special section on coding and coding theory-based signal

3688IEICE TRANS. COMMUN., VOL.E95–B, NO.12 DECEMBER 2012

PAPER Special Section on Coding and Coding Theory-Based Signal Processing for Wireless Communications

Performance Evaluation of Joint MLD with Channel CodingInformation for Control Signals Using Cyclic Shift CDMAand Block Spread CDMA

Teruo KAWAMURA†a), Ryota TAKAHASHI††, Members, Hideyuki NUMATA††, Student Member,Nobuhiko MIKI†, and Mamoru SAWAHASHI††, Members

SUMMARY This paper presents joint maximum likelihood detection(MLD) using channel coding information for orthogonal code division mul-tiple access (CDMA) to decrease the required average received signal-to-noise power ratio (SNR) satisfying the target block error rate (BLER), andinvestigates the effect of joint MLD from the conventional coherent detec-tion associated with channel coding. In the paper, we assume the physi-cal uplink control channel (PUCCH) as specified in Release 8 Long-TermEvolution (LTE) by the 3rd Generation Partnership Project (3GPP) as theradio interface for the uplink control channel. First, we clarify the bestscheme for combining correlation signals in two frequency-hopped slotsand in two receiver diversity branches for joint MLD. Then, we show thatthe joint MLD without channel estimation, in which correlation signals arecombined in squared form, decreases the required average received SNRcompared to that for joint MLD with coherent combining of the correlationsignals using channel estimation. Second, we show the effectiveness ofjoint MLD in terms of the decrease in the required average received SNRcompared to the conventional coherent detection in various delay spreadchannels. Third, we present a comparison of the average BLER perfor-mance levels between cyclic shift (CS)-CDMA and block spread (BS)-CDMA using joint MLD. We show that when using joint MLD, BS-CDMAis superior to CS-CDMA due to a lower required received SNR in short de-lay spread environments and that in contrast, CS-CDMA provides a lowerrequired received SNR compared to BS-CDMA in long delay spread envi-ronments.key words: CDMA, cyclic shift, block spread, MLD, LTE

1. Introduction

Commercial service of the Long-Term Evolution (LTE)based on Release 8 (hereafter simply Rel. 8 LTE) by the3rd Generation Partnership Project (3GPP) [1] was recentlylaunched worldwide with high expectations for real broad-band mobile services. In channel bandwidths wider than5 MHz, which is the main focus of LTE, among transmis-sion bandwidths supported in LTE, multipath interference(MPI) impairs the achievable data rate and diminishes thecoverage. Thus, orthogonal frequency division multiple ac-cess (OFDMA) was adopted as the downlink radio accessscheme because of its inherent immunity to MPI due to alow symbol rate, the use of a cyclic prefix (CP), and its affin-ity to different transmission bandwidth arrangements. In the

Manuscript received April 24, 2012.Manuscript revised August 6, 2012.†The authors are with NTT DOCOMO, INC., Yokosuka-shi,

239-8536 Japan.††The authors are with the Department of Information Network

Engineering, Tokyo City University, Tokyo, 158-8557 Japan.a) E-mail: [email protected]

DOI: 10.1587/transcom.E95.B.3688

LTE uplink, single-carrier frequency division multiple ac-cess (SC-FDMA) using discrete Fourier transform (DFT)-precoded OFDMA was adopted for its prioritization of widearea coverage provisioning due to its low peak-to-averagepower ratio (PAPR) feature [2].

In the LTE, only packet-based radio access is sup-ported. Hence, all traffic types are carried by packet radioaccess including real-time type traffic with restrictive delayrequirements. Thus, in the downlink, key techniques are ap-plied to the shared data channel such as frequency and timedomain channel-dependent scheduling, adaptive modulationand coding (AMC) using QPSK, 16QAM, and 64QAM, andhybrid automatic repeat request (HARQ) with soft com-bining. To enable accurate operation of these techniquesin the downlink shared data channels, the channel qual-ity indicator (CQI) and acknowledgement (ACK)/negative-acknowledgement (NACK) information must be fed backto the base station (BS). In the 3GPP specifications, theuplink control channel called the physical uplink controlchannel (PUCCH) is defined to carry CQI and ACK/NACKinformation when a set of user equipment (UE) does notcarry data traffic at the same time [2]. In this paper, weaim to achieve high quality reception of the CQI informa-tion in the PUCCH. Multiple PUCCHs from different UEsare multiplexed using orthogonal code division multiple ac-cess (CDMA) within the same frequency-time block, i.e.,resource block (RB), in the same subframe [2]. For CQI in-formation, orthogonal CDMA is achieved using orthogonalsequences, which are generated by cyclic-shifting the orig-inal constant amplitude zero auto-correlation (CAZAC) se-quence [3], [4] (hereafter simply cyclic shift (CS)-CDMA).This is based on the fact that the cross-correlation is quitelow among cyclic shifted CAZAC sequences. However, itwas reported that orthogonality is destroyed due to increas-ing inter-code interference when the delay times of delayedpaths approach the cyclic shift interval [5]. Another or-thogonal CDMA scheme is block spread (BS)-CDMA [6],[7]. In the PUCCH carrying CQI information, BS-CDMAwas not adopted due to the smaller number of multiplexedPUCCHs per subframe compared to that for CS-CDMA, al-though it provides good performance.

