Analysis of Electromagnetic Wave Propagation in Indoor Environments

Transcription

1 Analysis of Electromagnetic Wave Propagation in Indoor Environments Paulo G. Esperante, Raquel Cymrot, Paulo A. Garcia, Marcos S. ieira, Marcelo Perotoni School of Electrical Engineering Mackenzie University Rua da Consolação, ZIP CODE 2-7 SÃO PAULO - SP - BRAZIL paulo.esperante@mackenzie.br, raquel.cymrot@mackenzie.br, paulo.garcia@mackenzie.com.br, marcos_sv@mackenzie.com.br, marcelo.perotoni@cst.com Abstract: The wireless networks have been the object of many studies and analyzes of current technology industry, providing not only communication with mobility to end users, but also incorporating new applications. One such technology is known as Wireless Fidelity (Wi-Fi) 82.. This paper aims to present the behavior of the propagation of electromagnetic waves radiated from an access point Wi-Fi (AP), with different positions of the antenna. These analyses were based on measurements taken in an environment considering line of sight (LOS) at different distances from the AP, but in a confined environment. Consequently, although there were no obstacles (LOS) between transmitter and receiver, there were conditions of confinement on the propagated signal, given the characteristics of this environment (such as the height of the ceiling and the walls themselves). Thus, measurements were made by switching the antenna positioning of the access point, vertically and horizontally. From the analysis of these measurements, it was possible to verify the positioning of the antenna in the access point that generated improved signal coverage, even moderately. In addition, from the measured data (statistically based) the technique of linear regression was used in order to generate mathematical models for each specific situation measured. These proposed models were compared to the Friis model plus correction factors, and were used both for validating the measurements, as a basis for installation of new access points in similar environments. Key-Words: antenna, electromagnetic waves, Friis, line of sight, propagation, statistic analysis, wireless, Wi-Fi Introduction Two decades ago, telecommunications networks were predominantly wired, implying some limitations due to the fact there was a need for a physical connection among the parties. With the growth of telecommunications, wireless networks have taken over many of the of communications services, since that kind of communications offers services that facilitate people and companies life [][2]. The Wireless Fidelity (Wi-Fi) is a set of specifications for wireless local area networks (WLAN - Wireless Local Area Network) based on IEEE 82.g standards (Institute of Electrical and Electronics Engineers, 2) []. Due to the flexibility of Wi-Fi, it has become widespread the implementation of networks that use this technology in different places, mainly as a result of the previous mentioned advantages and by the reduction of costs. It is common to find available Wi-Fi services in hotels, airports, bus stations, bars, restaurants, malls, schools, universities, offices, hospitals etc. that offer Internet access, often free of charge. For the user to connect to this network it is necessary to have a notebook, desktop, smartphone, or any compatible Wi-Fi device. Wi-Fi transmission occurs through electromagnetic waves. The propagation of electromagnetic waves might be analyzed and modeled by many models and equations. One way can be Friis Equation that is a mathematical model that represents a signal transmitted in a medium in which there is a loss of signal power as a result of free space loss. Friis Equation is relevant once other models that explain these phenomena are based on it. This equation is based on transmission in Line Of Sight (LOS). Other models of electromagnetic waves propagation are compounded by variables that attenuate the signal due to obstacles, number of building floors, kind of flooring, kind and number of ISBN:

2 walls, furniture lay-out, opening of doors and distance from the antenna [][]. It is extremely important the comprehension of the factors that cause the multiple paths, however they are practically inevitable especially in indoor environments. The multipath effect occurs due to four phenomena: diffraction, scattering, reflection and refraction. The prediction of such phenomena might be best addressed with the design of transmitters in a confined environment. The Line Of Sight (LOS) situation does not consider multipath effects. It is really necessary to specify the kind of multipath, since it is not unusual for the electromagnetic wave to be blocked by doors, walls, floors and other obstacles [][][]. There are simple mathematical models, for example, the Line Of Sight (LOS), in which there is no obstacle between the transmitter and the receiver. That model is the Friis Equation. Performing a series of transformations and substitutions [][7][8], we obtain the following free space attenuation model: 2 Problem Formulation The objective of this paper is to analyze the WiFi signal, and the behavior of electromagnetic wave propagation in indoor environment. Measuring the attenuation levels during a certain time then based on the collected data, later it was performed a linear regression analysis that was compared with the Friis Equation. For transmitting the Wi-Fi signal a WiFi Access Point D-LINK model DL-2 AirPlus Xtreme G with a monopole-type antenna of cm, using the channel frequency (2.7 Gz). To measure the received signal level, an Itautec InfoWay model N8 series notebook was used. Any kind of notebook could have been used since they do not impose any changes in the performed measurements. The measurements in Line Of Sight occurred in the hallway on the ground floor of the building Engineering School of Mackenzie Presbyterian University. Measurements started after meters in a hallway meters wide. A total of measurement points were defined. The access point antenna was installed at. meters of height from the ground. To check the received power on the notebook it was used the Wireless-Mon software, which ensures the measurement of only one Access Point (AP's) even in the presence of others signal sources. The regression analysis aims to model and investigate the relationship between a response variable and one or more predictor variables (regressor). The linear models coefficients are estimated to minimize the quadratic errors sum (least squares methods) []. A way of quantifying part of the explain variability by the model is calculating the coefficient of determination, R 2, which is a number that varies from to. Fig. Wireless Transmitter - starting point and final point in the corridor to meters The closer this variable is to one the better the model is. The addition of new variables always increases the value of R 2, regardless of the relevance of this variable. It has to be thought over if the increment of this variable in the regression is worthwhile, because of the model s degrees of freedom lost in the residual. After the model is built, it has to be done the residual analysis to verify if the theory model suppositions were satisfied []. It was realized an experiment in line of sight (L.O.S.) condition, the independent variable was the distance and the dependent variable was the signal level. After that, it was done an analysis in the obtained data as to find out the linear regression model that best models or represents the measured results. The computed of electromagnetic wave propagation model was then compared with preexistent models like Friis equation. In order to perform a regression analysis, ANOA tables were built and tested the significance of each variable model, comparing the measured variability for each factor with the residual variability. The factors that are considered significant are the ones with descriptive level ISBN:

3 (P-value) less than the significance level fixed for each test, in general equal to % []. The suppositions that have to be verified about the residuals are that they have Normal distribution, with zero mean, constant variability and their independent relation. The Normal distribution of the residuals is verified using the Normal Probability Plot. Using the thick pencil rule, it can be asserted that the residuals obeyed a Normal distribution when all the points can be hidden by a straight line drawn with a thick pencil. This is a descriptive test. It is desired that statistical tests for testing normality are performed, with the hypothesis of Normal distribution not rejected when the descriptive level (P-value) test is larger than the significance level. The histogram helps to test the data normality; however its use is only meaningful when the number of collect data is large enough, such as the distribution form is very well represented in this graph. The supposition that the residual mean is zero is verified looking at the residuals versus fit graph. It is required an approximate symmetry of the dots in relation of the origin in the x axis. The supposition of constant variances is verified looking at the same residuals versus fit graph. When it is not noted an extreme difference when the fitted values changes, it can be concluded that the dispersion is approximately constant. The supposition of independence is verified by the residual versus order graph, i.e., when the order of the collected data is unknown, this graph is meaningless. The residuals have to be distributed randomly as the time goes on, without any established pattern. The uses of graphs are important to interpret a result. The Boxplot is a statistical tool that e helps the results analysis and contain information in a graphical format. This graph has a box format, with the superior level given by the rd quartil and the inferior level given by the st quartil. The median is represented by a line in the box interior and two line segments are drawn in the extreme of the box until maximum and minimum. alues that are not inside the box are called outliers and are shown as asterisks. The graphic representation given by boxplot provides, among other information, the data variability and symmetry. Problem Solution The experiment can be divided in two analyses. At first the antenna was in the horizontal position and in the second analysis, the antenna was in vertical position. By performing the regression in order to obtain the regression models, it was found equation 2, with the antenna in a horizontal position and equation with the antenna in a vertical position. Then Friis equation is presented (equation ), which represents the theoretical model. The coefficient of determination for the regressions presented in 2 and equations were respectively equal to 8,7% e 2,2%, results that shows how the total variability of the measures were explained by the models. The equation 2 and the equation differ slightly, but these differ from the theoretical Friis equation. This happened because in indoor narrow environments with Line Of Sight, it is very likely that multipath effects take place must occur. The data were analyzed using the software Minitab. Figure presents the results of the residual analysis with the antenna positioned horizontally. It is noted that the residual s of the experiment presented a Normal distribution with P-value =,2. The other model assumptions were also verified, that is, the residuals had approximately zero mean, approximately constant variance, as shown in the graph of residual versus fitted values, and they seem apparently independent since the graph of residues versus order did not present a standard. Percent Frequency,, Plots for attenuation with antenna horizontally Normal Probability Plot istogram N AD,8 P-alue,2 Fig. plots for line of sight with antenna positioned horizontally Figure 2 shows the results of residual analysis with the antenna positioned vertically. The experiment did not show Normal distribution with P-value =.7, when the Anderson-Darling test was applied. owever, when the Ryan-Joiner test ersus Fits Fitted alue ersus Order Observation Order 7 ISBN:

