Age of Sensed Information in a Cognitive Radio Network

Age of information is often studied as a primary objective to be optimized, but for problems where age is not the primary objective, it can still have a major role that can be utilized. This work studies a two-user, single-channel cognitive radio network, where the primary user’s transmit/idle dynamics are modeled as a binary Markov chain, and the secondary user decides to either sense or transmit. Under this setup, the age of the information sensed by the secondary user has a direct impact on its performance. The secondary user aims to maximize its throughput subject to a constraint on the probability of collision experienced by the primary. Using the Markov chain model of the primary user, the secondary user decides on its transmission and sensing strategy based on the estimated evolution of the primary user transmission state. For a stationary randomized transmission policy that depends on the sensed state, we derive the secondary throughput and the collision probability. Due to the complexity of the resulting expressions, we develop an alternative formulation of the problem by recognizing that the throughput and collision probability are functions of the age of each type of sensed information. Therefore, we transform the problem by converting the randomized policy to its induced age distribution function. As a result, the age distribution-based formulation results in a linear program, which can be solved efficiently. We include numerical results and simulations, and discuss the role of the age distribution and other related qualities of the information.