Nonbinary Turbo-Coded Spatial Modulation over PAPR-Limited

Nonbinary Turbo-Coded Spatial Modulation over PAPR-Limited Channel

Shigeaki Hashimoto and Koji Ishii

Graduate School of Engineering, Kagawa University,2217-20 Hayashi, Takamatsu, Kagawa 761-0396, Japan

E-mail: [email protected], [email protected]

Abstract This paper proposes a novel coded spatial modulation technique with nonbinary signaling basedon a nonbinary turbo-coding approach. The aim of this work is to improve the average bit error rate (BER)performance over a peak-to-average power ratio (PAPR)-limited channel. The use of nonbinary signaling suchas hexagonal quadrature amplitude modulation (HQAM), has been studied as a technique that can mitigate thePAPR. However, it is not suitable for the transmission of binary information because the number of modulationlevel cannot be given by a power of two, which leads to translation loss from nonbinary to binary numbers. On theother hand, generalized spatial modulation (GSM) has been proposed as an extended version of spatial modulation(SM) and it can boost the transmission rate. However, the number of modulation levels of GSM cannot be given bya power of two. This work proposes to jointly design coded spatial modulation composed of nonbinary signalingand nonbinary SM i.e., GSM, by using nonbinary turbo coding. Simulation results demonstrate the improved BERthe proposed coded SM over a PAPR-limited channel.

Keywords: spatial modulation, nonbinary turbo code, peak-to-average power ratio limited channel

1. Introduction

It is essential for future wireless communications to re-alize bandwidth, and energy-efficient transmission. Asbandwidth-efficient transmission techniques, multiple-input multiple-output (MIMO) techniques such as spa-tial multiplexing and space-time coding have been inten-sively studied. However, most MIMO systems have highpower consumption due to the necessity of multiple ra-dio frequency (RF) chains. Recently, spatial modulation(SM) has been proposed as a new type of MIMO trans-mission [1]. Unlike MIMO systems, the transmitter ofSM activates only one transmit antenna at a given timecorresponding to the transmission of information. As aresult, the transmitter can be composed of only one RFchain, which leads to simplification of the transmitter.Meanwhile, the receiver of SM estimates which trans-mit antenna has been activated and can then decode thetransmitted signal. SM can be decomposed into spatial-domain modulation, generally called space-shift keying(SSK) [2], and conventional IQ-domain modulation forexample, phase-shift keying (PSK) and quadrature am-plitude modulation (QAM). Thus, the transmission rateof SM depends on the number of transmit antennas andthe modulation level of the IQ-domain signal. In order toboost the transmission rate with the same number of trans-

mit antennas, generalized space-shift keying (GSSK) hasbeen proposed as an extended version of SM, where thetransmitter activates an arbitrary number of transmit an-tennas [3]. However, GSSK requires the same number ofRF chains as activated antennas since the transmitter mustactivate more than one transmit antenna at a given time.Furthermore, the modulation level of GSSK cannot be apower of two, and thus, some modification is needed totransmit binary information.

To achieve higher bandwidth efficiency of SM, a higherorder of modulation in the IQ-domain signal is a rea-sonable solution. QAM and amplitude phase shift key-ing (APSK) are suitable for high-order modulation, forexample, 16APSK and 64QAM, from the viewpoint ofminimum Euclidean distance. Generally, the bit errorrate (BER) depends on the minimum Euclidean distance.Thus, square QAM such as 16QAM and 64QAM canachieve a superior BER performance to APSK and PSKsignals. However, square QAM has a higher peak-to-average power ratio (PAPR) than PSK and APSK, whichleads to the degradation of the power amplifier (PA) ef-ficiency. To avoid the performance degradation causedby the nonlinearity of PA, input power backoff (IBO) iswidely utilized. Several types of modulation with a lowPAPR and a large Euclidean distance have been proposed,such as star-QAM. It is a well-known fact that hexago-

Journal of Signal Processing, Vol.19, No.6, pp.235-242, November 2015

PAPER

Journal of Signal Processing, Vol. 19, No. 6, November 2015 235

nal QAM (HQAM) can achieve the largest Euclidean dis-tance from lattice theory [4, 5] and has a good PAPR [6].However, the modulation level of HQAM is not a powerof two, which means that it is not suitable for the trans-mission of binary information.

