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

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 QMMcalibrations 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 indoorto-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. Planning for wireless communications network deployment may consequently select any basic model of choice for QMM-calibration, and hence, identify relative contributions to pathloss by the model's component parts.

On the Quasi-Moment-Method as a Rain Attenuation Prediction Modeling Algorithm

“…As pointed out in [33] and [35] and demonstrated in [34], the solution to the prediction problem given by ( 6) is unique when all the basis functions in the set are linearly independent.…”

“…assumes its smallest possible value: that is, [33], the numerical value of the quantity (3) in which is a weighting function, is the minimum possible. In particular, is required to be derivable from a 'base' function known to have, with reasonable accuracy, predicted rain attenuation, and which will admit representation in the form [33], [34],…”