Spatially resolved sub-Nyquist sensing of multiband signals with arbitrary antenna arrays

In recent years it has been shown that wideband analog signals can be sampled significantly below the Nyquist rate without loss of information, provided that the unknown frequency support occupies only a small fraction of the overall bandwidth. The modulated wideband converter (MWC) is a particular architecture that implements this idea. In this paper we discuss how the use of antenna arrays allows to extend this concept towards spatially resolved wideband spectrum sensing by leveraging the sparsity in the angular-frequency domain. In our system each antenna element of the array is sampled at a sub-Nyquist rate by an individual MWC block. This results in a trade-off between the number of antennas and MWC channels per antenna. We derive bounds on the minimal total number of channels and minimal sampling rate required for perfect recovery of the 2D angular-frequency spectrum of the incoming signal and present a concrete reconstruction approach. The proposed system is applicable to arbitrary antenna arrays, provided that the array manifold is ambiguity-free.