Determination of Wireless Communication Links Optimal Transmission Range Using Improved Bisection Algorithm

Abstract

In this paper, an improved bisection algorithm for computing the optimal transmission range of wireless communication links was presented. The optimal path length is based on the link budget equation for line-of-sight wireless communication links. Specifically, free space path loss model was used for the clear-air path loss while multipath fading and rain fading were the two fade mechanisms considered in the determination of the expected fade margin. Sample numerical example was carried out for a frequency of 10 GHz and a site located in the International Telecommunication Union (ITU) rain zone N. The result showed that at 10 GHz and with the given network and link parameters, the improved bisection algorithm converged at the 7th cycle while the classical bisection method converged at the 12th cycle. Further numerical examples were examined for frequencies ranging from 10 GHz to 200 GHz. In all, the improved bisection method had at least 41 % reduction in the convergence cycle when compared with that of the classical bisection method. A similar study with the classical Newton-Raphson method converged at the 4th cycle for a 12 GHz signal while the improved bisection method converged at the 6th cycle. Essentially, the Newton-Raphson method converges faster than the bisection and the improved bisection methods. However, it is very difficult to apply the classical Newton-Raphson method when several clear-air path losses are to be considered or when complex path loss model such as the Hata model is used in the path loss computation. As such, the improved bisection method is preferred due to its simplicity and also it offers convergence performance that is comparable to that of the classical Newton-Raphson method.