Impact of Factor Graph on Average Sum Rate for Uplink Sparse Code Multiple Access Systems

In this paper, we first study the average sum rate of sparse code multiple access (SCMA) systems, where a general scenario is considered under the assumption that the distances between the mobile users and the base station are not necessarily identical. Closed-form analytical results are derived for the average sum rate based on which an optimal factor graph matrix is designed for maximizing the capacity of the SCMA systems. Moreover, we propose a low-complexity iterative algorithm to facilitate the design of the optimal graph matrix. Finally, Monte Carlo simulations are provided to corroborate the accuracy of the theoretical results and the efficiency of the proposed iterative algorithm.