ISSN 1751-8628

High user capacity collaborative code-division multiple access I.L. Shakya F.H. Ali E. Stipidis Communications Research Group, School of Engineering and Design, University of Sussex, Brighton, UK E-mail: [email protected]

Abstract: In this study, the authors propose a novel collaborative multi-user transmission and detection scheme for the uplink of code-division multiple access (CDMA) that exploits the differences between users’ fading channel signatures to increase the user capacity well beyond the spreading length in multiple access interference (MAI) limited environment. The authors show that it is possible to achieve this increase at a low complexity and high bit error rate (BER) performance in ﬂat fading channels, which is a major research challenge for overloaded CDMA systems. In this approach, instead of using one sequence per user as in conventional CDMA, the authors group a small number of users to share the same spreading sequence and enable group spreading and despreading operations. The proposed collaborative multi-user receiver consists of two stages: group multi-user detection (MUD) stage to suppress the MAI between the groups and a low complexity maximum-likelihood detection stage to recover jointly the co-spread users’ data using minimum Euclidean distance measure and users’ channel gain coefﬁcients. The scheme is investigated analytically and by extensive simulations and comparisons with conventional CDMA, overloaded CDMA using group pseudo-decorrelation (G-PD) and layered space – time (LAST) MUD. It is shown that the total number of full-rate users supported by the scheme is substantially higher than the available sequences. Moreover, it achieves much lower complexity and signiﬁcantly improved BER for the same user capacity compared with G-PD. It is also shown that, with antenna diversity reception, collaborative CDMA considerably outperforms LAST scheme, particularly when more transmit antennas per group than available receive antennas are employed.

1

Introduction

1.1 Background Code-division multiple access (CDMA) has been adopted as the multiple access scheme for the third generation cellular mobile systems because of it’s ﬂexibility in cell planning, support for different rate trafﬁcs, user capacity and robustness to multipath fading channel conditions. One of the most important aims of CDMA is to increase the number of simultaneous users (user capacity) with acceptable error performance. In the uplink of CDMA, where orthogonality among users is difﬁcult to maintain, conventional single-user receivers that ignore the multiple access interference (MAI) exhibit very poor detection performance. Multi-user detection (MUD) techniques [1 – 4], can potentially eliminate the detrimental effects of

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the MAI, leading to much improved detection performance and hence, the user capacity. It is, however, well known that the maximum number of users supported with many MUD techniques, for example, linear decorrelators [5] and decorrelating decision feedback detectors are usually less than the spreading length or the number of available spreading sequences. Although other MUD schemes such as maximum-likelihood (ML) and minimum mean squared error (MMSE) are not bound by this limitation, they are constrained by impractical complexity and heavy loss in signal-to-noise ratio (SNR) or sum rate, respectively, as the number of users increases beyond the spreading length [6]. In addition, it is shown, for example, in [7 –9] that with the use of high complexity advanced MUD techniques, more users than the number of the spreading sequences can be supported, but at the expense of considerable errorperformance degradation.

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www.ietdl.org The work in [7] proposes to reuse the available orthogonal spreading sequences for two sets of users where their spread signals are scrambled by two distinct random scrambling sequences. At the receiver side, a highly complex iterative multistage detection technique is used that detects the users signals in the ﬁrst set and then performs cancellation from the total signal to detect the users data in the second set. This approach has shown to support, for example, 12 additional users when using orthogonal sequences of length 64, amounting to an overloading ratio of about 120%. The work in [9] proposes group based MUD for an overloaded CDMA systems in additive white Gaussian noise (AWGN) channel where it is assumed that the users are assigned random phases and their spreading sequences are linearly dependant. To address the rank deﬁciency of crosscorrelation matrix that severely degrades the performances of conventional decorrelation, MMSE and decorrelating decision feedback techniques in such overloaded condition, new methods called ‘group pseudo-decorrelation’ (G-PD), ‘group MMSE detection’ and ‘pseudo-decorrelating decision feedback detection’, respectively, are proposed. However, these techniques still suffer from considerable loss in detection performance of the desired user because of residual MAI, not to mention the higher computational complexity demand compared with the conventional counterparts. Another approach for an overloaded CDMA in AWGN channel environment is investigated by Pavola and Ipatov in [10, 11], where the total users were divided into groups of a small number of T users, and each group is assigned U , T orthogonal spreading sequences giving an overloading ratio of 1 + (T 2 U )/U. To ensure separability of the composite group data, a form of collaborative coding of grouped users data is used. Their scheme was designed for a simple correlator receiver assuming that orthogonal spreading sequences are employed and tight synchronisation between all the users is maintained. Although synchronisation is easily maintained in the downlink, the scheme may not be applicable for the uplink where the MAI because of non-ideal cross-correlation of users renders simple correlator receivers ineffective. Earlier work investigating collaborative coding and decoding schemes for multiple access channels (MAC) without requiring subdivision in time, frequency or CDMA codes can be found, for example, in [12, 13]. These schemes rely on unique decodability feature of the composite signal of code words employed by the users for ensuring separability at the receiver. Also more recently, a group-based collaborative spreading CDMA (CS-CDMA) scheme for the downlink of synchronous CDMA is proposed by current authors in [14], which allows the sharing of the same orthogonal sequence by more than one user. At the transmitter side, each group of T users data are separately collaborative coded using unique decodable codes similar to that used in [12, 13] and summed, then a single orthogonal sequence is used for spreading each group composite signals. At each user’s receiver, two stages of 308 & The Institution of Engineering and Technology 2011

