paper complexity reduction in joint decoding of block...

IEICE TRANS. COMMUN., VOL.E97–B, NO.4 APRIL 2014905

PAPER

Complexity Reduction in Joint Decoding of Block Coded Signals inOverloaded MIMO-OFDM System

Yoshihito DOI†a), Student Member, Mamiko INAMORI†b), Member, and Yukitoshi SANADA†c), Senior Member

SUMMARY This paper presents a low complexity joint decodingscheme of block coded signals in an overloaded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) sys-tem. In previous literature, a joint maximum likelihood decoding schemeof block coded signals has been evaluated through theoretical analysis. Thediversity gain with block coding prevents the performance degradation in-duced by signal multiplexing. However, the computational complexity ofthe joint decoding scheme increases exponentially with the number of mul-tiplexed signal streams. Thus, this paper proposes a two step joint decod-ing scheme for block coded signals. The first step of the proposed schemecalculates metrics to reduce the number of the candidate codewords usingdecoding based on joint maximum likelihood symbol detection. The sec-ond step of the proposed scheme carries out joint decoding on the reducedcandidate codewords. It is shown that the proposed scheme reduces thecomplexity by about 1/174 for 4 signal stream transmission.key words: multiple-input multiple-output (MIMO), overloaded MIMO,joint maximum likelihood decoding

1. Introduction

Recently the demands of larger capacity and higher daterates are increasing due to the appearance of new mobiledevices and services in wireless communications especiallyfor high data rate and short range communications such aswireless LANs. The technology of multiple-input multiple-output (MIMO) makes use of multiple transmit and receiveantenna elements to increase the capacity over single-inputmultiple-output (SIMO) transmission. MIMO has beenshown to offer significant improvements in terms of bothhigher data rates and better reliability [1], [2]. Suppose thatthe numbers of transmit antennas and receive antennas areNT and NR, the capacity reaches up to min(NT , NR) times[3], [4]. On the other hand, a wireless mobile terminal haslimitations in its form factor. The number of receive anten-nas in the mobile terminal has to be minimized while main-taining the throughput performance.

Thus, overloaded MIMO systems with NT > NR havebeen investigated in the literature. It has been shown in [5]that demodulation performance deteriorates with joint max-imum likelihood detection (MLD) when there are fewer re-ceive antennas than transmit antennas. [6] presents a ge-netic algorithm based detection scheme for an overloaded

Manuscript received July 27, 2013.Manuscript revised December 12, 2013.†The authors are with the Dept. of Electronics and Electrical

Engineering, Keio University, Yokohama-shi, 223-8552 Japan.a) E-mail: [email protected]) E-mail: [email protected]) E-mail: [email protected]

DOI: 10.1587/transcom.E97.B.905

MIMO system. Though this scheme reduces the computa-tional complexity of signal detection, the bit error curveshave shown error floors. [7] employs sphere decoding insymbol detection followed by turbo decoding. However, theproblem of the performance degradation in joint symbol de-tection remains. The system in [8] also implements morenumber of transmit antennas than that of receive antennas. Itonly selects one transmit antenna for each subcarrier basedon the channel response and no joint detection or decodingis assumed. In [9], the effect of channel estimation accu-racy in the overloaded MIMO system has been investigatedthrough computer simulations and experiments.

It has been suggested in [5] that diversity receptiondiminishes the amount of performance degradation due tospatial signal multiplexing. Therefore, the joint decodingscheme of block coded signals in an overloaded MIMO-orthogonal frequency division multiplexing (OFDM) sys-tem has been investigated [10]. Through soft decision de-coding of the block coded signals, diversity over codewordreception is realized. The problem of this scheme is that thecomputational complexity of joint decoding increases expo-nentially with the number of the multiplexed signal streams.Therefore, reducing this complexity is essential.

This paper proposes a two step joint decoding schemefor the reduction of the complexity. In the first step of theproposed scheme, the metric of each coded symbol in themultiplexed signals is calculated. A reduced number of can-didate codewords are then selected and joint decoding is car-ried out with the reduced set of codewords.

