A Tight Lower Bound for the Symbol Error Performance of the Uplink Sparse Code Multiple Access

We derive a tight lower bound for symbol error rate (SER) performance of the sparse code multiple access (SCMA) uplink operated over Rayleigh fading channels. In particular, based on the working principle of message passing algorithm receiver and the special structure of the sparse binary matrix, which is used to control the collisions of SCMA system, the system can be simplified to a single user single input multiple output (SU-SIMO) system employing maximal ratio combining (MRC) reception. In this way, the average SER lower bound of SCMA is obtained by calculating the average SER of SU-SIMO system employing MRC reception. Our results show that the derived lower bound is not only an efficient means of analyzing the SER performance, but also is tight, especially in the high signal-to-noise ratio regime.