Block-Compressed-Sensing-Based Multiuser Detection for Uplink Grant-Free NOMA Systems

Grant-free non-orthogonal multiple access (NOMA) has recently gained significant attention for reducing signaling overhead in machine-type communications (MTC). In this context, compressed sensing (CS) has been identified as a good candidate for joint activity and data detection due to the inherent sparsity nature of user activity. This paper augments activity and data detection for frame based multi-user uplink scenarios where users are (in)active for the duration of a frame, namely frame-wise joint sparsity model. Firstly, we formulate the block CS (BCS)-based sparse signal recovery framework, by fully extracting and exploiting the underlying frame-wise joint sparsity of the user activity. Then, to make explicit use of the block sparsity inherent in the equivalent block-sparse model and consider that the user sparsity level should be unknown for multiuser detection, two enhanced BCS- based greedy algorithms are developed, i.e., threshold aided block sparsity adaptive subspace pursuit (TA-BSASP) and cross validation aided block sparsity adaptive subspace pursuit (CVA- BSASP). Specifically, the proposed TA-BSASP algorithm can approach the oracle least squares (LS) performance, by reasonably setting the threshold based on the AWGN noise floor. And the proposed CVA-BSASP algorithm is a highly practical algorithm design that does not require any prior knowledge, by adopting the statistical and machine learning mechanism cross validation (CV) to determine the stopping condition of the algorithm. Superior performance of the proposed algorithms is demonstrated by numerical experiments.