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Signed Quadrature Spatial Modulation for MIMO Systems Ammar M. Abu-Hudrouss, Senior Member, IEEE, M.-T. O. El Astal, Member, IEEE Alaa H. Al Habbash, and Sonia A¨ ıssa, Fellow, IEEE Abstract—Quadrature spatial modulation (QSM) was recently proposed to increase the spectral efficiency of spatial modulation. In QSM, the real and imaginary parts of a symbol are transmitted independently from different antennas. A new spatial modulation technique, termed signed quadrature spatial modulation (SQSM), is introduced in this paper. Unlike QSM, SQSM creates four- dimensional spatial constellation, and hence results in higher system throughput. This technique extends the traditional spatial- constellation dimension into ± in-phase and quadrature-phase dimensions. The ensuing constellation consists of four antenna indices, which are chosen independently in order to transmit the real and imaginary parts of the modulated symbols and their inverse. The performance of the proposed technique is compared to the most-recent SM techniques, namely, QSM, double SM, and improved QSM (IQSM). Numerical results demonstrate that SQSM provides significant performance gains (3-7dB), particularly when a large number of transmit antennas is used. This comes with a marginal increase in computational complexity compared to QSM and SM. Also, while IQSM can be competitive with SQSM in some cases, SQSM has a much lower computational complexity, e.g., 46% reduction in complexity in case of 16 transmit antennas and 16 bps/Hz. Index Terms—MIMO, quadrature spatial modulation, spatial modulation, spectral efficiency. I. I NTRODUCTION In the last few years, there have been remarkable research efforts in developing multi-antenna transmission techniques with high spectral efficiency [1] or increased link reliability [2]. The vertical Bell labs layered space-time coding (V- BLAST) of [1] has a high spectral efficiency, but at the expense of high complexity and stringent restrictions on the number of receiver antennas needed to achieve minimal error rates [2]. Index modulation schemes, such as spatial modulation (SM), offer a trade-off between spectral efficiency and com- putational complexity. These schemes have higher spectral efficiency and lower decoding complexity compared to V- BLAST [3]. SM utilizes the indices of the transmit antennas to This work was supported in part by the PALAST/FRQ (Palestine Academy for Science and Technology/Fonds de Recherche du Quebec) Science Bridge grant program. The associate editor coordinating the review of this article and approving it for publication was Yiqing Zhou. (Corresponding author: A. M. Abu-Hudrouss.) A. M. Abu-Hudrouss is with the School of Engineering, Islamic University of Gaza, Gaza, Palestine; email: [email protected]. He was with the Institut National de la Recherche Scientifique (INRS), Montreal, QC, Canada H5A 1K6, when part of this work was done. M.-T. O. El Astal and A. H. Al Habbash are with the Palestinian ICT research agency (P-ICTRA), Gaza, Palestine; email: {mtastal, ahabbash}@p- ictra.org. S. A¨ ıssa is with the Institut National de la Recherche Scientifique (INRS), Montreal, QC, Canada H5A 1K6; email: [email protected]. convey information bits in addition to those bits mapped with conventional M -ary amplitude phase modulation (APM) [4]. A special case of SM is space-time shift keying (STSK) [5], where the modulation is limited to the antennas’ indices and, hence, lower spectral efficiency is obtained. Different schemes of generalized spatial modulation (GSM) [6], [7] were reported in the literature to increase the spectral efficiency by allowing multiple transmit antennas to be simultaneously active during transmission. Quadrature spatial modulation (QSM) is another novel technique that surpasses the performance of GSM [8]. In QSM, an M -ary APM symbol is decomposed into its real (in- phase, I) and imaginary (quadrature, Q) components, which are transmitted independently using selected antennas. The QSM technique has the same computational complexity of SM [8]. A generalized framework for QSM (GQSM) which can achieve higher spectral efficiency but at the cost of higher complexity is introduced in [9]. Also, a special case of GQSM, the improved quadrature spatial modulation (IQSM), is presented in [10]. In the latter scheme, the real and imaginary parts of two modulated symbols are transmitted simultaneously. The enhanced spatial modulation (ESM) scheme introduced in [11], [12] allows transmission from two independent antennas. These antennas transmit two different symbols which are drawn from basic and secondary symbol constellations. The secondary constellation is obtained by using single geometric interpolation. Accordingly, ESM is not a straightforwardly scalable scheme and is reported only for limited network configurations. On the other hand, in double spatial modulation (DSM) [13] and complex quadrature spatial modulation (CQSM) [14], two symbols are transmitted from one/two independent antennas. The rotation angle between the symbol constellations is used to distinguish between two symbols if they are to be transmitted from the same indexed antenna. The minimum Euclidian distance between the two sets of the signal constellation is maximized by a simple optimization approach. However, this minimum distance becomes very small, and almost impractical for high-order modulation schemes. As for IQSM, a lookup table is needed for binary assignment, as the binary input cannot be divided and assigned to different dimensions. In summary, most existing SM schemes use a single dimen- sion of the spatial domain, e.g., SSK and SM, or a maximum of two dimensions, such as in DSM and QSM. Taking this feature as a starting point, the main contribution of this paper is to introduce a four-dimensional spatial space by using the sign of the I and Q components of the transmitted symbol.
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Page 1: Signed Quadrature Spatial Modulation for MIMO Systems

