Comparison Between Known Propagation Models Using Least Squares Tuning Algorithm on 5.8 GHz in Amazon Region Cities

— This paper presents a performance comparison between known propagation Models through least squares tuning algorithm for 5.8 GHz frequency band. The studied environment is based on the 12 cities located in Amazon Region. After adjustments and simulations, SUI Model showed the smaller RMS error and standard deviation when compared with COST231-Hata and ECC-33 models.


I. INTRODUCTION
Since the constant increase of the wireless networks, studies of signal propagation are needed to ensure an efficient Pre-Project Stage in coverage and quality of services.This paper presents a study of the signal propagation in 5.8 GHz on Amazon region cities.
A performance comparison between known propagation models is made for an Amazon Region environment.The least squares tuning algorithm has been used to adjust the models to the measurements.It is important to remember that the terms related to reception and transmission heights in the models equations have been left unchanged.Although the models adjustments, differences in how the models work with reception and transmission height have influence in RMS error and standard deviation which are the metrics adopted in this work.This paper is organized as follows.In section II is presented explanations about the environment and the data acquisition.In section III a description of the propagation models is made.In section IV the least squares tuning algorithm is presented.In section V simulations and results are shown and finally, section VI shows the conclusions.

II. ENVIRONMENT AND DATA ACQUISITION
The collected data have been carried out in 12 cities on Pará State at Amazon Region, Brazil.These cities are known by their woodland environments.The vegetation normally appears mixed with the residential and commercial constructions resulting in a single medium.An example of Amazon region  The process for obtaining the distances between the clients and base stations is based on the coordinates that was collected during the implantation stage of these networks.

III. PROPAGATION MODELS
The propagation models used in this paper are COST231-Hata, SUI Model and ECC-33 model whose have reference in some performance comparison works [4]- [5]- [6].

A. Stanford University Interim (SUI) Model
SUI Model has had in your development the Stanford University participation.Variables involved in model prediction process are adopted for frequencies below 11 GHz.It is interesting to evaluate model performance for this case because SUI Model employs terrain properties on its equations so the base for calculating the propagation loss can be accomplished in an non-ideal way different of the free space equation method.
The base of the propagation model and the environment characterization are represented by the following equations [7]: for terrains type A and B (5) Where: Parameters , e chosen according to Table I:  Least Squares (LS) criterion is useful for linear adjustment cases.In this situation, the algorithm is represented by the idea of minimizing the sum of the squares of the differences between measured data and predicted data.These differences become an error function expressed as follows: ( ) The distance and frequency terms in the models equations were adjusted by the algorithm, however, the transmission and reception heights terms were not included in least squares tuning.
More details about LS algorithm applied in tuning method are described in [1]- [2].

V. SIMULATIONS AND RESULTS
Simulations have been done considering the mean and specific installation heights of the clients located at the 12 cities in study.The data obtained in the simulations are shown in Fig. 2-5.changing some parameters or adding a term which is related to some new environment feature.It is also foreseen an adjustment in SUI model for path loss prediction in mobility conditions.For such a purpose, measurement campaigns will be carried out.

Fig. 1 .
Fig. 1.Aerial view of Santarém city in Pará State, Brazil height, m IV.LEAST SQUARES ALGORITHM Due to the different characteristics of the environment where the models have been made, a tuning proceeding is needed to adjust model parameters to the measured data.

-
Number of total used data -Measured data 110

Fig. 2 .
Fig. 2. Propagation models performance using mean reception heights of the clients

Fig. 4 .
Fig. 4. Propagation models performance using specific reception heights of the clients

TABLE II .
RESULTS FOR MEAN INSTALLATION HEIGHT

TABLE III .
RESULTS FOR SPECIFIC INSTALLATION HEIGHT Results are relevant because RSSI collecting process has been performed in peculiar site-specific clients.Variations in models predictions, from Fig.4and Fig.5, are justified because each client has a specific CPE (customer premises equipment) installation height.RMS error (RE) and standard deviation (SD) values for all 12 cities in study are shown in TableIV.

TABLE IV .
RESULTS FOR SPECIFIC INSTALLATION HEIGHTIn this paper, a performance comparison between COST231-Hata, Stanford University Interim (SUI) and ECC-33 models is made for an Amazon Region environment.At the final performance evaluation, SUI Model has shown a better behavior than COST231-Hata and ECC-33 Models.Based on the obtained results, a proposal for future works can consider an adjustment of SUI Model by