False alarm probability estimation for Compressive Sensing radar

In this paper false alarm probability (FAP) estimation of a radar using Compressive Sensing (CS) in the frequency domain is investigated. Compressive Sensing is a recently proposed technique which allows reconstruction of sparse signal from sub-Nyquist rate measurements. The estimation of the FAP is based on an empirical model derived from simulations of the probability density function (pdf) of the noise samples reconstructed using the basis pursuit denoising (BPDN) algorithm. During simulations noise levels were assumed to be known; in practice noise or clutter power is not known a priori, and must be estimated from the radar data. As in radar applications it is desirable to have a Constant False Alarm Rate (CFAR), the aim here is to understand the statistical behavior of noise after CS reconstruction for designing CFAR radar detection schemes.