Joint PHY-MAC Design for Opportunistic Spectrum Access in the Presence of Sensing Errors

We address the design of opportunistic spectrum access (OSA) strategies that allow secondary users to independently search for and exploit instantaneous spectrum availability. The design objective is to maximize the throughput of secondary users while limiting the probability of colliding with primary users. Integrated in the joint design are three basic components: a spectrum sensor at the physical (PHY) layer that identifies spectrum opportunities, a sensing strategy at the medium access control (MAC) layer that determines which channels in the spectrum to sense, and an access strategy, also at the MAC layer, that decides whether to access based on sensing outcomes that are subject to errors. We formulate the joint PHY-MAC design of OSA as a constrained partially observable Markov decision process (POMDP). Constrained POMDPs generally require randomized policies to achieve optimality, which are often intractable. By exploiting the rich structure of the underlying problem, we establish a separation principle for the joint design of OSA. Specifically, the optimal joint design can be carried out in two steps: first to choose the spectrum sensor and the access strategy to maximize the instantaneous throughput under a collision constraint, and then to choose the sensing strategy to maximize the overall throughput. This separation principle reveals the optimality of myopic policies for the design of the spectrum sensor and the access strategy, leading to closed-form optimal solutions. Furthermore, decoupling the design of the sensing strategy from that of the spectrum sensor and the access strategy, the separation principle reduces the constrained POMDP to an unconstrained one, which admits deterministic optimal policies. Numerical examples are provided to study the design tradeoffs, the interaction between the PHY layer spectrum sensor and the MAC layer sensing and access strategies, and the robustness of the ensuing design to model mismatch.