Complexity reduction for vehicular channel estimation using the filter divergence measure

A key component in vehicular communications systems is the channel estimation filter that suppresses the additive noise in the channel estimates from pilot symbols. A filter which offers the best performance in terms of mean square error (MSE) is the well known Wiener filter. A drawback of using filters based on second order statistics is that they have to be recalculated when the statistical properties of the channel have changed. In vehicular communications the observed channels do not follow the wide-sense stationary (WSS) uncorrelated-scattering (US) properties, and therefore their power spectral density varies over time. A non-stationary process can be divided in time into consecutive stationarity regions where the WSS and US properties are assumed to hold, allowing to calculate the coefficients of a Wiener filter. In this paper we analyze the increase of the MSE observed when using a mismatched Wiener filter. The mismatch results from using the filter coefficients calculated for a past stationarity region. We relate this concept of performance degradation to spectral distance metrics. We use the spectral divergence between scattering functions at different time instances. Furthermore, we introduce a new metric, the filter divergence, which takes noise into account. We show that, by accepting an increase of MSE, the same filter coefficients can be used for several time regions, which allows computational complexity reduction in a real system.