On the Time Distribution of White Space Access Opportunities

In the future, secondary radios may exploit to use the spectrum holes (or white space) available over a given frequency band for transmission, provided the performance of the primary radio using the same spectrum is not significantly degraded. However, primary transmissions occur in bursts and hence spectrum holes are available sporadically. We define the duration in which a spectrum hole is first available to the instance it immediately becomes unavailable as the duration of white space access opportunities for secondary radios. In this paper, our model assumes a portion of the licensed spectrum is partitioned into N frequency bins, with the primary radio activities between any two frequency bins follow independent exponential on/off process. Our previous analysis showed that the probability density function of the white space access opportunities follows a hyper-exponential distribution. We present the approach to compute the theoretical probability density function of the duration of white space access opportunities for two frequency bins using an irreducible Markov chain model. For more frequency bins, the theoretical expression consists of many terms and may be difficult to handle. We perform extensive simulations and our results showed that in general only three exponential terms are needed to describe the continuous time distribution of white space access opportunities for secondary radios. The probability density function provides insightful information for the secondary usage of frequency bands.