A strict bound for dimension of measurement matrix for CS beamformer MUSIC algorithm

The issue of reducing computational burden and its complexity while maintaining the adequate resolution has been a major problem in the area of DOA estimation. Compressive Sensing (CS) has been used in this regard to a great effect to address this issue. In recent works, it has been shown that by exploiting the sparsity of the observations obtained from the sensors, the computations can be greatly reduced without affecting resolution of the algorithm. This is done by introducing CS beamformers (CSB) to the picture. The dimension measurement matrix suggested by traditional CS theory however is found to be sub-optimal as CS beamformer doesn't use the regular CS recovery methods while implementing it. In this paper, we introduce a new strict and improved bound to the dimensions of the measurement matrix to be used in the CS beamformer MUSIC algorithm which decrease the number of measurements still further. We provide simulations to demonstrate the results and a comparison with the original algorithm hence showing that this bound is superior for CSB-MUSIC algorithm.