Digital Signal Processing 23 (2013) 1712–1719
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Digital Signal Processing
www.elsevier.com/locate/dsp
Robustness analysis of nearfield subband beamformers in the presence
of microphone gain and phase errors
Huawei Chen
∗
College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
article info abstract
Article history:
Available online 25 April 2013
Keywords:
Microphone array
Nearfield subband beamformer
Wideband beamformer
Robustness analysis
Microphone gain and phase errors
Subband beamforming has found many applications in microphone array processing field, due to
its advantages over the fullband counterpart. In this paper, the performance of nearfield subband
beamformers for arbitrary arrays in the presence of microphone gain and phase errors is studied from
the perspective of statistical analysis. Through the bias and variance analysis of array response, some
insightful properties on the robustness of nearfield subband beamformers have been derived. It is shown
that the robustness of nearfield subband beamformers is dependent on the source-to-array distance, i.e.,
the robustness will deteriorate when the source is close to microphone arrays. Moreover , the variation
in sound speed, i.e., the temperature in homogeneous environments, has little effect on the robustness
performance of subband beamformers. The theoretical results are further verified by several numerical
examples on nearfield subband beamformers.
© 2013 Elsevier Inc. All rights reserved.
1. Introduction
Wideband beamforming is one of the key techniques in micro-
phone array processing, and has found many applications in tele-
conferencing, hands-free telephony, hearing aids, and speech input
devices to computers, just to name a few [1,2]. In general, wide-
band beamformers can be classified into two categories: farfield
and nearfield wideband beamformers [3]. In most of practical ap-
plications, microphone arrays are usually used in the nearfield
[4–9]. For these scenarios, it has been known that using the farfield
beamformers may lead to significant degradation in the beam-
forming performance [4]. As a common rule-of-thumb, nearfield
beamformers are required when the distance between the array
and source signal is approximately less than 2l
2
/λ, where l is
the largest array dimension, and
λ denotes the operating wave-
length [4].
Conventional wideband beamforming methods usually assume
the ideal microphone characteristics, i.e., there are no mismatches
in microphone gain and phase. However, it has been well known
that, in practice, microphone characteristics are usually not exactly
available to the designers and can even change over time [10].
Unfortunately, conventional wideband beamformers designed with
ideal models are highly sensitive to microphone mismatches [10].
Therefore, the robustness of wideband beamformers in the pres-
ence of microphone mismatch errors is crucial in practical appli-
cations of microphone arrays. In recent years, robust wideband
*
Fax: +86 25 84892430.
E-mail address: hwchen@nuaa.edu.cn.
beamformer design has drawn increasing attention, and various
design approaches have been proposed in the literature [10–17].
Based on the beamforming structure, the existing wideband
beamforming techniques for microphone arrays can also be clas-
sified into another two categories: fullband and subband beam-
formers. The conventional wideband beamforming techniques be-
long to the fullband beamformers, which usually employ the
filter-and-sum structure, i.e. each microphone signal is filtered
by an finite impulse response (FIR) filter, and then summing
all the FIR filter outputs. In subband beamforming, each micro-
phone signal is split into several frequency subbands by a set
of analysis filter banks, then the beamforming operation is per-
formed in each subband [18]. Compared with fullband beam-
forming, it has been found that subband beamforming has sev-
eral advantages [19]: 1) lower computational complexity; 2) faster
convergence for adaptive beamforming; and 3) improved inter-
ference suppression. Therefore, subband beamforming has been
found wide applications in microphone array processing [18–24].
Recently, in order to solve the over-constraint problem suffered
by the fullband robust beamformers, subband beamforming has
also been used to improve the nearfield beamforming perfor-
mance [16]. In this paper, we would like to go a step further to
study theoretically the robustness performance of nearfield sub-
band beamformers in the presence of microphone gain and phase
errors. In [25,26], the sensitivity analysis of the mean array re-
sponse for farfield fullband beamformers has been performed in
the presence of microphone mismatches. However, the perfor-
mance analysis of nearfield subband beamformers has not been
reported in the literature. In this paper, we would like to bridge
this literature gap. Through the statistical analysis, including the
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http://dx.doi.org/10.1016/j.dsp.2013.04.008