This paper proposes joint maximum likelihood detec-tion (MLD) based on channel coding information (hereafterjoint MLD) for control signals, i.e., CQI information, for

Copyright c© 2012 The Institute of Electronics, Information and Communication Engineers

KAWAMURA et al.: PERFORMANCE EVALUATION OF JOINT MLD WITH CHANNEL CODING INFORMATION3689

CS-CDMA and BS-CDMA to decrease the required averagereceived signal-to-noise power ratio (SNR) satisfying thetarget block error rate (BLER). Then, we investigate the ef-fect of joint MLD from the conventional coherent detectionassociated with a channel decoder. Although the BLER per-formance using joint MLD in CS-CDMA was briefly givenin a technical paper in the 3GPP [8], the detailed config-uration of MLD was not given. Hence, the current paperdiffers from [8] from the following three viewpoints. In thePUCCH, intra-subframe frequency hopping (FH) is appliedto mitigate the influence of flat fading caused by a narrowtransmission bandwidth such as one RB with the bandwidthof 180 kHz. Moreover, use of two-branch antenna diversityreception at a BS is mandatory. The two frequency-hoppedslots and the two receiver branches experience different in-stantaneous fading characteristics. Hence, in joint MLD, thecorrelation signals of the two frequency-hopped slots and ofthe two-antenna diversity branches are combined to producethe final correlation signal for estimating the transmitted bitsequence using MLD. We first present the best combiningscheme for the correlation signals in the two frequency-hopped slots and in the two-antenna diversity branches forjoint MLD in CS-CDMA. We decide the best combiningscheme for the correlation signals in terms of the averageBLER performance from the trade-off relationship betweenthe effective suppression of the noise component and theinfluence from channel estimation (CE) error. Second, weshow the effectiveness of joint MLD in terms of the decreasein the required average received SNR compared to the con-ventional coherent detection in various delay spread chan-nels. Third, we compare the achievable BLER performancelevels between CS-CDMA and BS-CDMA using joint MLDcomprehensively in various delay spread environments toclarify the best orthogonal CDMA scheme considering jointMLD. The rest of the paper is organized as follows. Sec-tion 2 describes the PUCCH radio interface and multiplex-ing scheme in CS-CDMA and BS-CDMA. Then, in Sect. 3,among the configurations for joint MLD, we propose jointMLD without CE, in which four correlation signals are com-bined in squared form (hereafter, squared combing), andthat with coherent combing for the correlation signals us-ing decision-feedback channel estimation (DFCE). After thecomputer simulation conditions are given in Sect. 4, Sect. 5presents computer simulation results followed by our con-clusions.

2. PUCCH Multiplexing Using Orthogonal CDMA

In the Rel. 8 LTE uplink, SC-FDMA is adopted to achievea low PAPR, which leads to the provisioning of wider areacoverage. The minimum granularity for radio resource as-signment to one UE called a RB is a 12-subcarrier band-width, which corresponds to 180 kHz. The PUCCH is trans-mitted using one RB bandwidth since the number of con-trol bits is small. Hence, orthogonal CDMA is used formultiplexing multiple PUCCHs with one RB bandwidth.This is to prevent a reduction in the number of available

Fig. 1 Subframe structure of PUCCH.

cell-specific codes using a CAZAC sequence multipliedin the frequency domain. Moreover, orthogonal CDMA-based multiplexing achieves a larger randomization effectof the inter-cell interference compared to the narrower-bandFDMA-based multiplexing within the same RB. Hence,while maintaining one RB bandwidth, orthogonal CDMAis employed to achieve simultaneous PUCCH multiplexingof as many channels as possible. The number of RBs forthe PUCCH for CQI and ACK/NACK transmission can bere-configured according to the number of accessing UEs.

Figure 1 shows the PUCCH subframe structure as-sumed in the paper, which is based on the Rel. 8 LTE radiointerface [2]. One subframe comprises 2 time slots, eachof which is 0.5-msec long. One slot comprises seven SC-FDMA symbols, i.e., fast Fourier transform (FFT) blocks.One SC-FDMA symbol consists of an effective symbol partthat is 66.7-μsec long and a CP part that is 4.7-μsec long.In the PUCCH carrying CQI information, a reference signal(RS) is multiplexed at the 2nd and 6th SC-FDMA symbolpositions within each slot. Since the PUCCH is transmittedfrom one RB bandwidth, the achievable frequency diversitygain is reduced compared to the uplink shared data channelwith wider transmission bandwidth. Hence, intra-subframeFH is applied to achieve a high frequency diversity gain [2].In the paper, we assume that the entire reception bandwidthat a BS is 10 MHz for the uplink. Hence, intra-subframe FHis applied over a 9-MHz frequency separation.

• CS-CDMA for PUCCHIn the PUCCH, it was decided that cyclic shifted sequencesthat originate from the same CAZAC sequences should beused to multiplex PUCCHs carrying CQI information in thesame RB from different UEs [9]. Figure 2(a) illustratesthe principle of CS-CDMA. The Zadoff-Chu sequence [10],which belongs to the family of CAZAC sequences, with thesequence length of N (we assume N is an odd number), an(i)(i = 0, 1, . . . ,N − 1), is represented as

an(i) = exp

(− j2π nN

· i(i + 1)2

), (1)

where n denotes the sequence index, which is an arbitraryinteger that is relatively prime to N. The number of cyclic-shifted CAZAC sequences becomes NCS = �N/ΔCS � for theCS length of ΔCS . Parameter ΔCS is set to less than themaximum path delay time. The cyclic-shifted sequence forCS-CDMA, which is generated from the same CAZAC se-quence, an,k(i), is given in the following equation.

an,k(i) = an ({i + N − k · ΔCS } mod N) , (2)

where k (k = 0, 1, . . . ,K − 1) is the sequence index gener-


Fig. 2 Principle of orthogonal CDMA.

ated by the CS, where K is the number of multiplexed PUC-CHs (K ≤ NCS ). Using the cyclic-shifted sequence in (2),different UEs within the same cell use the same CAZACsequence with different cyclic-shift values, e.g., k1ΔCS andk2ΔCS in the figure, for each FFT block. Different CAZACsequences are used at different cell sites. The same modula-tion scheme is used within all samples in one FFT block tomaintain the orthogonality among the control signals. Thus,the modulation pattern among 10 FFT blocks over a 1-msecsubframe indicates the control signals. When the maximumpath delay time is much shorter than ΔCS , the cyclic-shiftedCAZAC sequence achieves orthogonality among simulta-neous accessing PUCCHs using the zero auto-correlationproperty. However, it was reported in [5] that when themaximum path delay time approaches the ΔCS value, therequired received SNR satisfying the target BLER increasesdue to the destruction of the orthogonality among the cyclic-shifted CAZAC sequences. In the figure, d(k)(v, j) representsthe j-th data symbol ( j = 0, 1, . . . , 4) of the v-th slot (v = 0,1) for the k-th PUCCH.

