Optimal Throughput Analysis of Random Access Policies for Cognitive Radio Networks with Multiple Channel Access

In this paper we consider a time slotted cognitive radio (CR) network with N wireless channels and M secondary users (SUs). We focus on a random access policy where each SU stochastically decides whether to access idle channels or not based on the given access probability (AP) that is adapted to the channel state information (CSI), if possible. The AP plays an important role in the random access policy because it can control the number of SUs who can access idle channels in a simple manner and hence alleviate packet collisions among SUs. We assume that each SU can access at most L idle channels simultaneously at a time slot whenever possible. We consider two extreme cases - a) where all SUs have full CSI and b) where all SUs have no CSI. We analyze the throughput of an arbitrary SU for the two extreme cases, and rigorously derive a closed-form expression of the optimal AP values that maximize the throughput of an arbitrary SU for the two extreme cases. In the analysis, we also show the impact of multiple channel access and the acquisition of CSI on throughput performance.