Estimation and Control over Cognitive Radio Channels with Distributed and Dynamic Spectral Activity

TL;DR

This paper explores the integration of control and estimation over cognitive radio channels modeled as two-switch systems, revealing that optimal control laws are nonlinear and the separation principle does not hold in this context.

Contribution

It derives the optimal linear estimator for CR links, analyzes the nonlinear nature of LQG control laws, and discusses stochastic stability conditions in cognitive radio-based control systems.

Findings

Optimal linear estimator for CR links derived

LQG control law over CR links is nonlinear in the state estimate

Separation principle is violated in CR-based control systems

Abstract

Since its first inception by Joseph Mitola III in 1998 cognitive radio (CR) systems have seen an explosion of papers in the communication community. However, the interaction of CR and control has remained vastly unexplored. In fact, when combined with control theory CR may pave the way for new and exciting control and communication applications. In this paper, the control and estimation problem via the well known two switch model which represents a CR link is considered. In particular, The optimal linear estimator subject to a CR link between the sensor and the estimator is derived. Furthermore, it is shown that in the Linear Quadratic Gaussian (LQG) Control law for a closed-loop system over double CR links is not linear in the state estimate. Consequently, the separation principle is shown to be violated. Several conditions of stochastic stability are also discussed. Illustrative numerical examples are provided to show the effectiveness of the results.