TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES

Published online 6 November 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ett.2905

RESEARCH ARTICLE

Quadrature spatial modulation–performance analysisand impact of imperfect channel knowledgeRaed Mesleh1*, Salama S. Ikki2 and Hadi M. Aggoune1

1 Electrical Engineering Department and Sensor Networks and Cellular System (SNCS) research center, University of Tabuk, POBox: 741, 71491 Tabuk, Saudi Arabia

2 Department of Electrical Engineering, Faculty of Engineering, Lakehead University, Thunder Bay, Ontario, Canada

ABSTRACT

In this paper, a new multiple-input multiple-output transmission technique called quadrature spatial modulation (QSM)is proposed and analyzed in the presence of imperfect channel estimation at the receiver. In QSM, conventional spatialconstellation diagram of spatial modulation (SM) system is expanded to include both in-phase and quadrature components.As such, significant enhancement in the overall spectral efficiency is achieved while retaining all inherent advantages ofSM technique, such as inter-channel interference avoidance, single radio frequency chain transmitter and low receivercomplexity. It is shown that significant performance enhancements can be achieved as compared with SM, Alamouti, andspatial multiplexing systems. Besides, the impact of Gaussian imperfect channel estimation on the performance of QSMsystem is studied. A closed-form expression for the pairwise error probability of generic QSM system is derived and used tocalculate a tight upper bound of the average bit error probability over Rayleigh fading channels with perfect and imperfectchannel knowledge. Also, simple asymptotic expression is derived and analyzed. Obtained Monte Carlo simulation resultshighlight the accuracy of the conducted analysis. Copyright © 2014 John Wiley & Sons, Ltd.

*Correspondence

R. Mesleh, Electrical Engineering Department and Sensor Networks and Cellular System (SNCS) Research Center, University ofTabuk, PO Box: 741, 71491 Tabuk, Saudi Arabia.E-mail: rmesleh.sncs@ut.edu.sa

Received 6 June 2014; Revised 20 August 2014; Accepted 12 October 2014

1. INTRODUCTION

In recent years, the demand for wireless services andthe number of mobile subscribers have seen tremendousgrowth. This growth motivated researchers to develop newtransmission technologies, protocols, and network infras-tructure solutions to enhance the achievable throughput andthe overall spectral efficiency. The scarcity of the wire-less spectrum is the main factor that hinders the visionfor wireless access everywhere anytime, and perhaps thetoughest challenge that wireless research has to under-take. Overcoming this challenge requires innovations invarious areas including novel ways for spectrum sensingand reuse, mechanisms for using higher frequencies suchas 60 GHz and the visible light, novel ideas for dealingwith interference, multiple-input multiple-output (MIMO),and generally more efficient protocols and systems [1–12].MIMO technology promises a linear gain in capacity withthe number of antennas [13], but it is yet to be adopted ona scale commensurate with its true potential [14–16].

Space modulation techniques, as space shift keying(SSK) [17] and spatial modulation (SM) [18], are MIMOmethods that use the multiple transmit antennas in an inno-vative fashion. Transmit antennas are considered as spatialconstellation points and utilized to carry additional infor-mation bits to boost the overall spectral efficiency. Eachantenna index is utilized to carry additional informationbits and a spatial multiplexing (SMUX) gain of base-twologarithm of the overall number of transmit antennas isachieved. Besides, activating single transmit-antenna at atime eliminates inter-channel interference, relaxes inter-antenna synchronization requirements, reduces receivercomplexity, and allows the use of a single radio fre-quency chain at the transmitter. In addition, it has beenshown that space modulation techniques enhance error per-formance with moderate number of transmit antennas ascompared with other conventional MIMO techniques. Aswell, it is demonstrated that these techniques are morerobust to channel imperfections, such as spatial channelcorrelation and channel estimation errors, as comparedwith other MIMO techniques, because the probability of

Trans. Emerging Tel. Tech. 2017; 28:e2905

Copyright © 2014 John Wiley & Sons, Ltd. of1 9

R. Mesleh, S. S. Ikki and H. M. Aggoune

error of space modulation systems is not determined bythe actual channel realization, rather by the differencesbetween channels associated with the different transmitantennas [2, 3, 19–22].

Nonetheless, a major criticism of space modulation tech-niques is that the data rate enhancement is proportional tothe base-two logarithm of the number of transmit anten-nas. This is unlike other SMUX techniques, where data rateincreases linearly with the number of transmit antennas.To overcome this limitation, several attempts were made toenhance the overall spectral efficiency of such techniques.In [21], a generalized SM algorithm is proposed where acombination of transmit antennas is activated at each timeinstant. A similar algorithm is proposed in [22] for SSKsystem. However, the performance of these systems areshown to be slightly worse than the conventional SM/SSKsystems. Another algorithm proposed in [23] creates a newconstellation diagram for SSK system by combining realand imaginary symbols. The scheme is shown to performnearly the same as conventional SSK system with similarsystem configuration but with double spectral efficiency.

