Sparsity-Promoting Direction Finding of Superimposed Signals Using Nonuniform Arrays: A Variational Bayesian Treatment

This paper develops a general variational Bayesian algorithm for obtaining sparse solutions to direction-of-arrival (DOA) estimation tasks utilizing nonuniform arrays. In this context, we focus on a fully Bayesian treatment, also known as maximum a posteriori (MAP) estimation using priors that induce sparsity in such estimates. We introduce a hierarchical form of the multivariate K prior to model the sparsity of the unknown signal coefficients, and use this hierarchy to establish variational representations of latent variables in probabilistic graphical model. We then discuss how the parameters within this framework can be estimated in an iterative procedure, where we interpolate the observed data to a virtual uniform linear array (ULA) in order to enhance the achievable degrees-of-freedom (DOF). The proposed algorithm iterates back and forth, using the current parameter estimates to interpolate the observed data better and then increase the likelihood of the next parameter estimates. Experimental results with synthetic signals are used for illustrating the superior performance of the proposed approach as compared with other state-of-the-art DOA estimation algorithm.