Abstract
Sparse Bayesian learning (SBL) has given renewed interest to the problem of direction-of-arrival (DOA) estimation. It is generally assumed that the measurement matrix in SBL is precisely known. Unfortunately, this assumption may be invalid in practice due to the imperfect manifold caused by unknown or misspecified mutual coupling. This paper describes a modified SBL method for joint estimation of DOAs and mutual coupling coefficients with uniform linear arrays (ULAs). Unlike the existing method that only uses stationary priors, our new approach utilizes a hierarchical form of the Student t prior to enforce the sparsity of the unknown signal more heavily. We also provide a distinct Bayesian inference for the expectation-maximization (EM) algorithm, which can update the mutual coupling coefficients more efficiently. Another difference is that our method uses an additional singular value decomposition (SVD) to reduce the computational complexity of the signal reconstruction process and the sensitivity to the measurement noise.
Highlights
The problem of estimating the direction-of-arrival (DOA) of multiple narrow-band sources has received considerable attention in many fields, e.g., radar, sonar, radio astronomy and mobile communications [1]
Note that the effect of mutual coupling is negligible between two sensors that are far enough away from each other, because the mutual coupling coefficient is inversely proportional to their distance
We assume that the number of mutual coupling coefficients is m = 2 with c1 = 0.5 − 0.4i and c2 = 0.3 + 0.1i
Summary
The problem of estimating the direction-of-arrival (DOA) of multiple narrow-band sources has received considerable attention in many fields, e.g., radar, sonar, radio astronomy and mobile communications [1]. Many high-resolution DOA estimation algorithms have been proposed in the last few decades. Their excellent performance relies crucially on perfect knowledge of the array manifold. The array manifold usually suffers from imperfections, such as unknown mutual coupling between antenna elements, imperfectly-known sensor positions and orientations and gain-phase imbalances. The performance of DOA estimation may degrade substantially. It is necessary to calibrate imperfections prior to carrying out DOA estimation
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