This paper relies on the idea in [23] to propose a newhigh spectral efficiency MIMO scheme called quadraturespatial modulation (QSM) [24]. The authors in [23] pro-poses a new SSK scheme called ‘Bi-SSK modulation’.Bi-SSK extends the constellation diagram of conventionalSSK system by considering dual antenna constellation; oneto transmit real symbol and another to transmit an imagi-nary one. It is shown in [23] that a negligible performancepenalty is achieved but with double the data rate. QSMis a method for processing the signal before transmission.In QSM, the spatial constellation symbols are expandedto in-phase and quadrature components. One componenttransmits the real part of a signal constellation symboland the other transmits the imaginary part. In conventionalSM system, these two parts are transmitted from a singletransmit antenna to avoid inter-channel interference (ICI)at the receiver input. Similarly, in QSM system, ICI isalso avoided entirely because the two transmitted data areorthogonal and modulated on the real part and the imag-inary part of the carrier signal. But with the additionaltransmission of base-two logarithm of the number of trans-mit antenna bits. The proposed Bi-SSK system in [23] isshown to be a special case of QSM and called quadratureSSK (QSSK) for convenience. In QSSK, a group of data

bits activates one antenna to transmit the real symbol ‘C1’,and another group activates another or the same antenna totransmit the quadrature symbol ‘Cj’. Combining all pos-sible antenna combinations and symbols gives exactly theproposed constellation diagrams of [23].

Detailed analysis of QSM system with imperfect chan-nel knowledge at the receiver is conducted, and results arecompared with conventional SM, Alamouti, and SMUXsystems under similar spectral efficiency. The pairwiseerror probability (PEP) of QSM is computed in closed formwithout resorting to Monte Carlo numerical simulations,which besides being computationally intensive, only yieldlimited insights about the system performance and cannotbe exploited for a systematic optimization of it. In addi-tion, a tight upper bound on the overall average bit errorprobability (ABEP) is provided. As well, an approximateexpression for the error probability is obtained to clearlysee the impact of different system parameters on the overallperformance.

The remainder of this paper is organized as follow: InSection 2, QSM system and channel models are presented.Performance analysis is presented in Section 3. Resultsare discussed in Section 4, and the paper is concluded inSection 5.

2. SYSTEM AND CHANNELMODELS

A baseband system model for QSM/QSSK systems isdepicted in Figure 1. A generic Nt � Nr MIMO configu-ration is considered with Nt and Nr being the number oftransmit and receive antennas, respectively.

At one particular time instant, m D log2�N2

t M�

databits are to be transmitted, with M D log2.q/ denotingthe modulation order of arbitrary M-quadrature amplitudemodulation (M-QAM)/ phase shift keying (M-PSK) orother constellation diagrams. The incoming data bits areprocessed and partitioned into three groups. Two groupseach with log2.Nt/ bits are mapped into spatial constel-lation symbols. The other log2.M/ bits is mapped intoa signal constellation symbol. The signal constellationsymbol, x, is further decomposed to its real, x<, and imag-inary, x=, parts. The real part is transmitted from onetransmit antenna among the existing Nt transmit anten-nas, where the active antenna index is determined by the

Figure 1. System model of the quadrature spatial modulation (QSM)/quadrature space shift keying (QSSK) systems highlighting therequired transmitter/receiver blocks for baseband transmission in the presence of imperfect channel knowledge at the receiver.

of 9 © 2014 John Wiley & Sons, Ltd.DOI: 10.1002/ett

Trans. Emerging Tel. Tech. 2017; 28 :e29052

R. Mesleh, S. S. Ikki and H. M. Aggoune

first log2.Nt/ bits. Similarly, the imaginary part is transmit-ted by another or the same transmit antenna depending onthe other log2.Nt/ bits. However, the transmitted real andimaginary parts are orthogonal representing the in-phaseand the quadrature components of the carrier signal. Thesignal at the antenna input and after baseband to bandpassconversion can be written as

s D Rehxe�j2� fct

iD x< cos .2� fct/Cx= sin .2� fct/ (1)

which is the same for either SM or QSM systems forcertain carrier frequency, fc. In SM system, the completedata symbol, x, is transmitted from one antenna deter-mined by log2.Nt/ bits to avoid ICI. However, in QSM,an additional log2.Nt/ bits are transmitted by utilizingan additional spatial constellation dimension. While, ICIis entirely avoided and single radio frequency chain atthe transmitter can still be used as in the case of SM.But, the transmit antennas should be synchronized to starttransmission simultaneously.

An example for QSM bits mapping and transmissionis given in what follows assuming 4 � 4 MIMO systemand 4-QAM modulation. The number of data bits thatcan be transmitted at one particular time instant is m Dlog2.N

2t M/ D 6 bits. Assume that the following incoming

data bits, m D

2664 0 1 0 0 1 1„ ƒ‚ …

log2.M/Clog2.N2t /

3775 are to be transmitted.

