Joint Active User Detection and Channel Estimation for Massive Grant-free Access via Difference of Convex Programming

Compressed sensing-based joint active user detection and channel estimation (JADCE) algorithms play a key role in massive grant-free access systems. However, current compressed sensing-based JADCE approaches cannot perform well when the sampling matrix has strong coherence, which results in expensive implementations of JADCE as the number of pilot decreases. To address this, we formulate the JADCE as a joint sparse signal recovery problem and then propose an efficient solver from difference of convex programming (DCP) perspective. The proposed DCP-based algorithm leverages the weighted
$\mathcal{L}_{2,1-F}$
minimization to solve the multiple measurement vector of JADCE problem. Simulation results demonstrate that the proposed DCP-based
$\mathcal{L}_{2,1-F}$
minimization algorithm achieves effective active user detection and accurate channel estimation compared to conventional compressed sensing-based JADCE approaches.