Collaborative space-time spreading scheme for higher than unity rate CDMA downlink I. Shakya, F.H. Ali and E. Stipidis A novel scheme referred to as collaborative space-time spreading is proposed to provide a higher than unity rate with spatial diversity gain for the downlink of a CDMA system operating in a fading channel. This is achieved by performing collaborative coding and spreading over groups of T users, each of which is assigned a single orthogonal spreading sequence and followed by space-time encoding on the total composite signal of all groups. A user terminal simply despreads the incoming signal to recover the composite T-user group data and then extracts its intended data after space-time and collaborative decoding. Extensive comparisons with other relevant schemes are provided to show the superiority of this approach.

Introduction: A system that supports more users than the available sequences in an attempt to increase the sum rate beyond the unity rate capacity of fully orthogonal CDMA is termed as ‘overloaded’ or ‘oversaturated’ CDMA. For example, the schemes in [1, 2] allow user overloading and consider different transmission signal designs for single antenna base station and user terminals to minimise the impact of multiple access interference (MAI) to improve the overall signal-tointerference and noise ratio (SINR) performance. In the downlink of wireless systems operating in fading environments, owing to the size and power limitations mobile users cannot afford multiple antennas to achieve the spatial diversity. This problem can be effectively solved by employing multiple antennas at the base station using space-time transmission techniques. For example, an interesting scheme called space-time spreading is proposed in [3], that can offer full transmitter diversity for the downlink of non-overloaded CDMA. Supporting an overloaded system while providing high diversity gain is a significant challenge that has not been addressed in [1– 3]. In this Letter, an effective scheme referred to as collaborative space-time spreading (C-STS) that addresses these issues is proposed and analysed. Particularly, it employs a multiple access collaborative coding similar to that in [4, 5] to allow sharing of the same spreading sequence by more than one user and space-time coding over the total users’ composite signals at the base station and reverse operations at the receiver. System description: A system block diagram of the C-STS transmission and reception scheme is shown in Fig. 1. The total K users in the system is divided into G groups each of T users. Each user within a group is assigned a set of collaborative codewords. The same code can be reused for all G user groups since they are separable owing to the use of distinct orthogonal sequences. The combination of encoded group signals are spread using the group specific G orthogonal spreading sequences. The spread signals from all user groups are then summed to form a composite transmit signal S( j), 1  j  n to be transmitted from ith antenna where i [ f1, 2g. The signals S( j), 1  j  n are assumed to undergo two independent flat fading channels using the two antennas i [ f1, 2g. Note that two antenna cases are considered for simplicity and the scheme can be extended to more antennas if desired. A receiver first despreads the incoming signal rkl (t) and collects the resulting signal over two consecutive symbol periods to form soft estimates of the user’s data ykl( j) and ykl( j þ 1). These signals are then space-time combined to form the estimates of the composite codeword of kth user group, s^ k . Using the s^ k , the final estimate of the user’s transmitted data bkl is obtained using collaborative decoding and demapping of the codewords. g(1) k1

bkT

∑ encoder CT

{0 → 1} {1 → –1}

Sk

υκT

×

∑

rk1(j+1) +

× nk1

S S(j+1) S*(j)

g(1) kT g(2) kT

∫(.) yk1

ck

space-time decoding

collaborative decoding

>

g(2) k1

–S*(j+1)

υκ1 C k

bk1

sk

rkT(j) +

rkT(j+1) × nkT

ck

∫(.) ykT

space-time decoding

sk

collaborative decoding

>

bk1

{0 → 1} {1 → –1}

>

S(j) encoder C1

rk1(j)

