Sparsity-Inducing DOA Estimation of Coherent Signals under the Coexistence of Mutual Coupling and Nonuniform Noise

Abstract

The sparse reconstruction techniques can improve the accuracy and resolution of the direction of arrival (DOA) estimation using sensor arrays. However, due to reflective objects and nonidealities of the antennas and circuitry, the received signals may be coherent and coupled to each other in nonuniform noise environments, causing severe performance degradation of the signal sparse reconstruction. In this paper, a novel sparsity-inducing DOA estimation method is proposed to adapt to such a challenging scenario. To mitigate the nonuniform noise, its power components are first eliminated by a linear transformation. Then, leveraging the steering vector parametrization based on the banded symmetric Toeplitz structure of the mutual coupling matrix (MCM), a reweighted \mathcal {\ell }-{1} -norm minimization subject to an error-constrained \mathcal {\ell }-{2} -norm is designed to determine the DOA estimates, further enhancing the sparsity and providing robustness against the noise. In addition, a new stochastic Cramér-Rao lower bound (CRLB) of the DOA estimation is derived for the considered adverse condition. The simulation results demonstrate the superiority of the proposed method over its state-of-the-art counterparts.