Signed Quadrature Spatial Modulationfor MIMO Systems

Ammar M. Abu-Hudrouss, Senior Member, IEEE, M.-T. O. El Astal, Member, IEEE Alaa H. Al Habbash, andSonia Aıssa, Fellow, IEEE

Abstract—Quadrature spatial modulation (QSM) was recentlyproposed to increase the spectral efficiency of spatial modulation.In QSM, the real and imaginary parts of a symbol are transmittedindependently from different antennas. A new spatial modulationtechnique, termed signed quadrature spatial modulation (SQSM),is introduced in this paper. Unlike QSM, SQSM creates four-dimensional spatial constellation, and hence results in highersystem throughput. This technique extends the traditional spatial-constellation dimension into ± in-phase and quadrature-phasedimensions. The ensuing constellation consists of four antennaindices, which are chosen independently in order to transmitthe real and imaginary parts of the modulated symbols andtheir inverse. The performance of the proposed technique iscompared to the most-recent SM techniques, namely, QSM,double SM, and improved QSM (IQSM). Numerical resultsdemonstrate that SQSM provides significant performance gains(3-7dB), particularly when a large number of transmit antennasis used. This comes with a marginal increase in computationalcomplexity compared to QSM and SM. Also, while IQSM can becompetitive with SQSM in some cases, SQSM has a much lowercomputational complexity, e.g., 46% reduction in complexity incase of 16 transmit antennas and 16 bps/Hz.

Index Terms—MIMO, quadrature spatial modulation, spatialmodulation, spectral efficiency.

I. INTRODUCTION

In the last few years, there have been remarkable researchefforts in developing multi-antenna transmission techniqueswith high spectral efficiency [1] or increased link reliability[2]. The vertical Bell labs layered space-time coding (V-BLAST) of [1] has a high spectral efficiency, but at the expenseof high complexity and stringent restrictions on the number ofreceiver antennas needed to achieve minimal error rates [2].

Index modulation schemes, such as spatial modulation(SM), offer a trade-off between spectral efficiency and com-putational complexity. These schemes have higher spectralefficiency and lower decoding complexity compared to V-BLAST [3]. SM utilizes the indices of the transmit antennas to

This work was supported in part by the PALAST/FRQ (Palestine Academyfor Science and Technology/Fonds de Recherche du Quebec) Science Bridgegrant program. The associate editor coordinating the review of this article andapproving it for publication was Yiqing Zhou. (Corresponding author: A. M.Abu-Hudrouss.)

A. M. Abu-Hudrouss is with the School of Engineering, Islamic Universityof Gaza, Gaza, Palestine; email: [email protected]. He was with theInstitut National de la Recherche Scientifique (INRS), Montreal, QC, CanadaH5A 1K6, when part of this work was done.

M.-T. O. El Astal and A. H. Al Habbash are with the Palestinian ICTresearch agency (P-ICTRA), Gaza, Palestine; email: {mtastal, ahabbash}@p-ictra.org.

S. Aıssa is with the Institut National de la Recherche Scientifique (INRS),Montreal, QC, Canada H5A 1K6; email: [email protected].

convey information bits in addition to those bits mapped withconventional M -ary amplitude phase modulation (APM) [4].A special case of SM is space-time shift keying (STSK) [5],where the modulation is limited to the antennas’ indices and,hence, lower spectral efficiency is obtained. Different schemesof generalized spatial modulation (GSM) [6], [7] were reportedin the literature to increase the spectral efficiency by allowingmultiple transmit antennas to be simultaneously active duringtransmission.

Quadrature spatial modulation (QSM) is another noveltechnique that surpasses the performance of GSM [8]. InQSM, an M -ary APM symbol is decomposed into its real (in-phase, I) and imaginary (quadrature, Q) components, which aretransmitted independently using selected antennas. The QSMtechnique has the same computational complexity of SM [8]. Ageneralized framework for QSM (GQSM) which can achievehigher spectral efficiency but at the cost of higher complexityis introduced in [9]. Also, a special case of GQSM, theimproved quadrature spatial modulation (IQSM), is presentedin [10]. In the latter scheme, the real and imaginary partsof two modulated symbols are transmitted simultaneously.The enhanced spatial modulation (ESM) scheme introduced in[11], [12] allows transmission from two independent antennas.These antennas transmit two different symbols which aredrawn from basic and secondary symbol constellations. Thesecondary constellation is obtained by using single geometricinterpolation. Accordingly, ESM is not a straightforwardlyscalable scheme and is reported only for limited networkconfigurations.