• BS-CDMA for PUCCHFigure 2(b) illustrates the principle of BS-CDMA. Thespreading factor (SF) is set to the number of SC-FDMAsymbols, i.e., FFT blocks, within one slot (denoted as NBS =

5). Let ck(i) = e2πik/NBS be the i-th code (i = 0, 1, . . . ,NBS −1) of the k-th BS sequence (k = 0, 1, . . . ,NBS − 1). Then,the j-th signal of the i-th FFT block for the k-th PUCCHis spread by the orthogonal sequence with the SF of 5 asck(i)d(k)(v, j). Hence, the number of PUCCHs multiplexedwithin one subframe by BS-CDMA corresponds to the num-ber of FFT blocks per slot, i.e., 5. Thus, the achievable num-ber of PUCCHs multiplexed into one subframe becomessmaller than that for CS-CDMA.

Assuming the subframe structure in Fig. 1, the numberof CQI bits is set to 10 both for CS-CDMA and BS-CDMAfor fair comparison. A tail-biting convolutional code with

the constraint length of three bits is used as the channel cod-ing scheme. In the Rel. 8 LTE radio interface, the Reed-Muller code is used for channel coding. It was reported in[11] and [12] that a tail-biting convolutional code achievesalmost the same BLER performance level as that for theReed-Muller code when the number of CQI bits is approxi-mately 10. Hence, the influence of the difference in channelcoding on the achievable performance of joint MLD is negli-gible. In CS-CDMA, 10 CQI bits are channel-encoded withthe coding rate of R = 1/2. Then, after modulation mappingwith QPSK, 10 QPSK data symbols are multiplexed into 10FFT blocks except for the 4 FFT blocks for RS symbolswithin 1 subframe. Meanwhile, 12 QPSK symbols can bemultiplexed into the duration of 1 slot in BS-CDMA. Hence,10 CQI bits are channel-encoded with the coding rate of R =5/24. Then, the 48 coded bits are modulated with QPSK and24 QPSK symbols are multiplexed into two slots belongingto 1 subframe. Thus, BS-CDMA achieves a higher chan-nel coding gain than CS-CDMA, although the number ofmultiplexed PUCCHs becomes smaller assuming the samenumber of CQI bits and subframe structure. In the evalua-tions, we assume that RS symbols of different PUCCHs aremultiplexed using CS-CDMA.

3. Joint MLD Using Channel Coding Information

3.1 Conventional Coherent Detection with Soft-DecisionViterbi Decoder

Figure 3 shows a block diagram of the conventional coherentdetection associated with the soft-decision Viterbi decoder[13] for the tail-biting convolutional code. At a receiver,two-branch antenna diversity reception is assumed. We as-sume ideal FFT timing detection. The received signal, rm(t)(t = 0, 1, . . . ,NFFT − 1), at the m-th receiver branch (m = 0,1) can be expressed as

rm(t) =L−1∑l=0

hm,l s(t − τl) + nm(t), (3)

where s(t) =√

2Es/Tsd(t) is the transmitted signal withE[|d(t)|2] = 1, where operation E[·] denotes the ensembleaverage. Terms Es and Ts represent the symbol energy andthe symbol duration, respectively, and nm(t) is the noisecomponent with zero mean and with variance of 2N0/Ts

(N0 is the one-sided power spectrum density of the addi-tive white Gaussian noise (AWGN)). Terms hm,l and τl are

the channel impulse response with∑ L−1

l=0 E[∣∣∣hm,l

∣∣∣2] = 1 andthe time delay of the l-th path (l = 0, 1, . . . , L − 1) at the m-th receiver branch, respectively (we assume identical timedelays for all paths at the two receiver branches). Let rm

= [rm(0), rm(1), . . . , rm(NFFT − 1)]T be the received signalblock at the m-th receiver branch. Operation [·]T denotes atranspose operation. It is given in matrix notation as

rm = hms + nm =

√2Es

Tshmd + nm, (4)


Fig. 3 Block diagram of conventional coherent detection with decoder.

where s = [s(0), s(1), . . . , s(NFFT − 1)]T is the transmit-ted signal vector, d = [d(0), d(1), . . . , d(NFFT − 1)]T isthe transmitted symbol vector, nm = [nm(0), nm(1), . . . ,nm(NFFT − 1)]T is the noise vector, and hm is the cir-culant matrix of channel impulse response with the sizeof NFFT × NFFT . The received signal block is trans-formed to the frequency domain signal vector, Rm =

[Rm(0),Rm(1), . . . ,Rm(NFFT − 1)]T by FFT and it is ex-pressed as

Rm = Frm =

√2Es

TsHm D + Nm, (5)

where Hm = FhmFH is the channel matrix in the fre-quency domain, D = Fd = [D(0),D(1), . . . ,D(NFFT − 1)]T

is the frequency domain signal vector, Nm = Fnm =

[Nm(0),Nm(1), . . . ,Nm(NFFT − 1)]T is the frequency domainnoise vector, F is the FFT matrix with the size NFFT ×NFFT ,and (·)H denotes the Hermitian transpose operation. The u-th frequency component, Rm(u), of Rm at the m-th receiverbranch is given as

Rm(u) =

√2Es

TsHm(u)D(u) + Nm(u), (6)

where Hm(u) =∑ L−1

l=0 hl,m exp(− j2πuτl/NFFT ), D(u) =(1/√

NFFT

)∑ NFFT−1t=0 d(t) exp(− j2πut/NFFT ), and Nm(u) =(

1/√

NFFT

)∑ NFFT−1t=0 nm(t) exp(− j2πut/NFFT ). In the fre-

quency domain, the frequency-hopped PUCCH, which ismapped at both ends of the entire transmission bandwidthwith one RB bandwidth each, is de-mapped. In CS-CDMA,each subcarrier component, Rm(u), is multiplied by thecorresponding cyclic-shifted CAZAC sequence in the fre-quency domain and despread, i.e., coherently averaged, overthe duration of NCS subcarriers to extract each PUCCH sig-nal to produce R(k)

m (u). In BS-CDMA, each symbol belong-ing to five SC-FDMA symbols is despread for each slot toproduce R(k)

m (u).The frequency domain channel response is estimated

using 2 RS symbols, i.e., the 2nd and 6th FFT blocks, ineach slot. Let H(k)

m,1(u) and H(k)m,5(u) represent the estimated

channel impulse responses using RS at the u-th frequencycomponent at the m-th receiver branch at the 2nd and 6thFFT block for the k-th PUCCH. They are generated by mul-tiplying the corresponding cyclic-shifted CAZAC sequenceto each subcarrier component. Then, the channel responseof each slot, H(k)

m (u), is computed as

H(k)m (u) =

112

11∑u′=0

H(k)m,1(u′) + H(k)

m,5(u′)

