Statistical models of spectrum opportunities for cognitive radio

Dynamic Spectrum Access (DSA) is widely seen as a feasible solution to the problem of illusive radio spectrum clogging. The fundamental concept of DSA is to opportunistically access unutilised spectrum bands while respecting the rights of privileged incumbent users. DSA and spectrum policies depend on meticulous statistics of spectrum opportunities as well as spectrum occupancy models. In this paper, we develop a model to characterise the number of spectrum opportunities available using the probability and approximation theory. In particular, we derive the probability mass function (PMF) of the total number of spectrum opportunities available depending on the probability of each channel being free. We further analyse the complexity involved in calculating the PMF of the total number of available channels at any time and location and develop approximate models. Numerical results are provided showing that the proposed approximation models of spectrum opportunities achieve good accuracy at significantly lower computational cost.