Study of non-Markovian distributed primary radio activities on the opportunity time for secondary usage of spectrum

In this paper, the impact of non-Markovian distributed primary radio (PR) on/off activities on the opportunity time for secondary radio (SR) transmission is studied. The licensed spectrum is partitioned into N frequency bins (FBs) and each primary user is assumed to require only one FB for transmission. The PR activity in each FB is modeled as an independent on/off process. The sojourn time for PR activity in the `on´ state and in the `off´ state is described by the Pareto distribution and the hyper-Erlang distribution, respectively. Numerous cases are examined in this paper. In the first case, we assume the PR activity factors statistically identical in all the FBs. For this case, we examine the scenarios in which the PR traffic is light and also when it is heavy. In the second case, we assume that the PR activity factors between any two FBs are statistically different. Through the performance of extensive simulations, the probability density function (PDF) of the opportunity time is modeled and studied for different number of FBs, which is varied from N = 2 to N = 10. The goodness-of-fit of the statistical model to the simulated opportunity time is verified by the Kolmogorov-Smirnov test at 5% level of significance. The results show that when the PR activities are statistically identical, the PDF of the opportunity time can be described by a Gamma distribution. However, when the PR activities are statistically different, a hyper-Gamma distribution (mixture of Gamma distributions) provides a very good fit to the PDF of the opportunity time. We highlight the inadequacy of the exponential and hyper-exponential distribution fits for the PDF of the opportunity time in these cases. From these modeling results, the opportunity time can be reproduced with relative ease, and its statistics can be exploited for future SR performance studies.