signal processing are employed. In the ﬁrst stage it employs simple correlator-based despreading to separate the user’s signal at the group level and an additional ML joint detection stage is used to separate the user’s own data from a group composite signal. Recently, multi-input multi-output (MIMO) based CDMA techniques, such as [15 – 17] employing both spatial and temporal signal processing were also investigated to improve user capacity as well as diversity. The work in [15], also referred to as layered space– time (LAST) MUD, proposes to group several users to share the same spreading sequence and employs multiple receive antennas and LAST based multiuser detection. Also, more recently, there has been an interesting work known as MIMO-SCDMA in [16] which shows improved BER and user capacity of CDMA uplink. It employs multiple antennas and space– time spreading at user terminals and base station receiver using single or multiple antennas and various combinations of linear MUD, for example, in [5, 18]. MIMO techniques are also investigated to improve only the spatial diversity gain for the uplink of CDMA. For example, the work in [17] assumes multiple antenna user terminals and base station receiver where the users employ space– time coding-based transmission and investigate various MUD combined with space– time decoding for users’ data estimation. Against this background, in this paper we propose a new approach to signiﬁcantly increase the user capacity of CDMA far beyond the number of available spreading sequences without using multiple antennas. Speciﬁcally, we employ group collaborative transmission of more than one user (T user) to share the same spreading sequence assuming independent channel fading magnitudes of the users within each group. Unlike the multiple antenna schemes in [15, 16], the proposed schemes achieves the high user capacity by utilising only single antennas both at user terminals and the base station receiver. In addition, we show that multiple receive antennas can also be employed in our scheme if desired, to further improve the link BER performance. Hence, our scheme is not limited, for example, by the condition that the number of receive antennas at the base station must be higher than the number of users in a group for ensuring full rank of LAST MUD detection as in [15]. That is, our scheme permits number of transmitters or spatial streams to be higher than the number of receive antennas, that is, antenna overloading is also supported. Our scheme is different from [10, 11] in that, it utilises the same that is, one rather than U . 1 sequences for T ≥ 2 users, which means that a much higher overloading ratio that is, K/N can be supported, for example, T compared to 1 + (T 2 U )/U. Compared with the recent work in [14], which relies on the use of multiple symbol length uniquely decodable multiple-access collaborative coding to allow multiple users to share the same sequence, the proposed IET Commun., 2011, Vol. 5, Iss. 3, pp. 307– 319 doi: 10.1049/iet-com.2010.0150

www.ietdl.org scheme does not require any such coding and hence, achieves a much higher sum rate. Speciﬁcally, the decodability/ separability of grouped users data is achieved by exploiting the users’ channel gain differences by calculating Euclidian distances for each possible transmitted data and selecting the one giving the minimum distance. This allows multiple users to transmit their independent data with full rate at the same symbol period, leading to sum rate increase by the factor of T which is much higher than 1.5 in [14]. Furthermore, unlike the scheme in [14], which is designed for fully synchronous and MAI free downlink systems, the proposed scheme is designed to tackle both MAI and co-channel interference (CCI) to ensure minimum loss of signal to noise ratio compared with single user bound. Hence, it is naturally applicable for asynchronous uplink of CDMA. The proposed receiver design consists of a group MUD stage, followed by ML detection stage to address the MAI at the group level and the CCI effects among the co-spread users, respectively, which is in contrast to the above work that uses a single ML detection stage only.

1.2 Contributions Our main focus in this paper is to increase the user capacity K far beyond the spreading factor N to maximise the system spectral efﬁciency with least possible complexity while utilising the same resources as in conventional single antenna CDMA uplink. In line with these objectives, speciﬁc contributions of this work are highlighted as follows: 1. Our scheme is designed speciﬁcally to achieve the high user overloading capacity K/N in a heavily MAI limited environment, where conventional detection techniques such as linear decorrelators simply fails to work because of the rank deﬁciency of cross-correlation matrix. Instead of treating each user of a system as an potential contributor of MAI as in conventional CDMA, here we group two or more that is, T users to share the same sequence so that their MAI contribution to other group is minimised. 2. To recover the users data under such an overloaded scenario, we propose a novel collaborative multiuser receiver which consists of despreading and linear decorrelation stages as in decorrelating MUD receiver but these are performed at the group level rather than per user to suppress the MAI between the groups. This is followed by additional ML joint detection stage to deal with CCI created by the use of same sequence within each group and recover the group users data exploiting the differences in fading channel gains because of spatial diversity. 3. On the practical side, we achieve considerable saving in computational complexity by the factor of T for the despreading and decorrelation operations, because these are performed only once per group rather than per user. Although the joint detection stage requires an additional ML search over all the possibilities of grouped T cochannel users data, since T is usually a small number, IET Commun., 2011, Vol. 5, Iss. 3, pp. 307– 319 doi: 10.1049/iet-com.2010.0150

T ¼ 2, 3, additional computational cost for this search is much smaller compared with the saving we achieve by performing the group despreading and decorrelation. Furthermore, we will also show that our approach while requiring much lower computational complexity compared with the G-PD based overloaded MUD scheme in [9], also offers signiﬁcantly improved BER to achieve the same user capacity. 4. We also investigate antenna diversity reception scenario with A ¼ 2 antennas as an example to show that, with the additional dimension provided by the antenna diversity, more efﬁcient grouping conﬁgurations can be formed to achieve much higher user overloading with further improved BER. Furthermore, we compare its performance with the LAST CDMA MUD scheme [15] for different group sizes T to conﬁrm its superior performance speciﬁcally under the rank deﬁcient MIMO channel condition for each group that is, A , T. 5. Quantitatively, with this new approach using only G spreading sequences, K ¼ GT full-rate users are shown to be supported at only small degradation in BER compared with conventional CDMA using the same multiuser detection method that supports G users only. We demonstrate that scheme can support, for example, an overloading ratio of 160% and still have better BER performance than that of the conventional CDMA loaded to 90%. We also show that the required computational complexity for this approach is still very low under the same target user capacity. The remainder of the paper is organised as follows. In Section 2, system model of the proposed collaborative CDMA is presented. Design of collaborative multiuser receiver is described in Section 3. Computational complexity and BER performance analyses are carried out in Section 4. Brief discussions on synchronisation and channel estimation are provided in Section 5. Section 6 presents theoretical and simulation results and comparisons with other relevant schemes. Finally the paper is concluded in Section 7.