The first log2.M/ bits�

0 1�, modulate a 4-QAM sym-

bol, x D �1 C j. This symbol is divided further intoreal and imaginary parts, x< D �1 and x= D C1. Thesecond log2.Nt/ bits

�0 0

�modulate the active antenna

index used, `< D 1 to transmit x< D �1 resulting in thetransmitted vector s< D

��1 0 0 0

�T. The last log2.Nt/

bits,�

1 1�

modulate the active antenna index, `= D 4,used to transmit x= D C1, resulting in the vector s= D�

0 0 0 C1�T

. The transmitted vector is then obtained byadding the real and imaginary vectors, s D s< C js= D��1 0 0 j

�T. In case of QSSK system, the first antenna

transmits the real symbol C1 while the second antennatransmits the imaginary symbolCj.

The vector, s, is transmitted over an Nr � Nt wirelesschannel H and experiences an Nr-dim additive white Gaus-sian noise, n. H is a complex channel matrix with Nr � Nt

dimension. Its element hr,t denotes the complex channelpath gain between the tth transmit antenna and rth receiveantenna, and h`< is the `<

th column of H, that is, h`< D�h1,`< , � � � , hNr ,`<

�T . The channel entries are assumed tobe i.i.d. complex Gaussian random variables with zeromean and variance �2

h . The n D�n1, n2, � � � , nNr

�T is thecomplex Gaussian noise vector with zero mean and vari-ance N0 (both real and imaginary parts having a double-sided power spectral density equal to N0=2). The receivedsignal at the output of the channel is given by

y Dp

Es�h`<x< C jh`=x=

�C n, `<, `= D 1, 2, � � � , Nt

(2)where Es denotes the transmitted energy.

Let the estimate of the hr,t channel be Qhr,t. We assumethat hr,t and Qhr,t are jointly ergodic and stationary Gaus-sian processes. Further, assuming orthogonality betweenthe channel estimate and the estimation error, we have

hr,t D Qhr,t C ehr,t (3)

where ehr,t is the channel estimation error, which is com-plex Gaussian with zero mean and variance �2

e . Note that�2

e is a parameter that captures the quality of the channelestimation and can be appropriately chosen depending onthe channel dynamics and estimation schemes. Assumingorthogonal pilot channel estimation sequences, the estima-tion error reduces linearly with increasing the number ofpilots.

With this, the optimum ML decoder for QSM system atthe receiver is given by

hO<, O=, Ox<, Ox=

iDarg min

`<,`=x<,x=

���y�p

Es

�Qh`<x< C j Qh`=x=

����2

D arg min`<,`=,x<,x=

kgk2 � 2<˚yHg

(4)

where .�/H is the Hermitian of a vector or a matrix, k � k

denotes the norm, and g Dp

Es

�Qh`<x< C j Qh`=x=

�. The

detected antenna indices O< and O= along with the detecteddata symbols Ox< and Ox= are used to retrieve the originalinformation bits.

In case of QSSK system, (4) reduces to

hO<, O=

iD arg min

`<,`=

���y �p

Es

�Qh`< C j Qh`=

����2(5)

In the next section, the PEP of ML-decoder QSM systemis computed in closed form. Also, a tight upper bound onthe overall ABEP is provided, and an approximate expres-sion for the error probability is obtained. The obtainedasymptotic equation clearly highlight the impact of differ-ent system parameters on the overall performance and canbe used for future optimization studies.

3. PERFORMANCE ANALYSIS

Let Og Dp

Es

�QOh`< Ox< C j QOh`= Ox=

�, then

Pr .g! OgjH/ D Pr�dg ! dOgjH

�D Pr

w >

ˇˇrEs

2

�QOh`< Ox< �

Qh`<x<�

C j

rEs

2

�QOh`= Ox= �

Qh`=x=�ˇˇ21A

(6)

© 2014 John Wiley & Sons, Ltd.DOI: 10.1002/ett

of 9Trans. Emerging Tel. Tech. 2017; 28 :e2905 3

R. Mesleh, S. S. Ikki and H. M. Aggoune

where

w D 2<

( rEs

2

�Qh`<x< �

QOh`< Ox<�

C j

rEs

2

�Qh`=x= �

QOh`= Ox=�!

�

rEs

2

�e`<x< C je`=x= C n

�!)(7)

Note that w is a complex Gaussian random variable withvariance

�2w D 4

ˇˇrEs

2

�Qh`<x< �

QOh`< Ox<�C j

rEs

2

�Qh`= x= �

QOh`= Ox=�ˇˇ2

�

N0

2C�2

e Es

4jx<j

2 C�2

e Es

4jx=j

2

�.

