceFoundation of China (NSFC), contract/grant number: 60872007;National 863 High Technology Program of China, contract/grantnumber: 2009AA01Z239; The Ministry of Science and Technology(MOST), China, International Science and Technology CollaborationProgram, contract/grant number:0903; the UK-China Science BridgesProject: R&D on (B)4G Wireless Mobile Communications from theRCUK; EU FP7-PEOPLE-IRSES, project acronym S2EuNet, con-tract/grant number: 247083.

X. Ge (*) : J. Hu : J. Zhang :X. YangDepartment of Electronics and Information Engineering,Huazhong University of Science and Technology,Wuhan, Hubei, Chinae-mail: xhge@mail.hust.edu.cn

C.-X. WangJoint Research Institute for Signal and Image Processing,School of Engineering & Physical Sciences,Heriot-Watt University,Edinburgh EH14 4AS, UK

C.-H. YounGRID Middleware Research Center of ICC,Korea Advanced Institute of Science and Technology,Taejon 305, South Korea

Mobile Netw Appl (2012) 17:29–35DOI 10.1007/s11036-011-0296-4

which is realized by a micro-sleep operation in the userterminal [6]. Reference [7] investigated the relationshipbetween the transmission power and embodied power in basestations of cellular networks. Shun-Ren Yang analyzed powersaving of generic access networks (GAN) and UniversalMobile Telecommunications Systems (UMTS) interworkingmodel [8]. Considering the optimization of cell deployment,[9] details a novel concept and architecture of cell zoomingin mobile cellular networks to solve the problem of trafficimbalance and reduce the total energy consumption. A newscheme adapting both overall transmit power and itsallocation according to the states of all subchannels andcircuit power consumption to maximize energy efficiencywas proposed in [10]. Moreover, an upper bound on energyefficiency was developed to characterize its variation withbandwidth, channel gain and circuit power [11]. However,users in cellular networks generally do not accept the energyefficiency improvement by the cost of transmission rate.Therefore, how to evaluate the energy efficiency of commu-nication systems with power and capacity constraints is a greatchallenge for the next generation communication system.

In this paper, we formulate a new model to describe thepower allocation of multi-input single-output (MISO) andOFDM communication systems with power and capacityconstraints. Furthermore, a new algorithm is developed toevaluate the energy efficiency of MISO-OFDM communica-tion systems. Simulation results show that the energyefficiency of MISO-OFDM communication systems is in-creased with the minimum subchannel transmission capacityand is decreased with the total BS transmission power.

The rest of the paper is organized as follows. InSection 2, the system model is illustrated and the powerallocation problem of MISO-OFDM communication sys-tem is formulated. Moreover, a new power allocationalgorithm is developed to obtain a globally optimal solutionwith power and capacity constraints. In Section 3, the

minimum subchannel transmission power constrained bythe total power and the minimum subchannel transmissioncapacity is analyzed based on the new algorithm. InSection 4, total capacity and energy efficiency of MISO-OFDM communication systems are simulated and analyzedwith different BS transmission powers. Finally, conclusionsare drawn in Section 5.

2 System model and problem formulation

2.1 System model

To investigate the energy efficiency of MISO-OFDMcommunication systems with power and capacity con-strains, a basic MISO-OFDM communication system isillustrated in Fig. 1. Considering that multiple antennas areeasier to be integrated into base stations (BSs) than the userterminals in practice, in this paper, we just investigate theenergy efficiency of MISO-OFDM communication sys-tems. In Fig. 1, the BS is integrated with MT antennas andevery user terminal just is integrated with one antenna.There are K users and a BS distributed into a MISO-OFDMcommunication system. In this communication system, allorthogonal N subcarriers are regrouped into N or less Nsubchannels by the OFDM scheme. Therefore, the interfer-ence in this MISO-OFDM communication system isignored. The total bandwidth of communication system isassumed as B. Every subchannel of MISO-OFDM commu-nication system in Fig. 1 is assumed as a quasi-staticchannel, which means there is no change within a block oftransmission. Every selected user is allocated a subchannelfor transmission data. In the following context, the usernumber K is assumed larger than the maximum subchannelnumber. Hence, a user scheduling algorithm accounting forthe QoS of subchannels, such as [12] is used for user

UE

Base Station

UE

UE

UE

UE

UE

UEIFFT andparallelto serial

Subchannel 1

Subchannel 2

Subchannel N

Encoder ...

Addcyclicprefix

and D/A

...

...

UE 1 data

UE K data

UE 2 data

Channel information feedback

Base station transmitter using OFDM modulation scheme

Controller at base station

UE 1 CSI

UE K CSI

UE 2 CSISubchannelallocation...

