Adaptive deterministic maximum likelihood using a quasi-discrete prior

A block algorithm is presented to solve the joint blind channel identification and blind symbol estimation problem. It is based on a Deterministic Maximum Likelihood (DML) method. A partial prior on the symbols is incorporated into the DML criterion in order to improve the estimation accuracy. We propose a test which permits to circumvent the local minima problem and which is pertinent for a large class of criteria. The structure of the block algorithm is well-suited for deriving recursive and adaptive versions. We prove that., in the noiseless case, the obtained recursive algorithm converges only towards the global minimum. Numerical results show that the prior on the symbols improves the accuracy of the estimators and brings robustness to the lack of channel diversity. At the same time, this method introduces fewer local minima than the use of a full prior.