Speech Enhancement Based on a Microphone Array and Log-Spectral Amplitude Estimation

1. Introduction Microphone array systems are often used for high quality hands-free communication in reverberant and noisy environments [1]. Compared to single microphone systems, a substantial gain in performance is obtainable due to the spatial filtering capability to suppress interfering signals coming from undesired directions. In cases of spatially incoherent noise fields, beamforming alone does not provide sufficient noise reduction, and postfiltering is normally required (see [2, 3] and references therein). Existing microphone array systems are based on beamforming and multi-channel Wiener postfiltering. However, a Wiener filter minimizes the mean-square error (MSE) distortion of the signal estimate, which is essentially not the optimal criterion for enhancing noisy speech. A more appropriate distortion measure for speech enhancement systems is based on the MSE of the spectral, or log-spectral, amplitude [4, 5]. Furthermore, abrupt transient interferences are not attenuated, since the postfilter is unable to track and adapt to fast changes in the noise statistics. Single-channel postfiltering techniques also lack the ability to attenuate transient noise, since transients are generally not differentiated from the desired speech components. In this paper, we present a multi-microphone speech enhancement approach for minimizing the log-spectral amplitude (LSA) distortion in non-stationary noise environments. An adaptive beamformer with a generalized sidelobe canceller structure is applied to the noisy observed signals. In addition to the beamformer primary output, it provides reference noise signals by projecting the input signals onto the noise-only subsapce. Presumably, a desired signal component is stronger at the beamformer output than at any reference noise signal, and a noise component is strongest at one of the reference signals. Hence, the ratio between the transient power at beamformer output and the transient power at the reference signals indicates whether such a transient is desired or interfering. Based on a Gaussian statistical model [4], and an appropriate decision-directed a priori SNR estimate [6], we derive an estimator for the signal presence probability. This estimator controls the rate of recursive averaging in obtaining a noise spectrum estimate by the Minima Controlled Recursive Averaging (MCRA) approach [7]. Subsequently, spectral enhancement of the beamformer output is achieved by applying an optimal gain function, which minimizes the MSE of the log-spectra. 2. Problem Formulation Let x(t) denote a desired speech signal, and let the observed signals at the output of M microphones be given by