Sparse sensing with coprime arrays

Coprime sampling has, in the past, been used for signal processing applications such as range and doppler improvement in radar, and for identifying sinusoids in noise. This paper considers a coprime pair of samplers in space or time from the point of view of the difference coarray, which is key to the increased freedom available for processing with such arrays. First, two uniform linear arrays with N and M elements in space are considered. With the interelement spacings in the two arrays given by Mλ/2 and Nλ/2 where M and N are coprime integers, it is shown that the difference coarray has O(MN) freedoms, so that the number of freedoms available for DOA estimation and beamforming is O(MN). This implies in particular that a passive array can identify O(MN) sources using only M + N sensor elements. It is then shown that by using an N-band DFT filter bank and an M-band DFT filter bank in conjunction with the two arrays, it is possible to create a virtual filter bank with MN bands (i.e., MN beams). The increased number of freedoms can be exploited either in a passive setting (using time-domain averaging) or in an active setting as in radar and sonar.