Convergence Analysis for Multiuser Detection in Sparse Code Multiple Access Systems

Sparse code multiple access (SCMA) is a promising non-orthogonal multiple access technique to achieve high system capacity. In this paper, a symbol-based extrinsic information transfer (EXIT) tool for SCMA systems is proposed to visualize and predict the convergence behavior of iterative processors. Specifically, an equivalent two-part model is presented to substitute the union sum-product algorithm in the multiuser detection for SCMA. The a priori probabilities of the input symbols are modeled using conditional Gaussian PDF generated by fully considering the unique feature of SCMA codebook and power allocation. Theoretical expressions and calculation methods of the EXIT curves are given for both function node and variable node. The proposed model is shown to match well with the trajectories in simulation results. Iteration- stopping criteria of SCMA detection under given channel condition is analyzed and the design guideline of SCMA codebook is also discussed.