On Estimation Error Outage for Scalar Gauss–Markov Signals Sent Over Fading Channels

Measurements of a scalar linear Gauss-Markov process are sent over a fading channel. The fading channel is modeled as independent and identically distributed random variables with known realization at the receiver. The optimal estimator at the receiver is the Kalman filter. In contrast to the classical Kalman filter theory, given a random channel, the Kalman gain and the error covariance become random. Then, the probability distribution function of expected estimation error and its outage probability can be chosen for estimation quality assessment. In this paper and in order to get the estimation error outage, we provide means to characterize the stationary probability density function of the random expected estimation error. Furthermore and for the particular case of the i.i.d. Rayleigh fading channels, upper and lower bounds for the outage probability are derived that provide insight and simpler means for design purposes. We also show that the bounds are tight for the high SNR regime and that the outage probability decreases linearly with the inverse of the average channel SNR.