On the Uniqueness of the Quasi-Moment-Method Solution to the Pathloss Model Calibration Problem

TL;DR

This paper investigates the conditions under which the Quasi Moment Method (QMM) provides a unique solution for calibrating pathloss prediction models, demonstrating that linear independence of model components ensures uniqueness.

Contribution

It establishes the theoretical conditions for the uniqueness of QMM solutions in pathloss model calibration, supported by empirical validation across different propagation scenarios.

Findings

QMM calibration solutions are unique when model components are linearly independent.

Recasting models for SVD calibration enhances the observability of solution uniqueness.

Empirical results show minimal differences in prediction errors confirming theoretical claims.

Abstract

Investigations in this paper focus on establishing the uniqueness properties of the Quasi Moment Method (QMM) solution to the problem of calibrating nominal radiowave propagation pathloss prediction models. Nominal (basic) prediction models utilized for the investigations, were first subjected to QMM calibrations with measurements from three different propagation scenarios. Then, the nominal models were recast in forms suitable for Singular Value Decomposition (SVD) calibration before being calibrated with both the SVD and QMM algorithms. The prediction performances of the calibrated models as evaluated in terms of Root Mean Square Prediction Error (RMSE), Mean Prediction Error (MPE), and Grey Relational Grade Mean Absolute Percentage Error (GRG MAPE) very clearly indicate that the uniqueness of QMM calibrations of basic pathloss models is more readily observable, when the basic models are recast in forms specific to SVD calibration. In the representative case of calibration with indoor to outdoor measurements, RMSE values were recorded for QMM calibrated nominal models as 5.2639dB for the ECC33 model, and 5.3218dB for the other nominal models. Corresponding metrics for the alternative (rearranged) nominal models emerged as 5.2663dB for the ECC33 model and 5.2591dB for the other models. A similar general trend featured in the GRG MAPE metrics, which for both SVD and QMM calibrations of all the alternative models, was recorded as 0.9131, but differed slightly (between 0.9138 and 0.9196) for the QMM calibration of the nominal models. The slight differences between these metrics (due to computational round off approximations) confirm that when the components of basic models are linearly independent, the QMM solution is unique.