Kalman Filter-Based Channel Estimation for Mobile-to-Mobile and Relay Networks

This letter deals with channel estimation in mobile-to-mobile communications, possibly including amplify and forward mobile relays, assuming a two-dimensional scattering environment. A second-order autoregressive [AR(2)] model with the Kalman filter is used to estimate the channel gain of the global multihop channel. The parameters of the AR(2) model can be tuned by using a classic correlation matching criterion. Alternatively, the use of a minimization of the asymptotic variance criterion permits a strong performance improvement, although the corresponding analytical study is still missing in the literature—which is the topic of this letter. The closed-form expressions for the optimal tuning of the AR(2) parameters and mean square error performance have been first established as a function of the second and fourth moments of the Doppler spectrum of the global channel. Because the analytical formulas of these moments were not given in the literature, we derive them by exploiting cumulant property of convolution of density functions, after decomposition of the global channel as a cascade of Jakes Doppler power spectral density channels. Consequently, the provided closed-form formula are helpful for the design of Kalman filters for a given state of the source, destination, and mobile relays [Doppler spread and signal to noise ratio].