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Error probability bounds for SCMA signals

In this paper, we investigated error probability bounds for sparse code multiple access (SCMA) signals. SCMA is one of proposed non-orthogonal multiple access schemes for Fifth generation (5G) wireless communication standard. This scheme allows to increase the number of active users inside a given time-frequency resource. For AWGN and Rayleigh (without diversity) channels, we calculated union bounds for symbol and bit error probability. Asymptotic bound based on minimal distance between signals is also calculated. Analytical bounds are compared with simulations results (Maximum Likelihood (ML) Algorithm and Message Passing Algorithm (MPA) were used for signal reception). For AWGN channel, the results show that analytical bounds (symbol and bit error probabilities) are tight in the high-SNR region. For Rayleigh channel, analytical bound for symbol error probability are pessimistic with the gap of approximately 0.7 dB in the medium- and high-SNR regions.