Fig. 1 MISO-OFDM communication system model

30 Mobile Netw Appl (2012) 17:29–35

selection and subcarriers allocation. In this case, the signalyk,n received by the user UEk is expressed as follows

yk;n ¼ffiffiffiffiffiffiffiPn

MT

r

Hk;nsk þ n0 ð1Þ

Where Pn is the transmission power in the subchannel n ∈{1,…,N}, Hk,n is the subchannel vector from BS to UEk

with the subcarrier n, sk is the signal vector from BS toUEk, n0 is the additive white Gaussian noise (AWGN) withvariance N0 in the wireless subchannels.

The OFDM scheme used in Fig. 1 is assumed toadaptively adjust the transmission power over subchannelsaccounting for the bit error ratio (BER) and transmissionrate, which can be expressed as follows

Ptotal ¼XN

n¼1

Pn ð2aÞ

Ctarget ¼XN

n¼1

Cn ð2bÞ

PBER target � PBERðnÞ ð2cÞwhere Ptotal is the total transmission power in a BS, Pn isthe transmission power over the given wireless subchanneln; Ctarget is the constraint of total bit number over allsubchannels within a block of transmission, Cn is the bitnumber over a subchannel n within a block of transmission;PBER_target is the BER threshold configured by MISO-OFDM communication systems, PBER(n) is the BER over agiven wireless subchannel n.

2.2 Problem formulation

To maximize the total capacity in wireless subchannels, thetraditional power allocation scheme always tries to allocatethe maximum transmission power into the wireless sub-channel with the best quality, such as water-fillingalgorithm. In the Fig. 1 communication system, we firsttry to select N users from all K users, whose wirelesssubchannels are better than other wireless subchannels. Inthis case, the allocated transmission powers over wirelesssubchannels are proportional with quality of wirelesssubchannels, which is expressed as follows

Pn

Pmin¼ Hk;n

��

��2F

ð Hk k2FÞmin

ð3Þ

Where Pmin is the minimum subchannel transmissionpower over the worst wireless subchannel in all selected

wireless subchannels, ð Hk k2FÞmin is the worst wirelesssubchannel in all selected wireless subchannels.

Moreover, considering the energy efficiency requirementin this MISO-OFDM communication system, the total BStransmission power is fixed. Therefore, the power alloca-tion problem can be formulated as follows

XN

n¼1

Pn ¼ Ptotal

Pn ¼Hk;n

��

��2F

ð Hk k2FÞmin

Pmin Ptotal

8>>>>><

>>>>>:

ð4Þ

Where Pmin Ptotal is the minimum subchannel transmis-sion power derived from the fixed total BS transmissionpower constraint.

On the other hand, considering the QoS requirementfrom user applications, the minimum capacity of subchan-nel is usually constrained by a given user application. Allsubchannel state information of MISO-OFDM communi-cation systems is assumed to be known by the BS. In thiscase, the minimum capacity of subchannel constrained by agiven user application from MISO-OFDM communicationsystems can be expressed as follows

Cmin ¼ B

Nlog2 1þ Pmin Cmin

N0ð Hk k2FÞmin

� �

ð5Þ

where Pmin Cmin is the minimum subchannel transmissionpower, which corresponds to the worst subchannel in MISO-OFDM communication systems and satisfies the minimumcapacity requirement from a given user application.

From (4) and (5), we can derive two minimum subchanneltransmission power thresholds for MISO-OFDM communica-tion systems. When the value of Pmin Ptotal is larger than orequal to the value of Pmin Cmin , the minimum subchanneltransmission power is configured by the Pmin Ptotal. When thevalue of Pmin Ptotal is less than the value of Pmin Cmin , theminimum subchannel transmission power is configured bythe Pmin Cmin in order to satisfy the QoS requirement from agiven user application. Therefore, considering the energyefficiency and QoS requirements from MISO-OFDM com-munication systems, the power allocation problem can befurther formulated as follows

Pmin Ptotal � Pmin Cmin

XN

n¼1

Pn ¼ PtotalPn ¼Hk;n

��

��2F

ð Hk k2FÞmin

Pmin Ptotal

Cmin ¼ B

Nlog2 1þ Pmin Cmin

N0ð Hk k2FÞmin

� �

8>>>>>>><

>>>>>>>:

ð6Þ

Based on the power allocation model in (6), the transmis-sion power over every subchannel can be calculated.

Mobile Netw Appl (2012) 17:29–35 31

Furthermore, the total capacity of MISO-OFDM communi-cation systems can be derived as follows

Ctotal ¼ BXN

n¼1

log2ð1þPn

N0Hk;n

��

��2FÞ ð7Þ

Based on the total capacity of MISO-OFDM communi-cation systems and total BS transmission power, the energyefficiency of MISO-OFDM communication systems can bederived as follows

EE ¼BPN

n¼1log2ð1þ Pn

N0Hk;n

��

��2FÞ

Ptotalð8Þ

2.3 Algorithm design considering power and capacityconstraints

According to power allocation constraints in (6), a newpower allocation scheme is designed accounting for powerand capacity constraints. Moreover, the number of selected

users is derived from (4) based on the minimum subchanneltransmission power. In the following, a new power and userjoint schedule (PUJS) algorithm is described in Table 1.

