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  • IEEE ICC 2015 - Wireless Communications Symposium

    Iterative Multiuser Receiver in Sparse Code Multiple Access Systems

    Yiqun Wu, Shunqing Zhang, and Yan Chen Huawei Technologies, Co. Ltd., Shanghai, China

    Email: {wuyiqun}@huawei.com

    Abstract-Sparse code multiple access (SCMA) is a novel non­ orthogonal multiple access scheme, in which multiple users access the same channel with user-specific sparse codewords. In this paper, we consider an uplink SCMA system employing channel coding, and develop an iterative multiuser receiver which fully utilizes the diversity gain and coding gain in the system. The simulation results demonstrate the superiority of the proposed iterative receiver over the non-iterative one, and the performance gain increases with the system load. It is also shown that SCMA can work well in highly overloaded scenario, and the link-level performance does not degrade even if the load is as high as 300%.

    I. INTRODUCTION

    To satisfy the demand of high spectral efficiency and mas­ sive connections in next generation cOlmnunication systems, non-orthogonal multiple access schemes have received more and more attention [ 1]. One important reason is that non­ orthogonal multiple access can theoretically expand the capac­ ity region [2]. A familiar example of non-orthogonal multiple access is code division multiple access (CDMA), which has been deeply investigated and successfully applied. However, the optimal multiuser detection in CDMA systems is of high complexity, which increases exponentially with the number of users [3]. Although many low-complexity receivers have been proposed, they usually perform worse than the optimal one, especially when the system is overloaded, i.e., the number of users is larger than the number of chips [4].

    Low density spreading (LDS) has been proposed to reduce the complexity of multiuser detection [5]-[8]. In the LDS system, modulated symbols are only spread over a part of total chips and the signatures on other chips are zero. Therefore, the number of interfering users on each chip is much lower than the traditional CDMA. Similar to low-density parity­ check (LDPC) code, LDS signatures can be represented by a sparse factor graph [9], with variable nodes (VNs) representing data symbols and function nodes (FNs) representing chips. By taking advantage of the sparsity, message passing algorithm can be applied for multiuser detection, which has much lower complexity than optimal maximum a posteriori (MAP) decoder but achieving almost the same performance.

    Sparse code multiple access (SCMA) was introduced in [ 10], which generalizes the idea of LDS. In the SCMA system, the QAM mapper and the symbol spreader are combined into a single block of SCMA encoder, which maps a group of bits to multidimensional complex domain codewords. Similar to LDS, the signatures of SCMA codewords are sparse and can

    SCMA decoder

    OFDM Demodulator

    AWGN

    Fig. 1: Block diagram of an uplink SCMA system.

    be represented by a sparse factor graph. By carefully designing the factor graph and mapping functions, SCMA can perform better than LDS with similar decoding complexity [11].

    Inspired by the turbo principle [ 12], iterative multiuser receivers have been investigated in CDMA systems [13], [14] and also in the LDS system [15]. In this paper, we consider an uplink SCMA system employing channel coding, and develop an iterative multiuser receiver for the SCMA system. It will be shown that how the soft decisions are exchanged between the SCMA decoder and channel decoders to fully utilize the diversity gain and coding gain, and how the decoding complexity can be reduced by exploiting the special structure of SCMA code book and tailoring the factor graph during the iterations. The simulation results demonstrate the superiority of the proposed iterative receiver over the non-iterative one. The simulation results also show that SCMA can work well in highly overloaded scenario, and the performance will not degrade even if the load is as high as 300%.

    In this paper, the set of binary and complex numbers are denoted by lR and C, respectively. We use x, x, and X to represent a scalar, a vector and a matrix. The rest of the paper is organized as follows. Section II introduces the system model. Section III presents the details of the iterative multiuser receiver. In Section IV, the receiver performance is evaluated. Section V concludes the paper.

    II. SYSTEM MODEL

    Consider a K -user uplink SCMA system depicted in Fig. 1. For each user k, the binary information data bk are encoded by a channel encoder with coding rate Rk. The coded bits Ck

    978-1-4673-6432-4/15/$31.00 ©2015 IEEE 2918

  • IEEE ICC 2015 - Wireless Communications Symposium

    o VNs D FNs

    Fig. 2: Example of factor graph (V = 12, N = 8).

