Contrast Functions for Deterministic Blind Source Separation

Blind Source Separation (BSS) is often carried out under the assumption that sources are statistically mutually independent, at least in the sense of cumulants of given order. However, this assumption is not mandatory, and can be replaced by some assumption on the source distribution, even if all sources are identically distributed. Contrast functions are optimization criteria that satisfy some identifiability conditions. In this paper, one defines a distance to any discrete constellation, and proves that this family of criteria indeed defines contrast functions. The advantage of such criteria is that they are deterministic, and do not involve the estimation of sample statistics, such as moments or cumulants, hence a potentially shorter convergence time. IEEE Workshop SPAWC’03, June 15-18, 2003, Rome, Italy 1. THE MIMO BLIND DECONVOLUTION PROBLEM Blind equalization or identification schemes have been the subject of growing interest since 1975. One of the main advantages of blind techniques is that, by deleting pilot sequences, one can increase the transmission rate. But there are other advantages, which stem from limitations of classical approaches. In fact, techniques based on pilot sequences are difficult to use when channel responses are long, or fast varying, compared to the length of the pilot sequence. The presence of a carrier residual can also make the equalization task more difficult. Instead of basing the identification or equalization schemes on input-output measurements (data-aided approaches), some properties about the inputs are exploited (blind approaches), as is now explained.