Underdetermined Wideband DOA Estimation for Off-Grid Sources with Coprime Array Using Sparse Bayesian Learning.

Yanhua Qin,Jianyi Liu,Zhongyuan Yu,Yumin Liu

doi:10.3390/s18010253

Abstract

Sparse Bayesian learning (SBL) is applied to the coprime array for underdetermined wideband direction of arrival (DOA) estimation. Using the augmented covariance matrix, the coprime array can achieve a higher number of degrees of freedom (DOFs) to resolve more sources than the number of physical sensors. The sparse-based DOA estimation can deteriorate the detection and estimation performance because the sources may be off the search grid no matter how fine the grid is. This dictionary mismatch problem can be well resolved by the SBL using fixed point updates. The SBL can automatically choose sparsity and approximately resolve the non-convex optimizaton problem. Numerical simulations are conducted to validate the effectiveness of the underdetermined wideband DOA estimation via SBL based on coprime array. It is clear that SBL can obtain good performance in detection and estimation compared to least absolute shrinkage and selection operator (LASSO), simultaneous orthogonal matching pursuit least squares (SOMP-LS) , simultaneous orthogonal matching pursuit total least squares (SOMP-TLS) and off-grid sparse Bayesian inference (OGSBI).

Highlights

Wideband direction of arrival (DOA) estimation using sensor arrays is an active research topic since it has broad applications requiring estimation the so-called angular spectrum, for example, in radar, sonar, wireless communication and localization, to name a few [1]
We focus on the underdetermined wideband DOA estimation for off-grid sources based on the coprime array using Sparse Bayesian learning (SBL) algorithm
Assume ∆θ = 0.0952 rad as half of the two closely incident signals, successful separation of least absolute shrinkage and selection operator (LASSO), simultaneous orthogonal matching pursuit least squares (SOMP-LS), SOMP-TLS, off-grid sparse Bayesian inference (OGSBI) and SBL is defined if the estimated DOA of each signal satisfies θk − ∆θ ≤ θk ≤ θk + ∆θ

Summary

Introduction

Wideband direction of arrival (DOA) estimation using sensor arrays is an active research topic since it has broad applications requiring estimation the so-called angular spectrum, for example, in radar, sonar, wireless communication and localization, to name a few [1]. In order to solve the problem that joint sparsity fails to capture the true structure of the signals, a novel wideband DOA estimation algorithm within the sparse Bayesian framework is proposed to allow a much more flexible occupation of the spectrum band, and automatically determine the underlying band occupation by imposing a Dirichlet process prior on the latent parametric space in [14]. We focus on the underdetermined wideband DOA estimation for off-grid sources based on the coprime array using SBL algorithm.

Wideband Signal Model for Coprime Array

Off-Grid Formulation

Sparse Bayesian Learning Algorithm

Simulation Result

Conclusions