Characterization of Non-Stationary Channels Using Mismatched Wiener Filtering

A common simplification in the statistical treatment of linear time-varying (LTV) wireless channels is the approximation of the channel as a stationary random process inside certain time-frequency regions. We develop a methodology for the determination of local quasi-stationarity (LQS) regions, i.e., local regions in which a channel can be treated as stationary. Contrary to previous results relying on, to some extent, heuristic measures and thresholds, we consider a finite-length Wiener filter as realistic channel estimator and relate the size of LQS regions in time to the degradation of the mean square error (MSE) of the estimate due to outdated and thus mismatched channel statistics. We show that for certain power spectral densities (PSDs) of the channel a simplified but approximate evaluation of the matched MSE based on the assumption of an infinite filtering length yields a lower bound on the actual matched MSE. Moreover, for such PSDs, the actual MSE degradation is upper-bounded and the size of the actual LQS regions is lower-bounded by the approximate evaluation. Using channel measurements, we compare the evolution of the LQS regions based on the actual and the approximate MSE; they show strong similarities.