Blind signal separation is the process of extracting unknown independent source signals from sensor measurements which are unknown combinations of the source signals. The term "blind" is used as the source signals and the method of combination are unknown, and hence the problem is related to the problems of blind deconvolution and blind equalization. Blind signal separation is sometimes referred to as independent component analysis (InCA), as it generalizes principal component analysis to produce independent signals rather than simply uncorrelated signals. The problem of blind signal separation has been investigated in detail during the past ten years. The work has been driven by a wide variety of interests and areas of application, such as array beam-forming, higher-order statistics, neural networks and artificial learning, noise cancellation, and speech enhancement. However, no review of the available literature has been published. This paper is one of two papers seeking to redress this point. It focuses on the simplest form of the blind separation problem: the separation of sources that have combined in a linear, instantaneous fashion.