Robust Two-Dimensional FIR Filter Design for Broadband Beamformers

Document type: Researchreports
Full text:
Author(s): Sven Nordebo
Title: Robust Two-Dimensional FIR Filter Design for Broadband Beamformers
Series: Research report
Year: 1995
Issue: 6
ISSN: 1103-1581
Organization: Blekinge Institute of Technology
Department: Dept. of Signal Processing (Institutionen för signalbehandling)
Dept. of Signal Processing S-372 25 Ronneby
+46 455 780 00
Authors e-mail:
Language: English
Abstract: With conventional least squares or Chebyshev approximation methods in the design of a fixed, broadband, delay{and{sum beamformer, the filter weight values may become excessively large.
This anomaly is due to large, unspecified regions of the corresponding two{dimensional FIR filter frequency plane. With large filter weight values, the frequency response of the resulting beamformer may be severely degraded due to inaccuracies in sensor positions and/or sensor frequency response.
For an adaptive beamformer, such as the Generalized Sidelobe Canceller (GSC), an anomalous design of the upper and lower branch may cause reduced jammer suppression, and target signal cancellation, respectively. A robust design of these branches is therefore vital.
In this paper, robust design procedures for both the least squares, and the Chebyshev error design criterion, are given. The resulting beamformer frequency responses are robust with respect to model imperfections in sensor positions, amplitudes and phases.
When a probabilistic model of the inaccuracies is given, the least squares and Chebyshev approximations can be made robust by modifying the corresponding inner product and max{norm, respectively, so that the effect of perturbations is taken into account.
When no probabilistic model is given, the straightforward approach is to keep control both on the approximation error, and on the magnitudes of the beamformer weights simultaneously. A robust weighted Chebyshev design criterion is defined, where a small Chebyshev error is traded off against small beamformer weights in an optimal way.
Subject: Signal Processing\Active Noise and Vibration Control
URN: urn:nbn:se:bth-00003