(8)

Hence, the conditional PEP in (6) can be written as

Pr .g! OgjH/ D Q

sjAC jBj2

4N0 C 2�2e Es

�jx<j2 C jx=j2

�!(9)

where

A Dp

Es

�<�Qh`<x<

�� =

�Qh`=x=

��

<�QOh`< Ox<

�C=

�QOh`= Ox=

��B D

pEs

�=�Qh`<x<

�C<

�Qh`=x=

��

=�QOh`< Ox<

��<

�QOh`= Ox=

��(10)

and Q.x/ denotes the Q-function.Please note that x< and x= are the real and imaginary

parts of the complex symbol constellation, that is, both arereal values. Hence, A and B are independent Gaussian ran-dom variables, and � D A C jB is a complex Gaussianrandom variable. Thereby, the Q-function variable in (9),which is the squared magnitude of �, j�j2 is an exponentialrandom variable with mean [25]

N� D

8ˆˆ<ˆˆˆ:

��jx<j

2 C jOx<j2 C jx=j

2 C jOx=j2�

,

if Qh`< ¤QOh`< , Qh`= ¤

QOh`=��jx< � Ox<j

2 C jx=j2 C jOx=j

2�

,

if Qh`< DQOh`< , Qh`= ¤

QOh`=��jx<j

2 C jOx<j2 C jx= � Ox=j

2�

,

if Qh`< ¤QOh`< , Qh`= D

QOh`=��jx< � Ox<j

2 C jx= � Ox=j2�

,

if Qh`< DQOh`< , Qh`= D

QOh`=

(11)

where � DEs.�2

h��2e /

4N0C2�2e Es.jx<j2Cjx=j2/

.

In case of QSSK system,

N� D

8ˆ<ˆ:

Es.�2h��

2e /

2N0C�2e Es

,

if Qh`< ¤QOh`< , Qh`= ¤

QOh`=Es.�2

h��2e /

4N0C2�2e Es

,

if Qh`<DQOh`< , Qh`= ¤

QOh`= or Qh`< ¤QOh`< , Qh`=D

QOh`=(12)

Thus, the average PEP can be written as

NPe .gn ! Ogk/ D1

2

0@1 �

sN�=2

1C N�=2

1A , (13)

and the ABEP of the QSM system can be evaluated usingthe following asymptotically tight union bound,

Pb D1

2m

2mXnD1

2mXkD1

1

kNPe .gn ! Ogk/ errn,k (14)

where errn,k is the number of bit errors associated with thecorresponding PEP event.

If the receiver is equipped with Nr receive antennas, theinstantaneous PEP is given by

Pe .gn ! Ogk/ D Q

0@vuut NrX

kD1

�k

1A , (15)

and the average PEP can be written as [26, 27],

NPe .gn ! Ogk/ D �Nr

�

Nr�1XkD0

Nr � 1C k

k

�Œ1 � ���

k (16)

where �� D12

1 �

rN�=2

1CN�=2

�. Taking the Taylor series

of (16) and ignoring higher-order terms gives the followingasymptotic average PEP of the QSM system,

NPe .gn ! Ogk/ D2Nr�1�.Nr C 0.5/p�.Nr/Š

1N�

�Nr

, (17)

where a diversity gain of Nr is clearly obvious in (17).Three different scenarios can be discussed based on the

definition of �2e as given in what follows.

(1) Fixed �2e : Without loss of generality, let us consider

the case where Qh`< ¤QOh`< , Qh`= ¤

QOh`= . Then, theasymptotic average PEP can be written as

PEP �4Nr 2Nr�1�.Nr C 0.5/

p�.Nr/Š

�

24 1

2�2e

�jx<j

2 C jOx<j2�

��2

h��2e

��jx<j2CjOx<j

2Cjx=j2CjOx=j2�35

Nr

.

(18)

of 9 © 2014 John Wiley & Sons, Ltd.DOI: 10.1002/ett

Trans. Emerging Tel. Tech. 2017; 28 :e29054

R. Mesleh, S. S. Ikki and H. M. Aggoune

It can be seen that (18) is not a function of Es=N0,that is, increasing the signal to noise ratio (SNR) doesnot improve the error performance, and the diversitygain is zero. In other words, error floor in the ABEPperformance will be noticed.

(2) Variable channel estimation error, �2e D

1Es=N0

: If thechannel estimation error is inversely proportional tothe SNR, the asymptotic PEP can be simplified to

PEP �4Nr 2Nr�1�.Nr C 0.5/

p�.Nr/Š

1

Es=N0

�Nr

�

24 1C 1

2

�jx<j

2 C jOx<j2�

�2h

�jx<j2 C jOx<j

2 C jx=j2 C jOx=j2�35

Nr

,

(19)

where a diversity gain of Nr is clearly noticed inthis case. Note that increasing the SNR enhancesthe transmitted pilots power as well and reduces thechannel estimation error, which enhances the ABEPperformance of the system.

(3) Perfect channel estimation, �2e D 0: Assuming ideal

system where the channel is perfectly known at thereceiver simplifies the asymptotic PEP to

PEP �4Nr 2Nr�1�.Nr C 0.5/

p�.Nr/Š

1

Es=N0

�Nr

�

24 1

�2h

�jx<j2 C jOx<j

2 C jx=j2 C jOx=j2�35Nr

.