For complexity reduction in decoding, the scheme in[11] has also been proposed. This scheme also investigatesthe two step decoding though the assumed conditions aredifferent. The first step of [11] selects the candidate code-word that has the smallest Hamming distance from the harddecision received sequence and error codewords associatedwith it. In the second step, the decoding is carried out by thecandidate codeword and error codewords. Only an AWGNchannel is assumed and no diversity gain can be obtainedwith this algorithm due to hard decision.

This paper is organized as follows. Section 2 explainsthe system model and the proposed joint decoding scheme.Numerical results obtained through computer simulation areshown in Sect. 3. Finally, conclusions are presented inSect. 4.

Copyright c© 2014 The Institute of Electronics, Information and Communication Engineers

906IEICE TRANS. COMMUN., VOL.E97–B, NO.4 APRIL 2014

2. System Model

2.1 Overloaded MIMO-OFDM System

Suppose there are NT transmit antennas and NR receive an-tennas in a MIMO system as shown in Fig. 1. The over-loaded MIMO is the case when NT>NR. The block diagramof the overloaded MIMO-OFDM system with a joint decod-ing scheme is shown in Fig. 2. The information bit stream isde-multiplexed to NT branches and encoded on each trans-mission branch. M information bits are converted to L codedsymbols by a block code with the coding rate of L/M. ND/Lcodewords are transmitted over one OFDM symbol whereND is the number of date subcarriers (for simplicity, here,ND is assumed to be a multiple of L). On the pth branch inthe ith codeword, the coded symbol sequences are given ina vector form as Ci

p = [Ci1p Ci

2p . . . CiLp]T . The coded sym-

bols are assigned to subcarriers to spread over the frequencydomain through interleaving as shown in Fig. 3. Supposethat S p[k] is the interleaved symbol on the kth subcarrier ofthe pth branch. ND/L×L block interleaving is carried out tospread the coded symbols over the subcarriers. The codedsymbol, Ci

lp, is assigned to the kth subcarrier as S [k] = Cilp

where k is given as

k = (l − 1) × ND/L + (i − 1) + 1. (1)

Fig. 1 Overloaded MIMO-OFDM system.

Fig. 2 Received signal model of one of antenna elements in overloadedMIMO-OFDM system.

The OFDM signal of the pth branch is given as

up[n] =N−1∑k=0

S p[k] exp

(j2πnk

N

)(2)

where n(n = 0, 1, ...,N−1) is the time index, N is the size ofthe inverse discrete Fourier transform (IDFT). The last partof the OFDM symbol is replicated and added at the begin-ning as a guard interval (GI). The OFDM signal then passesthrough a transmit filter and the transmit signal in the base-band is given as

xp(t) =N−1∑

n=−NGI

up[n]ptp(t − nTs) (3)

where xp(t) is the pth signal stream, ptp(t) is the impulseresponse of the transmit filter, Ts is the sampling intervalfor the OFDM signal, and NGI is the GI length. At the re-ceiver side NT signal streams are spatially multiplexed andreceived by a single antenna element. The received signalsby the qth receive antenna at the output of the receive filterwith the impulse response, pqr(t), is given by

yq(t) =NT∑p=1

yqp(t) + wq(t) (4)

where wq(t) is the noise in the qth receive branch and yqp(t)is the received signal from the pth transmit antenna to theqth receive antenna. yqp(t) is calculated as

yqp(t) =N−1∑

n=−NGI

up[n]hqp(t − nTs) (5)

where hqp(t) is the impulse response of the composite chan-nel including the transmit and receive filters as

hqp(t) = ptp(t) ⊗ cqp(t) ⊗ prq(t) (6)

where cqp(t) is the impulse response of the physical channelbetween the pth transmit antenna and the qth receive an-tenna, and ⊗ represents convolution. The received signal isconverted to digital samples by an A/D converter at the rate

Fig. 3 Symbol interleaving over subcarriers.

