Unbiased adaptive equalization: the Gaussian kernel contrast functions

We address the issue of blind adaptive equalization. We introduce a class of cost functions which basically exploit the finite alphabet property of the source (we restrict ourselves to the case of BPSK sources). In an un-noisy context, we show that these cost functions are contrast functions in the sense that their maximizing arguments are delayed zero-forcing equalizers. When Gaussian noise is present, these Gaussian kernel cost functions show the property that under a suitable norm constraint of the equalizer, their maximizing arguments remain zero-forcing solutions. The results extend to the multi-source case, where the above-mentioned functions allow to extract a source and remove the ISI.