(20)

Again, a diversity gain of Nr is achieved but the prob-ability of error in (20) is less than that of (19) due tothe perfect knowledge of the channel.

4. NUMERICAL ANALYSIS ANDDISCUSSION

Performance evaluation of the proposed QSM technique ispresented in this section. Analytical and Monte Carlo simu-lation results are presented assuming perfect and imperfectchannel estimation at the receiver. In all results, the ABEPis depicted versus the SNR. The SNR is defined as Es=N0,with Es denoting the overall transmit power from all activetransmit antennas in all systems. For Monte Carlo simu-lation results, at least 106 symbols have been transmittedto compute the ABEP for each SNR value. The channelis assumed to be static for each frame, and a frame lengthof 200 symbols is considered. Orthogonal Hadamard pilotsymbols are inserted at the beginning of each frame forchannel estimation purposes. A pilot sequences, each oflength Nh D Nt symbols, are transmitted simultaneouslyfrom the multiple transmit antennas. Four receive antennas,Nr D 4 are considered in all scenarios.

Results for 2�4 and 4�4 QSM systems are depictedin Figures 2 and 3, respectively. The impact of imper-fect channel knowledge at the receiver is evaluated and

0

100

10-1

10-2

10-3

10-4

10-5

10-6

10-7

5 10 15

SNR (dB)

AB

EP

20 25

Figure 2. Analytical, simulation, and asymptotic quadrature spa-tial modulation (QSM) average error probability with two trans-mit antennas, four receive antennas and 4-QAM modulation inthe presence of imperfect channel estimation. Also and for sakeof comparison, performance of conventional spatial modulation(SM) under similar system setup and with similar spectral effi-ciency and QSM with perfect channel knowledge are depicted

as well.

0

100

10-1

10-2

10-3

10-4

10-5

10-6

5 10 15 20 25

SNR (dB)

AB

EP

Figure 3. Quadrature spatial modulation (QSM) analytical, sim-ulation, and asymptotic average error probability with fourtransmit antennas, four receive antennas and using 4-QAMmodulation compared with conventional spatial modulation (SM)scheme with similar spectral efficiency and under practical

channel estimation at the receiver.

compared with the case of perfect channel knowledge.Analytical and asymptotic results are depicted as welland compared with simulation results. Results demonstrateclose-match for a wide and pragmatic range of SNR values.It is important to note that the considered Chernoff upperbound is loose at low SNR but tightens at asymptotical val-ues. Also in Figure 2, the performance of 2�4 conventionalSM scheme with 8-QAM modulation achieving similarspectral efficiency as 2�4 4-QAM QSM system is depictedin the figure. Obtained results demonstrate the significantenhancement of the QSM system over the SM system,where a gain of about 3 dB can be noticed in the figure.

© 2014 John Wiley & Sons, Ltd.DOI: 10.1002/ett

of 9Trans. Emerging Tel. Tech. 2017; 28 :e2905 5

R. Mesleh, S. S. Ikki and H. M. Aggoune

Also, the impact of imperfect channel estimation on QSMsystem is evident in the figure where performance degra-dation of about 2 dB can be noticed. Similarly, 16-QAM4�4 SM system is depicted in Figure 3 and compared with4-QAM 4�4 QSM system achieving similar spectral effi-ciency. Channel estimation errors are shown to degrade theperformance of QSM system by about 1 dB and significantperformance enhancements are achieved as compared withconventional SM where a gain of about 5 dB can be noticedin Figure 3.

Considering both figures, Figures 2 and 3, QSMachieves higher performance enhancements with largenumber of transmit antennas as compared with SM system.With Nt D 2, QSM shows 3 dB better performance as com-pared with SM while 5 dB gain is reported with Nt D 4.This can be attributed to two reasons. First, detection oftransmit antenna indices is robust to channel estimationerrors, as shown in [28–30], because error is not related toactual channel realizations, rather to the differences amongchannel paths associated with different transmit antennas.Second, QSM increases the spectral efficiency from 4 to6 b/s/Hz by increasing the number of transmit antennasfrom Nt D 2 to Nt D 4. However, SM system achieves6 b/s/Hz spectral efficiency by increasing the number oftransmit antennas to 4, and the 4-QAM modulation ordershould be increased to 16-QAM.

Another important advantage of QSM can be noticedalso in both figures. Increasing the achieved spectral effi-ciency from 4 to 6 b/s/Hz degrades the QSM performanceby only 1.5 dB. This is minor degradation performance ascompared with SM or other digital modulation schemeswhere such spectral efficiency enhancement requires morethan 5 dB increases in SNR [26]. Note that these advan-tages are attained at almost no cost. The receiver complex-ity of QSM and SM schemes are equivalent and depends onthe considered spectral efficiency. Estimating the data sym-bols in (4) require two complex multiplications for eachreceiving antenna and ML searches over m-dimensionalspace diagram. Hence, the overall number of needed realmultiplications and divisions of QSM scheme is given by,

D 8Nr2m, (21)

which is equivalent to SM complexity [18, 21, 31]. It isimportant to note that there exist several algorithms toreduce the SM ML receiver complexity [31, 32] and similaralgorithms can be developed for QSM. While this will besignificant for future developments of the proposed QSMidea, it clearly falls beyond the scope of this paper and willbe addressed in future works.