DOI et al.: COMPLEXITY REDUCTION IN JOINT DECODING OF BLOCK CODED SIGNALS IN OVERLOADED MIMO-OFDM SYSTEM907

of Ts. Therefore, the received digital signal is given as

yq[n] = yq(nTs). (7)

After removing the GI and taking the DFT of N samples, thesignal on the kth subcarrier is expressed as

Zq[k] =N−1∑n=0

yq[n] exp

(− j

2πnkN

)

=

NT∑p=1

Hqp[k]S p[k] +Wq[k] (8)

where Hqp[k] is the frequency response between the pthtransmit antenna and the qth receive antenna and Wq[k] isthe noise through the qth receive filter on the kth subcarrier,respectively. These are given as

Hqp[k] =N−1∑n=0

hqp[n] exp

(− j

2πnkN

), (9)

Wq[k] =N−1∑n=0

wq[n] exp

(− j

2πnkN

), (10)

where hqi[n] and wq[n] are given by

hqp[n] = hqp(nTs), (11)

wq[n] = wq(nTs). (12)

In a matrix form, Eq. (8) is rewritten as

Z[k] = H[k]Cil +W[k] (13)

where

Z[k] = [Z1[k] Z2[k] . . . ZNR [k]]T , (14)

H[k] =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣H11[k] · · · H1NT [k]

.... . ....

HNR1[k] · · · HNRNT [k]

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ , (15)

Hp[k] = [H1p[k] H2p[k] . . . HNR p[k]]T , (16)

Cil = [Ci

l1 Cil2 . . . Ci

lNT]T , (17)

W[k] = [W1[k] W2[k] . . . WNR [k]]T , (18)

and k is calculated from Eq. (1) with l and i.

2.2 Detection and Decoding Schemes

2.2.1 Decoding based on Joint Maximum LikelihoodSymbol Detection

In the conventional joint detection, detection metrics for allthe combinations of NT coded symbols are calculated. Sup-pose that each coded symbol is binary modulated and σ2 isthe variance of the noise. The detection metrics for the lthsymbol of the pth signal stream are calculated as [12]

d1lp = min

{Cilp′ |p′�p}

1σ2

∥∥∥∥∥∥∥∥Z[k]

−⎛⎜⎜⎜⎜⎜⎜⎝

NT∑{p′=1|p′�p}

Hp′[k]Cilp′ +Hp[k]

⎞⎟⎟⎟⎟⎟⎟⎠∥∥∥∥∥∥∥∥

2

(19)

and

d0lp = min

{Cilp′ |p′�p}

1σ2

∥∥∥∥∥∥∥∥ Z[k]

−⎛⎜⎜⎜⎜⎜⎜⎝

NT∑{p′=1|p′�p}

Hp′[k]Cilp′ −Hp[k]

⎞⎟⎟⎟⎟⎟⎟⎠∥∥∥∥∥∥∥∥

2

(20)

where Cilp denotes the lth candidate symbol of the pth signal

stream, d1lp and d0

lp are the metrics for Cilp = +1 and Ci

lp =

−1, respectively. d1lp and d0

lp are calculated for all the coded

symbols of the signal streams. The metrics of 2M codewordsfor each signal stream are calculated on the basis of {d1

lp} and

{d0lp}. The codeword with the minimum metric is selected for

each signal stream using the following equation.

CMLp = arg min

Cip∈Ω

L∑l=1

dlp(Cilp) (21)

where

dlp(Cilp) =

⎧⎪⎪⎨⎪⎪⎩ d1lp (Ci

lp = +1)

d0lp (Ci

lp = −1), (22)

Cip =

[Ci

1p Ci2p . . . Ci

lp . . . CiLp

]T, (23)

The power of the distance between Cip and the error

codeword, e = [e1 e2 . . . eL], is given as

DS D(Cip, e) =

L∑l=1

|Eip[l]|2

NR∑q=1

|Hqp[k]|2∣∣∣∣{H[k]} (24)

where k is given by Eq. (1) with l, Eip[l] is the lth element

of the error vector between the true codeword, Cip, and the

error codeword, e, and it is given as

Eip[l] = |(Ci

lp − el)|. (25)

From Eq. (24), the pairwise error probability can be calcu-lated under the conditions of the channel matrices, {H[k]}.

