Sparsity-Inducing Direction Finding for Narrowband and Wideband Signals Based on Array Covariance Vectors

Among the existing sparsity-inducing direction-of-arrival (DOA) estimation methods, the sparse Bayesian learning (SBL) based ones have been demonstrated to achieve enhanced precision. However, the learning process of those methods converges much slowly when the signal-to-noise ratio (SNR) is relatively low. In this paper, we first show that the covariance vectors (columns of the covariance matrix) of the array output of independent signals share identical sparsity profiles corresponding to the spatial signal distribution, and their SNR exceeds that of the raw array output when moderately many snapshots are collected. Thus the SBL technique can be used to estimate the directions of independent narrowband/wideband signals by reconstructing those vectors with high computational efficiency. The method is then extended to narrowband correlated signals after proper modifications. In-depth analyses are also provided to show the lower bound of the new method in DOA estimation precision and the maximal signal number it can separate in the case of independent signals. Simulation results finally demonstrate the performance of the proposed method in both DOA estimation precision and computational efficiency.