Design of CFAR radars using compressive sensing

In this work we propose the GLRT-MP algorithm which combines compressed sensing techniques and classical detection theory and explores its application to sparse arrays. Sparse arrays are large undersample arrays with nonuniform spacing that provides high resolution at the cost of high sidelobes. Compressed sensing techniques are able to minimize the undesired effects of the large array, while classical detection theory provides a way to perform detection while maintaining a desired false alarm probability. We provide analysis of the GLRT when the noise power is known and unknown, the latter which will allow one to design a CFAR radar. We provide numerical results to verify our results.