Blind Deconvolution and Channel Equalisation

Abstract

Blind deconvolution is the process of unravelling two unknown signals that have been convolved. An important application of blind deconvolution is blind equalisation for the restoration of a signal distorted in transmission through a communication channel. Blind equalisation/deconvolution has a wide range of applications, for example in digital telecommunications for removal of inter-symbol interference, in speech recognition for removal of the effects of microphones and channels, in deblurring of distorted images, in dereverberation of acoustic recordings, in seismic data analysis etc.)In practice, blind equalisation is only feasible if some useful statistics of the channel input, and perhaps also of the channel itself, are available. The success of a blind equalisation method depends on how much is known about the statistics of the channel input, and how useful this knowledge is in the channel identification and equalisation process. This chapter begins with an introduction to the basics of deconvolution and channel equalisation. We study blind equalisation based on the channel input power spectrum, equalisation through model factorisation, Bayesian equalisation, nonlinear adaptive equalisation for digital communication channels, and equalisation of maximum phase channels using higher order statistics.