A Robust Capon Beamformer against Uncertainty of Nominal Steering Vector
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A Robust Capon Beamformer against Uncertainty of Nominal Steering Vector Zhu Liang Yu1 and Meng Hwa Er2 1 Center 2 School
for Signal Processing, Nanyang Technological University, Singapore 639798 of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
Received 21 April 2005; Revised 19 October 2005; Accepted 21 October 2005 Recommended for Publication by Fulvio Gini A robust Capon beamformer (RCB) against the uncertainty of nominal array steering vector (ASV) is formulated in this paper. The RCB, which can be categorized as diagonal loading approach, is obtained by maximizing the output power of the standard Capon beamformer (SCB) subject to an uncertainty constraint on the nominal ASV. The bound of its output signal-to-interference-plusnoise ratio (SINR) is also derived. Simulation results show that the proposed RCB is robust to arbitrary ASV error within the uncertainty set. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
Adaptive array has been studied for some decades as an attractive solution to signal detection and estimation in harsh environments. It is widely used in wireless communications, microphone array processing, radar, sonar and medical imaging, and so forth. A well-studied adaptive beamformer, for example, the Capon beamformer [1], has high performance in interference suppression provided that the array steering vector (ASV) corresponding to the signal of interest (SOI) is known accurately. When adaptive arrays are used in practical applications, some of the underlying assumptions on the environment, sources, and sensor array can be violated. Consequently, there is mismatch between the nominal and actual ASVs. Common array imperfections causing ASV mismatch include steering direction error [2, 3], array calibration error [4], near-far field problem [5], multipath or reverberation effects [6], and so forth. Since ASV mismatch gives rise to target signal cancellation in adaptive beamformer, robust beamforming is required in practical applications. Some robust adaptive beamformers have been proposed to avoid performance degradation due to array imperfections (see [7, 8] and references therein). However, most of these methods deal with steering direction error only. When ASV mismatch is caused by array perturbation, array manifold mismodeling, or wavefront distortion, these methods cannot achieve sufficient improvement on robustness [9].
If ASV can be modeled as a vector function of some parameters, like steering direction error [10] and time-delay error or general-phase-error (GPE) between sensors [11, 12], robust beamformer can be constructed by maximizing the output power of the standard Capon beamformer (SCB) to those parameters in their feasible ranges. Efficient gradient descent-based method [13] can be derived to find the optimal parameters. With these estimated optimal parameters, the error in ASV can be compensated. The signal cancellation effect in the output is then reduced. In this paper, we further extend the idea use
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