Mathematical model for wimax

Propagation analysis of WiMAX (IEEE 802.16-2004) network signal on the Polytechnic Campus ESPE

Diego Almeida, Román Lara, Darwin Aguilar
Department of Electrical and Electronics
Army Polytechnic School
Quito, Ecuador

Abstract— Propagation analysis describes the methodology to find a mathematical model for the campus of the University through the study of several related projects. Itdetails the characteristics of the teams involved in this investigation. It also shows an analysis of the results obtained with the spectrum analyzer, after taking nine measurements in each of the 185 selected points. Consequently, using the measurements taken on campus, you get a unique mathematical model of propagation environments like the Polytechnic School. Furthermore, it validates the equationfollowing a comparative analysis of the mathematical expression found in other models of propagation loss. We also compile an interactive map of signal coverage with data measured at the ESPE and data obtained from the ESPE_MODEL model.
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Keywords: WiMAX, IEEE 802.16-2004, propagation model, attenuation of signal, coverage.

I. IntroductionWiMAX technology has been installed throughout the campus Army Polytechnic School (ESPE) for this reason the University's wireless network has advantages over other standards because it has a high capacity for a considerable number of users.

It needed the power measurement of the spread of radio signal transmitted by the base and through analysis of field data, finding a mathematical model ofpropagation, contributing to this by improving data transmission in the Campus of the ESPE . The more accurate the prediction model can more accurately determine the value of power that must cover a region of interest.

The study areas are characterized by high student flow, administrative, commercial, all those with access to the WiMAX network, which is why we must analyze the quality of thesignal using the equipment purchased.

II. Theoretical Framework
Related Projects
The models are often based on probabilistic expressions for which power can be calculated with some possibility that the signal comes or not a specific point. Most models are based on measurements made ​​at the site of interest. It takes an amount necessary measures which are averaged to establish the equations ofpropagation in these media, which is useful for each environment. Some of these models can serve as a basis for other expressions, which is why you can not separate the mathematical theories of statistical information, can be acquired from the environment under study.

Okumura model based his studies on experimental measurements performed in Japan. [1] Okumura-Hata empirical formula obtainedthrough a software. [2] Walfisch-Ikegami is the combination of models with empirical corrections for some parameters. [3] ERCEG and SUI model is based on extensive data collection were adopted by the group of the IEEE 802.16 as the recommended model for fixed WiMAX applications. [4] The model characterizes Allsebook British cities. [5] 3D Intelligent Ray Tracing is a geometric model. [6] The modelof propagation of electromagnetic waves for the City of Santo Domingo in the Dominican Republic following a similar methodology to this research. [7]
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Signal Propagation
The way in which the signal goes from the base station to the subscriber station can easily pass as the case of LOS (line of sight) in which there are no obstacles to an environmentin which such obstacles arise as buildings, forests and other elements that may interfere with the transmission. [8] The electromagnetic waves in a collision with a surface can be affected by several phenomena. The most common are: reflection, refraction, diffraction and scattering.

Mathematical models of propagation.
Table I. Modelos matemáticos de propagación de potencia
MODEL |...