2.2.2 Joint Maximum Likelihood Decoding

In the conventional joint maximum likelihood (ML) decod-ing of the block coded signals, the joint metrics are calcu-lated for all the combinations of the candidate codewordsover NT signal streams. It is necessary to calculate the met-rics for (2M)NT combinations. The joint ML decoding is ex-pressed as

CML = arg minCi

1,Ci2,...,C

iNT∈Ω

L∑l=1

∥∥∥∥∥∥∥∥Z[k] −NT∑p=1

|Hp[k]Cilp

∥∥∥∥∥∥∥∥2

(26)


where k is given in Eq. (1) and

Ci =[Ci

1 Ci2 . . . Ci

p . . . CiNT

]. (27)

If {Hqp[l]} are viewed as a set of a non-binary spreadingsequence, multiuser detection theory in [13] can be applied.From Eq. (4.71) in [13], the power of the distance betweenthe true codeword and error codeword, DML(Ci

p, e), is givenas

DML(Cip, e) =

L∑l=1

|Eip[l]|2

NR∑q=1

|Hqp[k]

+

NR∑{p=1|p′�p}

Hqp′[k]ρqpp′ [k]|2

∣∣∣∣{H[k]} (28)

where

ρqpp′[k] = 〈Hqp[k]Ci

lp·Hqp′[k]Cilp′ 〉, (29)

and ρqpp′[k] is the correlation value between the signal trans-

mitted by the pth signal stream and the p′th signal stream.The performance difference between the joint ML symboldetection and the joint ML decoding arises from the secondterm in the || parentheses in Eq. (28) which takes the inter-ference between the signal streams into account.

2.2.3 Proposed Two Step Joint Decoding

In the joint maximum likelihood decoding, the computa-tional complexity of the metric calculation increases expo-nentially with the number of the multiplexed signal streams.The proposed scheme reduces the number of the candidatecodewords. As preparation of decoding the average receivedpower of each signal stream over the codeword length is es-timated and the signal streams are ordered on the basis ofthe average power. The indexes of the streams are assignedas ι (1 ≤ ι ≤ NT ) in descending order of the average receivedsignal power. The joint ML decoding is carried out with thefollowing steps.

1. The first step of the proposed scheme calculates themetric as

∑Ll=1 dlι(Clι) and selects Kι candidate code-

words from the smallest metric. The number of thecandidate codewords for the ιth stream is Kι and gener-ally Kι ≤ Kι+1.

2. In the second step joint decoding is carried out after re-ducing the number of the candidate codewords. Thereare Kι candidates for a single stream, therefore all thecombination of the candidate codewords are given as(∏NT

ι=1 Kι)NR .

An example of the first step in the proposed two stepjoint decoding for the case of NT=2 transmit antennas, NR=1receive antenna, ι=1, and BPSK modulation is shown inFig. 4. It is assumed that one of four codewords ([0 1 1],[1 0 1], [1 1 0], [0 0 0]) with the length of L=3 symbolsare transmitted from each transmit antenna. The channel re-sponses of the transmitted signals of the 1st and 2nd signal

Fig. 4 Example of the first step in proposed scheme (NT=2, NR=1, ι=1,L=3, K1 = 2, and BPSK modulation).

streams are H1 = +1 and H2 = + j. This example focuseson the 1st signal stream and there are 2 signal candidatesfor each symbol index l. They are indicated as the red cir-cles that correspond to the candidates (±1) of the 2nd signalstream. For the candidate codeword of [0 1 1], the total met-ric is calculated as

∑3l=1 dl1(Cl1) = d0

11+d121+d1

31 = 1.2. Thetotal metrics are calculated for all the candidate codewords.Since K1 = 2, the receiver selects 2 candidate codewordswith smaller metrics. While the smallest codeword metric[0 1 1] is selected in the joint ML symbol detection, theproposed scheme selects [0 1 1] and [1 1 0] as the candidatecodewords in the second step. The second step processes theconventional joint ML decoding with these selected code-words. This process is repeated for all the signal streams.

3. Numerical Results

3.1 Simulation Conditions

The pairwise error probability and the upper bound of thedecoding schemes can be evaluated with Eqs. (24) and (28)under the conditions of {H[k]}. However, the correlationbetween the channel responses over the subcarriers preventsa closed form solution. Thus, numerical evaluation throughcomputer simulation is conducted.

