Bayesian learning scheme for sparse DOA estimation based on maximum-a-posteriori of hyperparameters

In this paper, the problem of direction of arrival estimation is addressed by employing Bayesian learning technique in sparse domain. This paper deals with the inference of sparse Bayesian learning (SBL) for both single measurement vector (SMV) and multiple measurement vector (MMV) and its applicability to estimate the arriving signal’s direction at the receiving antenna array; particularly considered to be a uniform linear array. We also derive the hyperparameter updating equations by maximizing the posterior of hyperparameters and exhibit the results for nonzero hyperprior scalars. The results presented in this paper, shows that the resolution and speed of the proposed algorithm is comparatively improved with almost zero failure rate and minimum mean square error of signal’s direction estimate

Subspace Methods for Joint Sparse Recovery

We propose robust and efficient algorithms for the joint sparse recovery problem in compressed sensing, which simultaneously recover the supports of jointly sparse signals from their multiple measurement vectors obtained through a common sensing matrix. In a favorable situation, the unknown matrix, which consists of the jointly sparse signals, has linearly independent nonzero rows. In this case, the MUSIC (MUltiple SIgnal Classification) algorithm, originally proposed by Schmidt for the direction of arrival problem in sensor array processing and later proposed and analyzed for joint sparse recovery by Feng and Bresler, provides a guarantee with the minimum number of measurements. We focus instead on the unfavorable but practically significant case of rank-defect or ill-conditioning. This situation arises with limited number of measurement vectors, or with highly correlated signal components. In this case MUSIC fails, and in practice none of the existing methods can consistently approach the fundamental limit. We propose subspace-augmented MUSIC (SA-MUSIC), which improves on MUSIC so that the support is reliably recovered under such unfavorable conditions. Combined with subspace-based greedy algorithms also proposed and analyzed in this paper, SA-MUSIC provides a computationally efficient algorithm with a performance guarantee. The performance guarantees are given in terms of a version of restricted isometry property. In particular, we also present a non-asymptotic perturbation analysis of the signal subspace estimation that has been missing in the previous study of MUSIC.Comment: submitted to IEEE transactions on Information Theory, revised versio