Low-order Kalman filters for channel estimation

This paper addresses the design of low-order Kalman filters to estimate radio channels with Rayleigh fading. Rayleigh fading cannot be perfectly modelled with any finite order auto-regressive (AR) process. Previously, only first and second order Kalman filters were used for channel estimation since higher order Kalman filters were found to not significantly improve accuracy. This is due to mismatches in the statistics of the AR models of the Kalman filters and the true Rayleigh fading. In this paper, the coefficients of the AR models for the Kalman filter are calculated by solving for the minimum square error solutions of an over-determined linear systems. The AR models generated have statistics closely matching the Rayleigh fading process. The Kalman filter using these AR models can accurately estimate the Rayleigh fading process. The accuracy of the new Kalman filters is demonstrated in the tracking of simulated Rayleigh fading processes of different bandwidths.