2. (7)

Using the estimated channel response, the linear minimummean square error (LMMSE) weight at the u-th frequencycomponent at the m-th receiver branch for the k-th PUCCH

can be given as W (k)m (u) = H(k)∗

m (u)/(∑ 1

m′=0

∣∣∣H(k)m′

∣∣∣2 + σ) [14].

It is assumed that the noise power for the LMMSE weightsis ideally estimated. Then, the u-th frequency component,R(k)(u), for the k-th PUCCH is obtained as

R(k)(u) =1∑

m=0

W (k)m (u)R(k)

m (u)

=

√2Es

TsH(k)(u)D(k)(u) + N(k)(u), (8)

where H(k)(u) =∑ 1

m=0W (k)m (u)H(k)

m (u) and N(k)(u) =∑ 1m=0W (k)

m (u)N(k)m (u) are the equivalent channel impulse re-

sponse and noise component after frequency domain equal-ization (FDE), respectively. Then, the inverse DFT (IDFT)converts the frequency domain signal into time domain se-quences, d(t) for BS-CDMA. From the soft symbol se-quence, d(t), we compute the squared Euclidian distance be-tween the received symbol after equalization and the sym-bol replica candidate using the estimated channel impulseresponse both for bit “0” and “1.” We compute the log like-lihood ratio (LLR) of a posteriori probability (APP) usingthe minimum squared Euclidian distances for bits “0” and“1” [15]. Finally, the LLR is soft-decision Viterbi decodedwith the tail-biting BCJR algorithm (A3) in [13] with 10iterations to recover the transmitted binary data. In the tail-biting convolutional code, the initial values for computingthe path metric in the forward and backward recursions atthe 1st iteration are set to equal the probability among allpossible states due to the lack of tail bits. Then, the initialvalues at the 2nd and later iterations are set to the last valuesof previous iterations for the decoder [13].

3.2 Joint MLD Using Channel Coding Information

Figure 4(a) shows a block diagram of the proposed jointMLD using channel coding information for CS-CDMA. Inthe figure, we omit FFT, subcarrier de-mapping, and so onand focus only on the joint MLD part. Let R(k)

m (v, j) be thedespread signal in the frequency domain for the j-th FFTblock ( j = 0, 1, . . . , 6) including the FFT block for the RSof the v-th slot received at the m-th receiver branch for thek-th PUCCH. Then, by despreading the received signal us-ing the corresponding cyclic-shifted CAZAC sequence foreach FFT block, the received symbol sequence is obtained.Let sq be the q-th set of the possible 10 CQI bits (q =0, 1, . . . , 210−1). From this set, symbol replica dq( j) is com-puted ( j = 0, 1, . . . , 13). Note that the dq( j) value is knownat a receiver for j = 1, 5, 8, and 12. The correlation betweenthe time domain signal at each slot for the k-th PUCCH atthe m-th receiver branch and symbol replica is computed for210 symbol replica candidates, d(k)

q (v, j), as

X(k)m, q(v, j) = R(k)

m (v, j) · d(k)q (v, j)∗, (9)


Fig. 4 Block diagram of Joint MLD.

where (·)∗ denotes the complex conjugate. In (9), the rela-tion for the parameters between j and (v, j) is j = 5 × v + jexcept for indices of j = 1, 5, 8, and 12, since these indicesrepresent RS symbols. In (9), we assume that the complexfading envelope, i.e., channel impulse response, is constantover the one-slot length, since the slot length is very short.The correlation between the time domain FFT blocks andsymbol estimate candidate at each slot and each receiverbranch is computed. Then, the correlation signals for thetwo frequency-hopped slots at the two receiver branches arecombined in squared form as

X(k)(q) =14

1∑m=0

1∑v=0

∣∣∣∣∣∣∣∣6∑

j=0

X(k)m, q(v, j)

∣∣∣∣∣∣∣∣2

. (10)

In (10), parameter q indicates the index of a codeword, i.e.,a set of 10 CQI bits among the 1024 combinations. In jointMLD, the maximum correlation in (10) to provide the mostprobable CQI bit set, s(k)

opt ={s(k)

qmax(0), s(k)

qmax(1), s(k)

qmax(2), . . .

}, is

computed without estimating the channel impulse responseas

qmax = arg maxq

X(k)(q). (11)

In squared combining, the four correlation signals are com-bined without the influence of CE error. However, the sup-pression effect of noise components included in the correla-tion signals is small.

In the joint MLD in (10), the correlation signals of thetwo frequency-hopped slots at the two receiver branches arecombined in squared form. Hence, the noise componentsare enhanced. Figure 5 illustrates the subframe structure ofPUCCH with intra-subframe FH again. As shown in thefigure, the frequency diversity is obtained by applying theFH between two slots within a subframe and the receiverdiversity is obtained by combining the received signals em-ploying two receiver antenna branches for each slot. Here,we consider the coherent combining of the four correlationsin the joint MLD, since coherent combining reduces the en-hancement of noise components compared to square com-bining. As will be appreciate from Fig. 5, however, accurate

Fig. 5 Subframe structure of PUCCH with intra-subframe FH.

CE is necessary to combine the four correlations, particu-larly between the two frequency-hopped slots. Therefore,we propose DFCE using decoded bits after the initial jointMLD to achieve accurate coherent combining for the fourcorrelations. Figure 4(b) shows a block diagram of jointMLD with coherent combining of correlations using DFCE.In the first iteration, the transmitted control bits are detectedusing the joint MLD. Then, the tentatively recovered bits arechannel-encoded using a tail-biting convolutional code andre-modulated using QPSK.

