A Low-Complexity Energy-Minimization-Based SCMA Detector and Its Convergence Analysis

Sparse code multiple access (SCMA) has emerged as a promising non-orthogonal multiple access technique for the next-generation wireless communication systems. Since the signal of multiple users is mapped to the same resources in SCMA, its detection imposes a higher complexity than that of the orthogonal schemes, where each resource slot is dedicated to a single user. In this paper, we propose a low-complexity receiver for SCMA systems based on the radical variational free energy framework. By exploiting the pairwise structure of the likelihood function, the Bethe approximation is utilized for estimating the data symbols. The complexity of the proposed algorithm only increases linearly with the number of users, which is much lower than that of the maximum a posteriori detector associated with exponentially increased complexity. Furthermore, the convergence of the proposed algorithm is analyzed, and its convergence conditions are derived. Simulation results demonstrate that the proposed receiver is capable of approaching the error probability performance of the conventional message-passing-based receiver.