Resource-Efficient Active Compressive Sensing Using Analog Beamforming and Sparse Arrays

This paper studies active sensing using sparse arrays and compressive measurements acquired by a fully analog beam-forming architecture. We consider a spatially sparse angular gridded model, where the unknown coherent sparse scattering coefficients are recovered by solving a convex optimization problem. We demonstrate that the number of resolvable scatterers is determined by the number of virtual sum co-array elements. Hence, properly designed sparse arrays can resolve vastly more scatterers than the number of physical sensors. We also quantify the sample complexity of the recovery procedure. Specifically, using well-known results form compressive sensing, we show that the lower bound on the number of independent measurements required for successful recovery can be achieved within a polylog factor. This holds even in the case of an extremely resource-efficient sparse array with a fully analog transceiver employing one-bit phase shifters.