2

System model

The system block diagram of a baseband model of the proposed collaborative CDMA for a fading MAC and AWGN is shown in Fig. 1. At the transmitter side, the total K users are divided into G groups, each consisting of T collaborating users. Each user within a group is assumed to use the same spreading sequence. The transmitted signal from each user skl , is given by skl =

Pkl ykl ck ,

1 ≤ k ≤ G, 1 ≤ l ≤ T

(1)

where Pkl is the signal power, ykl is binary phase shift keying (BPSK) mapped signal of the user’s data bkl of period Tb , c k is the spreading sequence used with rectangular chip pulses 309

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Figure 1 Proposed collaborative CDMA system block diagram √ (1/ N )[ −1, + 1], of period Tc giving the processing gain of N ¼ Tb/Tc . At the receiver’s end, the total received signal is chip matched-ﬁltered and sampled to form a received vector over the symbol period of N chips as: r = [r1 , r2 , . . . , rN ]T , where [.]T is a transpose operator, and is given by r=

T G l =1 k=1

hkl skl + w

(2)

where hkl is a channel gain of the klth user, w = [w1 , w2 , . . . , wN ]T is the AWGN vector with twosided power spectral density N0/2. The signals from all users are assumed to propagate via slowly varying and frequency ﬂat fading channels and remain constant over at least a symbol period. The channel gain can also be written as hkl = akl ejfkl

(3)

where hkl is modelled as independent and identically distributed (i.i.d.) complex Gaussian random variable with zero mean and unit variance that is, CN [0, 1], ∀k, l and consists of amplitude akl , that is, Rayleigh distributed and uniformly distributed phase component fkl . For better exposition of principles of this scheme, fully synchronised reception is assumed. In practice because of differences in users’ paths the system operates in asynchronous manner at the group level similar to conventional CDMA. However, the users within each group need to be synchronised to enable sharing of the same sequence. This can be achieved for example, by using a closed loop timing control algorithm such as the one proposed in [19], although at the cost of some additional complexity. For the modulation technique, BPSK is used for simplicity, however, higher order modulation, for example, M-ary phase shift keying (M-PSK) or M-ary quadrature 310 & The Institution of Engineering and Technology 2011

amplitude modulation (M-QAM) can also be used, where the usual SNR against bandwidth efﬁciency trade-off is applied. For the channel model used, the assumption of i.i.d. fading of users’ channels is satisﬁed in most practical wireless environments because of large enough spatial separation between the users, which is usually much higher than the minimum requirement of half the wavelength l/2, to ensure the independent fading [20]. It is also worth mentioning at this stage that the term ‘conventional CDMA’ used in this paper refers to the CDMA system that uses one sequence per user while using the same MUD technique as in our scheme. Speciﬁcally, in this paper a decorrelator MUD is used as a case to investigate and compare BER performance and computational complexity of different schemes considered. Decorrelator is a well-known MUD technique for MAI mitigation and used here owing to its simplicity in analysis.

3 Collaborative multiuser receiver design The proposed receiver is shown in Fig. 1. In this design, the MAI between groups is suppressed using a linear MUD on group basis, whereas the CCI owing to use of the same sequence by T users within a group is addressed using the ML joint detection stage. These processes are highlighted, ﬁrst for clarity and detailed next. 1. Group despreading stage: The wide-band received signal is despread separately for each group at every symbol period to obtain soft estimates zk , 1 ≤ k ≤ G of each composite signal. Therefore in a system with K ¼ GT users using random spreading sequences for example, the variance of MAI component at despreader output is only (G − 1)/N compared with (GT − 1)/N of conventional CDMA. 2. Group decorrelation stage: It employs a linear decorrelation operation [5] at the group despreaders’ outputs indicated in the ﬁgure by ‘R21’, which is used to remove the MAI component from zk , arising from the relative misalignment of groups and the use of non-orthogonal sequences. It IET Commun., 2011, Vol. 5, Iss. 3, pp. 307– 319 doi: 10.1049/iet-com.2010.0150

www.ietdl.org should be noted that other type of linear and non-linear multiuser detection techniques such as MMSE, decorrelating decision-feedback detectors as studied in [18] can also be employed here. These techniques can further improve the performance of our scheme as they can alleviate noise enhancement problem of the linear decorrelators. Also an improved decorrelator with reduced noise enhancement as proposed in [21] could also be investigated. 3. ML joint detection of T co-spread users stage: The estimates of each group’s composite data signal at decorrelator outputs ak , 1 ≤ k ≤ G, are used to provide ﬁnal estimates of grouped co-spread users’ data jointly by calculating the Euclidean distance for each possible transmitted data vector. This allows good separation of the users’ data while ensuring minimal performance degradation from their mutual CCI.

3.1 Group despreading Without any loss of generality we assume that klth user is the desired user. The received signal r is ﬁrst despread by using group spreading sequences ck , 1 ≤ k ≤ G to form a vector of output signals z = [z1 , z2 , . . . , zG ]T , which can also be written in a matrix form as follows z = Rh + w

(4)

where R is the cross-correlation matrix of dimension G × G formed by the spreading sequences with each element rku = cTk c u , k = 1, 2, . . . G; u = 1, 2, . . . G and w= [w1 , w2 , . . . , wG ]T is the correlated noise vector with variance s2n and covariance matrix N0 R and h = [h1 , h2 , . . . hG ]T is a vector consisting of products of users’ data and channels. It can be noted in (4) that, although there are GT users in the system, the size of noise vector is only G × 1. The h shown in (4), is obtained from the matrix of all users’ data and channels H , which can be shown as follows ⎡

h11 y11 ⎢ h21 y21 ⎢ ⎢ . ⎢ .. ⎢ H =⎢ ⎢ hk1 yk1 ⎢ ⎢ .. ⎣ . hG1 yG1

h12 y12 h22 y22 .. . hk2 yk2 .. . hG2 yG2

... ... .. . ... .. . ...