On the other hand, in double spatial modulation (DSM) [13]and complex quadrature spatial modulation (CQSM) [14], twosymbols are transmitted from one/two independent antennas.The rotation angle between the symbol constellations is used todistinguish between two symbols if they are to be transmittedfrom the same indexed antenna. The minimum Euclidiandistance between the two sets of the signal constellation ismaximized by a simple optimization approach. However, thisminimum distance becomes very small, and almost impracticalfor high-order modulation schemes. As for IQSM, a lookuptable is needed for binary assignment, as the binary inputcannot be divided and assigned to different dimensions.

In summary, most existing SM schemes use a single dimen-sion of the spatial domain, e.g., SSK and SM, or a maximumof two dimensions, such as in DSM and QSM. Taking thisfeature as a starting point, the main contribution of this paperis to introduce a four-dimensional spatial space by using thesign of the I and Q components of the transmitted symbol.

Page 2: Signed Quadrature Spatial Modulation for MIMO Systems

This is expected to yield higher spectral efficiency even withzero or low APM modulation orders.

In fact, significant performance improvements can beachieved by the proposed signed quadrature spatial modulation(SQSM) technique, as shown analytically and numerically inthe paper, particularly when a large number of transmit anten-nas is used. The gain of SQSM also comes with significantreductions in receiver-computational complexity compared toDSM and IQSM, or with a small cost compared to QSM.Furthermore, though IQSM can compete with the performanceof SQSM when the number of transmit antennas is small, itis significantly more demanding in terms of receiver com-putational requirements. Moreover, the proposed SQSM hasthe same advantage of QSM in that a single radio-frequency(RF) chain is needed to produce the I/Q components of thesymbol with an additional 180 ◦-phase shifter. This wouldthen produce the real and imaginary parts of the symbol andits inverse. On the other hand, spatial multiplexing systems(SMUX) such as V-BLAST require a dedicated RF chain foreach transmit antenna while IQSM needs two RF chains atthe transmitter. Moreover, transmitting the same data symbolfrom different antennas and the orthogonality between the I/Qcomponents maintain a key advantage of SM, which is theavoidance of inter-channel interference (ICI) at the receiver.Nevertheless, transmit antenna synchronization is needed toavoid inter-symbol interference at the receiver.

The following content of the paper is organized as follows.In Section II, the description of the SQSM transmissiontechnique is provided. Analysis of the bit-error probability per-formance is introduced in Section III. Section IV investigatesthe receiver complexity of SQSM in comparison with state-of-art schemes. Monte-Carlo simulation results and comparisonsare provided in Section V, and the paper is concluded inSection VI.

II. SIGNED QUADRATURE SPATIAL MODULATION

Consider a multiple-input multiple-output (MIMO) commu-nication system with Nt transmit antennas and Nr receiveantennas. In general, the proposed SQSM scheme transmitsa symbol x and its inverse −x within the same time period.Symbol x is drawn from the first quadrant of an M -ary APM.The real and imaginary parts of x and of its inverse −x aretransmitted from different antennas.

Specifically, the incoming information bits are divided intofive parts: log2

M4 bits are modulated to determine the signal

constellation symbol x, and four parts of length log2Nt bitseach are used to select the individual four transmit antennas.The selected transmit antennas are used to send the real andthe imaginary components of x and −x. It should be notedthat√

2xR is sent if the indices of the antennas chosen totransmit the real parts of symbols (x< and −x<) are identical.A similar concept is applied when the selected indices for theimaginary parts of symbols (jx= and –jx=) are identical, inwhich case

√2 jx= is sent. Illustration of the SQSM concept

with QPSK and Nt = 4 transmit antennas is shown in Fig. 1.The received signal can be expressed as,

y = Hz + n, (1)

Fig. 1. Illustration of the signed quadrature spatial modulation (SQSM)concept when using QPSK and Nt = 4 transmit antennas (TAs).

where y is the Nr × 1 receive signal vector, z is the Nt × 1transmit signal vector, n is the Nr×1 white noise vector, H isthe Nr×Nt channel matrix. Given that σ2

n is the noise power,the entries of H and n are drawn from complex Gaussiandistributions CN (0, 1) and CN (0, σ2

n), respectively.Assuming that l<℘ , l<η , l=℘ and l=η are the indices of the

activated antennas used to transmit x<, −x<, jx=, and −jx=,respectively, the received signal of (1) can be equivalentlyexpressed as

y = a(x, l<℘ , l<η , l=℘ , l=η

)+ n, (2)

where,

a(x, l<℘ , l<η , l=℘ , l=η

)

