Compressive Sensing for Joint User Activity and Data Detection in Grant-Free NOMA

Abstract

This letter studies the joint user activity and data detection problem in an uplink grant-free non-orthogonal multiple access system with binary phase-shift keying modulation. First, we propose a new compressive sensing (CS)-based algorithm, namely the information-enhanced adaptive matching pursuit (IE-AMP), which exploits both the frame-wise user sparsity and the ternary nature of transmit signals, to increase the detection performance with reduced computation complexity. Next, building upon this method, we propose a robust IE-AMP (RIE-AMP) algorithm for further performance improvement. The RIE-AMP first extracts the support information (i.e., the number of nonzero elements in every row) of the output signals of IE-AMP, and then employs a weighted $ {\ell }_{ {1, 2}}$ minimization to refine the result. Numerical results show that the IE-AMP outperforms several state-of-the-art CS-based algorithms, with reduced computational efforts required, while the RIE-AMP achieves a better and more robust detection performance than the IE-AMP at the cost of higher computation complexity.