Distance dependence of path loss models with weighted fitting

Abstract

The path loss model describing the power-law dependency on distance plus a log-normally distributed shadowing attenuation, is a staple of link budgets and system simulations. Determination of the parameters of this model is usually done from measurements and ray tracing. We show that the typical least-square fitting to those data points is inherently biased to give the best fitting to the link distances that happen to have more evaluation points; this bias might be highly undesirable in various types of simulations that use the resulting model. In this paper we present a weighted fitting method to address this issue. While it is unavoidable that fits are better for one distance range than another, we argue that such a decision should be made consciously, and adjusted to the type of simulation for which the path loss model should be used. We discuss the weighting functions for different purposes, and show their impact on prediction accuracy of signal level, interference level, and capacity in a hexagonal cellular grid simulation. As examples, weighted fitting models are presented for 28 GHz channels in urban macrocells, and it is shown that the fitting accuracy can be improved by our approach.