=

x<

(hl<℘ − hl<η

)+ jx=

(hl=℘ − hl=η

)if l<℘ 6= l<η and l=℘ 6= l=η√

2 hl<℘x< + jx=

(hl=℘ − hl=η

)if l<℘ = l<η and l=℘ 6= l=η

x<

(hl<℘ − hl<η

)+√

2 hl=℘x=if l<℘ 6= l<η and l=℘ = l=η√

2(

hl<℘x< + j hl=℘x=)

if l<℘ = l<η and l=℘ = l=η

(3)

in which hl<℘ denotes the l th<℘ column of H, i.e., [hl<℘ =h1,l<℘ , · · · ,hNr,l<℘ ]. It is assumed that the variance of thetransmitted signal vector is normalized to unity, or

E(a(x, l<℘ , l<η , l=℘ , l=η

)a∗(x, l<℘ , l<η , l=℘ , l=η

))= 1,

(4)where E(.) is the expected value function. Therefore, thesignal-to-noise ratio (SNR) is defined as SNR = 1/σ2

n.For illustration purposes, a 4 × 4 MIMO system with 8-

QAM modulation is considered. The bit rate for each channelused is 9 bits/s. The first bit is used to choose between thetwo symbols of the 8-QAM’s first quadrant: 0 for 1 + j and 1for 1+3j. The remaining four 2-bits are used to index the realand imaginary parts on antennas. For example, assume that

Page 3: Signed Quadrature Spatial Modulation for MIMO Systems

TABLE ITHE COMPUTATIONAL COMPLEXITY OF QSM, DSM, IQSM, SQSM, MIMO-SM AND SMUX.

Technique Real Multiplications (×) Real Additions (+)

QSM 4N2t NR2M 2N2

t (NR − 1)2M

DSM 8N2t NR22M 6N2

t (NR − 1)22M

IQSM 8c2NR22M 6c2(NR − 1)22M

MIMO-SM 4NtNR2M 2Nt(NR − 1)2M

SQSM 4N4t NR2M/4 6 4N4

t (NR − 1)2M/4

SMUX 2NtNR2M 2Nt(NR − 1)2M

where c = 2

⌊log2

(Nt2

)⌋.

the incoming information bits are [010011100]. Thus, x =1 + j, and its inverse is −x = −1 − j. The x< = 1 willbe transmitted from the 3rd antenna, jx= = j from the 2nd

antenna, −x< = −1 from the 4th antenna, and −jx= = −jfrom the 1st antenna. The transmitted vector is then given byz = [−j j 1 −1]. In the same manner, say [101011110] is theinput information, then the transmit vector will be z = [0

√2

−j3 j3].The maximum-likelihood (ML) detection at the SQSM

receiver consists in finding the estimates [x, l<℘ , l<η , l=℘ , l=η ]according to,[

x, l<℘ , l<η , l=℘ , l=η

]=

arg minx,l<℘ ,l<η ,l=℘ ,l=η

∣∣∣∣y− a (x, l<℘ , l<η , l=℘ , l=η) ∣∣∣∣2. (5)

III. PERFORMANCE ANALYSIS

The performance of SQSM is now analyzed, by using asimilar approach as in [8] and considering imperfect channelestimation scenarios. This is to see the impact of the chan-nel estimation error on the proposed scheme. The estimatedchannel coefficient is given as h, and

h = h+ e, (6)

where e represents the channel estimation error, modeled bya complex Gaussian variable with zero mean and varianceσ2e . Let a = hl<℘x< − hl<ηx< + jhl=℘x= − jhl=ηx= and

a = ˆhl<℘ x< −ˆhl<η x< + j ˆhl=℘ x= − j

ˆhl=η x= be two distinctcodewords assuming that a is estimated at the receiver giventhat a is transmitted. Then, the pairwise error probability (PEP)is given by,

Pr [a→ a|H] = Q

√‖a− a‖2

2σ2n

= Q

(√ζ), (7)

where Q (.) is the Q-function, and

ζ =1

2σ2n

(a− a)H

(a− a) , (8)

where (.)H denotes the Hermitian operator. The PEP in (7)

can be easily generalized to include all cases of transmitted

vectors defined in (2). The average PEP can be written as [15],

Pe (a→ a) =1

2

(1−

√ζ/2

1 + ζ/2

), (9)

where ζ is the expected value of ζ, given by

ζ =1

2σ2n + 4σ2

e

(|x<|2 + |x=|2

) 4∑k=1

Dk, (10)

where D1 =(∣∣x<℘∣∣2 +

∣∣x<℘∣∣2)A1 +(∣∣x=℘∣∣2 +

∣∣x=℘∣∣2)B1

and D2 =∣∣x<℘ − x<℘∣∣2A2 +

∣∣x=℘ − x=℘∣∣2B2, withA1 = 0, A2 = 1 l<℘ = l<℘A1 = 1, A2 = 0 l<℘ 6= l<℘B1 = 0, B2 = 1 l=℘ = l=℘B1 = 1, B2 = 0 l=℘ 6= l=℘ .

