Asymptotically optimal blind fractionally spaced channel estimation and performance analysis

When the received data are fractionally sampled, the magnitude and phase of most linear time-invariant FIR communications channels can be estimated from second-order output-only statistics. We present a general cyclic correlation matching algorithm for known order FIR blind channel identification that has closed-form expressions for calculating the asymptotic variance of the channel estimates. We show that for a particular choice of weights, the weighted matching estimator yields (at least for large samples) the minimum variance channel estimator among all unbiased estimators based on second-order statistics. Furthermore, the matching approach, unlike existing methods, provides a useful estimate even when the channel is not uniquely identifiable from second-order statistics.