Joint User Activity and Data Detection for NOMA via the Integrated Framework of Expectation Maximization and Expectation Propagation

By introducing a structured sparse prior distribution over the transmitted signals, the user equipment (UE) detection problem in grant-free non-orthogonal multiple access (NOMA) is formulated within the expectation maximization (EM) learning framework, where the active state of each user corresponds to the unknown parameters in the prior. The structure of the sparse prior comes from the fact that the active state of each user remains the same during one Time-Frequency block of the grant-free NOMA systems. However, direct implementation of the expectation step of EM is intractable which requires the computation of posterior distributions of transmitted symbols. To address this problem, we propose to combine the expectation propagation algorithm (EPA) with EM, thus leading to an iterative joint UE and symbol detection receiver with low-complexity implementation and high performance.