h1l y1l h2l y2l .. . hkl ykl .. . hGl yGl

... ... .. . ... .. . ...

h1T y1T h2T y2T .. . hkT ykT .. . hGT yGT

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

where rows contain the signals of each group of T co-spread users’ independent data multiplied by their corresponding channels. Since we assigned the same spreading sequence for each group of T users, the elements in each row of H form group composite signals hk , hence the matrix H is reduced to a vector h in (4). This arrangement, as will be shown in Section 4, also leads to signiﬁcant savings in required computation complexity of the proposed receiver. The composite signal for kth group consisting of the T IET Commun., 2011, Vol. 5, Iss. 3, pp. 307– 319 doi: 10.1049/iet-com.2010.0150

users’ data and channels can also be given by hk =

T l =1

hkl ykl

(5)

3.2 Group decorrelation It is well known that in a practical system where MAI exists because of non-orthogonal nature of users received signals, the output signal vector z obtained from conventional matched ﬁltering based despreading does not provide good estimate of the users’ data, specially under high loading conditions as MAI becomes the dominant source of disturbance. Therefore a group decorrelation stage is employed in the proposed receiver to remove the effects of MAI. This is achieved by multiplying z with inverse of the cross correlation matrix R21. The decorrelator output signal vector a, can be shown as follows a = R−1 [Rh + w] = h + R−1 w

(6)

As can be seen, the vector a is free from MAI; however, it suffers from the noise-enhancement problem that scales linearly with increase in number of users because of the diagonal elements of R21 being higher than unity [1, 5]. From (6) it can be observed that the variance of the decorrelator noise terms that are deﬁned by Dec Dec T are now greater wDec = R−1 w = [wDec 1 , w2 , . . . , wG ] than that of original AWGN noise w. This ampliﬁcation of noise by the decorrelator causes degradation in output SNR specially when loading of sequences is high, that is, when G/N − 1. Note that the group decorrelation method as shown in (6) removes MAI or cross-correlation contaminated signals from all the GT users with its linear matrix inversion operation. Therefore our scheme does very efﬁcient utilisation of the decorrelation method by reusing each operation for group of users rather than for each user that also leads to signiﬁcant reduction in complexity required per user. The Gaussian assumption of residual noise and any multiple user interference signals at the output of this stage usually leads to more accurate performance analysis compared with that of the despreader output as noted in [1] and will be used later for the BER analysis of our scheme. Individual elements of the vector a = [a1 , a2 , . . . aG ]T are then sent to bank of G ML joint detectors to estimate the data of T co-spread users’ for all groups. For the purpose of analysis, the signal ak can also be modelled as the sum of constituent users’ signals and a noise term as follows ak =

T l =1

hkl ykl + hk

(7)

+ Tl=1 ekl is the total noise, which consists where hk = wDec k and sum of possible channel of decorrelator noise wDec k 311

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www.ietdl.org estimation error signals ekl , 1 ≤ l ≤ T that is uncorrelated with the channel itself. To perform detection of composite symbol, channel of each user has to be estimated from the received signal. In this work, we do not use a speciﬁc channel estimation method, but employ a simple yet very effective channel model with estimation error and any residual signals assumed to be zero mean complex additive Gaussian noise. Using this model the channel estimate of klth user, hˆ kl is given by hˆ kl = hkl + ekl

(8)

(q)

2

where ekl is the estimation error signal with variance s (e). Following this model, perfect channel estimation condition corresponds to the case when s2(e) ¼ 0. The reader is referred to Section 5 for more discussion on synchronisation and channel estimation.

3.3 ML joint detection of T co-spread users With channel estimates available, the joint detection stage requires calculation of the maximum a posteriori probabilities (MAP) for all possible transmitted data vectors. The detector provides the ﬁnal estimates of users’ data by selecting the vector which has the maximum probability. For data signalling scheme with equal probability of occurrence for all possible vectors, the process is simpliﬁed and receiver makes decision based on the ML criterion based upon the minimum squared Euclidean distance measure. With T co-channel users each employing M-ary modulated data symbols, there are L ¼ M T possible composite data combinations to search. The squared Euclidean distance for each, that is, q [ {1, 2, . . ., L} possible transmitted data combination or vector for the kth group is calculated as follows 2 T (q) 2 (q) ˆ hkl yl , = ak − dk l=1

with the users are hk1 ¼ 0.5 + 0.0j and hk2 ¼ 0.7 2 0.0j, respectively. It is clear from Section 3.2 that the group decorrelator completely removes MAI at group level at the cost of some enhancement of AWGN noise. This leaves the ML joint detection stage to deal with the composite signal ak = hk1 y1 + hk2 y2 + hk consisting of the two users’ data weighted by their own channels and the noise term. Assume that the estimates of channel gains hˆ k2 and hˆ k2 are perfect and that the proposed scheme operates in high SNR region so that the noise term can be considered negligible. Now the task of the joint detector is to obtain estimate of the users’ data, yˆ 1 and yˆ 2 from the composite signal ak ¼ 1.2 + 0.0j. The detector calculates distances,

1≤q≤L

(9)

(q)

Based on the set of calculated distances {dk }2 , 1 ≤ q ≤ L, the detector obtains the ﬁnal estimates of transmitted (2) (T ) group data as the vector bq = [b(1) q , bq . . . , bq ] which yields the minimum of squared Euclidian distances (q) 2 bˆ k = arg min dk bq [B

(10)

where bˆ k is obtained from all the possibilities for users within the kth group bq [ {B : [b1 , b2 , . . . , bL ]}.

