Super-Resolution Using FMCW Radar via Reweighted Decoupled Matrix Atomic Norm Minimization

Abstract

In this article, we investigate the joint estimation of range and velocity of targets using a wideband frequency-modulated continuous wave (FMCW) radar in the presence of range-Doppler coupling. To mitigate the effects of range-Doppler coupling, we propose a phase compensation framework based on a decoupled matrix atomic norm minimization (DANM). Subsequently, we propose a concave log-det heuristic to bridge the gap between atomic $\ell _{0}$ -norm and atomic $\ell _{1}$ -norm. To enhance the resolution, we use the proposed heuristic to formulate a reweighted decoupled 2-D matrix atomic norm (RMAN) minimization scheme and propose a semidefinite programming (SDP) solution for RMAN to decouple range and Doppler frequencies. Furthermore, we propose a novel RMAN-based approach for joint estimation of range and velocity of targets. The proposed algorithm is a gridless method that achieves resolution beyond the Rayleigh resolution limit and outperforms the conventional Fourier transform-based method in terms of estimation accuracy and root-mean-square error (RMSE), which converges to the derived Cramér-Rao lower bound (CRLB) as the signal-to-noise ratio (SNR) increases. The super-resolution ability of the proposed method is validated through extensive simulations under different scenarios.