D3 and D4 are the same as D1 and D2 after replacing thesubscript ℘ with η in all symbols. The bit error rate (BER)of the SQSM system is upper bounded (asymptotically tightunion bound) by the following average bit-error probability(ABEP),

Pb =2

m2m

2m∑i=1

2m∑k=i

Pe (a→ a) ei,k, (11)

where m is the spectral efficiency given in bps/Hz and ei,k isthe number of bit errors related with Pe (a→ a). In the idealcase of perfect channel estimation (i.e. σ2

e = 0), ζ (10) reducesto

ζ =1

2σ2n

4∑k=1

Dk. (12)

With Nr receive antennas, the PEP is given by

Pr [a→ a|H] = Q

√√√√ Nr∑

i=1

ζi

= Q

(√Z), (13)

which results in Z being a chi-squared random variable witha probability density function (PDF) given by

PZ(Z) =1

Γ(Nr)ζNrZNr−1 exp

(−Zζ

), (14)

Page 4: Signed Quadrature Spatial Modulation for MIMO Systems

where Γ(.) denotes the Gamma function. The average uncon-ditional PEP is given by [16], [17],

Pe (a→ a) = γNrNr−1∑k=0

(Nr − 1 + k

k

)[1− γ]

k, (15)

where γ = 12

(1−

√ζ/2

1+ζ/2

). The PDF of Z around the origin

can be approximated using Taylor series as [18],

PZ(Z) =1

Γ(Nr)ζNrZNr−1 +O, (16)

where O represents the ignored higher terms. The average PEPis computed as [18],

Pe (a→ a) =

∫ ∞0

Q(√Z)

1

Γ(Nr)ζNrZNr−1dZ

≈ 2Nr−1Γ (Nr + 0.5)√π (Nr)!

(1

ζ

)Nr.

(17)

It is clear that the SQSM system can achieve a diversity gainof Nr.

IV. RECEIVER COMPLEXITY ANALYSIS

The computational complexity of SQSM is analyzed here. Itequals the total result of the number of real-addition operationsand the number of real-multiplication operations multiplied bythe number of ML searches. The detection process in (5) re-quires 4N4

t Nr real multiplications, 4N4t (Nr − 1) average real

additions, and ML searches over M/4-dimensional modulationspace.

For comparison purpose, the complexity of recent SMtechniques is shown in Table I . In Fig. 2, the computationalcomplexities of all systems under consideration are comparedusing 16 × 16 MIMO configuration and achieving m = 16bps/Hz (with different constellation size M for each schemeto guarantee a fair comparison).

Fig. 2. Comparisons of receiver complexity of 16×16 systems and m = 16bps/Hz.

As observed from Table I, the SQSM scheme offers anextra-considerable complexity reduction compared to SMUXand IQSM systems. This can be easily seen from Fig. 2.Clearly, there is a complexity reduction of 44% compared to

0 5 10 15 20 2510−5

10−4

10−3

10−2

10−1

100

EsN0

[dB]

BE

R SQSM, QPSK, 12 b/s/Hz

SQSM, 12 b/s/Hz (analytical)

IQSM, QPSK, 12 b/s/Hz

DSM, 8-QAM, 12 b/s/Hz

QSM, 64-QAM, 12 b/s/Hz

SQSM, 16-QAM, 14 b/s/Hz

SQSM, 14 b/s/Hz (analytical)

IQSM, 8-QAM, 14 b/s/Hz

DSM, 16-QAM, 14 b/s/Hz

QSM, 256-QAM, 14 b/s/Hz

Fig. 3. BER performance of (8×4) DSM, QSM, IQSM, and SQSM systemsfor m = 12 and m = 14 bps/Hz.

0 5 10 15 20

10−4

10−3

10−2

10−1

100

EsN0

[dB]

BE

R

SQSM, QPSK

IQSM, QPSK

SMUX, BPSK

DSM, 16-QAM

QSM, 256-QAM

SM, 4096-QAM

Fig. 4. BER performance of (16 × 16) SM, SMUX, DSM, QSM, IQSM,and SQSM systems for m = 16 bps/Hz.

IQSM. Although the SQSM scheme requires an acceptableincrease in complexity (≤ 24%) compared to SM and QSM,it provides significant BER improvement as will be seen inthe next section. Moreover, for large-scale MIMO systems,suboptimal low decoding complexity schemes can be modifiedto suit the SQSM [19], [20], [21].

