Multi-Channel Signal Separation by Decorrelation

In a variety of contexts, observations are made of the outputs of an unknown multiple-input multiple-output linear system, from which it is of interest to identify the unknown system and to recover the input signals. This often arises, for example, with speech recorded in an acoustic environment in the presence of background noise or competing speakers, in passive sonar applications, and in data communications in the presence of cross-coupling effects between the transmission channels. In this paper we specifically consider the two-channel case in which we observe the outputs of a 2 x 2 linear time invariant system. Our approach consists of reconstructing the input signals by assuming that they are statistically uncorrelated and imposing this constraint on the signal estimates. In order to restrict the set of solutions, additional information on the true signal generation and/or on the form of the coupling systems is incorporated. Specific algorithms are developed and tested. As a special case, these algorithms suggest a potentially interesting modification of Widrow's least-squares method for noise cancellation, when the reference signal contains a component of the desired signal.