Filter design for a compressive sensing delay and Doppler estimation framework

The theory of compressive sensing (CS) aims to find efficient signal acquisition and recovery techniques with the aid of prior knowledge about the signal. While traditionally applied to sparse vectors, CS has been extended to analog signals with more general structures. The use of CS in delay and Doppler estimation in radar application has recently received attention from the signal processing community. In this paper, we adopt one of the available CS frameworks for delay and Doppler estimation and optimize the deployed filter in this framework. The optimization criterion is the Bayesian Crámer Rao Bound of delay estimation and Doppler in general additive Gaussian interference. An iterative algorithm is proposed to solve the optimization problem and the results are compared with the prototype filter design available in the literature.