Path Loss Prediction Using Fuzzy Inference System and Ellipsoidal Rules

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1 Amerian Journal of Applied Sienes, 2012, 9 (12), ISSN: Siene Publiation doi: /ajassp Published Online 9 (12) 2012 ( Path Loss Predition Using Fuzzy Inferene System and Ellipsoidal Rules 1 Mario Versai, 1 Salvatore Calagno, 1 Fabio La Foresta and 2 Biagio Cammaroto 1 Department of MECMAT, University Mediterranea, Reggio Calabria, Italy 2 Department of Civil Engineering, University of Messina, Contrada di Dio, I Messina, Italy Reeived , Revised ; Aepted ABSTRACT It is well known as the predition of radio wave path loss in urban environment plays a key role in order to orretly plan wireless systems and mobile ommuniation networks. To obtain more flexible predition models able to give aurate results, in reent years Soft omputing Tehniques has been exploited. In this study, a novel approah based on ellipsoidal fuzzy inferene system EFIS is investigated. Results ompared with those provided by the Okumura Hata model and the standard Fuzzy Inferene System approah (FIS) show superior performanes of the EFIS approah. Keywords: Path Loss, Soft Computing, Fuzzy Inferene System, Ellipsoidal Rules 1. INTRODUCTION with suess to solve a wide variety of problems suh as modeling lustering of entropy topography in epilepti The predition of the path loss in an urban eletroenephalography (Mammone et al., 2011a; 2011b; environment is of paramount importane for the design Labate et al., 2011a; 2011b; Mammone et al., 2012; and planning of the modern mobile ommuniation Morabito et al., 2012), dynamial reonstrution of road systems. As a matter of fat, information on the behavior longitudinal profiles (Costantino et al., 2012), predition of this parameter is ruial in determining link budgets, problems in nulear fusion appliations (Versai and ell sizes and reuse distanes. At this purpose, empirial Morabito, 2003), for modeling mirowave devies and and theoretial models for the path loss predition have antennas (Angiulli and Versai, 2002; 2003). In been developed during the years. However, both the partiular, among the different methodologial lass of models suffered of some drawbaks. Classial approahes provided by Soft Computing, in this study, a empirial models are often unsatisfatory in term of novel approah based on the fuzzy inferene system predition auray and rarely they adapt well to EFIS oupled with ellipsoidal rules to foreast the path different types of propagation environment, while loss behavior, is investigated. Atually, in the literature theoretial models are laking of omputational the ellipsoidal fuzzy systems have not muh been used effiieny. To obtain more flexible empirial models beause are haraterized by means of geometrial apable to give aurate predition results, in reent omplexity. So, their exploitation is often limited to years Soft Computing Tehniques have been exploited appliations where a better preision is required. The (Neskovi et al., 2000). Soft omputing tehniques study is organized as follows: The next setion realls (artifiial neural networks, geneti algorithms, fuzzy basis on the path loss onept and the Okumura-Hata logi models, partile swarm tehniques) are an model. Then, an overview the EFIS fuzzy approah is attrative alternatives to the standard, well established given. Finally numerial results and onlusions are hard omputing paradigms and they have been exploited drawn. Corresponding Author: Mario Versai, Department MECMAT, University Mediterranea, Reggio Calabria, Italy 1940