Impact of fixed �2e values on the performance of QSM

is shown in Figure 4. Two values of �2e are assumed, �10

and �15 dB. 4�4 QSM system with 4-QAM modulationis considered. Fixing the channel estimation error vari-ance means that increasing pilot symbols power would notreduce the channel estimation error, and an error floor isexpected as can be seen in the figure. In fact, (18) is nota function of the SNR and evaluating (18) will lead to theexpected ABEP value at high SNR.

010-4

10-3

10-2

10-1

100

5 10 15 20 25 30

SNR (dB)

AB

EP

Figure 4. Quadrature spatial modulation (QSM) analytical andsimulation average error probability with four transmit antennas,four receive antennas and using 4-QAM modulation for fixed �2

e

values. Two values of �2e of �10 and �15 dB are considered.

010-7

10-6

10-5

10-4

10-3

10-2

10-1

100

2 4 6 8 10 12 14 16 18 20

SNR (dB)

AB

EP

Figure 5. Performance analysis of quadrature space shift keying(QSSK) system in terms of analytical, simulation, and asymp-totic average error probability with two transmit antennas, fourreceive antennas in the presence of imperfect channel knowl-edge. QSSK results are compared with conventional space shiftkeying (SSK) system with similar spectral efficiency and QSSK

system with perfect channel knowledge.

Results for 2�4 QSSK system are shown in Figure 5and for 4�4 QSSK system in Figure 6. Again, analyti-cal, asymptotic, and simulation results demonstrate closematch for wide and pragmatic SNR values. Imperfectchannel knowledge is shown to degrade QSSK perfor-mance by about 1–1.5 dB. Also, QSSK system is shown tooutperform its counterpart SSK system by about 2 dB.

In the final set of simulation results, depicted inFigures 7 and 8, QSM performance is compared with otherMIMO techniques, including QSSK, SMUX, and Alam-outi scheme for two spectral efficiencies, m D 4 b/s/Hzand m D 8 b/s/Hz and under the assumption of imper-fect channel knowledge at the receiver. In SMUX system,data are transmitted simultaneously from all existing trans-mit antennas, and ML decoder is applied at the receiver

of 9 © 2014 John Wiley & Sons, Ltd.DOI: 10.1002/ett

Trans. Emerging Tel. Tech. 2017; 28 :e29056

R. Mesleh, S. S. Ikki and H. M. Aggoune

010-7

10-6

10-5

10-4

10-3

10-2

10-1

100

2 4 6 8 10 12 14 16 18 20

SNR (dB)

AB

EP

Figure 6. Performance analysis of quadrature space shift keying(QSSK) system in terms of analytical, simulation, and asymp-totic average error probability with four transmit antennas, fourreceive antennas in the presence of imperfect channel knowl-edge. QSSK results are compared with conventional space shiftkeying (SSK) system and QSSK with perfect channel knowledge.

100

10-1

10-2

10-3

10-4

10-5

10-6

10-7

0 5 10 15

AB

EP

SNR (dB)20

Figure 7. Simulation results of quadrature spatial modulation(QSM), quadrature space shift keying (QSSK), spatial multi-plexing (SMUX), and Alamouti schemes achieving a spectralefficiency of m D 4 b/s/Hz under the assumption of imperfect

channel knowledge at the receiver.

to decode the received signal. Alamouti scheme considerstwo transmit antennas and uses the optimum decoder pro-posed in [33] to decode the received message. In Figure 7,results for all schemes achieving a spectral efficiency ofm D 4 b/s/Hz are depicted. The significant enhancement ofthe proposed QSM system is evident in the figure. Whileperforming similar to SMUX and QSSK systems at lowSNR, 3–4 dB SNR gain is reported at high SNR values.Besides, more than 6 dB SNR gain is achieved as comparedwith Alamouti scheme at an ABEP of 10�4. However, it isanticipated that the Alamouti performance will enhance athigher SNR values due to diversity gain, and it may outper-form all other systems at very high, but impractical, SNRvalues.

In Figure 8, performance comparison of all systems fora spectral efficiency of m D 8 b/s/Hz is shown. QSM and

010-7

10-6

10-5

10-4

10-3

10-2

10-1

100

2 4 6 8 10 12 14 16 18 20

SNR (dB)

AB

EP

Figure 8. Simulation results for quadrature spatial modulation(QSM), quadrature space shift keying (QSSK), spatial multi-plexing (SMUX), and Alamouti schemes achieving a spectralefficiency of m D 8 b/s/Hz under the assumption of imperfect

channel knowledge at the receiver.

