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

The problem of joint activity detection and channel estimation at a multi-antenna base-station in massive random access can be posed as a joint sparse recovery problem for recovering row sparse matrices from multiple measurement vectors (MMVs), Recently, the Trainable Iterative Soft Threshold Algorithm (TISTA) for sparse recovery was extended to the MMV setting and applied to this joint activity detection and channel estimation problem. Two variants were proposed: one with an MMSE shrinkage function and another with a learning-based denoiser based on a model-based learning approach. In this paper, we generalize MMV-TISTA to the practical setting where different users suffer unequal path loss. In particular, we: (1) derive the maximum likelihood estimate of the path loss and use this to define the MMSE shrinkage function, and (2) propose a modified learning-based denoiser network for learning-based MMV-TISTA in the unequal path loss setting. We also use a probability of error based threshold for defining convergence instead of the MSE-based convergence used in existing literature. Simulation results show that the proposed methods are able to handle unequal path loss, and reduce the training overhead required for a given performance requirement significantly.