arXiv:2611.11810v2 Announce Type: replace Abstract: Range-Doppler profile (RDP) recovery is a fundamental task in adaptive radar signal processing, whose performance can be severely degraded by Doppler grid mismatch and colored interference. This article develops a unified sparsity-aware framework for on-grid and off-grid RDP recovery in the presence of correlated clutter with unknown spectral properties. The problem is formulated within a regularized maximum likelihood framework by exploiting both primary and secondary data, where the sparse RDP and interference covariance are jointly inferred, while Doppler frequency displacements are additionally estimated in the off-grid case to mitigate basis mismatch. Both covariance-adaptive one-step formulations and their sample-covariance-matrix-based two-step alternatives are developed within the mentioned framework. The resulting challenging nonconvex optimization problems are efficiently tackled by a majorization-minimization (MM) algorithm for the on-grid case and an MM-minimum block improvement (MBI) approach for the off-grid counterpart. Furthermore, Bayesian information criterion (BIC)-based refinement strategies are introduced to improve RDP recovery and Doppler frequency displacement estimation. Numerical results under colored interference demonstrate the superior recovery performance of the proposed methods over representative benchmarks.