>

collaborative space-time spreading

bkT

Fig. 1 System model of C-STS for kth group

Collaborative space-time spreading: At the base station, each user’s data bkl [ [1, 0] of period Tb is first encoded with one of Nl collaborative

codewords Cl [ W each of length n bits and BPSK mapped to form coded symbols vlj where W is the set of codewords of all T users. There are various multiple access collaborative codes that achieve a higher than unity sum rate such as the work in [4, 5] and references therein. In this Letter, we use a simple uniquely decodable collaborative code for the case of T ¼ 3 and n ¼ 2 as an example to illustrate the principle of the proposed technique. It should be noted that there are also codes with some additional error control capabilities that could be equally used though this is not within the scope of this Letter. The code used here gives the sum rate of Rsum ¼ STl¼1 log2 Nl/n ¼ 1.5 bits per channel use and all possible codeword combinations are shown in Table 1. The composite signal of the T users is given by sk ð jÞ ¼

T P

vkl ð jÞ; 1  j  n

ð1Þ

l¼1

The composite signals of all G groups are spread independently and summed to form the total composite via pffiffiffisignal S( j), to be transmitted p ffiffiffi the two antennas: Sð jÞ ¼ SG k¼1 ð1= 2Þsk ð jÞck ; 1  j  n, where 1= 2 is used for ensuring that the same power of single antenna transmission is used, ck is the common orthogonal sequence of the T users within kth pffiffiffiffi group with chip values 1= N ½1; þ1 of period Tc and the spreading factor is N ¼ Tb/Tc. The transmission scheme we propose here uses the well-known two-antenna Alamouti space-time block code, which can also be presented in a matrix form as follows:   Sð jÞ Sð j þ 1Þ S¼ S ð j þ 1Þ S ð jÞ where S denotes a complex conjugate of S. As can be noted, in the first row or the period, S( j) and S( j þ 1) are transmitted from antennas 1 and 2, respectively and in the second period, 2S ( j þ 1) and S ( j) are transmitted from antennas 1 and 2, respectively.

Table 1: Three-user uniquely decodable code (T ¼ 3, n ¼ 2) C1 þ C2 þ C3 C3

C1 (0 1) (0 1) (1 0) (1 0) C2 (0 0) (1 1) (0 0) (1 1)

(0 0) (1 0)

01 11

12 22

10 20

21 31

Channel model and receiver design: Without loss of generality klth user is chosen as the desired user. The received signal rkl (t) can be given by: rkl (t) ¼ gkl (t) S (t) þ nkl (t), where gkl (t) ¼ akl (t) e jfkl (t) is the channel gain assumed i.i.d. Rayleigh flat fading for each user with amplitude akl (t) and phase components fkl (t) remains constant over at least one codeword period of n and nkl (t) is the AWGN noise with variance N0. The rkl (t) is chip matched filtered within each symbol period to form a vector rkl. This is despread using the group sequence ck to obtain soft estimates ykl of the transmitted composite codeword: ykl ð jÞ ¼ rTkl ð jÞck ; ykl ð j þ 1Þ ¼ rTkl ð j þ 1Þck . Space-time combining: The signals ½ykl ð jÞ; ykl ð j þ 1Þ are sent to a combiner that uses space-time decoding to separate the multiple antenna signals. This ensures that the symbol level estimates of transmitted codewords from the two antennas are the maximum ratio combined by the following process s^ k ð jÞ ¼ ykl ð jÞfgklð1Þ g þ ykl ð j þ 1Þgklð2Þ ; s^ k ð j þ 1Þ ¼ ykl ð jÞfgklð2Þ g  ykl ð j þ 1Þgklð1Þ

ð2Þ

Collaborative decoding: The receiver performs joint detection of T-user group data and maximum likelihood decoding over a small number of codeword combinations to simultaneously provide the estimates of the desired user’s data b^ kl . The squared Euclidian distance of the spacetime combined signals s^ k ð jÞ; 1  j  n with each transmitted codeword ðqÞ 2 combination vðqÞ kl ð jÞ; 1  j  n is denoted as fdkl g . The distances are ð1Þ calculated by utilising the channel estimates g^ kl and g^ klð2Þ over the set of all possible q [ f1; Qg transmitted codeword combinations as shown in Table 1, given by fdklðqÞ g2 ¼

 T 2 n   P s^ k ð jÞ  {jg^ ð1Þ j2 þ jg^ ð2Þ j2 } p1ffiffiffi P vðqÞ ð jÞ  kl kl kl   2 j¼1 l¼1

ELECTRONICS LETTERS 22nd October 2009 Vol. 45 No. 22 Authorized licensed use limited to: UNIVERSITY OF SUSSEX. Downloaded on November 1, 2009 at 11:30 from IEEE Xplore. Restrictions apply.

