Performance Analysis and Phase Shift Design of IRS-Aided Uplink OTFS-SCMA

In this paper, we consider an intelligent reflecting surface (IRS)-aided orthogonal time frequency space (OTFS)-based uplink sparse code multiple access (SCMA) communications system. We first conduct performance analysis in terms of pairwise error probability (PEP) and derive an upper bound on word error probability (WEP). According to this bound, we establish a system design criterion and propose two IRS phase shifts design algorithms using semidefinite relaxation (SDR) and gradient ascent (GA) methods. The computational complexity of these algorithms is discussed. Next, we derive an upper bound on the average bit error rate (BER) and investigate the system performance in terms of diversity and signal-to-noise (SNR) gains. Further, to recover transmitted information bits, we present a modified joint iterative Gaussian approximated message passing (MP) detection and SCMA decoding algorithm, enabling detection and SCMA demapping to occur in each iteration. Finally, simulation results demonstrate that our proposed IRS design algorithms achieve better error performance compared to the known approaches.