Determination of Distribution Function for Large-Scale Wireless Communication Network

Abstract

This paper deals with the determination of signal distribution which is stochastic in nature in terms of transmitted and received signals in a metropolitan base station. An experiment was set up using a DS-CDMA system to transmit and receive signals at various places at the base station in the metropolitan wireless communication system.  Both transmitted and received signals were recorded. The paper analyses their mathematical modeling, relationship, and their statistics based on large-scale measurement data from a metropolitan wireless network. The result indicates that the distribution of signal at the base station in terms of transmission is alpha-stable Weibull probability density function whereas the receive signals are Weibull extreme value distribution because the maximum log-likelihood estimate from Matlab 2021a is -1553.5 and -1147.87 respectively. Since the pdf of alpha-stable distribution is not analytically expressible except for certain parameter values, the researchers mathematically modelled the alpha-stable distribution in which the pdf exists . The theoretically modelled alpha-stable pdf and that of the data are compared and are found to be the same.  Hence, it is theoretically and practically recommended that this method should be used in any field of Mathematics, Communication, and any other field where it uses is demanded.  It also recommended for further study to unearth how the characteristic function transforms to the modelled pdf.