Entropy Analysis of Broadband Wireless Access Systems

Abstract

A Broadband Wireless Access (BWA) system consists of a base station and a set of $M$ users within its antenna sector, with $N$ simultaneously active users, $0\le N\le M$ , working in Point-to-Multipoint (PMP) mode. We model this system as family of Birth–Death Processes (BDPs), with size $M+1$ , in equilibrium, indexed by system utilization parameter $\rho$ , ratio of its primary birth and death rates. Relying on the fundamental concepts of system information $i$ and system entropy $S=E(i)$ , we develop an entropy analysis of BWA systems. Thereby, by definition, the system entropy, as the mean value of system information, is the uncertainty, related to the system. Taking system information as loss function, we identify risk and uncertainty, related to the system. Using the maximization of entropy, given the average number $\overline{N}$ of active users, we promote belt-zone of deviation from maximum uncertainty and a function of relative risk, regarding $\overline{N}$ , for a BWA system. This analysis is illustrated on BWA systems with finite user population, such as the binomial $M$ -server BWA systems, modeled by the family of BDPs with binomial distribution, and the delay single-server BWA systems, modeled by the corresponding family of BDPs; both systems represent private networks.