This paper proposes nonbinary coded spatial modula-tion with nonbinary SSK and nonbinary signals to realizepower-efficient transmission. Firstly, we propose a novelnonbinary turbo coding for nonbinary SM. In [7], we pro-posed and discussed nonbinary turbo-coded modulationwithout considering the nature of the PA, namely, thePAPR limitation. Thus, this paper extends the discussionof nonbinary turbo-coded spatial modulation (NTCSM)to the case of a PAPR-limited channel. Furthermore, wediscuss the best combination of SSK and APSK signalsover a PAPR-limited channel. This paper is organized asfollows. In Sect. 2, we introduce the system model ofnonbinary coded SM and the PAPR-limited channel. Sec-tion 3 proposes two types of nonbinary turbo codes anddiscusses optimal coding structure. In Sect. 4, we ap-ply nonbinary turbo coding to nonbinary SM and give theperformances over PAPR-unlimited and limited channels.Finally, we conclude this paper.

2. System Model

This section provides the system model of nonbinarycoded SM. We explain the channel with PAPR limitationand then give the CCDF performances of several nonbi-nary signals.

2.1 Nonbinary coded spatial modulation

Fig. 1 Transmitter and receiver with nonbinary codedspatial modulation

We assume that a transmitter and receiver have Nt andNr antennas, respectively, as shown in Fig. 1. SM can

be decomposed into spatial-domain modulation calledSSK and conventional IQ-domain modulation, for exam-ple PSK and QAM, which will be referred to as ampli-tude phase shift keying (APSK). Thus, APSK in this pa-per means not only APSK (star-QAM) but also PSK andQAM. The individual modulation levels in the spatial andIQ domains are assumed to be MSSK and MAPSK, re-spectively, and thus the total number of SM levels can begiven by MSM = MSSK × MAPSK. At the transmitter,a binary information sequence d ∈ {0, 1}k of length k isfed into the nonbinary encoder and encoded to the non-binary codeword sequence c ∈ {0, 1, · · · ,MSM − 1}n

of length n. Thus, the coding rate can be calculated asr = k/n [bit/sym]. The nonbinary codeword sequencec is divided into two parts and then mapped into spatialand IQ-domain signals. In this work, MSSK and MAPSK

need not to be restricted to powers of two. Therefore,unlike conventional binary SM, nonbinary coded SM canmake full use of its own ability even if the system exploitsgeneralized SSK (GSSK) [3], SSK a with nonbinary num-ber of antennas, and/or a nonbinary APSK signal such asTPSK [8] or HQAM [4, 6]. When the transmitter with Nt

antennas utilizes MAPSK-APSK and GSSK, where it se-lects two transmit antennas from Nt transmit antennas1,the modulation levels of APSK and SSK can be given byMAPSK and MSSK = NtC2, respectively. In this case, ifthe transmitter selects the mSSKth SSK-modulated signal(0 ≤ mSSK ≤ NtC2 − 1) and the mAPSKth APSK mod-ulated signal (0 ≤ mAPSK ≤ MAPSK), the transmittingsymbol matrix xmSSK,mAPSK (∈ X and |X | = MSM ),which is an Nt × 1 matrix, can be given by

xmSSK,mAPSK

= [0, · · · , smAPSK , · · · , 0, · · · , smAPSK , · · · , 0]T (1)

where smAPSK is the mAPSKth APSK modulated signaland [·]T denotes the transpose operator. In the case ofNtC2 GSSK, there are two nonzero components in thetransmitting symbol matrix xmSSK,mAPSK since two trans-mit antennas are activated. If conventional SSK [1] isapplied, only one transmit antenna is activated and thusthere is only one nonzero component in the transmittingsymbol matrix. The received signal y ∈ CNr×1 is ex-pressed as

y = HxmSSK,mAPSK + w (2)

where H ∈ CNr×Nt is the fading coefficient matrix,where each element is a zero-mean, mutually uncorre-lated, and circularly symmetric complex Gaussian ran-dom variable with unit variance and w ∈ CNr×1 is the

