Joint maximum-likelihood sequence and channel estimation for intersymbol interference channels

Abstract

We propose two joint maximum-likelihood estimation approaches. For joint time and data estimation we derive the joint likelihood function for jointly estimating data sequences and timing error for minimum shift keying signaling. The likelihood function utilizes samples taken in a free-running mode at some arbitrary sampling rate. Lower bounds on both the error-probability and mean-square timing-error are presented and seen to approach closely the optimum performance for sampling rates of two or more samples per symbol. Simulation results show that when the sampling rate is two samples per symbol, the performance of our joint estimation algorithm approaches the performance of binary phase-shift-keying with perfect synchronization. For joint channel and data estimation, we propose an iterative method which iterates between a maximum-likelihood channel estimator and a maximum-likelihood sequence estimator (Viterbi algorithm) to estimate channel impulse response and detect transmitted data jointly. The algorithm is designed so that the data sequences are detected on a block-by-block basis. For each received block of data, the channel impulse response is assumed to be unknown and must be estimated each time. Because each block of data is treated separately and detected independently, this approach could be useful for fast time-varying intersymbol interference channels. Simulation results show the symbol error probability of the algorithm closely follows the performance of a maximum-likelihood sequence estimation receiver that knows the channel impulse response.