Dynamic Models of Cognitive Radio Networks

Abstract

<p>A cognitive radio network is a multi-user system, in which different users compete for limited resources in an opportunistic manner, interacting with each other for access to the available resources. The fact that both users and spectrum holes (i.e., underutilized spectrum subbands) can come and go in a stochastic manner, makes a cognitive radio network a highly dynamic and challenging wireless environment. Finding robust decentralized resource-allocation algorithms, which are capable of achieving reasonably good solutions fast enough in order to guarantee an acceptable level of performance even under worst-case interference conditions, is crucial in such an environment. </p> <p>Considering a non-cooperative framework, the iterative waterfilling algorithm (IWFA) is a potentially good candidate for transmit-power control in cognitive radio networks for achieving a Nash-equilibrium point. IWFA is appealing because of its low complexity, fast convergence, distributed nature, and convexity. It can be reformulated as an affine variational inequality (AVI) problem. Employing the theory of projected dynamic (PD) systems, an affine dynamic model is obtained for the evolution of the network's state. This dynamic model allows us to study both equilibrium and disequilibrium behaviour of the network. The proposed dynamic framework also facilitates sensitivity and stability analysis of the system.</p> <p>The fact that changes happen in a cognitive radio network because of continuous dynamics as well as discrete events, makes it a hybrid dynamic (HD) system. Decision making is then a multiple-time-scale process. Modeling the system using the theory of PD lends itself to describing the cognitive radio network as a constrained piecewise affine (PWA) system and therefore, benefiting from various mathematical tools, which have been well demonstrated in control theory.</p> <p>Usually users use asynchronous update schemes and they update their transmit powers at different rates. The feedback channel introduces a time-varying delay in the control loop of a cognitive radio, which means sometimes users update their transmit powers using out-dated information. Therefore, the network is practically speaking a multiple-time-varying-delay system with uncertainty. Robust exponential stability of the network is studied in this framework.</p> <p>Theories of evolutionary variational inequalities and projected dynamic systems on Hilbert spaces were used to extend the developed framework further in order to address the multiple-time-scale nature of the cognitive radio network.</p>