A lower ordered HMM approach to blind sequence estimation

In this paper, the base-band signal collected from an unknown, multipath, multi-receiver FIR channel is viewed as a state sequence generated by a hidden Markov model (HMM) whose states and order are unknown and whose transition probability matrix with an unknown permutation is known once the order is given. Based on this view, two types of algorithms are developed for acquisition and tracking, respectively. The algorithms are suitable for both block and non-block transmissions, and for time-varying channels. For acquisition the states and the transition probability matrix of a fully-connected HMM with a possible lower order are estimated by using a clustering algorithm. Then a state sequence is estimated based on a maximum a posterior (MAP) estimator using the Viterbi algorithm with a fully-connected trellis. This state sequence is used to refine the estimated states and transition probability matrix of the HMM. Based on the fully-connected HMM, the states are properly assigned to symbol vectors and the non-fully-connected HMM is determined, which is used in the maximum likelihood (ML) sequence estimation. In tracking, the symbol sequence is estimated by the Viterbi algorithm, and the states of the HMM are updated at each release of estimated states. Simulation results show that the proposed blind algorithms with the lower-ordered HMM achieve a performance comparable with the ML estimator utilizing the known, channel parameters. Theoretical analysis confirms simulation results.