Compressed sensing for DOA estimation with fewer receivers than sensors

This paper addresses the problem of the direction-of-arrival (DOA) estimation using fewer receivers than sensors. Inspired by the Compressed Sensing (CS) theory developed in recent years, we present a new preprocessing scheme for a large array using a small size receiver. Unlike the traditional ℓ
₂
-norm-based algorithms by judicious selection of the preprocessing matrix, the proposed scheme uses a random weight generator as a measurement of the compressed sensing to form the output data for each time interval. The formulated CS problem for DOA estimation is then solved based on the convex programming via ℓ
₁
-norm approximation such as Dantzig Selector. We consider two different scenarios in the CS domain, i.e., the angle domain and the angle-frequency domain. It is shown that the number of receivers can be reduced significantly for a given number of sensors by using the proposed CS-based DOA estimation approach.