2 Mario Versai et al. / Amerian Journal of Applied Sienes, 9 (12) (2012) MATERIALS AND METHODS 2.1. Path Loss and the Okumura-Hata Model Path Loss L is a measure of the signal level attenuation aused by propagation mehanisms. It is defined as Eq. 1: L P t db = 10log P r (1) where, P t and P r are the transmitted and reeived power, respetively. The Okumura-Hata model is likely to be the most used and widespread path loss predition model. It is based on experimental data olleted in Japan at different frequenies inluding in the range MHz, for a height of the transmitting antenna ranging between meters. It gives the average path loss for urban areas as Eq. 2: L = log(f ) UA,dB 13.82log(h ) + a(h ) + log(d) eff rx (2) f = The arrier frequeny in MHz d = The antenna separation distane (ranging between 1-20 Km) h eff = The effetive height of the transmitting antenna h rx = The height of the reeiving antenna (ranging between 1-10 m) a(h rx ) = The orretion fator (db) and is Eq. 3: = log(h eff ) (3) This model also assumes that there are no dominant obstales between the transmitting and reeiving antennas and that the ground profile hanges slowly. The average path loss for suburban area is formulated as Eq. 4: LSUA,dB = LUA,dB 2 log f 28 (4) while in the rural open environment assumes the form Eq. 5: 2.2. Fuzzy Inferene System and Ellipsoidal Rules: A Brief Review NFIS approah is a logial tool that maps inputs to outputs by bank of fuzzy rules providing a basi from whih it is possible to take important deisions. Typially, a Sugeno-FIS an be strutured into three setions: Membership funtions, fuzzy operators and bank of if then rules whih represents the inferene of the proedure. Sugeno inferene performs by the four following setions Fuzzifiation of the Inputs It is imperative to determine the degree to whih inputs (represented by fuzzy sets in Sugeno s inferene) belong to eah fuzzy set by means of membership funtions. This degree represents the degree to whih eah if-part of eah rules has been satisfied Appliation of Fuzzy Connetives If the anteedent of a rule has more than one part, the fuzzy operator is applied to obtain one number representing the results of the anteedent for that rule. Using AND onnetive, the anteedent of eah rules is ative to the minimum values Impliation Proedure The onsequent part of eah rules, that Sugeno s inferene strutures by singletons, is ativated to the results of the anteedent for that rules Defuzzifiation The output is omputed by a linear ombination of the single fuzzy singletons ative as reported to previous step. Nevertheless, to generate optimal FIS it is possible to exploit GENFIS proedure that exploits fuzzy subtrative lustering to determine the number of rules and anteedent membership funtions and then uses linear least squares estimation to determine eah rule s onsequent equations (Jang, 1993). Regarding EFIS, the ovariane of date identify ellipsoidal rules (pathes). In partiular, eah rule is represented by an ellipsoid overing a portion of inputs-outputs spae and they overlap. Geometrially, an ellipsoid z an be represented by eigenvetors and Eigen values of a positive definite matrix A: If n and p are is the number of inputs and outputs respetively, q = n + p represent the ellipsoid dimension Eq. 6: L L 4.78(log(f )) 2 ROE,dB = UA,dB (log(f )) (5) 2 T α = (z ) A(z ) = Λ T T (z ) P P (z ) (6) 1941

3 Mario Versai et al. / Amerian Journal of Applied Sienes, 9 (12) (2012) α = R + = Centre of ellipsoid A = Diagonal matrix of Eigen values of A P = Orthogonal matrix that orient the ellipsoid Its olumns are the unitary eigenvetors while the lengths of semi axis are omputed by Eq. 7: α λ,..., α λ 1 q λ k = Eigen values of A = Centre of ellipsoid (7) Finally, eah ellipsoid represents a fuzzy rule and then, its projetion on eah possible values axis represents the support of membership funtion. In our ase, triangular membership funtions are onsidered (Dikerson and Kosko, 1996). 3. RESULTS AND DISCUSSION In order to fae the path loss predition problem by means of the EFIS approah, we have onsidered an EFIS network having the following inputs: (i) the arrier frequeny, (ii) the transmitting antenna gain, (iii) the reeiving antenna gain, (iv) the distane from the radiobase station, (v) the height of the building (vi) the length of the street, (vii) the building separation, (viii) the height of the transmitting antenna, (ix) the height of the reeiving antenna, while the output is the path loss value. For the designing and training our NFIS model, we have exploited the MatLab Genfis toolbox (Jang, 1993). A database of 2000 path loss values has been built exploited a syntheti urban senario model using Wireless InSite, a ommerial software based on the ray-traing method. Afterwards, a testing dataset of further 1000 path loss values has been built for testing the predition ability of the model. Table 1 shows some parameter used in simulations. All omputations have been arried out using a PC with two Intel Core2 CPUs at 1.66 GHz and 4 GB of RAM. The performanes of the EFIS network are ompared with those offered by the Okumura Hata model and by a standard Fuzzy Inferene System (FIS) network. The foreasting auray of these models have been evaluated in term of Root Mean Square Error (RMSE) and Mean Absolute Perentage Error (MAPE). Figure 1 shows a omparison among the ray traing value and the estimated path loss values as a funtion of the distane for the onsidered Okumura Hata, NFIS and EFIS models. It an be observed as, in the onsidered ase, EFIS and NFIS networks give more better results than the Okumura Hata model, desribing in a more faithful way the path loss trend. Fig. 1. Ray Traing, NFIS, EFIS and Okumura-Hata path loss values versus distane 1942

