Compressive sensing with unknown parameters

This work addresses target detection from a set of compressive sensing radar measurements corrupted by additive white Gaussian noise. In previous work, we studied target localization using compressive sensing in the spatial domain, i.e., the use of an undersampled MIMO radar array, and proposed the Multi-Branch Matching Pursuit (MBMP) algorithm, which requires knowledge of the number of targets. Generalizing the MBMP algorithm, we propose a framework for target detection, which has several important advantages over previous methods: (i) it is fully adaptive; (ii) it addresses the general multiple measurement vector (MMV) setting; (iii) it provides a finite data records analysis of false alarm and detection probabilities, which holds for any measurement matrix. Using numerical simulations, we show that the proposed algorithm is competitive with respect to state-of-the-art compressive sensing algorithms for target detection.