A sparse MLE approach for joint interference mitigation and data recovery

Consider the scenario where a receiver acquires information (data) corrupted by interference and noise. Both the information and interference have a sparse structure. To fully exploit the individual sparse structure of the information and interference, the joint interference mitigation and data recovery is formulated as a sparse maximum likelihood estimation (MLE) problem which maximizes the associated likelihood function under individual sparsity levels (ISLs) constraints. We propose an alternating optimization (AO) recovery algorithm to solve the non-convex sparse MLE problem. Under certain restricted isometry property (RIP) conditions, we show that the proposed AO algorithm converges to the optimal solution of the sparse MLE problem. We also derive an upper bound of the corresponding estimation error for the information. Simulations show that the proposed solution achieves significant gain over various baselines.