Two Weighted $l_{p}$-Norm Based Multiuser Detection Algorithms for Uplink Grant-Free NOMA

Grant-free non-orthogonal multiple access (GFNOMA) has become increasingly sophisticated in supporting massive machine-type communications (mMTC) in recent years. One of the current challenges in mMTC is multiuser detection (MUD). In this work, we propose two focal underdetermined system solver (FOCUSS) algorithms to address MUD in mMTC. Specifically, FOCUSS effectively addresses the issue of transmitting user information within a single time slot by introducing norm factor and regularization parameter. In practical MUD scenarios, the user's activity status remains unchanged within a certain timeframe. To enhance the efficiency of MUD, we devise the M-FOCUSS algorithm for data transmission in multiple time slots. Simulation results indicate that both the FOCUSS and MFOCUSS algorithms outperform conventional detectors.