Example: Let us assume that there are T ¼ 2 users with

their individual BPSK (M ¼ 2) modulated data y1 = −1 and y2 = +1, respectively, sharing the same spreading sequence ck and that the fading channel gain associated 312 & The Institution of Engineering and Technology 2011

{dk }2 given in (9) for each of L ¼ M T ¼ 4 possible combination of the users’ data that is, [+1, +1], [+1, 21], [21, +1] and [21, 21] giving distances of 1.0, 0.16, 0.0 and 1.96, respectively. Based on the list of distances, the detector selects the data combination with minimum distance that is, [21, +1], as the ﬁnal estimates of the users’ data. It should be noted that the joint detector is able to distinguish users’ data when the channel gains hk1 and hk2 are not too similar; when they are, for example, because of the channel fading correlation or error in channel estimation processes, there may be more than one case of minimum distance to select from, resulting in detection ambiguity. However, in real world mobile wireless channel environments with geographically separated users, probability of channels being too similar is very small indeed. This assumption is valid for many practical schemes found in the literature, for example [15, 16, 20]. This dissimilar or uncorrelated channel fading gains of individual users in wireless environments is exploited in the proposed scheme to signiﬁcantly increase the number of users.

4

Performance analysis

4.1 Computational complexity The proposed group-based collaborative CDMA approach, compared with conventional CDMA that uses one sequence per user, requires only an additional ML joint detection stage for T co-spread users. This is because the group despreading and decorrelation operations involve the same amount of complexity as the despreading and decorrelation operations of the conventional CDMA. Although the joint detection stage requires ML search over L ¼ M T possible combinations of data vectors for each group of T users, since both M and T are usually small numbers, for example, 2 – 4, the complexity for this search is still low compared with the standard CDMA despreading and decorrelation operations performed over the spreading length N as {M, T } ≪ N . Assuming that random sequences are used, the overall computational complexities required for different receivers are shown in Table 1. The complexity required for the proposed receiver to support K ¼ G × T users can be obtained as: O[GN + G 2 N + GM T ] ﬂoating point operations (FLOPs) IET Commun., 2011, Vol. 5, Iss. 3, pp. 307– 319 doi: 10.1049/iet-com.2010.0150

www.ietdl.org Table 1 Approximate computational requirement for the CDMA MUD schemes to support K ¼ G × T users Schemes

Required spreading factor, N

Total complexity, FLOPs

proposed collaborative CDMA multiuser receiver

N≥G

GN + G 2N + GM T

conventional CDMA using a decorrelator

N ≥ GT

GTN + (GT)2 N + GTM

CDMA MUD scheme in [6] using a G-PD

N≤K

(K/|G|) {M|G| |G|4 K 4 N6 (K − |G|)4 } + {M|G| (K − |G|)2 N2 |G|3

LAST CDMA MUD scheme in [15]

N≥G

2K 4 + 2K 3 + (N + 2)K 2 + KN

per symbol decision. In contrast, for the same number of K ¼ G × T users, the conventional CDMA will require O[GTN + (GT )2 N + GTM] FLOPs. The FLOP counts are taken for the number of complex multiplications required for the despreading, decorrelation, and ﬁnal symbol decision operations, respectively. Looking at Table 1, it can be also be noted that the proposed scheme actually requires much lower spreading factor and hence lower computational complexity to support the same K ¼ G × T users compared with the conventional CDMA. For example, even when sequences of same spreading factor N ¼ 31 are used to achieve the user capacity of K ¼ 15 × 2 ¼ 30 users, it only requires 7.5 × 103 FLOPs compared with 28.9 × 1023. Also, the proposed receiver scheme has much lower complexity compared with the MUD scheme for overloaded CDMA in [9]. The computational complexity of this scheme using a G-PD technique based on its system parameters is also included in Table 1. For this scheme, the complexity is calculated for the G-PD detection operation obtained from equation (8) of [9] where |G| is the group size used for the G-PD detector. The reader is referred to this reference for more details on the decision rule and deﬁnition of speciﬁc parameters. It can be clearly seen from the table that the proposed scheme is much less complex than the scheme in [9], complexity of which increases much faster with N. Finally, the table also shows the computational complexity required for the LAST CDMA MUD scheme in [15] where each sequence is reused by group of T users similar to our scheme, but requires A ≥ T antennas at the receiver to be able to detect users’ data satisfactorily. The total complexity for our scheme that uses A antennas can be calculated as: A{GN + G 2 N } + GM T . It can be noted from the table that the complexity of the LAST CDMA receiver increases in fourth power of the number of users K, which, even for small K becomes signiﬁcantly higher than that of the proposed collaborative multiuser receiver with A antennas. Note that we have assumed that long random sequences are used in the calculation of computational complexity, which necessiates updating of inverse of the matrix R21 IET Commun., 2011, Vol. 5, Iss. 3, pp. 307– 319 doi: 10.1049/iet-com.2010.0150

every symbol for the linear MUD stage. When symbol length sequences such as short Gold sequences are employed, the R21 can be computed during the ﬁrst symbol period and stored in memory to be used for the detection of subsequent symbols [1, 2]. Although both types of sequences have their own merits and disadvantages in terms of system performance and complexity [2], the use of short sequences is found to be attractive for a low complexity linear MUD implementation for the uplink of CDMA, investigated, for example, in [22]. In practice, deployment of decorrelation based detectors may complicate the system design because of dynamic nature of data trafﬁc in the system arising from random arrival and departure of users’ calls. This process can be modelled using Markov chain having K states for K active users as in [23, 24]. Since the proposed scheme supports K users with only G ¼ K/T sequences, each entry and exit of a user k [ [1, K ], may not prompt for an update of crosscorrelation matrix R[G×G] at the decorrelation stage. If we assume, for example, that in average K ≥ 3G/2 users are active, then it is highly likely that any newly entering user is accommodated without requiring to update the matrix R because G sequences are almost always occupied by previous users and any additional user can be assigned a sequence occupied by one of the earliest connected users. Therefore our group-based collaborative CDMA is less sensitive to the dynamic channel access environment of users compared with conventional CDMA using a decorrelator. The design of dynamic call admission control protocol for optimisation of the proposed system’s performance and complexity similar to the one proposed in [25] for 3G/4G CDMA is an interesting topic for research. This however, is beyond the scope of this paper and is left for future study.

