Approximate Message Passing-Based Joint User Activity and Data Detection for NOMA

This letter focuses on joint user activity and data detection in the uplink grant-free non-orthogonal multiple access systems based on approximate message passing (AMP) and expectation maximization (EM) algorithms. The proposed Joint-EM-AMP detection algorithm consists of three steps in each iteration. First, AMP decouples the superimposed received signal into uncoupled scalar problems. Then, at the denoising step, AMP computes the posterior means and variances of the transmitted symbols with the extended modulation constellation. The third step is to estimate user activity parameters using EM based on the frame-wise joint sparsity of user activity. In contrast to existing state-of-the-art algorithms, the proposed Joint-EM-AMP algorithm demonstrates significant performance gain in terms of bit error rate, which will be verified in simulation results.