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Publication# Minimum Mutual Information Beamforming for Simultaneous Active Speakers

2007

Report or working paper

Report or working paper

Abstract

In this work, we consider an acoustic beamforming application where two speakers are simultaneously active. We construct one subband-domain beamformer in \emph{generalized sidelobe canceller} (GSC) configuration for each source. In contrast to normal practice, we then jointly optimize the \emph{active weight vectors} of both GSCs to obtain two output signals with \emph{minimum mutual information} (MMI). Assuming that the subband snapshots are Gaussian-distributed, this MMI criterion reduces to the requirement that the \emph{cross-correlation coefficient} of the subband outputs of the two GSCs vanishes. We also compare separation performance under the Gaussian assumption with that obtained from several super-Gaussian probability density functions (pdfs), namely, the Laplace, $K_0$, and $\Gamma$ pdfs. Our proposed technique provides effective nulling of the undesired source, but without the signal cancellation problems seen in conventional beamforming. Moreover, our technique does not suffer from the source permutation and scaling ambiguities encountered in conventional blind source separation algorithms. We demonstrate the effectiveness of our proposed technique through a series of far-field automatic speech recognition experiments on data from the \emph{PASCAL Speech Separation Challenge} (SSC). On the SSC development data, the simple delay-and-sum beamformer achieves a word error rate (WER) of 70.4%. The MMI beamformer under a Gaussian assumption achieves a 55.2% WER, which is further reduced to 52.0% with a $K_0$ pdf, whereas the WER for data recorded with a close-talking microphone is 21.6%.

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Beamforming or spatial filtering is a signal processing technique used in sensor arrays for directional signal transmission or reception. This is achieved by combining elements in an antenna array in such a way that signals at particular angles experience constructive interference while others experience destructive interference. Beamforming can be used at both the transmitting and receiving ends in order to achieve spatial selectivity. The improvement compared with omnidirectional reception/transmission is known as the directivity of the array.

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

Gaussian function

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form and with parametric extension for arbitrary real constants a, b and non-zero c. It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell".

Digital Signal Processing I

Basic signal processing concepts, Fourier analysis and filters. This module can
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