Academic journal article Journal of Digital Information Management

Robust Adaptive Beamforming with SSMUSIC Performance Optimization in the Presence of Steering Vector Errors

Academic journal article Journal of Digital Information Management

Robust Adaptive Beamforming with SSMUSIC Performance Optimization in the Presence of Steering Vector Errors

Article excerpt

ABSTRACT: A novel subspace projection approach was proposed to improve the robustness of adaptive beamforming and direction finding algorithms. The cost function of the signal subspace scaled multiple signal classification (SSMUSIC) is minimized in the uncertainty set of the signal steering vector, the optimal solution to the optimization problem is that the assumed steering vector can be modified as the weighed sum of the vectors orthogonally projected onto the signal subspace and the noise subspace. Using the estimated steering vector with small error to the true steering vector, the spectral peaks in the actual signal directions are guaranteed. Consequently, the problem of signal self-canceling encountered by adaptive beamforming due to steering vector mismatches is eliminated. Simulation and lake trial results show that the proposed method not only possesses high resolution performance, but also is robust to a few steering vector errors. Furthermore, the modified MUSIC algorithm outperforms the conventional MUSIC and SSMUSIC methods excellently.

Categories and Subject Descriptors

C. 3 [Special purpose and application based systems]; Signal Processing Systems G.4 [Mathematicsl Software]

General Terms

Signal processing, Signal Classification, Noise detection

Keywords: Robust adaptive beamforning, steering vector error, direction of arrival, diagonal loading, subspace projection matrix. Received 30 November 2006; Revised 15 February 2007; Accepted 12 March 2007

1. Introduction

Multi-channel array signal processing has been widely and successfully used in radar, sonar, seismology, wireless communications, audio and speech processing, etc. Adaptive beamforming and high resolution direction-of-arrival (DOA) estimation algorithms have received much attention in the past a few decades, and among which, the minimum variance distortionless response (MVDR) [1] and multiple signal classification (MUSIC) algorithm [2] are the most popular two techniques.

Adaptive beamforming is utilized to enhance the signal of interest (SOI) corrupted in unwanted interferers and noises. In order to maximize the signal-to-interference-plus-noise-ratio (SINR) of the adaptive beamforming, the array steering vector of the SOI usually needs to be known precisely. It is well known that the MVDR method may suffer significant performance degradation even when there are very small array steering vector errors [3], which may result from many factors, e.g., signal local scattering, DOA mismatch, small number of data snapshots, nonstationary propagating environment, and individual sensor errors of positions, gains and phases, etc. The performance of adaptive beamforming is even worse when the SOI is contained in the training data snapshots. Therefore, robust beamforming has been a key issue in array applications when there are signal model errors.

The most widely used method to improve the robustness of adaptive beamforming is diagonal loading (DL), for its simplicity and effectiveness [1], [5]. The idea is to add a scaled identity matrix to the array covariance matrix prior to inversion, so that the norm of the weight vector and the white noise gain are constrained, and the noise eigenvalues are equalized. The key problem of DL method is how to choose the proper diagonal loading parameter [4]. Recently, some worst case performance optimization methods have been proposed to determine the DL value properly [6]-[8], by which the array output power is minimized subject to the constraint that the SOI with steering vectors lying in an uncertainty set not being suppressed, and hence, the output SINR is maximized when there are steering vector errors, and the robustness is improved. Besson [9] had derived the theoretical SINR performance analysis of the generalized diagonal loading beamformers when existing random steering vector errors, it was pointed out in [9] that for higher uncertainties, the remedy to improve robustness must be to estimate the steering vector or to obtain additional information about the actual steering vector, rather than to preserve the array's response over a larger uncertainty ellipsoid. …

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