^{1}

^{1}

^{1}

^{1}

^{*}

This paper shows a comparison between theoretical and experimental coverage analysis. Theoretical work is based on Okumura-Hata propagation model, which are compared with the measured data obtained through an experimental analysis en México City. It is important because all the network designers and managers have to take in account how the signals will arrive to the mobile devices. If they know it, they can install Nodes B (base stations) in the better place in the area in order to take advantage of the power radiated by the antenna.

A propagation model is a set of mathematical expressions, diagrams and algorithms used to represent the radio characteristics of a given environment. Generally, prediction models can be classified as empirical or statistical, theoretical or deterministic or a combination of these two (semi-empirical). While empirical models are based on measurements, theoretical models are based on the fundamental principles of the phenomena of radio wave propagation. Propagation models predict the path loss for an RF signal can be between a base station and a mobile or fixed receiver. The advantage of doing a radio channel model taking into account the characteristics of the path between transmitter (Tx) and receiver (Rx), is to determine the feasibility of projects that wish to plan in certain areas, so you can make a estimate of the need, costs and required equipment capacity (technical specifications). The performance of the propagation models is measured by the accuracy of the results compared with actual field measurements. The model described in this article has a good correlation in terms of the comparisons mentioned both in simulation and field measurements. The applicability of a model depends on this specification requires such as: the type of terrain (mountainous, hilly or quasi-smooth), the characteristics of the propagation environment (urban, suburban, and open), characteristics of the atmosphere (refraction index, rainfall intensity), soil electrical properties (conductivity ground), type of urban construction material etc. [

Several existing path loss models such as the Free Space Path Loss Model, Okumura-Hata’s Model, and Egli’s Model are chosen as reference for optimized path loss model development. The best existing path loss model with the smallest mean relative error to the measured path loss will be chosen as a reference for the development of the optimized path loss model. The regression fitting method is used to develop a new empirical linear line by combining the best existing path loss model with the measurement data which is collected from the WCDMA network. The new empirical linear line is used as a reference during optimization to develop an optimized path loss model [

The Okumura-Hata’s model is an empirical model based on extensive measurements made in Japan at several frequencies within the range of 150 to 1920 MHz. Okumura-Hata’s model is developed for macro cells with cell diameters of 1 to 100 km [

The Okumura’s Model is expressed as:

where:

L50 (dB): is the 50th percentile value of propagation path loss;

LF: is free space path loss;

Amu: is free space attenuation;

G(ht): is base station antenna height gain factor;

G(hr): is mobile antenna height gain factor, and G_{area}: is gain corresponding to specific environment.

This paper describes how Okumura’s model can be chosen for urban outdoor coverage in the Wide Code Division Multiple Access (WCDMA) system. This optimized path loss model is based on the empirical measurements collected in the WCDMA network focusing on Mexico City.

Wide Code Division Multiple Access is a channel access method that allows several simultaneous information transmissions over a single communication channel, with different distinguishing code patterns. WCDMA employs both the spread-spectrum technology and a special coding scheme to allow multiple users to be multiplexed over the same physical channel. In the WCDMA system, duplex channel is made of two 1.25 MHz-wide bands of spectrum. WCDMA is a technology of the direct sequence of Spread Spectrum; this technology expands the signals over a bandwidth of 5 MHz, buried in the noise in the channel, and has the capacity to carry voice and data simultaneously. WCDMA provides high transfer rates, efficient support of asymmetric traffic, transmission using packet switching through the radio interface and high efficiency in spectrum use. The Base Station (BS) also known as a Node B; is part of the UMTS Terrestrial Radio Access Network (UTRAN). The Node B is to perform fundamental tasks of transmission and reception of radio, filtering of the signal, amplification, modulation and demodulation of the signal and be an interface to the Radio Network Controller (RNC) [

The Common Pilot Channel (CPICH) transmits a carrier used to estimate the cannel parameters. It is the physical reference for other channels. It is used to control power, coherent transmission and detection, measurement of adjacent cells and obtaining the Scrambling Code (SC) [

Measurements were done, along the test area, (

The measurement procedure was performed in the band V (UMTS Channels), which has a center frequency of 887.5 MHz; which is used in Mexico for WCDMA services. The measurements were made with a spectrum analyzer, BTS Master MT8222A with frequency range of 9 KHz to 7.1 GHz, which has applications software for the analysis of WCDMA signal. The BTS Master can measure the performance of Node B by connecting directly to the Node B equipment or through the air by the connection of an omni-directional antenna, which operates in the frequency band of 870 to 960 MHz. To obtain the location information of each metering requires a GPS (Global Positioning System) antenna.

The first step for a correct analysis of the performance of a Node B is to delineate the area of interest where the measurements will be made; this area is shown in the ^{2}. In each measurement the spectrum analyzer was placed at a height between 1.10 and 1.30 meters, since it is the average height to which the user carries his mobile equipment.

For this work, the latitude and longitude were selected as a geographical reference of the system, and the CPICH power level because through the measurement of this power level, the user terminal is able to establish a connection with the Node B near, which provides the best service. This will allow that the user station know which is the dominant pilot that would define the coverage area.

The measurement equipment is capable of taking grab samples of the power levels at certain points. For adequate analysis requires the proper spacing between measurements, making it easy to apply statistical techniques such as Krige Method [

The Method of Krige is a family of generalized algorithms for least squares that from a set of observations provides the optimal linear predictor for the variable in any position. Daniel G. Krige developed the technique in an attempt to predict more accurately the mineral reserves. In recent decades the Krige Method has become a fundamental tool in the field of the geostatistics because founded the basis of linear geostatistical initially developed this method. It is a geostatistical method for estimating points that using a variogram model to obtain data. It is based on the premise that the spatial variation continues with the same pattern.

The variogram or semivariogram is a tool that allows analyzes the spatial behavior of a variable on a defined area, resulting in the influence of data at different distances. From the data provided by the theoretical variogram the estimation is performed by the method of Krige. The semivariogram is a measure of how similar the points are in the space when they are farther apart. To develop a variogram first requires creating an experimental variogram based on the selected simple, and choose a theoretical variogram that fit the experimental, because this is not a function where we can make interpolations. The semivariogram provides information of the spatial behavior of a variable. To quantify the degree and scale of spatial variation is necessary adjusting a function that describes the behavior of the variable [

The experimental semi-variogram (see

To minimize the variance of the mean square error of estimate is necessary to have a function that describes the behavior of the phenomenon discussed, as an interpolation between the points of the experimental variogram does not guarantee the existence and uniqueness of the solution of the Kriging system, that is why, based on the experimental variogram, we construct a theoretical variogram that resembles the actual behavior of the variable through the least squares approximation as is showing in the red line in the

The

The validation step shown in

The number of measurements needed to ensure a correct prediction of the measured power levels, depend on the range of variability of this power level. That is to say, if the power level is very variable, a greater number of measurements must be taken that when the power does not change quickly. Knowing the function most appropriate to the behavior of the measured power level the information is plotted so that geographical coordinates define the axes, and the power level determines the color, which represents the sample [

For complete analysis requires the use of different models of Geographic Information Systems (GIS, Geographic Information System) which is an organized integration of hardware, software and geographic data, designed to capture, store, manipulate, analyze and display

all forms of geographically referenced information, to solve complex problems of planning and management to meet specific information necessary for a general vision of the area of interest [