On estimation error outage for scalar Gauss-Markov processes sent over fading channels

Measurements of a complex scalar linear Gauss-Markov process are sent over a fading channel. The fading channel is modeled as independent and identically distributed complex normal random variables with known realization at the decoder. The optimal estimator at the decoder is the Kalman filter with random instantaneous gain and error variance. To evaluate the quality of estimation at the receiver, the probability distribution function of the instantaneous estimation error variance and its outage probability are of interest. For the special case of the Rayleigh fading channels, upper and lower bounds for the outage probability are derived which provide insight and simple means for design purposes.