Abstract
Direction of arrival (DOA) estimation has recently been developed based on sparse signal reconstruction (SSR). Sparse Bayesian learning (SBL) is a typical method of SSR. In SBL, the two-layer hierarchical model in Gaussian scale mixtures (GSMs) has been used to model sparsity-inducing priors. However, this model is mainly applied to real-valued signal models. In order to apply SBL to complex-valued signal models, a general class of sparsity-inducing priors is proposed for complex-valued signal models by complex Gaussian scale mixtures (CGSMs), and the special cases correspond to complex versions of several classical priors are provided, which is helpful to analyze the connections with different modeling methods. In addition, the expression of the SBL form of the real- and complex-valued model is unified by parameter values, which makes it possible to generalize and improve the properties of the SBL methods. Finally, the SBL complex-valued form is applied to the offgrid DOA estimation complex-valued model, and the performance between different sparsity-inducing priors is compared. Theoretical analysis and simulation results show that the proposed algorithm can effectively process complex-valued signal models and has lower algorithm complexity.
Highlights
Direction of arrival (DOA) estimation of spatial signals is an important content of array signal processing research
One merit of Sparse Bayesian learning (SBL) is its flexibility in modeling sparse signals, which can improve the sparsity of its solution [10]. erefore, research work on DOA estimation based on SBL has been gaining momentum in recent years [11, 12]
By using the complex Gaussian scale mixtures hierarchy, it has been shown that this signal model includes complex versions of a number of signal models commonly used for sparse signal modeling
Summary
Direction of arrival (DOA) estimation of spatial signals is an important content of array signal processing research. An offgrid DOA estimation model was first studied in [13], where the true DOAs are no longer constrained in the sampling grid, and they proposed a sparsity cognizant total least-squares (S-TLS) method for the perturbed compressive sensing under sparsity constraints It has been shown in [13] that the S-TLS can yield a MAP (maximum a posteriori) optimal estimate if the matrix perturbation caused by the basis mismatch is Gaussian. Based on the OGSBI method, a linear interpolation between two adjacent grids is adopted in [15] to approximate the true DOA steering vector, and they proposed a perturbed sparse Bayesian learning (PSBL) algorithm to solve the offgrid DOA estimation problem. Both ongrid and offgrid methods are grid-based methods. A comment on notation: we use boldface lowercase letters for vectors and boldface uppercase letters for matrices. (·)T, (·)− 1, (·)∗, and (·)H denote the transpose, inverse, conjugation, and conjugation-transpose operations, respectively. ‖ · ‖F and ‖ · ‖2 are the F-norm and 2-norm of a matrix, respectively. tr(·) denotes the trace operation of a matrix. ⊙ describes Hadamard product operator. p(·) represents the probability density function of random variables
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