1This work focuses only on GSSK with two activated antennas tokeep the complexity of the transmitter low, since the transmitter re-quiress the same number of RF chains as activated antennas.

236 Journal of Signal Processing, Vol. 19, No. 6, November 2015

corresponding noise sample sequence comprising a zero-mean Gaussian random variable with variance σ2. Thiswork assumes that the fading coefficient matrix is con-stant within one frame and varies independently from oneframe to another. We further assume that the symbol-level synchronization at the receiver is perfect and that thechannel state information (CSI) is unknown at the trans-mitter but is perfectly known at the receiver. At the re-ceiver side, similar to the soft decoding for a nonbinarycode [9], an SM demapper calculates a log-likelihood ra-tio (LLR), which is the logarithmic ratio between the sym-bol γ and the reference symbol 0 (γ = {1, · · · ,MSM −1}) and is defined as

LcSM=γ = lnPr(y|cSM = γ)Pr(y|cSM = 0)

= ln

∑

xm,n∈XcSM=γ

p(y|x̂ = xm,n) Pr(cSM = γ)

∑

xm,n∈XcSM=0

p(y|x̂ = xm,n) Pr(cSM = 0)(3)

where

p(y|x̂ = xm,n) ∝ exp(− ||y − Hx̂||F

σ2

)(4)

where || · ||F is the Frobenius norm, XcSM=γ denotes thesubset of X for which the labeling of the transmittingsymbol is equal to the codeword symbol γ, and Pr(cSM =γ) is the a priori probability that the codeword symbol isequal to γ. Obviously, the computational complexity isgreater than that in the case of a binary symbol since thetotal number of constellation points increases. However,we emphasize that a complexity reduction method, for ex-ample, Max-Log-MAP or sphere packing, can be applied.By using the input LLRs given by Eq. (3), the maximuma posteriori probability (MAP) decoder calculates the a-posteriori probability of the information sequence and theextrinsic values of the codeword sequence. The detailsof the encoding and decoding for this system will be de-scribed in Sect. 3.

2.2 Peak-to-average power ratio limited channel

This work focuses on the coded SM over a PAPR-limited channel. Thus, this section provides the com-plementary cumulative distribution functions (CCDFs) ofinstantaneous power for several types of APSK signals.Square constellation signals such as 16 QAM signal usu-ally have poor PAPR performance, which results in inef-ficient transmission power. In contrast, nonsquare QAMand PSK signals such as 18 HQAM and 16 star-APSKsignals can achieve good PAPR performance. Althoughthere have been many analyses of the CCDF for binary

signals [10, 11], there have been no analysis of the CCDFfor nonbinary signals. Thus, this subsection will provideCCDF performances of nonbinary signals.

The complex baseband linear modulation signal whosetime scale is normalized the time scale by the symbol pe-riod is given by

s(τ) =∞∑

k=−∞skg(k + τ) (5)

where τ is the normalized time scale, sk denotes the kthcomplex baseband signal, and g(τ) is the impulse re-sponse of the square-root raised cosine (SRRC) filter andis expressed as

g(τ) =

1 − α + 4απ τ = 0

α√2(1 + 2

π ) sin π4α + (1 − 2

π ) cos π4α τ = ± 1

4αsin π(1−α)τ+4ατ cos π(1+α)τ

πτ(1−(4ατ)2) otherwise(6)

where α denotes the roll-off factor. The probability thatthe instantaneous power |s(τ)|2 is below a given level zis given by

F (z, τ) = Pr[|s(τ)|2 < z

](7)