4 Mario Versai et al. / Amerian Journal of Applied Sienes, 9 (12) (2012) Table 1. Wireless Insite parameters Parameter Range Carrier frequeny 900 [MHz] Transmitting antenna gain 16 [dbi] Transmitting antenna height 30 m Reeiving antenna height 1.5m Range of the building heights m Buildings material Conrete: ε r = 15, σ = [S/m] Table 2. Root mean square error and means absolute perentage error Method RMSE MAPE NFIS EFIS Okumura Hata Table 3. NFIS and EFIS networks: Number of rules Method Number of rules NFIS 21 EFIS 12 In Table 2 are reported the performanes of the onsidered models in term of RMSE and MAPE. It an be said that both NFIS and EFIS network show a good performane in terms of estimation. Nevertheless, referring to the number of rules (Table 3), the best performane is provided by EFIS network beause, by means of 29 ellipsoidal rules, is able to evaluate the path loss with a RMSE and a MAPE smaller than 2%. 4. CONCLUSION In this study, a novel method for the path loss predition Exploiting the Fuzzy Inferene System in onjuntion with ellipsoidal rules (EFIS) is presented. Results ompared with those provided by the Okumura Hata model and the standard Fuzzy Inferene System Approah (FIS) show superior performanes of the proposed approah. 5. REFERENCES 1. Angiulli, G. and M. Versai, A neurofuzzy network for the design of irular and triangular equilateral mirostrip antennas. Int. J. Infrared Millimeter Waves, 23: DOI: /A: Angiulli, G. and M. Versai, Resonant frequeny evaluation of mirostrip antennas using a neural-fuzzy approah. IEEE Trans. Mag., 39: DOI: /TMAG Costantino, D., F.C. Morabito, F.G. Pratio and M. Versai, Dynamial reonstrution of road longitudinal profiles: A theoretial and experimental study. Int. J. Model. Simul. Atapress, 32: DOI: /Journal Dikerson, J.A. and B. Kosko, Fuzzy funtion approximation with ellipsoidal rules. IEEE Trans. Syst. Man Cybernetis-Part B: Cybernetis, 26: DOI: / Jang, J.S.R., ANFIS: Adaptive-networkbased fuzzy inferene system. IEEE Trans. Syst. Man Cybernetis, 23: DOI: / Labate, D., F.L. Foresta, G. Inuso and F.C. Morabito, 2011a. Remarks about wavelet analysis in the EEG artifats detetion. Proeedings of the 20th Italian Workshop on Neural Nets, (NN 11), IOS Press Amsterdam, Netherlands, pp: Labate, D., F.L. Foresta, G. Inuso and F.C. Morabito, 2011b. Multisale entropy analysis of artifatual EEG reordings. Frontiers Artif. Intell. Appli., 234: DOI: / Mammone, N., G. Inuso, F.L. Foresta, M. Versai and F.C. Morabito, 2011a. Clustering of entropy topography in epilepti eletroenephalography. Neural Comput. Appli., 20: DOI: /s Mammone, N., F.L. Foresta and F.C. Morabito, 2011b. Disovering network phenomena in the epilepti eletroenephalography through permutation entropy mapping. Proeedings of the 20th Italian Workshop on Neural Nets, (NN 11), IOS Press Amsterdam, Netherlands, pp:

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