Adaptive blind equalisation of FIR channels using hidden Markov models

The problem of blind equalization of digital communications signals passed through a finite impulse response (FIR) channel with additive Gaussian white noise on the output is addressed. The input signal is modeled as a finite state Markov process, and the fixed lag smoother equations for estimating this input sequence are derived. The unknown channel taps are simultaneously estimated, using an incomplete data version of the recursive least squares (RLS) algorithm, where the (unknown) regressed data error and covariance are replaced by their expectations conditioned on the observations. A sufficient condition for local convergence of the tap estimates is given in terms of a sufficiency of excitation condition of the input Markov chain. Sub-optimal algorithms of reduced computation requirement, which utilize reduced state estimation (via decision feedback), are specified. The performance of the algorithms is illustrated using simulations employing quadrature phase shift keying (QPSK) signals