In addition, the probability which exceeds the given levelis

Γ(z, τ) = 1 − F (z, τ) (8)

On the basis of the above equation, Fig. 2 shows theCCDF characteristics of the instantaneous power of thenonbinary signals of 12 PSK, 12 QAM, and 18 HQAMsignals. We applied the roll-off factor α = 0.22 to theSRRC filter. Moreover, the symbol period J is equalto 18, and then the one-sided symbol length is 32. The4+12 star-QAM (star-APSK) signal consists of two cir-cles whose ratio between the inner radius and outer ra-dius is given by

√2(1 +

√3) since this ratio can achieve

the largest Euclidean distance. From Fig. 2, 16 QAMsignal has the highest instantaneous power at CCDF =10−3. Compared to the square 16 QAM, 12 QAM, and18 HQAM signals. 12 QAM and 18 HQAM signal sig-nal can achieve better CCDF performances than 16 QAMsignal because the constellation points of these modu-lations are close to the circular shape. Besides, the4+12 star-QAM signal can further improve the CCDF per-formance compared to with those of 12 QAM, 18 HQAM,and 16 QAM signals. Furthermore, the 12 PSK signal hasthe best performance since its constellation has a con-stant amplitude, namely, it is a circular constellation. Onthe basis of the above analyses, we will discuss the codedesign of nonbinary SM and the optimal combination ofSSK and APSK in Sect. 4.


Fig.2 CCDF of instantaneous power (α = 0.22)

Fig.3 Structure of nonbinary turbo encoder and decoder

3. Nonbinary Turbo Encoder

This section describes the nonbinary turbo coding fornonbinary SM. For brevity of code design, we focus onlyon nonbinary numbers that can be decomposed into pow-ers of two and three. For example, 18 can be decom-posed as 18 = 32 × 2. From this constraint of the non-binary numbers, in order to efficiently encode a binarydata sequence to a nonbinary code sequence, the encodershould be composed of encoders with binary and ternaryoutputs. Thus, our proposed turbo encoder is a combina-tion of ternary-output and binary-output convolutional en-coders. Moreover, the design of the proposed nonbinaryturbo encoder is based on a serial concatenated convolu-tional encoder, namely, a serial turbo encoder [12]. Fig-ure 3 shows the proposed nonbinary turbo encoder anddecoder. The encoder consists of an outer binary-inputbinary-output (BIBO) convolutional encoder and inner

encoder that consists of BIBO and binary-input ternary-output (BITO) encoders. From [12], the inner and outerencoders of the serial turbo code should be nonrecur-sive and recursive encoders, respectively. Furthermore,a turbo code with a low-rate outer code can achieve su-perior performance to one with a high-rate outer code iftheir overall coding rates are identical.

In a similar fashion, our proposed nonbinary turboencoder consists of low-rate nonrecursive convolutionalouter encoder and high-rate recursive convolutional in-ner encoder. As seen in Fig. 3, a binary information se-quence d ∈ {0, 1}k is encoded by a nonrecursive BIBOconvolutional encoder. Then, the binary codeword se-quence is interleaved and divided into two sequences thatare respectively fed into the BITO and BIBO encoders.The codeword sequence encoded by the BITO encoderis the ternary sequence ct ∈ {0, 1, 2}nt , while the oneencoded by the BIBO encoder is the binary sequencecb ∈ {0, 1}nb . Note that the code length of both code-word depends on the decomposed number of modulationlevels of SM. For example, if the number is given by18 = 32 × 2, the relationship between nt and nb can beexpressed as nt = 2nb since two ternary codeword sym-bols and one binary codeword symbol are mapped intothe same spatial modulated symbol.