3 Performance analysis of power and capacityconstraints

In the PUJS algorithm, the minimum subchannel transmis-sion power is impacted by the total BS transmission power

Table 1 Algorithm PUJSðPmin Cmin Þ

Table 1 Algorithmminmin_( )CPUJS P

Input: the value of minmin_CP from a given user application

Output: the selected users and corresponding allocation subchannel power values

01 initial MISO-OFDM communication system and obtain all subchannel state

information;

02 select N users from all K candidates based on the subchannel quality;

03 calculate the minimum subchannel transmission power totalmin _ PP from (4);

04 iftotal minmin_ min_P CP P

05 then allocate the corresponding power values to N users based on (4);

06 else replace the value of minmin_CP into the value of

totalmin _ PP ;

substitute the new minimum subchannel transmission power value into (4) to

derive the number of selected users N’ and all subchannel power values allocated

to the N’ users;

07 return the selected users and corresponding allocation subchannel power values.

≥

Table 2 Simulation parameters

Simulation parameter Symbol Parameter value

Number of subcarriers N 50

Number of BS antennas MT 4

Number of users K 100

Total BS transmission power Ptotal normalized as 1

System bandwidth B normalized as 1

Variance of AWGN N0 0.01

32 Mobile Netw Appl (2012) 17:29–35

and the minimum subchannel capacity constrained by agiven user application. Thereby, evaluation of power andcapacity constraints in the PUJS algorithm is an interestingproblem, which can provide some practical guidelines fordeveloping new efficient algorithms to improve the energyefficiency and system capacity performance. The effect ofpower and capacity constraints on the minimum subchanneltransmission power is analyzed numerically in this section.In our numerical analysis, some parameters of MISO-OFDM communication systems are configured as Table 2.Without loss of generality, the number of subcarriersmodulated by the OFDM scheme in this paper is assumedas 50 and every subcarrier is allocated to a correspondingwireless subchannel for data transmission. Based on theMonte Carlo simulation method, every simulation result isobtained by averaging 500 times simulation calculation.

3.1 Minimum subchannel transmission power constrainedby the total BS transmission power

Based on (4), the relationship between the minimumsubchannel transmission power and the total BS trans-

mission power is illustrated in Fig. 2. From Fig. 2, theminimum subchannel transmission power increases withthe decreasing of number of selected users. Values ofminimum subchannel transmission power are not impact-ed by the subchannel minimum capacity. This result canbe explained by (4), which implies that the minimumsubchannel transmission power is linear with the numberof selected users if the total BS transmission power isfixed.

3.2 Minimum subchannel transmission power constrainedby the minimum subchannel capacity

Based on (5), the relationship between the minimumsubchannel transmission power and the minimum subchan-nel capacity is illustrated in Fig. 3. From Fig. 3, theminimum subchannel transmission power is impacted bythe minimum subchannel capacity and the number ofselected users. Moreover, the value of minimum subchanneltransmission power increases with the minimum subchan-nel capacity and the number of selected users.

00.01

0.020.03

0.040.05

0.06

30

35

40

45

500.01

0.015

0.02

0.025

0.03

Minimum subchannel capacityNumber of selected users

Min

imum

sub

chan

nel t

rans

mis

sion

pow

er

Fig. 2 Minimum subchannel transmission power constrained by thetotal BS transmission power Ptotal

00.01

0.020.03

0.040.05

0.06

3035

4045

500

0.02

0.04

0.06

0.08

0.1

Minimum subchannel capacityNumber of selected users

Min

imum

sub

chan

nel t

rans

mis

sion

pow

er

Fig. 3 Minimum subchannel transmission power constrained by theminimum subchannel capacity Cmin

00.01

0.020.03

0.040.05

0.06

3035

4045

500

0.02

0.04

0.06

0.08

0.1

Minimum subchannel capacityNumber of selected users

Min

imum

sub

chan

nel t

rans

mis

sion

pow

er

constrained by Ptotal

constrained by Cmin

Fig. 4 Minimum subchannel transmission power constrained by the totalBS transmission power Ptotal and minimum subchannel capacity Cmin

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

32

34

36

38

40

42

44

46

48

50

Minimum subchannel capacity

Num

ber

of s

elec

ted

user

s

N vs Cmin

source data

N vs Cmin

curve fitting

Fig. 5 Fitting the joint line from the two dimensionality space ofnumber of selected users N and minimum subchannel capacity Cmin

Mobile Netw Appl (2012) 17:29–35 33

3.3 Minimum subchannel transmission power constrainedby the total BS transmission power and the minimumsubchannel capacity

Based on (6), the minimum subchannel transmission powerconstrained by the total BS transmission power and theminimum subchannel capacity is illustrated in Fig. 4. FromFig. 4, we can find there is a joint line between the minimumsubchannel transmission power constrained by the total BStransmission power and the minimum subchannel transmis-sion power constrained by the minimum subchannel capacity.Values in this joint line can simultaneously satisfy theconstraints from the total BS transmission power and theminimum subchannel capacity.

