Kernelized method for compressive beamforming

Beamforming is a powerful processing tool for direction-of-arrival (DOA) estimation. The performance of a beamformer is limited by physical characteristics of the array in use, and searching space is often crowded in the form expressed in Euclid space. When the input space is transformed into a feature space with high dimension, e.g. infinite dimension in Hilbert space, it exhibits highly sparse characteristics. On that basis, the beamforming problem can be included in the framework of the compressive sensing (CS). In this paper, we map the sampled data into a high dimensional feature space with sparse representation induced by a kernel function. The DOA estimation is solved by using a kernel-based matching pursuit algorithm. When compared with the traditional CS, the new method improves the feature separability, and produces a better performance distinguishing coherent sources with fewer snapshots.