Sparsity-Smoothness-Aware Power Spectral Density Estimation with Application to Phased Array Weather Radar

In this paper, we propose a sparsity and smoothness regularized model for the estimation of nonnegative power spectral densities (PSDs) of complex-valued random processes from mixtures of realizations. The proposed model is designed to jointly estimate frequency components of the realizations and the PSDs. The PSDs are estimated by the nonnegative variable in the proposed model, which enables that the sparsity and the smoothness can be exploited via convex optimization. Numerical experiments on the phased array weather radar, which is an advanced weather radar system, show that the proposed approach achieves superior performance to the existing sparse estimation models combined with post-smoothing.