4 was performed, the adherence to Normal distribution was proved, with P-value =.. The others model assumptions were verified, so the model can be used. Figure presents the test of equal variances for all the measurements in all of the distances and considering the two antenna positions. The Barlett test was used, once it adhered to the Normal distribution and such hypothesis was not rejected (P =,). Percent Frequency,, Plots for attenuation with antenna vetical Normal Probability Plot -2 istogram 2 N AD, P-alue,7 Fig.2 plots for line of sight with antenna positioned vertically, use of the Anderson-Darling test Distance Test for Equal ariances for mesurements 2 8 % Bonferroni Confidence Intervals for StDevs Fig. Test for equal variance for measurements with data of the antenna vertically and horizontally positioned With the calculated mean, figure was generated, which presents the interaction between the variables distances and positions of the antenna, which shows the behavior of attenuation for both antenna vertically and horizontally positioned. It can be seen that there is little difference between the signals received by 2 meters and meters. This phenomenon probably occurred because there is a lowering in the ceiling to 2 meters where the multipath probably masked the measurements to 2 meters. As can be seen in Figure. Figure shows the Boxplot chart that allows analyzing the symmetry of the measurements and ersus Fits Fitted alue ersus Order Observation Order Bartlett's Test Test Statistic 2,7 P-alue, Levene's Test Test Statistic, P-alue, the dispersion of the data, which is bigger as the spacing of the boxes grows. There is also the presence of some outliers in the graph, which are represented by asterisks. There are lines of segments joining the averages for each distance with the antennas in both positions. Note that the location influences the measures, which are always higher when the antenna is vertically positioned. Mean 8 7 Interaction Plot for medições Data Means 2 8 Distance Fig. Interaction plot for analysis in line of sight with antenna vertically and horizontally positioned alues of measurements 8 7 Distance (m) 2 Fig. Boxplot of data for line of sight with antenna vertically and horizontally positioned Conclusion Analyzing the behavior of electromagnetic wave in free space, which means has no obstacle between transmitter and receiver, the distance factor had expected behavior since the greater the distance the greater the attenuation. Performing comparisons with the Friis model, one can verify that the created models have different equations, which is justified since the measures were obtained in a hallway, which leads to the multipath signal. owever, in both cases (AP antennas in the vertical and horizontal position), the attenuation showed similar behavior. The generated models also showed constant variance attenuation with distance, similar to the Friis model. This shows that the models created can be used to scale the 2 2 Boxplot of measurements ISBN:

5 placement of AP s in confined ambient with a good degree of accuracy and, in its absence, the basic model of Friss serve at least as an initial basis for this purpose. References: [] LOPES, R.; FREIXO, P.; SERRADOR, A., Indoor Propagation Models and Radio Planning for WLANs, INTERNATIONAL CONFERENCE ON E-BUSINESS AND TELECOMMUNICATION NETWORKS, ol., 2, pp [2] LASSABE F.; CANALDA P.; CATONNAY P.; SPIES F., Indoor Wi-Fi positioning: techniques and systems, Annals of telecommunications, ol., No -, 2 pp.. [] IEEE 82. Working Group, 2 < ml>. [] NAJNUDEL, M., Estudo de propagação em ambientes fechados para o planejamento de WLANs. Disertação (Mestrado em Engenharia Elétrica)-Pontifícia Universidade Católica do Rio de Janeiro, 2. Disponivel em: < eq=@>. [] SARKAR, T. K.; JI, Z.; KIM, K.; MEDOURI, A.; SALAZAR-PALMA, M., A Survey of various propagation models for mobile communication, IEEE Antennas and Propagation Magazine, v., n., p. -82, June 2. [] SAUNDERS, S. R. Antennas and Propagation for Wireless Communication Systems, John Willey&Sons, London,. [7] RAPPAPORT, S.T. Wireless Communications: Principles and Practice, Pearson Prentice all, 28. [8] DAIES, J.N.; GROUT,.; PICKING, R., Prediction of Wireless Network Signal Strength within a Building, Proceedings of the Seventh International Network Conference (INC 28), University of Plymouth, 8- July 28, pp-. [] MONTGOMERY, D. C.; RUNGER, G. C., Applied Statistics and Probability for Engineers, John Wiley & Sons, 2. ISBN: