Stability conditions for optimal filtering over cognitive radio system

Cognitive radio system is a very popular area in the communication community as it saves money and bandwidth by sensing the available licensed spectrum for unlicensed users. This advantage provides a promising future for the application of cognitive radio in control systems. In this paper, we propose to communicate through a cognitive radio link between the sensor and the estimator. In this way, the state estimator needs to adjust to this new communication link as the link is affected by the interruptions from primary users. We assume the emergence of primary users results in packet losses. The link is assumed to be governed by multiple semi-Markov processes each of which can capture and represent one channel in it. We derive sufficient conditions for the stability of the peak covariance process of the optimal filter. A numerical example is given to demonstrate the theorems.