Side-Information Aided Compressed Multi-User Detection for Up-Link Grant-Free NOMA

Grant-free non-orthogonal multiple access (NOMA) is considered as one of the most important methodologies for the machine-type communications (MTC). In the field of MTC, compressed sensing based multi-user detection (CS-MUD) has been recognized as an excellent candidate for joint user activity and data detection, since many users sporadically transmit short-size data packets at low rates. This article focuses on the CS-MUD problem in the up-link grant-free NOMA scenario, where users are (in)-active randomly in each time slot yet with high temporal correlation. First, we investigate the CS framework to fully extract the underlying side information in the temporal correlation and propose a novel CS-MUD algorithm. Then, to mitigate the performance degradation due to the imperfect channel estimation in practice, the proposed algorithm is further extended by utilizing the perturbed CS, where the impact of channel estimation errors is modeled as certain perturbation in the measurement matrix. Different from most of the state-of-the-art CS-MUD algorithms, both proposed algorithms can apply even in the absence of prior knowledge on the number of active users. Simulation results indicate that the proposed algorithms achieve better performance than the existing CS-MUD methods. Their convergence and complexity issues are also discussed theoretically and numerically.