4.2 BER performance In this section, we derive BER expression for the proposed scheme in Rayleigh ﬂat fading channel environment. Since combined decorrelator output noise and AWGN signals are Gaussian distributed [1], the probability of bit error of a user conditioned on channel fading realisation hkl given by Pe(ykl |hkl ), can be obtained from the output signal to 313

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www.ietdl.org interference plus noise ratio (SINR) Gkl for each time instance as follows Pe(ykl |hkl ) = Q Gkl

2

(11)

√ 1 2 where Q(x) = (1/ 2p) x e−t /2 dt is a standard Gaussian error integral function. The average error probability, Pe (ykl ), is then obtained by calculating (11) over all instances of fading distribution of the klth user by utilising the Gkl , which is given by 1 Pe (ykl ) =

0

Pe (ykl |hkl )p(Gkl ) dGkl

(12)

where p(Gkl ) is the probability density function of SINR distribution based on fading channel magnitude of the klth user. To obtain SINR at the ﬁnal detector, that is, Gkl , ﬁrst the SINR has to be calculated at the group level. The group level SINR at the output of the decorrelator for all the users within the kth group Gk , can be obtained from the single user SNR that is without any MAI or additional noise, G0 , which for the klth user can be given by G0 = E{a2kl }/N0 . Using G0 , the SINR for the user at the group level, Gk , can be obtained by utilising the method proposed in [1] as follows (ak /T )2 2 T −1 = (ak /T ) G0 (1 − f k Rk f k ) Gk = var(ak /T )

(13)

where fk is the kth column of R without the diagonal element and Rk is obtained from R by discarding from it the elements of the kth row and column. Note that when, for example, long random or pseudo-noise (PN) sequences are employed instead of symbol length sequences as it was assumed in will consist of random rather than ﬁxed cross (13), the R21 k correlation values during each symbol period. Therefore statistical average rather ﬁxed cross correlation values should be used for the performance analyses of such systems. Final BER for the klth user at the output of the ML joint detector stage can be obtained using the BER obtained at the output of the decorrelator using the SINR in (13), where loss of the desired user’s power because of presence of other T 2 1 co-spread users in the same group has to be considered. For this purpose, a simple measure called average squared error 2 distance per bit d , that is obtained by averaging over all L possible composite symbols, is used here. This is done by calculating distances {de(q) }2x , corresponding to each of the L 2 1 error symbols for each signal point representing the T users’ data. This process is repeated for all L possible 2 signal points and the ﬁnal average value d , is obtained as follows L 2

d =

L−1

q=1

x=1

E{de(q) }2x

TL(L − 1)

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2 where E{d (q) e }x is the expected distance, that is obtained by 2 collecting {d (q) e }x for each symbol period and averaging over

(14)

all channel fading realisations. The d value is used to calculate the relative SNR loss l in dB compared with fully 2 2 2 orthogonal signalling: l = 10 log {d 0 /d } dB, where d 0 = 4 2 for BPSK modulated signals. The distance measure, d , can also be used along with the average SINR at the decorrelator output to obtain an approximate probability of error for a user. Averaging Pe(ykl |hkl ) over all the fading distribution gives the average probability of error Pe(ykl ). For the proposed scheme this can be obtained simply by modifying the standard BPSK probability of error formula by substituting the single user SNR G0 , by the average 2

2

SINR Gk , and weighting it by the ratio d /d 0 . This is because using group decorrelation and the ML joint detection stages, we have effectively decoupled the MAI and CCI effects and made our receiver analogous to a single user detector but obviously with some loss in the desired user’s signal power as discussed above. The modiﬁed BER formula is given as follows ⎤ ⎡ (d 2 /d 2 )G 1⎣ 0 k ⎦ 1− Pe(ykl ) ≃ 2 2 2 1 + (d /d )G 0

(15)

k

where Gk is the average of all SINR values Gk corresponding to each channel fading amplitude of the desired user in the kth group.

5 Synchronisation and channel estimation Although the focus of this paper is design of transmission and detection techniques for improved user capacity and performance analysis while simplifying assumptions of perfect synchronisation and channel estimation, it is important to consider the effects of these practical issues on the system performance. These issues are brieﬂy discussed next.

Synchronisation: In the proposed scheme, similar to conventional CDMA initial spreading code acquisition or coarse delay estimation of a user can be achieved by correlating the incoming signal with locally generated copy of a spreading sequence. This process allows for the delay estimation within a chip interval by exploiting the good autocorrelation property of the sequences used. There are different code acquisition schemes investigated for the uplink of CDMA for both AWGN and fading channel environments, for example [2, 26]. To allow more than one user to simultaneously access the same channel, each cospread user has to periodically insert a known orthogonal pilot sequence in its data stream similar to one investigated, for example, in [27] so that the interference effects of other co-spread users will be minimised. The acquisition process will then be accompanied by code tracking to ﬁne tune the delay estimate within a small fraction of a chip period [2]. IET Commun., 2011, Vol. 5, Iss. 3, pp. 307– 319 doi: 10.1049/iet-com.2010.0150

www.ietdl.org It has to be stressed here that imperfect delay estimation can severely effect the performance of linear MUD methods as noted in [28]. Therefore for the purpose of investigating this issue, we model the delay estimation error signal as complex Gaussian random variable with standard deviation in fraction of chip period similar to the work in [18] and show its impact on the performance of the proposed system.

