Off-grid DOA estimation under nonuniform noise via variational sparse Bayesian learning

In this paper, the problem of direction-of-arrival (DOA) estimation in the presence of nonuniform noise is investigated, where the inherent off-grid effects in traditional sparsity-inducing algorithms are also considered. By formulating a sparse signal recovery problem for weighted partial virtual array (PVA) response, we develop a sparse Bayesian learning based method by exploiting joint sparsity between the power distribution of incident signals and the off-grid difference. In our proposed algorithm, a weighted partial covariance vector is obtained through the deliberate projection and decorrelation operations, which facilitates a sparse representation free from the nonuniform noise variances. Meanwhile, a variational Bayesian inference is implemented upon a hierarchical Bayesian learning model with an almost Jeffrey's prior adopted, which strongly induces the sparsity and involves adaptively tuning sparseness-controlling parameters. Moreover, the proposed method works without the knowledge of the number of sources. Simulation results demonstrate it provides superiority in estimation precision and robustness against nonuniform noise.