SMUX achieve the targeted high spectral efficiency withmoderate number of transmit antennas and signal modula-tion order. While, QSSK requires 16 transmit antennas andAlamouti needs 256-QAM modulation order to achievethis spectral efficiency. In addition, QSM system is shownto outperform all other systems and 5 dB SNR gain canbe noticed when compared with QSSK and SMUX. Thisis while, Alamouti scheme is shown to suffer significantlyfrom the use of very high modulation order to achieve thetargeted spectral efficiency and an ABEP lower than 10�1

cannot be achieved even at 20 dB SNR.

5. CONCLUSIONS

A new high spectral efficiency MIMO scheme, calledQSM, is reported in this paper and detailed performanceanalysis in the presence of Gaussian imperfect channelestimation is presented. Derived analyses are shown tobe accurate for a wide range of system parameters andSNR values. The QSM system is also shown to be veryrobust to channel estimation errors as compared with theconventional SM system while achieving higher spectralefficiency and maintaining most of its inherit advantages.In addition, QSM is shown to outperform other MIMOschemes such as SMUX and Alamouti for the samespectral efficiency. As such, QSM is very promising fordeployment in future wireless systems. Reported resultsdemonstrate that the QSM system requires 3–5 dB less sig-nal power as compared with conventional SM and SMUXsystems for the same error performance and spectral effi-ciency in the presence of imperfect channel knowledgewithout any additional receiver complexity.

© 2014 John Wiley & Sons, Ltd.DOI: 10.1002/ett

of 9Trans. Emerging Tel. Tech. 2017; 28 :e2905 7

R. Mesleh, S. S. Ikki and H. M. Aggoune

ACKNOWLEDGMENT

The authors gratefully acknowledge the support of SNCSresearch center at University of Tabuk under the grant fromthe Ministry of Higher Education in Saudi Arabia.

REFERENCES

1. Marzetta TL, Caire G, Debbah M, Chih-Lin I,

Mohammed SK. Special issue on massive MIMO.

Journal of Communications and Networks 2013; 15(4):

333–337.

2. Maleki M, Bahrami H, Beygi S, Kafashan M, Tran

NH. Space modulation with csi: constellation design and

performance evaluation. IEEE Transactions on Vehicu-

lar Technology 2013; 62(4): 1623–1634.

3. Maleki M, Bahrami HR, Alizadeh A, Tran NH. On

the Performance of spatial modulation: optimal constel-

lation breakdown. IEEE Transactions Communications

2014-01; 62(1): 144–157.

4. Burton A, Ghassemlooy Z, Rajbhandari S, Liaw

SK. Design and analysis of an angular-segmented

full-mobility visible light communications receiver.

Transactions on Emerging Telecommunications Tech-

nologies 2014; 25: 591–599.

5. Hoydis J, Ten Brink S, Debbah M. Massive MIMO:

How many antennas do we need? In 2011 49th Annual

Allerton Confrence on Communications, Control, and

Computing (Allerton), Illinois, USA, 2011; 545–550.

6. Zhao L, Zheng K, Long H, Zhao H. Performance

analysis for downlink massive MIMO system with ZF

precoding. Transactions on Emerging Telecommunica-

tions Technologies 2013. DOI: 10.1002/ett.2745

7. Masouros C, Chen J, Tong K, Sellathurai M, Ratnarajah

T. Towards massive-MIMO transmitters: on the effects

of deploying increasing antennas in fixed physical space.

In Future Network and Mobile Summit (FutureNetwork-

Summit), 2013, Lisbon, Portugal, 2013; 1–10.

8. Jang YU, Joung J, Shin WY, Jeong ER. Frame design

and throughput evaluation for practical multiuser MIMO

OFDMA systems. IEEE Transactions on Vehicular Tech-

nology 2011; 60(7): 3127–3141.

9. Choi RU, Ivrlac M, Murch R, Utschick W. On strategies

of multiuser MIMO transmit signal processing. IEEE

Transactions on Wireless Communications 2004; 3(6):

1936–1941.

10. Shen WL, Lin KJ, Gollakota S, Chen MS. Rate adapta-

tion for 802.11 multiuser mimo networks. IEEE Trans-

actions on Mobile Computing 2014; 13(1): 35–47.

11. Shin SS, Choi H, Jang JE, Choi JW. A low-

complexity iterative MIMO detection and decoding

scheme using dimension reduction. Transactions on

Emerging Telecommunications Technologies 2014. DOI:

10.1002/ett.2839

12. Gesbert D, Kountouris M, Heath RW, Byoung Chae C,

Slzer T. From single user to multiuser communications:

shifting the MIMO paradigm. IEEE Signal Processing

Magazine 2007; 24(5): 36–45.

13. Telatar E. Capacity of multi-antenna Gaussian channels.

European Transaction on Telecommunication 1999;

10(6): 585–595.