ð3Þ

C^ kl ¼ arg

min

fC1ðqÞ ...;CTðqÞ g[W

fdklðqÞ g2

ð4Þ

Finally, the data decision b^ kl is obtained by demapping the codewords C^ kl to symbols as used in the transmitter. We made a reasonable assumption in (4) that each user has the knowledge of its own codewords and the Q allowable codeword combinations of Table 1. Note that the sum rate of the proposed scheme can be increased by employing higher dimensional constellation points. For example, a factor of two increase in the rate can be achieved by introducing the second dimension with the above processes performed independently on the two, i.e. in-phase and quadrature (IQ) dimensions, which is also referred to as ‘C-STSIQ’. It should also be noted that, though the MAI between groups is eliminated by the orthogonality of spreading sequences, the use of the same sequence by the T users generates self-interference owing to mutual projections of the users’ signals on each other. This has direct impact on the distance separation between the resulting composite single points used in the data decision-making process. It is a wellknown fact that the normalised distance measure averaged over all Q 2 possible data combinations or constellations points, d , determines the 2  average BER performance. Therefore, we will use d as one of the means to compare the performances of different schemes considered.

the ‘CMGO-STS (2 þ 4, 2)’ for the same Rsum ¼ 3 bits/s and user overloading ratio of K/N ¼ 3. This is because the ‘C-STS-IQ’ still employs a single sequence for T users rather than L sequences and hence the despreaders for L þ s users. In fact, the ‘CMGO-STS’ requires signal mapping to accommodate L þ s ¼ 6 users, leading to much tighter 2 packing of 2Lþs ¼ 64 signal points and a low d ’ 0:6 and higher data decision complexity. It also outperforms the ‘STS 8-PSK’ for the Rsum ¼ 3 bits/s. Finally, the performance of ‘OO-STS’ is shown under the Rsum ¼ 1.5 bits/s. As expected, the ‘C-STS’ largely outperforms the ‘OO-STS’ owing to group orthogonality and good distances between composite codewords. In Fig. 2 we plot the average BER against Eb/N0 of the ‘C-STS’ and ‘C-STS-IQ’ compared to that of ‘STS BPSK’ and ‘STS-QPSK’, respectively, to show the BER trends and how far apart their BER curves are. It can be seen that the ‘C-STS’ and ‘C-STS-IQ’ provide the sum rate gain of 0.5 and 1 bits, respectively, however at the cost of 2.2 dB, as expected. 100 C-STS-IQ (Rsum = 3 bits/s)

L

STS BPSK 1 STS QPSK 2 STS 8-PSK 2 C-STS 1 CMGO-STS (2 þ 1, 2) 2 OO-STS 1 C-STS-IQ 2 CMGO-STS (2 þ 4, 2) 2

Complexity Rsum SINR (dB) per decision K/N d¯ 2 (bits/s) 1 4 SNR 2 0 1.0 2 1 4 SNR 2 0 2.0 4 1 1.76 SNR 2 3.57 3.0 8 1.5 3 2.4 SNR 2 2.2 8 1.5 1.5 2.67 SNR 2 1.76 8 1.5 1.5 – 4.2 [1] 2 3 3 2.4 SNR 2 2.2 16 3 3 ’0.6 SNR 2 8 64

