Blind identification/equalization using deterministic maximum likelihood and a partial information on the input

A new algorithm for jointly estimating the channels and the symbols sent through these channels is presented. Although the symbols are assumed to belong to a finite set, we use this prior information only partially. The rationale is that under some precise circumstances the plain deterministic maximum likelihood method seldom, if ever, exhibits local minima, while a full use of the finite alphabet property is more efficient, but introduces numerous local minima. The use of a partial information allows to considerably improve the performance in terms of symbol estimation without adding a new local minimum. Our algorithm combines a least-squares estimation of the channels and a constrained minimisation of a quadratic criterion for the symbols. If the data are noise-free, it is shown that the global minimum is attained only for the true filter and symbols. Furthermore, me propose a growing window technique which permits to evaluate whether the actual solution is a global minimum or not. In the second case, our technique permits to escape from this local minimum. Numerical simulations illustrate the accuracy of our algorithm in the presence of noise.