Simulation conditions are presented in Table 1. Someof the specifications such as the bandwidth or the number ofsubcarriers follow the IEEE 802.11 standards. (8, 4) Ham-ming coding is used as the block coding. This is because thenumber of codewords is limited to 16 that relates to the de-coding complexity. Also the diversity order achievable withthe joint ML decoding is 4 since the minimum Hammingdistance is 4. Other block codes can be used according tothe requirement of performance and the limitation of com-putational complexity in the mobile terminal. A coded sym-


Table 1 Simulation conditions.

Modulate scheme BPSK, QPSK/OFDMNumber of subcarriers 64

Number of 48date subcarriers

Bandwidth 312.5 [kHz]of a subcarrierGuard interval 16 samples

lengthNumber of 1-4

signal streamsNumber of BPSK:1-4, QPSK:1, 2

transmit antennasNumber of 1, 2

receive antennasBlock coding (8, 4) Hamming code

Interleaver Block interleaver (6×8)1 path Rayleigh

Channel model Indoor Office-BIndoor Residential-A

Channel estimation IdealNumber of trials ≥1.6×105 bits

bol is modulated with BPSK or QPSK on each subcarrierand multiplexed with OFDM. In QPSK modulation, 2 inde-pendently coded signal streams are transmitted on the I andQ phases orthogonally. Thus, the number of transmit anten-nas reduces to a half. The transmitted symbol with QPSKmodulation is given as

S [k] = Cilp + jCi

l(p+1), p = 1, 2, . . . ,(NT

2− 1

). (30)

The number of data subcarriers are 48 and the DFT size is64. The guard interval length is set to 16 samples. The band-width of each subcarrier is 312.5 kHz. The number of trans-mit antennas are from 1 to 4 for BPSK and 1 or 2 for QPSKwhile the number of receive antennas is set to 1 or 2. Thus,the number of signal streams are from 1 to 4 (BPSK) and 2or 4 (QPSK). The BER for 1 signal stream with BPSK mod-ulation and 2 signal streams with QPSK modulation with theML decoding is included as a reference. The channel mod-els in computer simulation are 1 path Rayleigh fading, In-door Office-B, and Indoor Residential-A models [14]. Idealchannel estimation is assumed in the simulation. Channelestimation can be realized with the preamble symbols in-cluded in the frame format shown in Fig. 5. In the figureit is shown that the second long preamble of the secondstream is inverted to realize orthogonality between the twosignal streams over the 2 long preamble symbols in the caseof NT = 2. Thus, the channel responses are estimated foreach signal stream independently through the summation ofthe DFT outputs of those 2 long preamble symbols. Eventhough the number of transmit signal streams increases, or-thogonality between the streams can be realized with thelong preamble symbols that are modulated by Hadamardcodes.

Fig. 5 Transmit signal format.

Table 2 Number of complex multiplications.

Decoding Jointwith joint ML Proposed

ML symbol decoding schemedetection

Candidatecodeword - (2M)NT NRL (

∏NTι=1 Kι)NRL

selectionML symbol

detection (2NT )NRL - (2NT )NRL

Fig. 6 Computational complexity vs. number of signal streams (1 receiveantenna, Indoor Office-B, BPSK).

3.2 Numerical Results

3.2.1 Computational Complexity of Joint DecodingSchemes

Table 2 compares the computational complexity of the de-coding schemes in terms of the number of complex multi-plications. Fig. 6 shows the numbers of complex multiplica-tions for the joint decoding schemes by changing the num-ber of the signal streams with BPSK modulation. Here, theperformance degradation of the proposed scheme from thejoint ML decoding is within 0.2 dB at BER=10−3 on the In-door Office-B channel model. The numbers of selected can-didate codewords with 2 signal streams are K1 = 2 and K2 =


Fig. 7 BER vs. Eb/N0 (2 signal streams, 1 receive antenna, IndoorOffice-B, BPSK).

2. In the joint ML decoding the computational complexity is{(24)}28=2048 as NT = 2, NR = 1, M = 4, and L = 8. On theother hand, it is (4+ 22)8=64 in the case of NT = 2, NR = 1,K1 = 2, K2 = 2, and L = 8. Therefore, the computationalcomplexity in terms of the number of complex multiplica-tions is about 64/2048=1/32. For 3 signal streams {Kι} areset as K1 = 2, K2 = 3, and K3 = 4 while the computa-tional complexity reduces (24 + 23)8/{(24)}38=1/128. Thecomplexity reduces to about (360 + 24)8/{(24)}48=1/174 for4 signal streams when K1 = 3, K2 = 4, K3 = 5, and K4 = 6.Therefore, the computational complexity normalized by thatwith the joint ML decoding reduces as the number of signalstreams increases.

