Modeling of initial contention window size for successful initial ranging process in IEEE 802.22 WRAN cell

Avoiding collision among contending customer premise equipments (CPEs) attempting to associate with a base station (BS) in a wireless regional area network (WRAN) is a challenging issue. The collision probability is highly dependent upon the size of the initial contention window and the number of contending CPEs. To reduce the collision probability among CPEs in order to start the ranging process in an IEEE 802.22 network, the BS needs to adjust the initial contention window size. This paper provides an analytical framework to estimate the ranging request collision probability depending upon the size of the initial contention window and the number of CPEs attempting to join the IEEE WRAN cell. The accuracy of the estimated curve is analyzed for various numbers of contention CPEs on the basis of the relative errors. The numerical results confirm that the approximation works reasonably well for finding the ranging request collision probability for any number of contention CPEs at a particular value of initial contention window size. Moreover, this approximation provides the threshold size for a contention window to start the initial ranging process for any number of CPEs in an IEEE 802.22 network.