Mathematical analysis of Primary Users characteristics effects on Cognitive Radios

Cognitive Radios (CRs) have been recently proposed for the problem of spectrum scarcity. The main principle of the operation of these radios is based on the opportunistic access to the frequency spectrum mainly dedicated to Primary Users (PUs). However, statistical characteristics of PUs, either their spatial distribution or time pattern of channel usage can affect the usability of a specific frequency band for CRs. In this paper, based on mathematical analysis, first, the effect of the spatial distribution of PUs on the number of CRs in an Ad-Hoc configuration will be investigated. Analysis of this case shows that there are limits on the number of CRs for full coverage of a given area when they transmit simultaneously with PUs. Then, based on the temporal statistics of PUs, i.e., their arrival rate and channel usage, the usability of a specific frequency band for CRs will be explored in a non-simultaneous scenario. Mathematical analysis shows that for a given temporal specifications of PUs, there is an upper bound for the achievable data rates CRs may obtain.