Channel estimation: Channel estimation in CDMA uplink is usually obtained after MAI suppression at the output of MUD [18] and with the use of periodically inserted pilot sequences in the data stream [27, 29]. The quality of channel estimation is usually dependent on system parameters such as user loading factor, types of spreading sequences used, pilot to data power ratio and type of MUDs used [4, 18]. In the proposed scheme, channel estimation of each group of T co-spread users is required for the ML joint detection stage. This can be achieved by assigning separate orthogonal pilot data sequences within the data streams of each of T users using for example the method used in [27] so that CCI from other users to the desired user is minimised. The estimate of the desired user’s channel can then be obtained by multiplying the group decorrelator’s output signal with the user speciﬁc orthogonal pilot sequence, summing of the products and averaging over ⌈T⌉ consecutive samples, where ⌈T⌉ is a ceiling operator for rounding towards the nearest larger number that is integer power of 2. Once the channel estimates of the T users are obtained, data estimation is carried out by using the processes in (9) and (10). For investigating the practical issue of impacts of channel estimation, in this paper we follow a simpler approach by using the model of (8) as discussed earlier in Section 3.2.

6

Numerical results

In this section, we present user capacity and BER performance results of the proposed scheme obtained from the theoretical analysis of Section 4.2 as well as from computer simulations. We also compare it with conventional CDMA using a decorrelator, the MUD scheme for overloaded CDMA in [9] using a G-PD and the LAST CDMA scheme [15], all of which are based on the decorrelation method, under the same system settings and channel conditions. Unless stated otherwise, synchronised reception for the uplink with K equal average power users and short Gold sequences with spreading factor of N ¼ 31 are assumed.

6.1 User capacity performance and effect of group size (T) Fig. 2 shows the theoretical and simulated BER performances of the proposed scheme and comparison with conventional CDMA in Rayleigh ﬂat fading channels under perfect channel estimation condition. For the proposed scheme, G ¼ 25 and T ¼ 2 are chosen giving total number of users K ¼ G × T ¼ 50. BER performances IET Commun., 2011, Vol. 5, Iss. 3, pp. 307– 319 doi: 10.1049/iet-com.2010.0150

Figure 2 User capacity performance and effect of group size T of collaborative CDMA in Rayleigh ﬂat fading channels, Gold sequences N ¼ 31 of conventional CDMA with K ¼ 25 × 1 and 30 × 1 users along with the single user BPSK bound are also generated. The results clearly show the superior performance of the proposed collaborative CDMA. It is evident that it can support K ¼ 50 users giving an overloading ratio of approximately K/N ¼ 160% at the same BER performance of approximately K ¼ 27 users. The signiﬁcant increase in the user capacity comes at no extra power and also with lower number of required spreading sequences. The BER simulation result of the proposed scheme can also be veriﬁed from the BER plot obtained using the theoretical analysis in Section 4.2 by using (15). For example, for K ¼ 25 × 2 ¼ 50 users, where 2 d = 2.66 for T ¼ 2, the equation predicts a SNR loss of l ≃ 1.8 dB compared with conventional CDMA that accommodates only K ¼ 25 × 1 users; this, as can be seen from the ﬁgure, is reasonably accurate. In Fig. 2 we also show BER of the proposed scheme for different group sizes T, while keeping the same number of groups as G ¼ 30. The BER curves are obtained for: (a) T ¼ 2, (b) T ¼ 3 giving the user capacity of K ¼ 60 and K ¼ 90, respectively. As can be seen from the ﬁgure, the proposed technique exhibits satisfactory BER performance even when T is increased from 2 to 3 and shows a SNR penalty of only ≃1.8 dB for each additional co-spread users in a group. Note that in most practical situations the number of users is of paramount interest for the cellular wireless system operators, hence, this loss in the SNR because of increased group size can be offset if required, by employing conventional techniques such as error control coding, although at the cost of users’ data rates. We also show using computer simulations, how the proposed scheme compares with the overloaded MUD scheme in [9] in terms of BER performance in Fig. 3. We 315

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Figure 3 BER comparison of collaborative CDMA using (G × T ¼ 4 × 2) with the MUD scheme in [9] using G-PD detector and (|G| ¼ 2) to support the same total K ¼ 8 users in Rayleigh ﬂat fading channels, random sequences N¼7 assume ﬂat Rayleigh fading channel environment and that both schemes employ BPSK data modulation and random spreading sequences of length N ¼ 7. The target user capacity is set to K ¼ 8 users giving an overloading ratio of K/N ¼ 114%. For the proposed scheme this is achieved by selecting for example, G ¼ 4 and T ¼ 2 and using the receiver processes as described in Section 3. For the latter, we assume the G-PD detector is used to handle the user overloading and select a small group size of |G| ¼ 2 for a fair comparison. The schemes are compared by obtaining the averaged BER over all K users for different Eb/N0 values. It can be clearly seen from the ﬁgure that the proposed collaborative CDMA offers signiﬁcantly improved BER for the same user overloading condition. This is because of the fact that, as the same sequence is shared by users in each group in the proposed scheme, MAI and CCI from all other groups to the desired group are completely removed at the output of the group decorrelation stage. In contrast, in the scheme [9] each user employs a separate random sequence and since the G-PD detector is not able to fully cancel the MAI, considerable amount of residual MAI still exists, leading to degraded performance.

6.2 Impact of receive antenna diversity BER performance of the proposed scheme under diversity reception is investigated next. For simplicity, we consider two receive antennas A ¼ 2 at the base station and assume that they are spaced sufﬁciently apart so that channels on the antennas experience independent fading and that the channels are estimated perfectly. We ﬁrst show the BER improvement with the diversity reception compared with the single antenna scheme. For reference, the BER of single-user BPSK bound employing maximum ratio 316 & The Institution of Engineering and Technology 2011