To evaluate the characteristics of joint line in the Fig. 4,we fit this joint line into different two-dimensionality spacesto investigate the change trend with different system param-eters. In Fig. 5, the number of selected users decreases withthe increasing of the minimum subchannel capacity in thisjoint line. In Fig. 6, the minimum subchannel transmission

power decreases with the increasing of selected users, butthis decreasing trend is not linear. In Fig. 7, the minimumsubchannel transmission power increases with the minimumsubchannel capacity in this joint line.

4 Simulation results and discussion

Based on the simulation configuration in Section 3, wefurther investigate the total capacity and energy efficiencyperformance of MISO-OFDM communication systems underdifferent total BS transmission powers. In the followingsimulations, the total BS transmission power is configuredfrom 1 to 10 to evaluate MISO-OFDM communicationsystems performance.

In Fig. 8, the value of total capacity remains unchangedwhen the value of minimum subchannel capacity starts toincrease, and then the value of total capacity increases after thevalue of minimum subchannel capacity exceeds a specificthreshold. Moreover, this specific minimum subchannel

30 32 34 36 38 40 42 44 46 48 50

0.014

0.015

0.016

0.017

0.018

0.019

0.02

0.021

0.022

0.023

0.024

Number of selected users

Min

imum

sub

chan

nel t

rans

mis

sion

pow

erP

min vs N source data

Pmin

vs N curve fitting

Fig. 6 Fitting the joint line from the two dimensionality space ofnumber of selected users N and minimum subchannel transmissionpower Pmin

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

0.014

0.016

0.018

0.02

0.022

0.024

Minimum subchannel capacity

Min

imum

sub

chan

nel t

rans

mis

sion

pow

er

Pmin

vs Cmin

source data

Pmin

vs Cmin

curve fitting

Fig. 7 Fitting the joint line from the two dimensionality space of theminimum subchannel capacity Cmin and the minimum subchanneltransmission power Pmin

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Minimum subchannel capacity

Tot

al c

apac

ity

Ptotal

=10

Ptotal

=8

Ptotal

=6

Ptotal

=4

Ptotal

=2

Ptotal

=1

Fig. 8 Impact of minimum subchannel capacity on the total capacityof MISO-OFDM communication system

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.5

1

1.5

2

2.5

3

3.5

4

Minimum Subchannel Capacity

Ene

rgy

Effi

cien

cy

Ptotal

=10

Ptotal

=8

Ptotal

=6

Ptotal

=4

Ptotal

=2

Ptotal

=1

Fig. 9 Impact of minimum subchannel capacity on the energyefficiency of MISO-OFDM communication system

34 Mobile Netw Appl (2012) 17:29–35

capacity threshold increases with the total BS transmissionpower. The total capacity of MISO-OFDM communicationsystem increases with the total BS transmission power.

In Fig. 9, the value of energy efficiency remainsunchanged when the value of minimum subchannel capacitystarts to increase, and then the value of energy efficiencyincreases after the value of minimum subchannel capacityexceeds a specific threshold.Moreover, this specific minimumsubchannel capacity threshold increases with the total BStransmission power. However, the energy efficiency decreaseswith the total BS transmission power.

5 Conclusion

In this paper, we have investigated the energy efficiency ofMISO-OFDM communication systems considering powerand capacity constraints. From these two constraints, wehave formulated a power allocation model for a MISO-OFDM communication system and developed a new PUJSalgorithm to realize the power allocation in the BS.Moreover, the minimum subchannel transmission powerperformance constrained by the total BS transmissionpower and minimum subchannel capacity has been ana-lyzed. Based on numerical simulations, there is a joint linewhich can simultaneously satisfy requirements from thetotal BS transmission power and minimum subchannelcapacity and the basic performance of joint line isinvestigated by the numerical fitting approach. Further-more, energy efficiency and total capacity performance ofMISO-OFDM communication systems with power andcapacity constraints have been analyzed by simulations.From simulations, we find there is a minimum subchannelcapacity threshold to impact on energy efficiency and totalcapacity of MISO-OFDM communication systems. Whenthe value of minimum subchannel capacity is less than aspecific threshold, the energy efficiency and total capacityof the MISO-OFDM communication systems remainunchanged. Otherwise, the energy efficiency and total

capacity of MISO-OFDM communication systems increasewith the minimum subchannel capacity.

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