V. PERFORMANCE COMPARISONS

This section provides simulation results to evaluate theperformance of the proposed SQSM, in terms of BER, whichis a function of the received SNR per antenna. Both analytical(upper bound) and Monte-Carlo numerical results are shownfor different spectral efficiency values. Results show a close-match between the analysis and simulations for a wide andpragmatic range of SNR. Specifically, SQSM is comparedto the most recent state-of-art spatial modulation schemes,

Page 5: Signed Quadrature Spatial Modulation for MIMO Systems

namely, QSM, IQSM and DSM. It should be noted that theESM scheme of [10] is ignored in the comparisons due toits lack of simple scalability. In contrast, DSM is adequatefor comparison due its superior BER performance comparedto ESM [11]. Simulations were conducted assuming Rayleighfading channels. Perfect channel estimation at the receivers isassumed unless otherwise stated.

In Fig. 3, 8 × 4 MIMO SQSM is considered to achievea spectral efficiency of 12 and 14 bps/Hz. Numerical andanalytical results are in close-match over high SNR values.The SQSM system demonstrates significant performance en-hancement compared to QSM. For example, a gain of 7 dB isobtained at 10−4 over traditional QSM system for 12 bps/Hztransmission. A higher enhancement can be noticed for thecase with higher bit-rate, i.e., 14 bps/Hz. Compared to DSM,an enhancement of 3.5 dB is obtained at 10−4 for 14 bps/Hztransmission, whereas the gain is 3 dB in case of 12 bps/Hz.This can be explained by to the use of a lower modulationorder and, hence, the SQSM effectiveness has not unleashedits merits yet.

In summary, SQSM outperforms both QSM and DSMin gain values that are realized by increasing the spectralefficiency needed and/or increasing the number of transmitantennas as shown in Fig. 4. The SQSM system demon-strates slight performance enhancement compared to IQSM(the most-recent) for 12 bps/Hz transmission or loses a gainof at most 1 dB in the high SNR range for 14 bps/Hztransmission, while it offers this gain at low SNR. It is to benoted that the performance achieved by IQSM comes at thecost of a considerable increase in computational complexity(see Section IV).

In Fig. 4, the performance of SQSM is further analyzed fora 16×16 MIMO system with a rate of 16 bps/Hz. Significantenhancement is achieved over QSM, DSM and SMUX, wheregains of 14.55 dB, 9.1 dB, and 1.05 dB are respectivelyobtainable at a BER of 10−4. It is worth to note that the SQSMtechnique starts to have a better performance than IQSM whilereducing the complexity by 44%.

In order to show SQSM effectiveness using different mod-ulation schemes, Fig. 5 shows the performance of 4 × 4SQSM system with data rates of 8, 9, and 10 bps/Hz, usingPSK and QAM constellations. It is worth noting that, sinceSQSM works with non-zero real and imaginary components ofconstellation points, the M -PSK constellation is rotated withπ/M . At a BER of 10−4, the gain losses of using PSK overQAM are 0.3 dB and 3 dB at data rates of 9 bps/Hz and 10bps/Hz, respectively. This can be easily justified by the factthat the minimum Euclidian distance of PSK constellation issmaller than its QAM counterpart.

In Fig. 6, the impact of imperfect channel knowledge atthe receiver for SQSM and QSM is evaluated and comparedto the case of perfect channel knowledge of 4 × 4 systemfor 10 bps/Hz. Two values of the channel estimation errorare considered, namely, the error variance is proportional to1/SNR and when it is fixed to -15 dB. Analytical results forSQSM are also depicted and compared to simulation results.The analytical results shows a good match with the simulationones at high SNR. In case of σ2

e = 1/SNR, a degradation of

0 5 10 15 20 25 3010−5

10−4

10−3

10−2

10−1

100

EsN0

[dB]

BE

R

16 PSK, 10 b/s/Hz

16 QAM, 10 b/s/Hz

8 PSK, 9 b/s/Hz

8 QAM, 9 b/s/Hz

QPSK, 8 b/s/Hz

SQSM (Analytical)

Fig. 5. BER performance of (4× 4) SQSM system for m = 8, m = 9 andm = 10 bps/Hz.

0 5 10 15 20 25 3010−5

10−4

10−3

10−2

10−1

100

EsN0

[dB]

BE

R

SQSM, 16 QAM, σ2e=0 dB

SQSM, 16 QAM, σ2e=1/SNR

SQSM, 16 QAM, σ2e=-15 dB

QSM, 64 QAM, σ2e=0 dB

QSM, 64 QAM, σ2e=1/SNR

QSM, 64 QAM, σ2e=-15 dB

SQSM (Analytical)

Fig. 6. The impact of imperfect channel estimation at the receiver of (4×4)SQSM and QSM systems for m = 10 bps/Hz.

