This chapter deals with blind deconvolution and blind separation of convolutive mixtures. Blind deconvolution is a signal processing problem that is closely related to basic independent component analysis (ICA) and blind source separation (BSS). In communications and related areas, blind deconvolution is often called blind equalization. In blind deconvolution, we have only one observed signal (output) and one source signal (input). | Independent Component Analysis. Aapo Hyvarinen Juha Karhunen Erkki Oja Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-40540-X Hardback 0-471-22131-7 Electronic 19 Convolutive Mixtures and Blind Deconvolution This chapter deals with blind deconvolution and blind separation of convolutive mixtures. Blind deconvolution is a signal processing problem that is closely related to basic independent component analysis ICA and blind source separation BSS . In communications and related areas blind deconvolution is often called blind equalization. In blind deconvolution we have only one observed signal output and one source signal input . The observed signal consists of an unknown source signal mixed with itself at different time delays. The task is to estimate the source signal from the observed signal only without knowing the convolving system the time delays and mixing coefficients. Blind separation of convolutive mixtures considers the combined blind deconvolution and instantaneous blind source separation problem. This estimation task appears under many different names in the literature ICA with convolutive mixtures multichannel blind deconvolution or identification convolutive signal separation and blind identification of multiple-input-multiple-output MIMO systems. In blind separation of convolutive mixtures there are several source input signals and several observed output signals just like in the instantaneous ICA problem. However the source signals have different time delays in each observed signal due to the finite propagation speed in the medium. Each observed signal may also contain time-delayed versions of the same source due to multipath propagation caused typically by reverberations from some obstacles. Figure in Chapter 23 shows an example of multipath propagation in mobile communications. In the following we first consider the simpler blind deconvolution problem and after that separation of convolutive mixtures. Many techniques for convolutive mix- 355
