A wideband compressive radio receiver

Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for the acquisition of sparse or compressible signals. Instead of taking periodic samples, CS measures inner products with M random vectors, where M is much smaller than the number of Nyquist-rate samples. The implications of CS are promising for many applications and enable the design of new kinds of analog-to-digital converters, imaging systems, and sensor networks. In this paper, we propose and study a wideband compressive radio receiver (WCRR) architecture that can efficiently acquire and track FM and other narrowband signals that live within a wide frequency bandwidth. The receiver operates below the Nyquist rate and has much lower complexity than either a traditional sampling system or CS recovery system. Our methods differ from most standard approaches to the problem of CS recovery in that we do not assume that the signals of interest are confined to a discrete set of frequencies, and we do not rely on traditional recovery methods such as l₁-minimization. Instead, we develop a simple detection system that identifies the support of the narrowband FM signals and then applies compressive filtering techniques based on discrete prolate spheroidal sequences to cancel interference and isolate the signals. Lastly, a compressive phase-locked loop (PLL) directly recovers the FM message signals.