An Adaptive Beamforming Perspective on Convolutive Blind Source Separation
Microphones in an acoustic environment typically capture a mixture of several sources. The goal of convolutive blind source separation (BSS) is to filter the signals from a microphone array to extract the original sources while reducing interfering signals. This chapter discusses the ambiguities of convolutive BSS. It reviews how geometric information is utilized in conventional adaptive beamforming and suggests that second-order BSS can readily be combined with adaptive beamforming methods, because they both operate on the power spectra of the signals. Most adaptive beamforming algorithms rely on a power criteria of a single output. The algorithms overcome the crosstalk problems of conventional adaptive beamforming and the ambiguity problems of convolutive BSS. An alternative to higher-order statistics is to constrain the crosstalk minimization to a second-order criteria and instead exploit the nonstationarity of the signals. Estimating second-order statistics is numerically more robust and the criteria lead to simpler algorithms.