The decoder calculates LLRs for the ternary and binarycodewords Lct and Lcb

from the received signal usingEq. (3). Individual decoders for the BITO and BIBO en-coders calculate the LLRs for the binary symbol. Thus,two soft values can be combined with a parallel-to-serial(P/S) converter to becomes the LLRs of the interleavedbinary codeword. The LLRs are de-interleaved and fedinto the BIBO (outer) decoder as the input LLR of bi-nary codeword. The BIBO outer decoder calculates thesoft values for binary codeword and binary informationsequences. The LLRs of the binary codeword sequenceare interleaved, S/P converted, and fed back to the BITOand BIBO decoders as the a priori probabilities. Thus,the decoder can operate this decoding process iteratively.

We provide two types of nonbinary turbo encoders.The only difference between them is the structure of theBITO encoder, which works as the component encoder inthe inner encoder shown in Fig. 3. The BITO encoderis composed of a binary-to-ternary (B/T) converter anda rate 1 recursive ternary-input ternary-output (TITO) en-coder2. The B/T converter converts a binary sequence to aternary sequence in according with the conversion rule de-picted in Table 1. The mapping rule given by Table 1 is aquasi-Gray mapping. According to this rule, three bits are

2Rate 1 recursive encoder is widely referred to as repeat-accumulate(RA) encoder and applied into serial the turbo encoder as an inner en-coder since the turbo encoder with RA encoder can easily and efficientlyobtain interleaver gain.


converted to two ternary symbols. Therefore, the codingrate of the BITO encoder composed of the B/T converterand rate-1 TITO encoder can be given by rBITO = 3/2,which is more than one. The other BITO encoder is basedon a recursive BITO encoder that directly encodes binaryinformation to a ternary codeword and can take advantageof the redundancy caused by B/T conversion. However, tothe best of our knowledge, there is no rate 3/2 BITO en-coder for the case of a constraint length of less than 4. Asa result, we should apply a BITO encoder whose maxi-mum coding rate is limited to less than or equal to 1 byextending the BITO encoder proposed in [8]. Therefore,the coding rate of the outer code depends on the type ofBITO encoder.

Table 1 BT converterGF(23) GF(32)0 0 0 0 00 0 1 0 10 1 0 1 00 1 1 2 01 0 0 1 11 0 1 1 21 1 0 2 11 1 1 2 2

/ 0 2

4. System Design over PAPR-Limited Channel

The purpose of this section is to describe our designof nonbinary turbo-coded SM (NTCSM) with good BERperformance over a PAPR-limited channel. To achievethis, we will first compare two types of nonbinary turbocode proposed in Sect. 4.1 and evaluate NTCSM over aPAPR-limited channel in Sect. 4.2. In this section, we as-sume that both the transmitter and the receiver have fourantennas and that the transmission rate is 4 bits/symbol.Thus, we exploit three types of signal combination, 4 SSK+ 18 HQAM, 4C2 SSK+12 QAM, and 4C2 SSK+12 PSK,where, the individual modulation levels are identical andgiven by MSM = 72. Note that the proposed NTCSMcan be extended to cases with more transmit antennas andmore receive antennas. However, if the transmitter hasmore than four antennas, some modification may be re-quired. For example, when the transmitter has five anten-nas, some binary-pentagonal conversion or a binary-inputpentagonal-output encoder is expected to be required inorder to make full use of the given ability. The general-ization of the modulation level should be carried out asfuture work.

4.1 Encoder design for nonbinary turbo codedspatial modulation

This subsection discusses which type of nonbinaryturbo coding is more suitable for nonbinary SM. Recallthat two types of turbo coding were proposed in Sect. 3.One is based on a B/T converter and a rate 1 TITO en-coder, which will be referred to as NTCSM type I. Theother is based on a BITO encoder, which will be referredto as NTCSM type II. A frame is composed of 3 000 piecesof binary information (k = 3 000). In the case where4 SSK + 18 HQAM is utilized, the modulation levels inthe spatial and IQ domains can be given by MSSK = 4and MAPSK = 18, while in the case where 4C2 SSK +12 QAM is utilized, each level can be given by MSSK = 6and MAPSK = 12. NTCSM type I consists of a rate 2/3nonrecursive BIBO convolutional outer encoder and rate1 TITO and rate 1 BIBO recursive convolutional innerencoders. As mention in Sect. 3, we apply a repeat-accumulate (RA) encoder as the inner TITO and BITOencoders in order to efficiently obtain the interleaver gainfrom the serial turbo code.