14. Alexiou A, Haardt M. Smart antenna technologies for

future wireless systems: trends and challenges. IEEE

Communications Magazine 2004; 42(9): 90–97.

15. Sanduleanu MAT, Vidojkovic M, Vidojkovic V, Van

Roermund AHM, Tasic A. Receiver front-end circuits

for future generations of wireless communications. IEEE

Transactions on Circuits and Systems II 2008; 55(4):

299–303.

16. Zander J, Mähönen P. Riding the data tsunami in

the cloud: myths and challenges in future wireless

access. IEEE Communications Magazine 2013; 51(3):

145–151.

17. Jeganathan J, Ghrayeb A, Szczecinski L, Ceron A. Space

shift keying modulation for MIMO Channels. IEEE

Transactions on Wireless Communications 2009; 8 (7):

3692–3703.

18. Mesleh R, Haas H, Sinanovic S, Ahn CW, Yun S. Spatial

modulation. IEEE Transactions on Vehicular Technology

2008; 57(4): 2228–2241.

19. Serafimovski N, Younis A, Mesleh R, Chambers P,

Renzo MD, Wang CX, Grant PM, Beach MA, Haas H.

Practical implementation of spatial modulation. IEEE

Transactions on Vehicular Technology 2013; 62(9):

4511–4523.

20. Mesleh R, Di Renzo M, Haas H, Grant PM. Trellis coded

spatial modulation. IEEE Transactions on Wireless Com-

munications 2010; 9(7): 2349–2361.

21. Younis A, Serafimovski N, Mesleh R, Haas H. Gener-

alized spatial modulation. In Asilomar Conference on

Signals, Systems, and Computers, Pacific Grove, CA,

USA, 2010; 1498–1502.

22. Jeganathan J, Ghrayeb A, Szczecinski L. Generalized

space shift keying modulation for MIMO channels. In

Proceedings of IEEE 19th International Symposium on

Personal, Indoor and Mobile Radio Communications

PIMRC 2008, Cannes, France, 2008; 1–5.

23. Liang HW, Chang R, Chung WH, Zhang H, Kuo SY. Bi-

space shift keying modulation for MIMO systems. IEEE

Communications Letters 2012; 16(8): 1161–1164.

24. Mesleh R, Ikki SS, Aggoune HM. Quadrature spatial

modulation system, U.S. Patent 61/897,894, October 31,

2013.

of 9 © 2014 John Wiley & Sons, Ltd.DOI: 10.1002/ett

Trans. Emerging Tel. Tech. 2017; 28 :e29058

R. Mesleh, S. S. Ikki and H. M. Aggoune

25. Simon MK, Alouini MS. Digital Communication overFading Channels: A Unified Approach to PerformanceAnalysis (1st ed.) John Wiley & Sons, Inc.: USA, 2000.

26. Proakis JG. Digital Communications. McGraw–Hill:NY, USA, 1995.

27. Simon MK, Alouini MS. Digital Communication overFading Channels (2nd edn), Wiley Series in Telecom-munications and Signal Processing. John Wiley & Sons,Inc.: USA, 2005.

28. Ikki S, Mesleh R. A general framework for perfor-mance analysis of space shift keying (SSK) modulationin the presence of gaussian imperfect estimations. IEEECommunications Letters 2012; 16(2): 228–230.

29. Mesleh R, Ikki S. On the effect of gaussian imperfectchannel estimations on the performance of space modu-lation techniques. In 2012 IEEE 75th Vehicular Technol-ogy Conference (VTC Spring), Yokohama, Japan, 2012;1–5.

30. Basar E, Aygolu U, Panayirci E, Poor HV. Performanceof spatial modulation in the presence of channel estima-tion errors. IEEE Communications Letters 2012; 16(2):176–179.

31. Younis A, Mesleh R, Haas H, Grant PM. Reducedcomplexity sphere decoder for spatial modulation detec-tion receivers. In 2010 IEEE Global Telecommunica-tions Conference Globecom 2010, Miami, USA, 2010;1–5.

32. Tang Q, Xiao Y, Yang P, Yu Q, Li S. A new low-complexity near-ml detection algorithm for spatial mod-ulation. IEEE Wireless Communications Letters 2013;2(1): 90–93.

33. Alamouti SM. A simple transmit diversity tech-nique for wireless communications. IEEE Journalon Selected Areas in Communications 1998; 16(8):1451–1458.

© 2014 John Wiley & Sons, Ltd.DOI: 10.1002/ett

of 9Trans. Emerging Tel. Tech. 2017; 28 :e2905 9

本文献由“学霸图书馆-文献云下载”收集自网络，仅供学习交流使用。

学霸图书馆（www.xuebalib.com）是一个“整合众多图书馆数据库资源，

提供一站式文献检索和下载服务”的24 小时在线不限IP

图书馆。

图书馆致力于便利、促进学习与科研，提供最强文献下载服务。

图书馆导航：

图书馆首页 文献云下载 图书馆入口 外文数据库大全 疑难文献辅助工具