Direction of Arrival Estimation for Off-Grid Signals Based on Sparse Bayesian Learning

The inherent limitation of the predefined spatial discrete grids greatly restricts the precision and feasibility of many sparse signal representation (SSR)-based direction-of-arrival (DOA) estimators. In this paper, we first propose a perturbed SSR-based model to alleviate this limitation by incorporating a bias parameter into the DOA estimation framework. Using this model, a perturbed sparse Bayesian learning-based algorithm, named PSBL, is developed to solve the DOA estimation problem, followed by a theoretical analysis of PSBL. We then present two algorithms based on the covariance matrix of the array output, named perturbed covariance matrix (PCM) and improved PCM (IPCM), respectively, to improve the convergence speed of PSBL. Extensive experiments show that the PSBL enjoys a high estimation accuracy in the cases of limited snapshots, low signal-to-noise-ratio, correlated, and spatially adjacent signals. In particular, PCM not only keeps the merits of PSBL, but also exhibits superiority over PSBL in terms of computational efficiency. IPCM has a better computational efficiency, but with a small sacrifice of its performance in a correlated signal scenario.