3.2.2 BER Performance with Multiple Signal Streams

Figure 7 show the BER versus Eb/N0 with BPSK modula-tion for 2 signal streams and 1 receive antenna on the IndoorOffice-B channel model. Fig. 8 shows the case of 4 signalstreams and 1 or 2 receive antennas. The numbers of se-lected candidate codewords are K1 = 2 and K2 = 2 for 2 sig-nal streams and they are K1 = 3, K2 = 4, K3 = 5 and K4 = 6for 4 signal streams. As it is clear that the proposed schemealso achieves the BER degradation within 0.2 dB while thecomputational complexity reduces up to about 1/174. Onthe other hand, the BER curves of the joint ML decodingdeteriorates as the number of the signal streams increasesfrom 2 to 4. When there are 2 receive antennas, the differ-ence of the BERs with the joint ML symbol detection andthe joint ML decoding diminishes. The proposed schemestill achieves equivalent BER performance as the joint MLdecoding.

Figures 9 shows the BER performance for 4 signalstreams and 1 receive antenna with QPSK modulation onthe Indoor Office-B channel model. The numbers of selectedcandidate codewords are K1 = 3, K2 = 4, K3 = 5 and K4 = 6

Fig. 8 BER vs. Eb/N0 (4 signal streams, Indoor Office-B, BPSK).

Fig. 9 BER vs. Eb/N0 (4 signal streams, 1 receive antenna, IndoorOffice-B, QPSK).

for 4 signal streams. It is observed that the proposed schemealso achieves the BER degradation within 0.2 dB while thecomputational complexity reduces by about 1/174.

3.2.3 Performance on Different Channel Models

The BER curves for 4 signal streams and 1 or 2 receive an-tennas with BPSK modulation on the 1 path Rayleigh fad-ing model and the Indoor Residential-A model are shown inFigs. 10 and 11. The numbers of selected candidate code-words with 4 signal streams are K1 = 3, K2 = 4, K3 = 5and K4 = 6. In the case of 2 receive antennas, the differenceof the BERs with the joint ML symbol detection and thejoint ML decoding also diminishes on the 1 path Rayleighfading model and the Indoor Residential-A model. The pro-


Fig. 10 BER vs. Eb/N0 (4 signal streams, 1 path Rayleigh, BPSK).

Fig. 11 BER vs. Eb/N0 (4 signal streams, Indoor Residential-A, BPSK).

posed scheme is still valid as the BER converges to that ofthe joint ML decoding.

In Figs. 12 and 13 the BER performance for 4 signalstreams and 1 receive antenna with QPSK modulation on the1 path Rayleigh fading model and the Indoor Residential-A model are presented. The numbers of selected candidatecodewords with 4 signal streams are K1=3, K2=4, K3=5,and K4=6.

Through the comparison of the performance shown inFigs. 8–13, the BER improves more with the joint ML de-coding and the proposed scheme as the delay spread in-creases. The reason is that frequency diversity is realizedthrough joint decoding and interleaving of the coded sym-bols. The performance degradation with signal multiplexingis then minimized owing to the diversity.

Fig. 12 BER vs. Eb/N0 (4 signal streams, 1 receive antenna, 1 pathRayleigh, QPSK).

Fig. 13 BER vs. Eb/N0 (4 signal streams, 1 receive antenna, IndoorResidential-A, QPSK).

3.2.4 Computational Complexity of Joint Decoding

The computational complexity of the joint ML symbol de-tection and the proposed scheme is shown in Figs. 14–16.The complexity is normalized by that of the joint ML de-coding and the BER of the joint ML decoding is shown withthe dashed line as a reference in each figure. The complex-ity and the BER of the joint ML symbol detection is alsoplotted for comparison. These figures show the relationshipbetween the BER and the normalized computational com-plexity with 4 BPSK modulated signal streams for 1 receiveantenna on the Indoor Office-B, Indoor Residential-A, and1 path Rayleigh fading models. Eb/N0 is set to 16 dB. Thenormalized complexity in the proposed scheme depends on


Fig. 14 BER vs. normalized computational complexity (4 signalstreams, 1 receive antenna, Indoor Office-B, Eb/N0 = 16 dB, BPSK).

