Joint spectrum sensing and direction of arrival recovery from sub-Nyquist samples

Joint spectrum sensing and direction of arrival (DOA) estimation is often necessary in communication applications, such as Cognitive Radio (CR). In this paper, we consider joint DOA and carrier frequency recovery of several transmissions as well as signal reconstruction from sub-Nyquist samples to overcome the sampling rate bottleneck of the wideband signals a CR typically deals with. We present two joint DOA and carrier frequency recovery approaches. The first is based on compressed sensing (CS) techniques and the second adapts a 2D-DOA recovery algorithm previously proposed in the Nyquist regime, the Parallel Factor (PARAFAC) analysis algorithm, to our sub-Nyquist samples. This technique allows us to solve the well known pairing issue between the DOA and carrier frequency to be recovered for each transmission. Once these are recovered, we show how the signal itself can be reconstructed from the samples. We also provide sufficient conditions for perfect blind signal recovery in terms of the sampling rate and the number of array elements.