Hardware-Efficient Direction of Arrival Estimation using Compressive Sensing

Compressed sensing (CS) based direction of arrival (DOA) estimation enables high performance with reduced hardware complexity. An important aspect affecting the performance of such systems is the measurement matrix that is used to reduce the number of samplers. Recent studies have proposed designing CS-DOA specific measurement matrices. However, these studies assume that each sensor is connected to each sampler channel. Such designs reduce the number of analog-to-digital samplers while increasing the number of other analog components required for mixing the sensor outputs. In this study, we tackle the problem of hardware-efficient measurement matrix design for CS based DOA estimation. We first propose constructing a hardware-efficient measurement matrix by projecting the hardware-inefficient full-matrix onto block-diagonal matrices. We rigorously derive the necessary equations and provide analytical solution for the proposed projection operation. Next, we propose a structured random permutation of the sensors to maximize the similarity between the full-matrix and the block-diagonal matrix. We thoroughly validate our proposed approach by comparing it to previously proposed block-diagonal Gaussian random matrices under a variety of simulated settings.