Support recovery in compressive sensing for estimation of direction-of-arrival

In the estimation of direction-of-arrival (DOA) problem, traditional array signal processing techniques normally use linear arrays sampled at Nyquist rate, and the inter-element distance in the linear array is required to be less than or equal to half of the wavelength to avoid angular ambiguity. The emerging Compressive Sensing(CS) theory enables us to use random array to sample the signal at much lower rate and still be able to recover it. To use this theory, the spatial signal should be sparse and it is always the case in practice. In this paper, we propose to apply the compressive sensing theory to reduce the spatial samples, i.e., to reduce the number of antenna elements. Instead of only showing the benefit of using CS theory, we analyze the performance of the angular estimation using the random array, i.e., we analyze the performance when the measurement is Fourier ensemble in terms of support recovery. We provide the sufficient and necessary conditions for the reliable support estimation.