areas of application, such as beam forming, higher-I. Linear, Instantaneous Combinations, Digital Signal order statistics, neural networks and artificial learn-Processing 6, 5-16. ing, noise cancellation, and speech enhancement. A major product of this work is the concept of indepen-Blind signal separation is the process of extracting undent component analysis (InCA). This paper forms known independent source signals from sensor measure-Part I of a two-part review of the literature in this ments which are unknown combinations of the source sigfield. It focuses on the simplest form of the blind nals. The term ''blind'' is used as the source signals and the method of combination are unknown, and hence the separation problem: the separation of sources that problem is related to the problems of blind deconvolution have combined in a linear, instantaneous fashion. and blind equalization. Blind signal separation is some-Part II [1] considers a more complicated separation times referred to as independent component analysis problem, where the combination of the sources is (InCA), as it generalizes principal component analysis to linear and convolutive, and also discusses a variety produce independent signals rather than simply uncorreof issues of importance to blind signal separation lated signals. The problem of blind signal separation has problems in general. been investigated in detail during the past ten years. The work has been driven by a wide variety of interests and 1.1. Problem Statement and Notation areas of application, such as array beam-forming, higherorder statistics, neural networks and artificial learning, Given m measured signals x 1 (k), x 2 (k), . . . , x m (k) noise cancellation, and speech enhancement. However, no that are combinations, linear or nonlinear, of n indereview of the available literature has been published. This pendent source signals s 1 (k), s 2 (k), . . . , s n (k), the paper is one of two papers seeking to redress this point. aim of blind signal separation is to produce n outputs It focuses on the simplest form of the blind separation y 1 (k), y 2 (k), . . . , y n (k) that recreate the original problem: the separation of sources that have combined in source signals, i.e., y 1 (k) ร
s 1 (k), y 2 (k) ร
s 2 (k), . . . , a linear, instantaneous fashion. แญง 1996 Academic Press, Inc.
y n (k) ร
s n (k). Nothing can be assumed about the sources except that they are statistically independent. Thus blind signal separation is the process of extracting the independent components s 1 (k), s 2 (k),