Fig. 15 BER vs. normalized computational complexity (4 signalstreams, 1 receive antenna, 1 path Rayleigh, Eb/N0 = 16 dB, BPSK).

the numbers of the selected candidate codewords and theyare shown in Appendix. It is obvious that the BER perfor-mance of the proposed scheme approaches that of the jointML decoding by increasing the amounts of the normalizedcomputational complexity. The BER converges to that withthe joint ML decoding at around the normalized complexityof 0.01 and no difference in terms of the convergence prop-erty is observed on the channel models with different delayspreads. The same tendencies can be observed with QPSKmodulation.

3.2.5 Number of Selected Candidate Codewords

Figures 17 and 18 show the BER performance with the dif-ferent number of the selected candidate codewords, K4 or

Fig. 16 BER vs. normalized computational complexity (4 signalstreams, 1 receive antenna, Indoor Residential-A, Eb/N0 = 16 dB, BPSK).

Fig. 17 BER vs. K4 (4 signal streams, 1 receive antenna, Indoor Office-B, Eb/N0 = 16 dB, BPSK).

K1, for 4 signal streams with BPSK modulation on the In-door Office-B channel model. Eb/N0 is set to 16 dB and thenumber of the receive antennas is 1. The number of theselected candidate codewords other than K4 are K1 = 3,K2 = 4, and K3 = 5 in Fig. 17. If K4 decreases, theBER performance of the proposed scheme increases rapidly.In Fig. 18 the number of the selected candidate codewordsother than K1 are set to K2 = 4, K3 = 5, and K4 = 6. TheBER performance degradation of the proposed scheme isless significant with a smaller number of K1. Therefore, itis necessary to select a larger number of the candidate code-words for K4 instead of K1.


Fig. 18 BER vs. K1 (4 signal streams, 1 receive antenna, IndoorOffice-B, Eb/N0 = 16 dB, BPSK).

4. Conclusions

This paper has proposed the two step joint decoding schemefor the block coded signals in the overloaded MIMO-OFDMsystem. It has been shown that the proposed scheme holdsthe performance degradation to within 0.2 dB at BER=10−3

from that of the joint ML decoding and reduces the numberof the complex multiplications by about 1/174 for 4 signalstreams with BPSK modulation. The proposed scheme hasreduced the complexity more with a larger number of sig-nal streams. The proposed scheme also works with QPSKmodulation as well as BPSK modulation. It has also beenshown that the BER of the proposed scheme approaches tothat of the joint ML decoding by increasing the number ofthe normalized computational complexity to about 0.01.

As the future research, the proposed scheme shouldbe combined with an outer code such as a Turbo code ora LDPC code to confirm if the total decoding complexityreduces.

Acknowledgments

This work is supported in part by a Grant-in-Aid for Scien-tific Research (C) under Grant No.22560390 from the Min-istry of Education, Culture, Sport, Science, and Technologyin Japan.

References

[1] G.J. Foschini, “Layered space-time architecture for wireless com-munication in a fading environment when using multi-element an-tennas,” Bell Labs Tech. J., vol.1, no.2, pp.41–59, Autumn 1996.

[2] G.J. Foschini and W.J. Gans, “On limits of wireless communicationin a fading environment when using multiple antennas,” WirelessPersonal Commun., vol.6, no.3, pp.314–335, March 1998.

[3] I.E. Telatar, “Capacity of multi-antenna gaussian channels,” Euro-pean Trans. Tel., vol.10, no.6, pp.585–595, Nov./Dec. 1999.

[4] A. Goldsmith, S.A. Jafar, N. Jindal, and S. Vishwanath, “Capacitylimits of MIMO channels,” IEEE J. Sel. Areas. Commun., vol.21,no.5, pp.684–702, June 2003.

