Compressive sensing for array signal processing

Compressive sensing (CS) is an emerging area in which the conventional two step process of data acquisition and compression can be integrated into a single step. Compressive sensing exploits the sparsity of a signal and allows the digital signal to be reconstructed from far fewer measurements than the original size of the signal. This is possible as long as the measurements satisfy certain reasonable conditions such as Restricted Isometry Property, Incoherence, etc. The theory of compressed sensing can also be applied to the field of sensor array processing . In this paper, compressive sensing is applied to the problem of Direction of Arrival estimation. We perform Compressive Beamforming using two different approaches. In the time domain approach, CS can be applied to reduce the sampling rate of the Analog-to-Digital Converter, i.e., the number of samples received by each sensor of the array. In the spatial domain approach, CS can be applied to compress the array of large number of elements into an array of much smaller number of elements. Both these approaches are compared to the conventional beamforming technique and found to be close to the ideal impulse output. Compressed sensing recovery is performed using Subspace Pursuit (SP) and the two approaches are compared. The results obtained using SP is found to outperform the results obtained in the previous papers.