Learning-Based Sparse Recovery for Joint Activity Detection and Channel Estimation in Massive Random Access Systems

We consider the problem of joint activity detection and channel estimation in massive random access. When the receiver has multiple antennas, this is a joint sparse recovery problem with multiple measurement vectors (MMV). For the general setting where the channels could be correlated across antennas, we first develop a modified minimum mean squared error (MMSE) shrinkage function to be used in the Trainable Iterative Soft Thresholding Algorithm (TISTA). Then, we learn this MMSE shrinkage function using a model-based neural network. In the simulation results, the proposed learning-based method, L-MMSE-MMV-TISTA, offers a 30-40% reduction in preamble length requirement compared to TISTA. We also compare L-MMSE-MMV-TISTA with the state-of-the-art MMV sparse Bayesian learning (M-SBL) method. While M-SBL can provide better performance at the cost of higher complexity in highly measurement-constrained settings, LMMSE-MMV-TISTA provides a significant complexity advantage when only a slightly larger number of measurements are available.