2.3 dB can noticed for SQSM and 3 dB for QSM as in [15],while SQSM has the superiority in performance with gain of2.3 dB at a BER of 10−4. When σ2

e = −15 dB, the errorprobability at high SNR is fixed to 1.5× 10−3 for SQSM and4× 10−3 for QSM.

The results demonstrate that SQSM is better suited toMIMO technology compared to the most recent SM schemes(QSM, IQSM and DSM) in terms of both performance andcomputational complexity. The results show that SQSM hasstronger immunity to channel uncertainties compare to QSM[15] while at the same time giving significant enhancement inperformance.

VI. CONCLUSION

This paper introduced a new spatial modulation scheme thatuses APM symbol from the positive quadrant and its inverse.

Page 6: Signed Quadrature Spatial Modulation for MIMO Systems

This was done by splitting a symbol and its inverse intoin-phase and quadrature-phase components; each transmittedfrom an independently selected antenna. This design allowsfor four-dimensional spatial constellations, unlike conventionalSM, QSM and DSM. Moreover, SQSM has a straightforwardscalability, unlike ESM. Therefore, SQSM has a higher spatialefficiency compared to QSM under the same number oftransmit antennas.

Performance evaluation of the proposed SQSM scheme wascarried out using analysis and simulations. In particular, it wasshown that SQSM has superior performance compared to QSMand DSM. Also, SQSM has a much lower decoding complexitythan IQSM (56% in the setting corresponding to Fig. 2), whileat the same time achieving a performance enhancement overIQSM when used as a signed quadrature shift keying (M = 4).

REFERENCES

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[4] R. Mesleh, H. Haas, S. Sinanovic, C. W. Ahn, and S. Yun, “Spatialmodulation,” IEEE Transactions on Vehicular Technology, vol. 57,pp. 2228–2241, July 2008.

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[6] A. Younis, N. Serafimovski, R. Mesleh, and H. Haas, “Generalisedspatial modulation,” in Signals, Systems and Computers (ASILOMAR),2010 Conference Record of the Forty Fourth Asilomar Conference on,pp. 1498–1502, IEEE, 2010.

[7] J. Wang, S. Jia, and J. Song, “Generalised spatial modulation systemwith multiple active transmit antennas and low complexity detectionscheme,” IEEE Transactions on Wireless Communications, vol. 11,pp. 1605–1615, Apr. 2012.

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[13] Z. Yigit and E. Basar, “Double spatial modulation: A high-rate indexmodulation scheme for mimo systems,” in Wireless CommunicationSystems (ISWCS), 2016 International Symposium on, pp. 347–351,IEEE, 2016.

[14] M. Mohaisen and S. Lee, “Complex quadrature spatial modulation,”ETRI Journal, vol. 39, pp. 514–524, Aug. 2017.

[15] R. Mesleh and S. S. Ikki, “On the impact of imperfect channel knowl-edge on the performance of quadrature spatial modulation,” in WirelessCommunications and Networking Conference (WCNC) on, pp. 534–538,IEEE, 2015.

[16] J. G. Proakis, “Digital communications mcgraw-hill series in electricaland computer engineering,” in Computer Engineering, McGraw-Hill,2001.

[17] M. K. Simon and M.-S. Alouini, Digital communication over fadingchannels, vol. 95. John Wiley & Sons, 2005.

[18] R. Mesleh and A. Alhassi, Space modulation techniques, vol. 288. WileyOnline Library, 2018.

[19] J. Li, X. Jiang, Y. Yan, W. Yu, S. Song, and M. H. Lee, “Low complexitydetection for quadrature spatial modulation systems,” Wireless PersonalCommunications, vol. 95, pp. 4171–4183, Aug. 2017.

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Ammar M. Abu-Hudrouss was born in Khan-Younis, Palestine, in 1977. He received the B.Sc.degree from Islamic University Gaza, Palestine, in2000. He received the MSc degree in Telecommuni-cation Engineering and the PhD degree in Commu-nication Engineering from Birmingham University,Birmingham, U.K., in 2003 and 2007, respectively.In 2012-2013, he was a visiting researcher at Uni-versity of York, as a holder of a DistinguishedScholar Award from the Arab Fund for Social andEconomic Development. He is currently a Professor

of Communications at Islamic University of Gaza (IUG), Palestine. He isalso a member of the Palestinian ICT research agency (P-ICTRA). Duringhis work at IUG, Prof. Abu-Hudrouss has been granted to presume severalscientific visits to international universities in Europe and Canada. Prof. Abu-Hudrouss is currently a member of many local and national committees andcouncils including the Palestinian Engineering Syndicate, the Higher Councilfor Innovation and Excellence, the Crisis and Disaster Master ProgramCommittee, and the Council for IUG Incubator. Prof. Abu-Hudrouss is a seniormember at the IEEE. His current research interests are in localization, digitalsignal processing for wireless communications, software defined radio, indexmodulation, and coding.

