LMS based arrays with compressed sensing

This paper examines the potential of reducing the computational complexity of adaptive antenna-array systems by reducing the number of measurements per antenna using compressive sensing techniques. Compressive sensing is particularly suited for signals that are K sparse on some basis Psi. These types of signals are common in radar systems, multipath propagation, terrain scattered interference, etc. The idea is to take M observations (with M ~ O(K log(N))) instead of the standard N observations dictated by the Nyquist sampling criterion and desired frequency resolution, thereby reducing the size of the covariance matrix, hence expediting the adaptive process and reducing the computational demand of the antenna-array system. The least mean squared (LMS) algorithm is thus applied to the reduced-size observation vector, and the original signal is reconstructed at the output of the array. This reduction in complexity is counterbalanced by the error incurred in reconstructing the array output from few observations.