A Unified Framework and Sparse Bayesian Perspective for Direction-of-Arrival Estimation in the Presence of Array Imperfections

Abstract

Self-calibration methods play an important role in reducing the negative effects of array imperfections during direction-of-arrival (DOA) estimation. However, the dependence of most such methods on the eigenstructure techniques greatly degrades their adaptation to demanding scenarios, such as low signal-to-noise ratio (SNR) and limited snapshots. This paper aims at formulating a unified framework and sparse Bayesian perspective for array calibration and DOA estimation. A comprehensive model of the array output is presented first when a single type of array imperfection is considered, with mutual coupling, gain/phase uncertainty, and sensor location error treated as typical examples. The spatial sparsity of the incident signals is then exploited, and a Bayesian method is proposed to realize array calibration and source DOA estimation. The array perturbation magnitudes are assumed to be small according to most application scenarios, and the geometries of mutually coupled arrays are assumed to be uniform linear and those of arrays with sensor location errors are assumed to be linear. Cramer-Rao lower bounds (CRLBs) for the array calibration and DOA estimation precisions are also obtained. The sparse Bayesian method is finally extended to deal with the DOA estimation problem when more than one type of array perturbation coexists.Index Terms-Direction-of-arrival (DOA) estimation, array calibration, perturbed array output formulation, Cramer-Rao lower bound (CRLB), sparse Bayesian reconstruction.

A direction finding method for spatial optical beam-forming network based on sparse Bayesian learning

“…Recently, many scholars intend to apply the SBL algorithms to solve spectrum estimation problem and have achieved favorable results [12][13][14]. These SBL-based methods [15][16][17] take advantage of the probability density distribution of the data to achieve a best matching between the reconstructed results and the observations, which means that SBL techniques do not depend on the phase-difference information.…”

“…Recently, the sparse reconstruction techniques have been introduced to solve the problems in various areas, such as spectrum estimation and array processing [12][13][14][15][16][17]. Among them, the sparse Bayesian learning (SBL) technique has been demonstrated to have favorable performance both theoretically and experimentally [16,17].…”

Single-Channel Compressive Sensing for DOA Estimation via Sensing Model Optimization

“…Furthermore, the authors in [15] investigate the CS-based DOA estimation in the presence of sensing model mismatching errors, proving that the performance of CS-based DOA estimation algorithm degrades dramatically in the presence of sensing model mismatching. [16] [17] [18] present a DOA estimation model under sensing model mismatching, and then use Bayesian method to realize DOA estimation. [19] proposes a joint Least-Absolute Shrinkage and Selection Operator (LASSO) algorithm to achieve DOA estimation in the presence of mismatching.…”

Radar coincidence imaging with phase error using Bayesian hierarchical prior modeling

“…[7][8][9][10][11] These methods are less sensitive to phase error but lack adaptation to demanding scenarios with low signal-to-noise ratio (SNR), limited snapshots, and spatially adjacent sources. 12 Recently, sparse recovery and compressive sensing 13 are introduced into signal processing by exploiting the sparsity. A sparsity-driven iterative method for joint synthetic aperture radar (SAR) imaging and phase error correction in a nonquadratic regularization-based framework is proposed in Ref.…”

“…To realize array calibration and direction-of-arrival estimation, a unified framework based on sparse Bayesian learning (SBL) is formulated and a sparse Bayesian array calibration method is then proposed in Ref. 12. Using variational Bayesian inference (VBI), an array autocalibration SBL algorithm in the full conjugate Bayesian framework is proposed to achieve DOA estimation with gain/phase errors in Ref.…”