The Role of AoI in a Cognitive Radio Network: Lyapunov Optimization and Tradeoffs

We study the problem of a two-user, single-channel cognitive radio network, in which the objective is to maximize the secondary user (SU) throughput subject to a constraint on the probability of collision experienced by the primary user (PU). The transmit/idle dynamics of the primary user is modeled as a binary Markov chain, and the secondary senses the channel and decides on its transmission and sensing strategy based on the estimated evolution of the primary user transmission state. Because of the Markov model of the primary user dynamics, the age of the information sensed by the secondary has an impact on its belief when it is not sensing. We apply a Lyapunov optimization algorithm to solve the constrained throughput optimization problem, which utilizes the AoI-dependent PU idle/transmit probability to make the SU's sense/transmit decision in each slot. We then apply the Lyapunov framework to identify the tradeoff between three fundamental information qualities: AoI, accuracy, and completeness. Characterizing these types of tradeoffs can be a useful intermediate step towards optimizing a variety of objectives.