Figure 4 BER performance of collaborative CDMA with dual antenna diversity reception (A ¼ 2) in Rayleigh ﬂat fading channels, Gold sequences N ¼ 31 combining (MRC) is also included in the ﬁgure. It can be noted from the Fig. 4 that, as expected the diversity reception offers signiﬁcant gain for all conﬁgurations of K ¼ G × T users investigated. For example, for K ¼ 30 × 2 ¼ 60 users and for the same BER of 1022, it requires only 11 dB of Eb/N0 compared with 20.5 dB for the single antenna case. We also investigate different conﬁgurations of user grouping to see the effect on the BER performance. Two conﬁgurations are considered here: (a) G ¼ 20 with T ¼ 3 and G ¼ 30 with T ¼ 2 are chosen to give the same total user capacity of K ¼ 60 users and (b) G ¼ 23 with T ¼ 4 and G ¼ 30 with T ¼ 3 are chosen to give similar user capacity of K ¼ 92 and K ¼ 90 users, respectively. We observe the following from the ﬁgure: for the case (a), to achieve the same user capacity of K ¼ 60 users, the conﬁguration of K ¼ 20 × 3 outperforms the K ¼ 30 × 2 by about 3.5 dB at BER of 1023; for the case (b), for the similar user capacities of K ¼ 92 and K ¼ 90, the conﬁguration of K ¼ 23 × 4 outperforms the conﬁguration K ¼ 30 × 3 by about 2.5 dB at BER of 1023. This suggests that it is best to increase the group size (T ) and lower the spreading factor N to increase the user capacity, if diversity reception is affordable. We can also observe from the ﬁgure that the diversity gain can actually close the gap in the BER degradation because of additional co-spread users in a group. Note that use of transmit antenna diversity methods such as space–time spreading [2] can also be used here and similar improvement in BER performance can be expected. In Fig. 5 we compare the BER of the proposed scheme with the LAST CDMA [15] using BPSK data modulation under the dual antenna diversity reception condition (A ¼ 2). The same number of sequences G ¼ 20 and the group size T are used, giving the total user capacity of IET Commun., 2011, Vol. 5, Iss. 3, pp. 307– 319 doi: 10.1049/iet-com.2010.0150

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Figure 5 Performance comparison of collaborative CDMA with LAST CDMA [15] under dual antenna diversity reception (A ¼ 2) in Rayleigh ﬂat fading channel condition, Gold sequences N ¼ 31 K ¼ G × T users. Two scenarios are considered: (a) T ¼ 2 giving K ¼ 20 × 2 users and (b) T ¼ 4 giving higher K ¼ 20 × 4 users. For the former, T ¼ A, hence the full rank condition of MIMO channel matrix for each group is satisﬁed; for the latter, since A , T, the MIMO channel matrix for each group is rank deﬁcient. From Fig. 5, it can be clearly seen that the proposed collaborative CDMA signiﬁcantly outperforms the LAST CDMA in both cases. More speciﬁcally, it offers more than 10 dB gain for the case of K ¼ 20 × 2 users to achieve the same BER of 1023. For the case of K ¼ 20 × 4 users, the proposed scheme archives BER performance near to that it achieves for K ¼ 20 × 2 users, whereas the LAST CDMA shows much larger BER degradation, rendering itself nonfunctional even under large Eb/N0 values. This is because very poor data estimation performance at each layer of detection of the LAST MUD detector caused by the rank deﬁciency of the MIMO channel matrix and error propagation to each subsequent layer.

6.3 Impact of imperfect synchronisation and channel estimation Here we investigate the practical issues of synchronisation and channel estimation on the BER performance. It is assumed that the synchronisation or delay estimation error signal is uncorrelated with the desired user’s signal and is modelled as complex Gaussian random variable with standard deviation in fraction of a chip s(t) ¼ 0.05, which is then added to the received signal. Fig. 6 shows the BER of the proposed scheme for K ¼ 30 × 2 ¼ 60 users and compares with conventional CDMA with K ¼ 30 users only. It can be seen that, as expected, synchronisation error gradually degrades the BER of both schemes that use the same linear decorrelation method. Similarly, the BER IET Commun., 2011, Vol. 5, Iss. 3, pp. 307– 319 doi: 10.1049/iet-com.2010.0150

Figure 6 BER performance of collaborative CDMA for K ¼ 30 × 2 users in Rayleigh ﬂat fading channels under synchronisation error with standard deviation of s(t) ¼ 0.05 and channel estimation error with variance s2(e), Gold sequences N ¼ 31 under imperfect channel estimation condition with estimation error variance of s2(e) ¼ 220 dB is investigated as shown in Fig. 6 for K = 30 × 2 = 60 users. It can be noted that, the proposed scheme retains its high user capacity performance with satisfactory BER at the low Eb /N0 region, however, it is noted to be slightly more sensitive to channel estimation error at the higher Eb /N0 region. This is because, although the AWGN vanishes in such condition, the non-vanishing complex additive noise because of channel estimation error becomes a dominant source of disturbance, leading to more erroneous decisions in the ML joint detection stage given in (10).

7

Conclusions

We proposed a high capacity and low complexity collaborative CDMA scheme for the uplink system that supports total number of full-rate users far beyond the spreading length. This is achieved by grouping a small number of users to share the same sequence and performing group linear MUD and ML joint detection based on the Euclidean distance to recover the co-spread users’ data exploiting their channel gain differences. The analytical and simulation results conﬁrmed that it offers signiﬁcantly higher user capacity and improved BER performance compared with conventional CDMA and the G-PD scheme. For example, using Gold sequence of length 31, it is shown to support 50 full-rate users compared with approximately 27 users offered by conventional CDMA and signiﬁcantly improved BER compared with the GPD under the same user overloading capacity of 114%. The computational complexity analysis also shows that the proposed scheme requires much lower FLOPs. Moreover, with multiple antenna diversity 317

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www.ietdl.org reception, substantial improvement in the BER has been demonstrated compared with LAST. For example, more than 10 dB gain is achieved at BER of 1023 for the same K ¼ 20 × 2 users, and even much higher gain for the antenna overloading condition of K ¼ 20 × 4 users. Finally, we also established that the user capacity gain is not much effected under imperfect delay and channel estimation conditions at low Eb /N0 . Investigation of channel correlation, synchronisation and channel estimation techniques are of practical importance and are the subjects for future work.

8

References

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