Joint Interference Mitigation and Data Recovery in Compressive Domain: A Sparse MLE Approach

We consider the problem where a receiver acquires information (data) corrupted by interference and noise. Both the information and interference are assumed to have a sparse structure. This problem occurs in many applications such as data demodulation in cellular systems. 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. This sparse MLE framework can fully exploit the individual sparse structure of the information and interference to improve the data recovery performance at the receiver. We propose an alternating optimization (AO) recovery algorithm to solve the non-convex sparse MLE problem. To analyze the performance of the proposed AO algorithm, we introduce a new kind of restricted isometry property (RIP) called the ISLs-RIP. Under the ISLs-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. Finally, we extend the above results and algorithms to the case when the receiver only has statistical knowledge of the ISLs. Simulations show that the proposed solution achieves significant gain over various baselines.