Low cost adaptive algorithm for blind channel identification and symbol estimation

A recursive/adaptive least squares algorithm (MLRA) is proposed to solve the joint blind channel identification and blind symbol estimation problem. It is based on Deterministic Maximum Likelihood methods (DML) which are pertinent in this field. We prove that when the MLRA converges then it converges towards the global minimum. The MLRA is able to track variations of the system by the introduction of an exponential forgetting factor in the DML criterion. The link between the adaptive algorithm and a Soft Decision Feedback Equalizer is emphasized. Update strategies of the filters can be either of a least squares type or of a stochastic gradient type. Both of them are derived in the paper. Numerical simulations show that the simplifications involved result in small degradations on the performances.