Let s(k)(v, j) be the estimated symbol replica at the j-th FFT block of the v-th slot for the k-th PUCCH. Heres(k)(v, j) is known for j = 1 and 5. By multiplying thecomplex conjugate of s(k)(v, j) to despread the symbol se-quence in the time domain, the channel impulse response atthe j-th FFT block at the m-th receiver branch, H(k)

m (v, j), iscomputed. The channel responses of seven FFT blocks in-cluding RS symbols within a slot are coherently averaged as

H(k)m (v) =

∑ 6j=0

�

H(k)

m (v, j) at the second iteration. Since thesignal energy of all symbols within a slot is used to computethe channel response, the CE error is significantly mitigated.By using the estimated channel impulse responses associ-ated with the two slots at the two receiver branches, the fourcorrelation signals are coherently combined as

�

X(k)

(q) =14

∣∣∣∣∣∣∣∣1∑

m=0

1∑v=0

⎡⎢⎢⎢⎢⎢⎢⎣6∑

j=0

X(k)m, q(v, j)

⎤⎥⎥⎥⎥⎥⎥⎦ H(k)m (v)∗

∣∣∣∣∣∣∣∣2

. (12)

Compared to (10), the noise components included in the cor-relation signals are efficiently eliminated for joint MLD in(12). The correlation in (12) still suffers from CE error, al-though it is reduced by the application of DFCE.

4. Computer Simulation Evaluations

Table 1 gives the link-level simulation parameters based onthe Rel. 8 LTE radio interface [2]. We used the GSM 6-pathTypical Urban (TU) [16] and ITU Vehicular-A (Veh.-A) [17]channel models (L = 6). The root mean square (r.m.s.) delayspread values for the GSM 6-path TU and Veh.-A channelmodels are τrms = 1.06 and 0.37 μsec, respectively. In or-der to investigate the BLER performance of joint MLD inlong delay spread environments, a six-path exponentially-decayed power delay profile model is also used. In thismodel, the average received signal power of each path isreduced by 1 dB from the first path and the τrms value is


Table 1 Simulation parameters.

parameterized by changing the delay time between contin-uous paths. We assume that each path follows independentRayleigh fading variation with the maximum Doppler fre-quency of fD = 5.55 Hz assuming pedestrian moving speedexcept for Fig. 12.

4.1 Investigations on the Best Joint MLD Structure

First, we compare the average BLER performance betweenjoint MLD with and without CE to determine the beststructure for joint MLD for CS-CDMA. Figure 6 showsthe mean-square error (MSE) of the DFCE based on hard-symbol estimation after the first iteration of the joint MLDas a function of the average received SNR per receiverbranch. The MSE is normalized by the amplitude of thetransmitted signal. The numbers of CSs and multiplexedPUCCHs are set to K = NCS = 6. We find that the MSE ofDFCE is clearly decreased compared to that for the CE us-ing RS only. Hence, we see that the CE accuracy for theDFCE significantly improves by employing the decision-feedback hard-decision symbols in addition to RS symbols.Figure 7 shows the average BLER performance for controlsignals using the joint MLD as a function of the averagereceived SNR per receiver branch for K = NCS = 6 in theGSM TU channel model. For coherent combining of thefour correlation signals for the respective slots and receiverdiversity branches, we employ a complex channel impulseresponse estimated using two RS symbols within a slot. Inthe figures, the squared combining and coherent combin-ing are represented as squared comb. and coh. comb., re-spectively. For comparison, the average BLER performancewith ideal CE for the coherent combining for the four cor-relations among the respective slots and receiver diversitybranches is also plotted in the figure. From Fig. 7, we findthat the achievable BLER performance using coherent com-bining for the correlations between two receiver branchesor/and between two frequency-hopped slots is degraded byapproximately 1 to 1.5 dB compared to that using squaredcombing for the correlations between two receiver branchesand between two frequency-hopped slots, i.e., without CE.Moreover, the figure shows that the influence of the CE errorfor two frequency-hopped slots on the BLER performanceis larger than that for two receiver branches. The reason for

Fig. 6 Mean-square error of channel estimation as a function of averagereceived SNR.

Fig. 7 Average BLER performance as a function of the average receivedSNR, coherent combining using RS based CE for GSM six-path TU model.

this is considered to be as follows. In the intra-subframeFH, the one coded symbol sequence belonging to the dif-ferent slots are received with low fading correlation due tothe sufficient FH separation as shown in Fig. 5. In mostcase, the difference of the correlation levels between the twofrequency-hopped slots is large. Hence, the large differenceof the correlation levels affects the BLER performance con-siderably. Therefore, it is considered that the influence ofthe CE error for coherently combining of the two correla-tions belonging to the different time slot on the achievableBLER performance is large. Meanwhile, the same signalis received at the two receiver antennas simultaneously inthe receiver diversity as shown in Fig. 5. Hence, the fluctu-ation in the combined correlation signals between the tworeceiver branches is not so large even if the fading correla-tion between the two receiver branches is low. Therefore,the influence of the CE error on the coherent combining ofthe two correlations between the two receiver branches be-comes smaller than that for the two frequency-hopped slots.The figure also shows that the coherent combining with idealCE further decreases the required average received SNR by


Fig. 8 Average BLER performance as a function of the average receivedSNR for coherent combining using DFCE.

approximately 1.5 dB compared to the squared combiningwithout CE due to the suppression effect of the noise com-ponents included in the correlation signals. However, evenwith coherent combining using the DFCE based on hard-symbol estimates after the initial iteration of the joint MLD,the required average received SNR is degraded by approxi-mately 1.5 dB from the coherent combining with ideal CE.As a result, the achieved BLER performance is almost thesame as that for the joint MLD using the squared combin-ing for the four correlation signals without CE in Figs. 8(a)and 8(b). That is, the joint MLD using the coherent combin-ing for the four correlations does not improve beyond thatusing the squared combing. Therefore, we conclude that injoint MLD using the channel coding information, squaredcombining without CE for the four correlation signals is thebest combing scheme between two receiver diversity andtwo frequency-hopping diversity branches.

