On the Distribution of Opportunity Time for the Secondary Usage of Spectrum

In the future, secondary radio (SR) may exploit the use of spectrum holes (SHs) that are available over a given spectrum band for transmission, provided that the performance of the primary radio (PR) using the same spectrum band is not significantly degraded. However, random or quasi-random PR activities result in SHs that will sporadically be available. Hence, to study their impact on SR transmission, it is first required to statistically characterize the duration of SHs. We define the duration in which an SH is first available to the instance when it just becomes unavailable as the opportunity time (OT) for SR transmission. Our model partitions the spectrum band under consideration into N frequency bins (FBs). Between any two FBs, the PR activities are assumed to be independent, and the PR activities in each FB follow an exponential on/off process. We derive the theoretical probability density function (pdf) of the OT using a lumped Markov chain model. Our analysis shows that the pdf follows a hyperexponential distribution, and when the PR activity factors are pair-wise distinct for all the N FBs, the pdf is given by the weighted sum of (2^N - 1) exponential terms. In particular, if the N FBs have identical PR activity factors, the pdf will only consist of N exponential terms. The statistics of the OT could provide insightful information for the secondary usage of the spectrum.