Signature Design of Sparsely Spread Code Division Multiple Access Based on Superposed Constellation Distance Analysis

Sparsely spread code division multiple access (SCDMA) is a non-orthogonal superposition coding scheme that allows concurrent communications between a base station and multiple users over a common channel. However, the detection performance of an SCDMA system is mainly determined by its signature matrix, which should be sparse to facilitate the belief propagation (BP) detection. On the other hand, to guarantee good maximum likelihood (ML) detection performance, the minimum Euclidean distance for the equivalent signal constellation after multi-user superposition should be maximized. In this paper, a code distance analysis is proposed for SCDMA systems with a finite number of users and spreading lengths. Based on this analysis, good signature matrices whose factor graphs have very few short cycles and possess large superposed signal constellation distances are designed. The proposed signature matrices have both good BP and ML detection performances. Moreover, their BP detection performances exactly converge to their ML detection performances with few iterations. It is worth pointing out that the proposed signature matrix design could be directly applied to the 5G non-orthogonal multiple access systems.