The generator matrix of the rate 2/3 BIBO outer en-coder is given by [1 + D + D2 + D3, 1 + D + D3] and ispuncturing from rate 1/2 to rate 2/3, which is the greatestnonrecursive convolutional code with constraint length 4[13]. Also, the generator matrices of the rate 1 recursiveTITO and BITO encoders are given by [1/(1 + D)] inGF(3) and [1/(1+D)] in GF(2), respectively. It is impor-tant to note that the rate 1 recursive TITO encoder i.e., theRA encoder in GF(3), outputs the ternary symbols withequal occurrence probabilities. Therefore, [1/(1 + D)] inthe GF(3) RA code can avoid reducing the entropy of theoutput. On the other hand, NTCSM type II consists of arate 4/5 BIBO nonrecursive convolutional outer encoderand rate 1 BITO and BIBO recursive convolutional in-ner encoders. The generator matrix of the rate 4/5 BIBOouter encoder is the same as that of NTCSM type I butthe puncturing pattern is different [13]. As mentioned inSect. 3, there are no three-bit-input two-ternary-symbol-output (BITO) encoders with a constraint length of lessthan 43. Thus, we must resort to the conventional BITOencoder. Moreover, from the fact that a recursive con-volutional code with a large effective free distance can bemade from a nonrecursive convolutional code with a largefree distance [14], we utilize the recursive BITO encoderwhose generator matrix is given by [1/(2+2D +D2)] inGF(3). Note that a [2+2D+D2] BITO encoder has a largefree distance and good BER performance when ternaryPSK is applied [6, 8]. The generator matrix of the BIBOrecursive encoder is the same as the one in NTCSM typeI. We would like to emphasize that NTCSM type I can

3We have confirmed this fact by an exhaustive computer search.


Fig.4 BER performances of NTCSM type I and type II

exploit a lower-rate (more powerful) outer encoder thanNTCSM type II. In the following evaluations, we utilize arandom interleaver.

Fig. 4 shows a comparison of the BER performancebetween NTCSM type I and type II. In each type, thenumber of iterative decodings (referred to as “it” in thefigures) is five, since the BER performances cannot beimproved with more than five iterative decodings. Here-inafter, we will evaluate the BER performance with fiveiterations. Fig. 4 reveals that NTCSM type I canachieve better performance than NTCSM type II whenboth 4 SSK+18 HQAM and 4C2 SSK+12 QAM are uti-lized, because NTCSM type I can be embedded in a morepowerful outer encoder owing to the nature of B/T con-verter. We conclude that NTCSM should have a low-rateouter code similar to that in the serial turbo code [12].In the following section, we exploit NTCSM type I as anonbinary error-correcting code.

4.2 Evaluations over PAPR limited channel

This subsection discusses the performance of NTCSMover a PAPR-limited channel. As described in Sect. 2.2,individual types of APSK signals have different CCDFperformances as well as different Euclidean distances,which results in different BER performances depend-ing on the channel model, namely, whether the chan-nel is PAPR unlimited or limited. Hereinafter, we dis-cuss the suitable structure of NTCSMs in the casesof PAPR-limited and -unlimited channels. Firstly, wecompare the proposed NTCSMs with 4 SSK+18 HQAM,