[5] S.J. Grant and J.K. Cavers, “Performance enhancement through jointdetection of cochannel signals using diversity arrays,” IEEE Trans.Commun., vol.48, no.8, pp.1038–1049, Aug. 1998.

[6] K. Wong, A. Paulraj, and R.D. Murch, “Efficient high-performancedecoding for overloaded MIMO antenna systems,” IEEE Trans.Wireless Commun., vol.6, no.5, pp.1833–1843, May 2007.

[7] N. Surajudeen-Bakinde, X. Zhu, J. Gao, and A.K. Nandi, “Improvedsignal detection approach using genetic algorithm for overloadedMIMO systems,” IEEE 4th Int. Conf. on Wireless Commun., Net-working and Mobile Computing, vol.2, pp.1–4, Oct. 2008.

[8] M. Sandell and J. Coon, “Per-subcarrier antenna selection withpower constraints in OFDM systems,” IEEE Trans. Wireless Com-mun., vol.8, no.2, pp.673–677, Feb. 2009.

[9] T. Yabe, M. Inamori, and Y. Sanada “Experimental investigation ofjoint decoding in overloaded MIMO-OFDM system,” IEICE Trans.Commun., vol.E96-B, no.12, pp.3101–3107, Dec. 2013.

[10] Y. Sanada, “Performance of joint maximum-likelihood decoding forblock coded signal streams in overloaded MIMO-OFDM system,”International Symposium on Intelligent Signal Processing and Com-munication Systems 2013, Nov. 2013.

[11] X. Wu, H.R. Sadjapour, and Z. Tian, “A new adaptive two-stagemaximum-likelihood decoding algorithm for linear block codes,”IEEE Trans. Commun., vol.53, no.6, pp.909–913, June 2005.

[12] A.J. Viterbi, “An intuitive justification and a simplified implemen-tation of the MAP decoder for convolutional codes,” IEEE J. Sel.Areas Commun., vol.16, no.2, pp.260–264, Feb. 1998.

[13] S. Verdu, Multiuser Detection, Cambridge University Press, 1998.[14] Joint Technical Committee of Committee T1 R1P1.4 and TIA

TR46.3.3/TR45.4.4 on Wireless Access, “Draft final report on RFchannel characterization,” Paper no.JTC(AIR)/94.01.17-238R4, Jan.1994.

Appendix: Number of Candidate Codewords

Table A· 1 Number of candidate codewords in Figs. 14–16.

Number of selected Normalized

candidate codewords computational

K1 K2 K3 K4 complexity

2 2 2 2 4.9×10−4

2 3 4 5 2.0×10−3

3 4 5 6 5.7×10−3

4 5 6 7 1.3×10−2

Yoshihito Doi was born in Wakayama,Japan in 1989. He received his B.E. degreein electronics engineering from Keio University,Japan in 2013. Since April 2013, he has been agraduate student in School of Integrated DesignEngineering, Graduate School of Science andTechnology, Keio University. His research inter-ests are mainly concentrated on MIMO-OFDMsystem.


Mamiko Inamori was born in Kagoshima,Japan in 1982. She received her B.E., M.E., andPh.D. degrees in electronics engineering fromKeio University, Japan in 2005, 2007, and 2009,respectively. Since October 2009, she has beenan assistant professor at Keio University. She re-ceived the Young Scientist Award from EricssonJapan in 2010. Her research interests are mainlyconcentrated on software defined radio.

Yukitoshi Sanada was born in Tokyo in1969. He received his B.E. degree in elec-trical engineering from Keio University, Yoko-hama, Japan, his M.A.Sc. degree in electri-cal engineering from the University of Victoria,B.C., Canada, and his Ph.D. degree in electricalengineering from Keio University, Yokohama,Japan, in 1992, 1995, and 1997, respectively. In1997 he joined the Faculty of Engineering, To-kyo Institute of Technology as a Research As-sociate. In 2000, he joined Advanced Telecom-

munication Laboratory, Sony Computer Science Laboratories, Inc, as anassociate researcher. In 2001, he joined the Faculty of Science and En-gineering, Keio University, where he is now a professor. He received theYoung Engineer Award from IEICE Japan in 1997. His current research in-terests are in software defined radio, cognitive radio, and OFDM systems.

paper complexity reduction in joint decoding of block...

Documents