M.-T. O. El Astal received his PhD. degree inelectrical engineering and ICT from University ofTasmania, Hobart, Australia, in 2015, and the B.Sc.and M.Sc. degrees in electrical and control engi-neering from Islamic University of Palestine (IUG),Gaza, Palestine. He has mentored, supervised andtrained researchers, technicians and developers invarious aspects of ICT technologies and research.Currently, he is an assistant professor in Engineeringand IT faculty of IUG and University of Palestine,respectively. In addition, he is working as a senior

researcher at the Palestinian ICT research agency (P-ICTRA), and the head ofconsultancy committee of smart-grid in GEDco, Palestine. Dr. El Astal is theco-leader of Facebook developer circle in Gaza for Artificial Intelligence,2017-2019; he acted as TPC co-chair at ICSCS 2016; and TPC memberat IEEE PICECE 2019, IEEE ICEPT 2018 and 2019. He is co-recipient of2018 IEEE ICEPT Best Paper Awards. His research interests are smart-citiessolutions, particularly smart-grid, wireless communications, and deep learning.

Alaa H. Al Habbash was born in Riyadh, SaudiArabia, in 1985. He received the B.Sc. degree andthe M.Sc. degree in Telecommunication Engineeringfrom Islamic University Gaza, Palestine, in 2008and 2013, respectively. He is currently working as ajunior researcher in wireless communications at thePalestinian ICT research agency (P-ICTRA), Gaza,Palestine. Al Habbash is co-recipient of 2018 IEEEICEPT Best Paper Awards. His current researchinterests are space-time coding, turbo codes, spatialmodulation, and deep learning.

Page 7: Signed Quadrature Spatial Modulation for MIMO Systems

Sonia Aıssa (S’93-M’00-SM’03-F’19) received herPh.D. degree in Electrical and Computer Engineer-ing from McGill University, Montreal, QC, Canada,in 1998. Since then, she has been with the InstitutNational de la Recherche Scientifique-Energy, Mate-rials and Telecommunications Center (INRS-EMT),University of Quebec, Montreal, QC, Canada, whereshe is a Full Professor. Her research interests includethe modeling, design and performance analysis ofwireless communication systems and networks.

From 1996 to 1997, she was a Researcher withthe Department of Electronics and Communications of Kyoto University,and with the Wireless Systems Laboratories of NTT, Japan. From 1998 to2000, she was a Research Associate at INRS-EMT. In 2000-2002, whileshe was Assistant Professor, she was a Principal Investigator in the majorprogram of personal and mobile communications of the Canadian Institute forTelecommunications Research, leading research in radio resource managementfor wireless networks. From 2004 to 2007, she was an Adjunct Professor withConcordia University, Canada. She was Visiting Invited Professor at KyotoUniversity, Japan, in 2006, and at Universiti Sains Malaysia, in 2015.

Professor Aıssa is the Founding Chair of the IEEE Women in EngineeringAffinity Group in Montreal, 2004-2007; acted as TPC Symposium Chair orCochair at IEEE ICC ’06 ’09 ’11 ’12; Program Cochair at IEEE WCNC2007; TPC Cochair of IEEE VTC-S 2013; TPC Symposia Chair of IEEEGlobecom 2014; TPC Vice-Chair of IEEE Globecom 2018; and serves as theTPC Chair of IEEE ICC 2021. Her editorial activities include: Editor, IEEETRANSACTIONS ON WIRELESS COMMUNICATIONS, 2004-2012; AssociateEditor and Technical Editor, IEEE COMMUNICATIONS MAGAZINE, 2004-2015; Technical Editor, IEEE WIRELESS COMMUNICATIONS MAGAZINE,2006-2010; and Associate Editor, WILEY SECURITY AND COMMUNICATIONNETWORKS JOURNAL, 2007-2012. She currently serves as Area Editor forthe IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. Her awardsinclude the NSERC University Faculty Award in 1999; the Quebec Govern-ment FRQNT Strategic Faculty Fellowship in 2001-2006; the INRS-EMTPerformance Award multiple times since 2004, for outstanding achievementsin research, teaching and service; and the 2007 Technical Community ServiceAward from the FRQNT Centre for Advanced Systems and Technologies inCommunications. She is co-recipient of five IEEE Best Paper Awards andof the 2012 IEICE Best Paper Award; and recipient of NSERC DiscoveryAccelerator Supplement Award. She served as Distinguished Lecturer of theIEEE Communications Society and Member of its Board of Governors in2013-2016 and 2014-2016, respectively. Professor Aıssa is a Fellow of theCanadian Academy of Engineering.


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