Two-Dimensional Off-Grid DOA Estimation With Metasurface Aperture Based on MMV Sparse Bayesian Learning

Metasurface aperture-based systems (MABSs) have recently attracted more attention due to their simple hardware structure, easy fabrication, and low-cost measurement, and they have been developed for the direction-of-arrival (DOA) estimation. In this article, we focus on the two-dimensional (2-D) off-grid DOA estimation problem for MABSs. Unlike the traditional multichannel array measurement mechanism, MABSs retrieve the directional of incident sources by generating multiple spatially incoherent quasi-random radiation patterns. Meanwhile, it will bring a new problem in that the measurement matrix of the MABS is a pseudorandom matrix and cannot be described by mathematical formulas. Besides, under the compressed sensing (CS) framework, the grid mismatch caused by discretization operation cannot be ignored. To handle these problems, we innovatively propose a 2-D off-grid DOA estimation model for MABSs using a Gaussian interpolation kernel. Then, based on the proposed model, a 2-D off-grid DOA estimation method, referred to as 2-D off-grid sparse Bayesian learning based on Gaussian interpolation (OGGISBL), is developed. Specifically, the off-grid errors are considered as parameters to be calibrated in the model, which are estimated by using the expectation–maximization (EM) algorithm under the framework of multiple measurement vector (MMV) sparse Bayesian learning (SBL) and eliminated via updating the grids using the Gaussian interpolation kernel. As shown by the simulation and experimental results, compared with the existing DOA estimation methods used for MABSs, the proposed method can calibrate more than 95% of the off-grid errors and works well even at low signal-to-noise ratio (SNR) (5 dB) and few numbers of snapshots, which significantly improves the measurement performance of MABSs.