Distortion Outage Analysis for Joint Space-Time Coding and Kalman Filtering

In this paper, we consider the scenario of transmitting a first-order Gauss–Markov vector signal over a multi-input multi-output (MIMO) Rayleigh nonfrequency selective fading channel. The signal is reconstructed at the receiver side with the help of a Kalman filter in order to minimize the mean squared error. Orthogonal space time codes are utilized in order to increase the quality of estimation and mitigate the destructing effects of the fading channel. As a criterion for estimation quality assessment, we use the distortion outage probability. We first obtain upper and lower bounds for the outage probability as a function of system parameters. We then perform high-SNR analysis of the bounds, through which we prove the achievability of the maximum diversity order for a $N\times K$ MIMO fading channel. In addition, we obtain upper and lower bounds for the coding gain of the distortion outage probability in the high-SNR regime, and outline the relation between system parameters and the coding gain.