4.2 Effect of Joint MLD for CS-CDMA and BS-CDMA

Figure 9 shows the average BLER performance using jointMLD and conventional coherent detection followed by the

Fig. 9 Average BLER performance using Joint MLD as a function of theaverage received SNR.

soft-decision Viterbi decoder as a function of the averagereceived SNR per receiver branch. For comparison, the av-erage BLER performance using the conventional coherentdetection with ideal CE in CS-CDMA is also plotted. Fig-ures 9(a) and 9(b) assume GSM TU and ITU Veh.-A chan-nel models, respectively. The numbers of CSs and PUC-CHs are set to K = NCS = 6 in CS-CDMA. The numberof PUCCHs, which corresponds to the SF, is set to K =NBS = 5 in BS-CDMA. From Fig. 9(a), we see that whenthe conventional coherent detection associated soft-decisionViterbi decoder is used, the required average received SNRat the average BLER of 10−2 using CS-CDMA is increasedby approximately 0.9 dB compared to that for BS-CDMA.This is due to the higher channel coding gain, i.e., the lowerchannel coding rate, in BS-CDMA assuming the same num-ber of CQI bits in the same subframe structure. By usingjoint MLD, the required average received SNR at the aver-age BLER of 10−2 for CS-CDMA is decreased by approxi-mately 1.6 dB compared to that for coherent detection. Ad-ditionally, even with ideal CE, the required received SNR forjoint MLD is decreased by approximately 1 dB compared tothat for the conventional coherent detection. Hence, we see


Fig. 10 Average BLER performance using Joint MLD as a function ofthe average received SNR considering an exponentially-decayed model.

that joint MLD is very effective in decreasing the requiredaverage received SNR. In BS-CDMA, the improvement inthe required average received SNR for joint MLD from thatfor the coherent detection is approximately 1.1 dB at most.This is explained as follows. The gain from joint MLD inBS-CDMA is small, since the impairment in the inter-codeorthogonality in the PUCCH is small due to a short sub-frame length. In contrast, joint MLD effectively suppressesthe increasing inter-code interference in CS-CDMA. The re-sultant loss in the required average received SNR of BS-CDMA from the CS-CDMA is reduced to approximately0.5 dB when joint MLD is used.

Figure 9(b) shows that the loss in the required aver-age received SNR in CS-CDMA compared to that for BS-CDMA is smaller. This is due to the lower level of inter-code interference caused by a smaller τrms value in theVeh.-A channel model than that for the TU channel model.Hence, when CS-CDMA or BS-CDMA is used, the requiredaverage received SNR at the average BLER of 10−2 em-ploying joint MLD is decreased by approximately 1.2 or1.0 dB, respectively, compared to those for coherent detec-tion. Moreover, the required average received SNR em-ploying joint MLD for CS-CDMA is decreased by approxi-mately 0.7 dB compared to that for coherent detection withideal CE. However, the improvement in the required aver-age received SNR by using joint MLD compared to that forcoherent detection in the Veh.-A channel model is almostidentical to that in the TU channel model.

To investigate the gains of joint MLD for the differ-ence in the delay spread values, we investigate the averageBLER performance assuming the six-path exponentially de-cayed power delay profile channel model. Figure 10 showsthe average BLER performance with CS-CDMA and BS-CDMA when τrms = 1.06 μsec, as a function of the aver-age received SNR. It is assumed that K = NCS = 6 for CS-CDMA and K = NBS = 5 for BS-CDMA. Figure 10 showsthat a large reduction gain in the required average receivedSNR is obtained using joint MLD compared to using coher-ent detection in CS-CDMA. More specifically, the required

Fig. 11 Required average received SNR at average BLER of 10−2 as afunction of τrms.

average received SNR at the average BLER of 10−2 usingjoint MLD is reduced by approximately 2.6 dB comparedto that for coherent detection. In contrast, the improvementin the required average received SNR using joint MLD be-comes smaller in BS-CDMA. Hence, the required averagereceived SNR at the average BLER of 10−2 with CS-CDMAbecomes almost identical to that for BS-CDMA when jointMLD is used for τrms = 1.06 μsec.

Figure 11 shows the required average received SNRsatisfying the average BLER of 10−2 as a function of ther.m.s. delay spread, τrms, for CS-CDMA. Figures 11(a) and11(b) assume K = NCS = 6 (ΔCS = 11.1 μsec) and 12 (ΔCS

= 5.5 μsec), respectively. In Fig. 11(a), the required averagereceived SNR using BS-CDMA is given as well assuming K= NBS = 5. The performance assuming one PUCCH (K = 1)is given as a reference without inter-code interference. Fig-ure 11(a) shows that when coherent detection is employed,the required average received SNR is significantly increasedaccording to the increase in the τrms value due to the increas-ing inter-code interference among simultaneous multiplexedPUCCHs. However, by using joint MLD, the increase in therequired average received SNR due to inter-code interfer-


ence particularly for a large τrms condition is suppressed toa low level. More specifically, the required average receivedSNR at the average BLER of 10−2 using joint MLD is de-creased by approximately 2.6 and 4.0 dB for τrms = 1.06 and1.59 μsec, respectively for CS-CDMA. When τrms is shorterthan approximately 1 μsec, joint MLD for K= 6 achieves alower required average received SNR compared to that forK = 1. Moreover, we find that the required average receivedSNR using BS-CDMA is reduced by approximately 1.3 dBcompared to that for CS-CDMA in the environment whereτrms is shorter than approximately 0.5 μsec. Hence, we seethat in a short delay spread environment, BS-CDMA is moreadvantageous than CS-CDMA from the viewpoint of the re-quired average received SNR when five-to-six PUCCHs aremultiplexed. According to the increase in the τrms value,however, the loss in the required average received SNR ofCS-CDMA compared to that for BS-CDMA is decreased.The required received SNR using joint MLD in CS-CDMAbecomes almost identical to that for BS-CDMA for the τrms

of approximately 1 μsec and that for BS-CDMA increasessignificantly when τrms is longer than approximately 1 μsec.In order to achieve orthogonal multiplexing among differentPUCCHs, BS-CDMA utilizes the block spreading over fiveFFT blocks, while CS-CDMA utilizes the cyclic shifting ofa sequence within only one FFT block. Therefore, sincethe influence of the loss of orthogonality due to a long delayspread is accumulated over 5 FFT blocks in BS-CDMA, andthe achievable BLER performance for BS-CDMA is drasti-cally degraded compared to that for CS-CDMA under longdelay spread conditions such as longer than τrms = 1 μsec.Moreover, in CS-CDMA the loss in the required averagereceived SNR using joint MLD from the K = 1 conditionis suppressed to within 0.2 dB when τrms is approximately1.5 μsec. Therefore, we see that the CS-CDMA using jointMLD is more effective in decreasing the required averagereceived SNR compared to BS-CDMA under long delayspread conditions such as longer than approximately τrms