Fig. 5 BER performances of BICSM and NTCSM overPAPR-unlimited channel

4C2 SSK+12 QAM, and 4C2 SSK+12 PSK with the bit-interleaved coded SMs (BICSMs) with 4 SSK+16 APSKand 4SSK+16QAM proposed in [15] over a PAPR-unlimited channel. BICSM consists of a rate 2/3 punc-tured convolutional code whose generator matrix is givenby [1 + D + D2 + D3, 1 + D + D3]. It can be seen fromFig. 5 that the conventional BICSMs with 16 APSK and16 QAM have almost the same BER performances since16 APSK and 16 QAM have similar BER performances.On the other hand, NTCSM with 4C2SSK+12QAMcan achieve better BER performance than the NTCSMswith 4 SSK+18 HQAM and 4C2 SSK+12 PSK becausethe minimum Euclidean distance of 12 QAM is largerthan those of 18 HQAM and 12 PSK. To summarize, theproposed NTCSMs can achieve better performance thanBICSM at high SNR region (SNR >11 dB). In particularNTCSM with 4C2 SSK+12 PSK can improve the SNR byabout 1.5 dB at BER=10−5 compared with the conven-tional BICSMs.

We further evaluate the proposed NTCSM over aPAPR-limited channel. The PA typically exhibits nonlin-ear characteristics as the signal input power approaches itssaturation region. To avoid this nonlinear distortion, thePA should operate with an input power backoff (IBO),which essentially degrades the PA efficiency. In orderto evaluate the effect of the incurred IBO, we introducea soft-envelope limiter as the PA model in the follow-ing. Then, the relative IBO gain can be defined as thedifference between the instantaneous powers achievingthe given value of the CCDF of two different modulationschemes [16]. In the BER evaluations, we defined the hor-


Fig. 6 BER performances of BICSM and NTCSM con-sidering CCDF performances (over PAPR limited chan-nel)

izontal axis as SNR + IBO [dB]. IBO depends on the in-stantaneous power of the input signal, i.e., the nonlinear-ity of PA. In this work, the required IBO is defined as theinstantaneous power that satisfies CCDF = 10−3 fromFig. 2. Fig. 6 reveals that the performance enhancementof the proposed NTCSM against the conventional BICSMis larger than in the case of a PAPR-unlimited channel,since the proposed NTCSM can efficiently exploit nonbi-nary signals with good CCDF performance. Concretely,the performance of NTCSM with 4C2GSSK and 12 PSKoutperforms the conventional BICSM by about 4 dB atBER = 10−5 . The proposed NTCSM can moreover im-prove the BER performance over PAPR limited channel.

5. Conclusions

In this paper, we proposed nonbinary turbo-coded spa-tial modulation in order to realize power-efficient trans-mission in terms of the PA. Furthermore, we discussedthe suitable structure of nonbinary turbo coding for spa-tial modulation considering the PAPR. Simulation resultsrevealed that the proposed NTCSM can achieve superiorBER performance to the conventional BICSM over bothPAPR-unlimited and -limited channels. As a result, ourproposed system can realize power-efficient transmission.

Acknowledgment

The work was supported by JSPS (26820147) and A-

STEP (AS262Z00353H) in Japan.

References

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Shigeaki Hashimoto re-ceived his B.S. and M.S. de-grees from the Departmentof Reliability-based Infor-mation System Engineer-ing, Faculty of Engineering,Kagawa University, Japan,in 2013 and 2015, respec-tively. Since April 2015,he has been working atMurata Manufacturing Co.,Ltd. His research interests

include multiple-antenna transmission and coding theory.

Koji Ishii received hisB.E., M.E., and Ph.D. de-grees from Yokohama Na-tional University, Japan, in2000, 2002, and 2005, re-spectively. Since April2005, he has been with theDepartment of Electronicsand Information Engineer-ing, Faculty of Engineering,Kagawa University, Japan,where he is currently an As-

sociate Professor. From 2012 to 2013, he was a VisitingScientist at the University of Sydney, Australia. His cur-rent research interests include wireless communications,information theory, iterative processing, and cooperativecommunications. He is a member of the IEEE Commu-nications and Information Theory Society. He is also amember of IEICE and RISP.

(Received Febrary 14, 2015; revised June 23, 2015)


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Nonbinary Turbo-Coded Spatial Modulation over PAPR-Limited