Robust Angle Estimation Within the Single Beamwidth Based on Nonlinear Wavefront Modulation and Sparse Recovery

Abstract

Accurate angle estimation of targets within a single beamwidth is highly desirable in radar applications. This article proposes a robust angle estimation method based on nonlinear wavefront modulation (NWM) and sparse recovery. First, a parameterized model is developed to reformulate the angle estimation problem as a linear inverse problem. The primary innovation lies in the introduction of NWM to ensure the solvability of the equations. To address the ill-posedness arising from high correlation between columns of the wavefront modulation matrix, sparse constraints are incorporated to stabilize the solution. Specifically, this work introduces the regularized modified sparse Bayesian learning (RM-SBL) algorithm for high-precision angle estimation under an additive white Gaussian noise (AWGN) model. The stabilizing mechanism of these sparse constraints is evaluated through the lenses of both Cramér–Rao bound (CRB) analysis and regularization theory. Finally, comprehensive implementation details are provided, encompassing system design, experimental setup, and the signal processing workflow. Experimental results demonstrate an angular root-mean-square error (RMSE) of 0.195°, which is equivalent to approximately 1/80 of the antenna beamwidth (16°). Consequently, high-precision angle estimation can be achieved through noninvasive hardware enhancements to existing system configurations. The method also demonstrates consistent robustness across varying signal-to-noise ratios (SNRs), different numbers of wavefront modulation states, calibration inaccuracies, and diverse target amplitude distributions. This work contributes to the advancement of wavefront modulation radar systems and exhibits significant potential to enhance angular estimation accuracy in practical deployments.