= 1 μsec.Figure 11(b) shows that for K = 12, the required aver-

age received SNR at the average BLER of 10−2 using jointMLD is reduced by approximately 6.6 dB compared to thatfor coherent detection at τrms = 0.64 μsec. We see that thejoint MLD is very effective in decreasing the required av-erage received SNR that satisfies the target average BLERparticularly under a large K condition such as 12. Therefore,we conclude that in a short delay spread environment, BS-CDMA is more advantageous in multiplexing PUCCHs thanCS-CDMA due to the reduction in the required average re-ceived SNR. In contrast, the loss in the required average re-ceived SNR for CS-CDMA compared to that for BS-CDMAbecomes smaller when using joint MLD. Furthermore, CS-CDMA is more advantageous than BS-CDMA under longdelay spread conditions such as longer than approximatelyτrms = 1 μsec.

Figure 12 plots the average received SNR at the aver-age BLER of 10−2 as a function of the maximum Dopplerfrequency, fD. It is assumed that K = 6 and 5 for CS-CDMA

Fig. 12 Required average received SNR at average BLER of 10−2 as afunction of fD.

and BS-CDMA, respectively, when τrms = 1.06 μsec. Wefind that the joint MLD is more robust for fast channel vari-ation due to the increasing Doppler frequency than the co-herent detection. We see, moreover, that the required av-erage received SNR at the average BLER of 10−2 usingjoint MLD increases when fD is larger than approximately300 Hz. This is due to the increasing error of the computedcorrelation through coherent averaging over one-slot dura-tion caused by the amplitude and phase variation over theduration. However, we find even at a high fD value such as460 Hz, the required average received SNR of joint MLD isreduced by approximately 2.0 dB compared to that for co-herent detection. For BS-CDMA, the loss in the requiredaverage received SNR using joint MLD is suppressed to alow level for such a high fD value where fading variationappears over the one-slot duration. This is due to the appli-cation of orthogonal spreading over the duration of five FFTblocks.

Finally, we compare the computational complexity be-tween the conventional coherent detection and joint MLDfor CS-CDMA. Table 2 gives the required number of multi-plications and additions for the conventional coherent detec-tion and joint MLD. FFT processing for the entire receptionbandwidth at the BS is common for all UEs. Thus, we fo-cus only on UE-specific processing. In both schemes, thedespreading operation is necessary to derive the own signalfrom the multiplexed signal with CSs. In the conventionalcoherent detection, the channel estimation using the RSs,the generation of the LMMSE weight at each subcarriercomponent, and multiplication of the weight to each sub-carrier component are necessary. As we mentioned earlier,we used the Max-Log-MAP decoder as soft-decision Viterbidecoder. In joint MLD, the operations of the generation ofthe symbol replica candidates and that of the correlation cal-culations for the number of control bits are necessary. In-stead, the frequency domain equalizer and decoder for theconvolutional code are unnecessary.

In Table 3, we assume that one complex-value multi-plier corresponds to four real-value multipliers and two real-


Table 2 Required number of multiplications and additions for conven-tional coherent detection and joint MLD for CS-CDMA.

Table 3 Comparison of computational complexity between conventionalcoherent detection and joint MLD.

value adders, one complex-value adder corresponds to tworeal-value adders, one comparison corresponds to one real-value adder, and the ratio of computational complexity of areal multiplier to a real adder is 10:1. From the table, thecomputational complexity of joint MLD increases by ap-proximately 68 times compared to that for the conventionalcoherent detection associated with the Max-Log-MAP de-coder. This is because that the correlations are computedfor all the possible control bit sequences that correspond to210 in joint MLD. We consider, however, that the impact ofthe increase in the computational complexity is not neces-sarily large due to the following reasons. First, we considerthe application to the BS receiver. Hence, the restrictionson power consumption and circuit size due to the increasingcomplexity are not as rigid as that for the UE. Second, sincethe code block size is only approximately 10 bits, the com-putational complexity is smaller compared to that for theturbo decoder for the code block size of larger than a fewthousand bits and signal detection for MIMO multiplexing.

5. Conclusion

This paper proposed joint MLD schemes without and withCE using channel coding information for control signals

for CS-CDMA and BS-CDMA using the PUCCH radio in-terface. We clarified the best combining scheme for cor-relation signals between the two frequency-hopped slotsand between two receiver diversity branches in the jointMLD. According to the results, we showed that the jointMLD without CE is very effective in decreasing the requiredaverage received SNR at the target average BLER com-pared to the conventional coherent detection with the soft-decision Viterbi decoder. We also presented comparisonsof the average BLER performance levels of CS-CDMA andBS-CDMA using joint MLD. Computer simulation resultsshowed the following results.

• Even with the enhanced DFCE the BLER performance ofjoint MLD using coherent combining for the correlationsignals does not improve compared to that for squaredcombing for the correlation signals. Hence, we concludethat the squared combining of the correlation signals forfrequency-hopped slots and receiver diversity branches isthe most appropriate scheme based on the trade-off rela-tionship between the effective suppression of noise com-ponents and the elimination of CE error for joint MLD.• When 6 (12) PUCCHs are simultaneously multiplexed by

CS-CDMA, by applying joint MLD, the required aver-age received SNR at the average BLER of 10−2 is sig-nificantly decreased compared to that for the coherentdetection, and the loss in the required average receivedSNR from a one PUCCH case is suppressed to within 1(1.2) dB for the τrms value of less than 1.5 (0.5) μsec.• In the environments where the τrms is less than approx-

imately 0.5 μsec, the required average received SNR ofBS-CDMA is reduced by approximately 1.3 dB com-pared to that for CS-CDMA when joint MLD is used.However, the required received SNR using joint MLDin CS-CDMA becomes almost identical to that for BS-CDMA for the τrms of approximately 1 μsec. Moreover,CS-CDMA decreases the required average received SNRsignificantly compared to BS-CDMA under long delayspread conditions such as longer than approximately τrms

= 1 μsec.

