Mean estimation MSE for Kalman filtering of large dimensional sources sent over fading channels

Uncoded transmission of a large dimensional Gauss-Markov vector process over a fading channel is considered. This problem is of interest in sensor network applications with data processing at the fusion center or in control and real-time monitoring where this method could be useful due to its simplicity and zero delay property. Assuming perfect channel knowledge at the receiver, the optimal estimator is the Kalman filter. In contrast to the classical Kalman filter, the prediction and estimation error covariance matrices are random. In this paper, by using Stieltjes transform analysis, we find an approximation to the pdf of the eigenvalue distribution of the estimation error covariance matrix for the high channel SNR regime. The approximated pdf is then used to obtain the mean estimation MSE of the Kalman filter.