Performance results: A baseband model of a downlink of CDMA using Walsh Hadamard sequences of length N ¼ 128 with G ¼ N and power control to maintain the same average power level for each user is considered. Fully synchronous system and perfect channel estimation are assumed to assess the best achievable performance. However, in practice they can be estimated using, for example, known pilot sequences in the data streams and are the subjects for future investigations. For comparison purposes, we show the key performances of the proposed scheme ‘C-STS’ with the following: (a) the space-time spreading [3] ‘STS’ under different spectral efficiency, (b) space-time spread collaborative mapping group orthogonal scheme [2] ‘CMGOSTS’ employing the (L þ s, L) configuration, where L and s are the number of signal dimensions and additional users accommodated, respectively, and (c) the space-time spread ‘Random OO’ scheme [1] ‘OO-STS’. Table 2 shows the key measures to compare the performance of the schemes considered. Specifically, it shows measures such as the relative signal-to-noise ratio (SNR) loss compared with the single user BPSK bound, l, and required computational complexity for data decision from each composite signal. The l is calculated as 2 2 2 l ¼ 10 log10 fd 0 =d g dB where d 0 ¼ 4 for the BPSK signals. The output SINR (SINR) in relation to the input SNR (SNR) in dB is given by: SINR ¼ SNR 2 l. The ‘STS’ [3] employing BPSK denoted as 2 2 ‘STS BPSK’ is a fully orthogonal scheme with d ¼ d 0 ¼ 4, and hence its SINR ¼ SNR dB. Although the proposed ‘C-STS’ with L ¼ 2 1 has a lower d and SINR compared with ‘CMGO-STS (2 þ 1, 2)’ using the densest packing of constellation points for the sum rate Rsum ¼ 1.5 bits/s, the ‘C-STS-IQ’ with L ¼ 2 significantly outperforms

STS-QPSK (Rsum = 2 bits/s) STS-BPSK (Rsum = 1 bits/s)

10–2 10–3 10–4

Table 2: Performance comparison of C-STS with different STS based schemes for CDMA downlink Scheme

C-STS (Rsum = 1.5 bits/s)

10–1 average BER

The fdklðqÞ g2 are used for decoding so that one with the minimum distance is selected to give the transmitted set of codewords of the T users as follows

0

5

10 15 Eb/N0, dB

20

25

Fig. 2 BER of C-STS using Walsh-Hadamard sequences of length N ¼ 128 with G ¼ N groups and T ¼ 3 users

Conclusion: A collaborative space-time spreading scheme for high rate overloaded CDMA downlink in fading is proposed and analysed. Compared with other considered schemes, it shows a significant gain especially under higher rate owing to maintenance of good distances of the composite group data signals. For example, to achieve the same overloading ratio of K/N ¼ 3 and sum rate of Rsum ¼ 3 bits/s, it requires a much lower complexity receiver and 5.8 dB less SNR. Performance analysis of the scheme under dispersive multipath fading channel conditions is for future investigations. # The Institution of Engineering and Technology 2009 30 March 2009 doi: 10.1049/el.2009.0884 I. Shakya, F.H. Ali and E. Stipidis (Communications Research Group, School of Engineering and Design, University of Sussex, Brighton BN1 9QT, United Kingdom) E-mail: [email protected] References 1 Vanhaverbeke, F., and Moeneclaey, M.: ‘An improved overloading scheme for downlink CDMA’, EURASIP J. Appl. Signal Process., 2005, pp. 604 –610 2 Paavola, J., and Ipatov, V.: ‘Performance analysis of oversaturated collaboratively coded group orthogonal CDMA in AWGN channel’. IEEE PIMRC, Helsinki, Finland, September 2006, pp. 1 –6 3 Hochwald, B., et al.: ‘A transmitter diversity scheme for wideband CDMA systems based on space-time spreading’, IEEE J. Sel. Areas Commun., 2001, 19, pp. 48–60 4 Ali, F.H., and Soysa, S.: ‘Complex-valued collaborative coding multiple access for fading channels’, IEE Proc., Commun., 2001, 148, pp. 327– 332 5 Mattas, M., and Ostergard, P.R.J.: ‘A new bound for the zero-error capacity region of the two-user binary adder channel’, IEEE Trans. Inf. Theory, 2005, 51, pp. 3289– 3291

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