References

[1] 3GPP, TS36.201 (V8.3.0), “E-UTRA; LTE physical layer —General description (Release 8),” March 2009.

[2] 3GPP, TS36.211 (V8.9.0), “E-UTRA; Physical channels and modu-lation (Release 8),” Dec. 2009.

[3] 3GPP, R1-050822, Texas Instruments, “On allocation of uplink pilotsub-channels in EUTRA SC-OFDMA,” Aug. 2005.

[4] T. Kawamura, Y. Kishiyama, K. Higuchi, and M. Sawahashi, “Or-thogonal pilot channel using combination of FDMA and CDMAin single-carrier FDMA-based Evolved UTRA uplink,” IEEEWCNC2007, pp.2403–2408, March 2007.

[5] T. Kawamura, Y. Kishiyama, K. Higuchi, and M. Sawahashi,“CDMA-based multiplexing scheme for multiple L1/L2 control sig-nals from different UEs in Evolved UTRA uplink,” WPMC2007,pp.903–907, Dec. 2007.

[6] S. Zhou, G.B. Giannakis, and C.L. Martret, “Chip-interleavedblock spread code division multiple access,” IEEE Trans. Commun.,vol.50, no.2, pp.235–248, Feb. 2002.


[7] X. Peng, K.-B. Png, Z. Lei, F. Chin, and C.C. Ko, “Blockspread IFDMA: An improved uplink transmission scheme,” IEEEPIMRC2007, Sept. 2007.

[8] 3GPP, R1-072705, Motorola, “Uplink CQI channel structure,” June2007.

[9] 3GPP, R1-062742, NTT DOCOMO, “CDM-based multiplexingmethod of multiple ACK/NACK and CQI for E-UTRA uplink,” Oct.2006.

[10] D.C. Chu, “Polyphase codes with good periodic correlation proper-ties,” IEEE Trans. Inf. Theory, vol.18, no.4, pp.531–532, July 1972.

[11] 3GPP R1-080096, Motorola, “CQI coding schemes,” Jan. 2008.[12] 3GPP R1-080531, Texas Instruments, “Details on block coding for

PUCCH,” Jan. 2008.[13] J.B. Anderson and S.M. Hladik, “Tailbiting MAP decoders,” IEEE

J. Sel. Areas Commun., vol.16, no.2, pp.297–302, Feb. 1998.[14] D. Falconer, S.L. Ariyavisitakul, A. Benyamin-Seeyar, and B.

Eidson, “Frequency domain equalization for single-carrier broad-band wireless systems,” IEEE Commun. Mag., vol.40, no.4, April2002.

[15] A. Stefanov and T. Duman, “Turbo coded modulation for wire-less communications with antenna diversity,” IEEE VTC’99-Fall,pp.1565–1569, Sept. 1999.

[16] 3GPP, TS45.005 (V7.3.0), “Radio transmission and reception,” Nov.2005.

[17] Recommendation ITU-R M.1225, “Guidelines for evaluation of ra-dio transmission technologies for IMT-2000,” 1997.

Teruo Kawamura received his B.E.and M.E. degrees from Hokkaido University,Sapporo, Japan in 1999 and 2001, respectively.In 2001, he joined NTT DOCOMO, INC. Sincejoining NTT DOCOMO, he has been engaged inthe research and development of chip equalizerfor HSDPA, radio interface of uplink data andcontrol channels for LTE and LTE-Advanced,and experimental evaluations for LTE and LTE-Advanced.

Ryota Takahashi received his B.E. andM.E. degrees from Musashi Institute of Tech-nology, Japan in 2008 and 2010, respectively.In the university, he was engaged in research onefficient detection of control signals for single-carrier FDMA. In 2010, he joined Fujitsu Lim-ited.

Hideyuki Numata received his B.E. degreefrom Musashi Institute of Technology, Japan in2011. Currently, he is a graduate student of theDepartment of Information Engineering, TokyoCity University. His research interest includesefficient detection of control signals for single-carrier FDMA.

Nobuhiko Miki received his B.E. and M.E.degrees from Kyoto University, Kyoto, Japan in1996 and 1998, respectively, and received hisDr. Eng. degree from Keio University, Yoko-hama, Japan in 2009. In 1998, he joined NTTMobile Communications Network, Inc. (nowNTT DOCOMO, INC.) His research interestsinclude mobile communication systems.

Mamoru Sawahashi received his B.S. andM.S. degrees from The University of Tokyo in1983 and 1985, respectively, and received hisDr. Eng. Degree from the Nara Institute of Tech-nology in 1998. In 1985, he joined the NTTElectrical Communications Laboratories, and in1992 he transferred to NTT Mobile Commu-nications Network, Inc. (now NTT DOCOMO,INC.). In NTT, he was engaged in the researchof modulation/demodulation techniques for mo-bile radio. He was also engaged in the research

and development of radio access technologies for W-CDMA mobile com-munications and broadband packet radio access technologies for 3G long-term evolution and for the systems beyond IMT-2000 in NTT DOCOMO.From April 2006, he assumed the position of Professor of the Depart-ment of Electronics and Communication Engineering, Musashi Instituteof Technology (now Tokyo City University). From 2007 to 2009, he wasa part-time director of the Radio Access Development Department of NTTDOCOMO. In 2005, 2006 and 2011, he served as a guest editor of theIEEE JSAC on Intelligent Services and Applications in Next-generationNetworks, 4G Wireless Systems, and Advances in Multicarrier CDMA,and Distributed Broadband Wireless Communications.

special section on coding and coding theory-based signal

Documents