    11 lO

    -a

    FN 1

    01 00

    a

    11 lO

    -a o

    FN2

    01 00

    a

    Fig. 3: Illustration of the mapping function of 4-point SCMA code book (M = 4).

    are then mapped into complex domain codewords Xk by an SCMA encoder. The signatures of SCMA codewords can be represented by a factor graph Q(V , N), which contains V VNs and N FNs. Fig. 2 shows an example of factor graph, in which V = 12, N = 8. The VNs represent data layers, and the FNs represent resources shared by data layers. The edges between VNs and FNs mean the corresponding data layers have non­ zero signatures on the associated resources. Since there are totally V data layers on N resources, define the system load

    v as p = N' For each data layer, every J = log2 M coded bits are

    mapped to an N-dimensional SCMA codeword. The asso­ ciated mapping function for the v-th data layer is defined as: Iv : ]RJ --+ X, where X E eN and IXI = M. Let Cv = (Cv,l , Cv,2 , " . , cv,J) be the coded bits, and Xv = (Xv,1 ,Xv,2 ,"' ,Xv,N) be the SCMA codeword. Let C = (CI, C2, . . . , cv ) be the coded bits of all data layers. Let 1> (v) = {n : xv,n -I- O} be the neighbor FNs of the VN v, and ll1 (n) = { v : xv,n -I- O} be the neighbor VNs of the FN n.

    Each SCMA codeword is a sparse vector with no more than half non-zero elements. The element xv,n is non-zero if and only if there is an edge between the VN v and the FN n in Q. Fig. 3 illustrates the mapping function of the 4- point SCMA codebook, which means M = 4. In this case, each VN has two neighbor FNs and every two coded bits are mapped to an N-dimensional codeword. Only two elements of the codeword are non-zero, which correspond to the two FNs. On the two FNs, the bits 00, 01, 10 and 11 are mapped to (a, 0), (0, a) , (0, -a) , ( -a , 0), respectively.

    Each user can have multiple data layers. Let Vk be the set of VNs for the user k, and I Vk I = Vb and 1); ( v) be the user

    corresponding to the VN v. For user k, the transmitted signal is the sum of the codewords from all the data layers in Vk:

    ( 1)

    The generated codewords x = {Xl, ... , XK} are then modu­ lated by OFDM modulators. Assume each OFDM symbol has Ntotal = SN subcarriers for transmission, which are divided into S subbands and each subband has N subcarriers. Thus, there are S SCMA codewords for each user per layer per OFDM symbol. Let hk,n(i , s) be the channel gain between the user k and the base station (BS) on the n-th subcarrier of the s-th subband of the i-th OFDM symbol, then the received signal on the same subcarrier is given by

    K

    Yn(i , s) = L hk,n(i , s)xk,n(i , s) + vn(i , s), (2) k=l

    where Vn (i , s) is additive Gaussian noise with power 0'2. As the processing procedure is the same for each subband and each OFDM symbol, we will drop the index i and s for notational simplicity in the following analysis. Let y = (Yl, Y2 , ... , Y N) be the received signals, and hk = (hk,l , hk,2 , ... , hk,N) be the channel gains between the user k and the BS.

    III. ITERATIVE MULTIUSER RECEIVER

    In this section, the details of iterative multiuser receiver for SCMA system are presented. The structure of the receiver is shown in Fig. 4, which consists of two types of blocks: a SCMA decoder and K parallel channel decoders, separated by deinterleavers and interleavers. Given the received signal y and channel knowledge h = ( h1, ''' , hK)' the SCMA decoder delivers the soft decision of every coded bit of every data layer, i.e., a posteriori log-likelyhood ratio (LLR), which is given by

    A ( .) -1 P{cv,j = 11Y} 1 CV,J - og P{cv,j = Oly}'

    By using Bayes' rule, we have

    (3)

    A ( ) 1 P{yicv,j = 1} 1 P{cvJ' = 1} 1 Cv,j = og + og ' (4) P{yicv,j = O} P{ Cv,j = O}

    = AI(Cv,j) + A�(Cv,j) ,

    In (4), the first term, denoted by Al(Cv,j), represents the extrinsic information by SCMA decoder, and the second term, denoted by A� (cv,j), represents the a priori LLR of Cv,j which is given by the corresponding channel decoder in the previous iteration. For the first iteration, assuming no prior information and A�(Cv,j) = O.

    To compute (4), we can apply the relation between C and x. Define

    c:'j £ {(Cl,l,'" , Cv,j-l, 1 , Cv,j+l, '" , CV,J) : Cu,i E {O, 1}, (u, i ) -I- (v,j)}. (5)

    2919

  • IEEE ICC 2015 - Wireless Communications Symposium

    y SCMA decoder

    Fig. 4: Structure of the iterative multiuser receiver for SCMA system.

    Similarly define C;;'j' Let X:j be the set of codewords mapped from the coded bits in Ct.j' and similarly Xv�j' By using Bayes' rule,

    . LCE c+ . P{cIY} A1(�,v) = log L

    V, J P{ I } cE C- . C Y V, J

    LXE x+ P