Uplink SCMA System With Multiple Antennas

Sparse code multiple access (SCMA) is a codebook-based nonorthogonal multiple access that exploits the coding gain of designed codebooks and the near-optimum performance of belief-propagation (BP) detection. In this paper, we study an uplink SCMA system equipped with multiple receive antennas utilized to get a diversity gain. Assuming that the maximum likelihood detection is applied to the system, we derive the upper bound on the average bit error rate (ABER) and analyze the diversity order which is shown to be the product of the number of receive antennas and the spreading gain. Exploiting the multiple received signals, we also propose a simplified detection method called Gaussian approximation based BP (GA-BP) detection with linear prefiltering. As the first step of the proposed detection, a conventional linear filter is applied to mitigate the multiuser interferences. Then, the GA-BP iteratively removes the residual interferences which may be approximated to a Gaussian random variable for the massive number of user equipments. Numerical results show that for moderate and high signal to noise ratio region the analyzed upper bounds on ABER of SCMA system tightly coincide with the simulation results. Also, for the moderate numbers of antennas, the ABER of GA-BP with matched filter closely approaches to that of the conventional BP detection with much lower computational costs.