An Efficient SCMA Codebook Design Based on 1-D Searching Algorithm

This letter proposes an efficient sparse code multiple access (SCMA) codebook design, in which 1-D searching algorithm is introduced to minimize the upper bound of pair-wise error probability (PEP). Firstly, an SCMA signal model is given according to superposition modulation. Our analysis shows that under the proposed amplitude and phase rotation settings, each user has the same mutual information lower bound. In addition, the superimposed constellation points on each sub-channel belong to the same set, which depends on only one amplitude variable. Therefore, 1-D searching on this variable is introduced and the performance metric is upper bound of PEP. It is demonstrated that the calculated upper bound can well predict the receiver performance with maximum likelihood detection. In addition, the performance of the proposed codebook is verified with message passing algorithm at the receiver. The simulation results show that the PEP and bit error rate of the proposed codebook is better than that of the existing codebooks.

I. Introduction

Code domain non-orthogonal multiple access (NOMA) was considered as an important technique in future 5G [1]. Low density signature CDMA (LDS-CDMA), which is the first kind of code domain NOMA, was proposed in [2] and message passing algorithm (MPA) was introduced to realize low complexity detection. Subsequently, sparse code multiple access (SCMA) [3], [4] was proposed to combine low density spreading with multi-dimensional constellation optimization. Since its birth, SCMA has attracted much attention from both academia [5]–[10] and industry [11]. Recently, codebook optimization algorithms for maximizing mutual information between the discrete input and continuous output were proposed in [8] and [9]. In addition, codebook design was optimized according to superposed constellation distance in [10]. In the above existing works [8]–[10], joint codebook optimizations over multiple variables are performed, which always requires high computational complexity.