A Generalized Regression Neural Network Model for Path Loss Prediction at 900 MHz for Jos City, Nigeria

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1 America Joural of Egieerig Research (AJER) 2016 America Joural of Egieerig Research (AJER) e-issn: p-issn : Volume-5, Issue-6, pp Research Paper Ope Access A Geeralized Regressio Neural Network Model for Path Loss Predictio at 900 MHz for Jos City, Nigeria Deme C. Abraham Departmet of Electrical ad Computer Egieerig, Ahmadu Bello Uiversity, Zaria, Nigeria. ABSTRACT: This study cosiders the applicatio of a Geeralized Regressio Neural Network (GR-NN) based model for path loss predictio across the city of Jos, Nigeria. The GR-NN model was created ad used to aalyze path loss data obtaied from Base Trasceiver Statios situated across the city. Results idicate that the GR-NN based model with a Root Mea Squared Error (RMSE) value of 4.52B, offers a sigificat improvemet i path loss predictio accuracy of more tha 6dB i RMSE, over widely used empirical propagatio models. Keywords: COST 231 Hata Model, COST 231 Walfisch-Ikegami Model,, Okumura Model, Geeralized Regressio Neural Network, Path loss. I. INTRODUCTION The determiatio of radio propagatio characteristics of give terrai is highly crucial i mobile etwork plaig. As such, umerous techiques have bee implemeted i radio propagatig modelig. Due to their simplicity, empirical models are some of the most widely used. Empirical models are those models that are formulated based o observatios ad measuremets aloe [1]. They are mathematical formulatios used i radio propagatio modelig of a give terrai. Although empirical models are quite straight forward i implemetatio, they are usually ot very accurate i path loss predictio whe used outside the terrai for which they were formulated. I recet times, computatioal itelliget techiques have bee used to model radio propagatio as demostrated by [2], [3], [4], [5]. Artificial eural etworks (ANNs) are some of the most widely used computatioal itelliget techiques i hadlig complex o-liear fuctio approximatio. They have bee prove to hadle complex o-liear fuctio approximatio with a greater accuracy tha those techiques which are based o liear regressio. Hece, radio propagatio models created o the bases of o-liear fuctio approximatio have bee prove to predict path loss with greater accuracy tha those that are based o liear regressio. This ca be attributed to the fact that path loss across a give terrai is best modeled usig o-liear fuctio approximatio sice path loss is depedet o heterogeeity of terrai clutter resultig from varyig obstacles that perturb radio propagatio. I this study, a Geeralized Regressio Neural Network (GRNN) Model is created ad compared for path loss predictio accuracy across the city of Jos, Nigeria, with the followig widely used empirical propagatio models: the Okumura Model, the COST 231 Hata ad the COST 231 Walfisch-Ikegami. The choice of these empirical models is based o their suitability for path loss predictio i built-up eviromets. II. THE GENERALIZED REGRESSION NEURAL NETWORK The Geeralized Regressio Neural Network (GRNN) is a type of Radial Basis Fuctio Neural Network (RBF-NN), classified uder Probabilistic Neural Networks (PNN). Give sufficiet iput data, the GRNN ca approximate virtually ay fuctio. I cotrast to back-propagatio eural etworks, which may require a large umber iteratios to coverge to the desired output, the GR-NN does ot require iterative traiig, ad usually requires a fractio of the traiig samples a back-propagatio eural etwork would eed [6]. The GRNN is used to solve a variety of problems such as predictio, cotrol, plat process modelig or geeral mappig problems [7]. As show i Figure 1, the GRNN comprises of four layers: iput layer, a hidde layer (patter layer), a summatio layer, ad a output layer. Accordig to [6], the GRNN ca approximate ay arbitrary fuctio betwee iput vector ad output vector directly from the traiig data. w w w. a j e r. o r g Page 1

2 Figure 1: Geeralized Regressio Neural Network Architecture [8] The geeral regressio as described by [6] is as follows: give a vector radom variable, x, ad a scalar radom variable, y, ad assumig X is a particular measured value of the radom variable y, the regressio of y o X is give by E y X = yf X,y dy f X,y dy If the probability desity fuctio f(x, y) is ukow, it is estimated from a sample of observatios of x ad y. The probability estimatorf(x, Y), give by equatio (2) is based upo sample values X i ad Y i of the radom variables x ad y, where is the umber of sample observatios ad p is the dimesio of the vector variable x. (1) f(x, Y) = 1 (2π) (p +1)/2 σ (p +1)/. 1 exp X Xi T (X X i ). exp (Y Yi ) 2 i=1 (2) 2σ 2 2σ 2 A physical iterpretatio of the probability estimatef(x, Y), is that it assigs a sample probability of width σ (called the spread costat or smoothig factor) for each sample X i ad Y i, ad the probability estimate is the sum of those sample probabilities. The scalar fuctio D i 2 is give by D i 2 = X X i T X X i (3) Combiig equatios (1) ad (2) ad iterchagig the order of itegratio ad summatio yields the desired coditioal mea Y(X), give by Y(X) = Y i exp D i 2 i=1 2σ 2 exp D i 2 i=1 2σ 2 It is further stated i [6] that whe the smoothig parameter σ is made large, the estimated desity is forced to be smooth ad i the limit becomes a multivariate Gaussia with covariace σ 2. O the other had, a smaller value of σ allows the estimated desity to assume o-gaussia shapes, but with the hazard that wild poits may have too great a effect o the estimate. III. THE OKUMURA MODEL The Okumura model [9], [10] is oe of the most widely used empirical propagatio models for path loss predictio across various terrai types, classified as urba, suburba, quasi-ope area ad ope areas. The model was developed based o empirical data collected i the city of Tokyo, Japa. The model is valid for the frequecy rage 150 MHz to 1920 MHz ad distaces up to 100 km. The path loss expressio is give by L = L FSL A MU H MG H BG G AREA (5) where, - L = Media path loss i Decibels (db) - L FSL = Free Space Loss i Decibels (db) (4) w w w. a j e r. o r g Page 2

3 - A MU = Media atteuatio i Decibels (db) - H BG = Base statio atea height gai factor give by 20log(h b /200) for 30m<h b <100m - H MG = Mobile statio atea height gai factor give by 10log(h m /3) for h m <3m - G AREA =Gai due to type of eviromet IV. THE COST 231 HATA MODEL The COST 231 Hata [11] Model was formulated from the Hata Model, to suit the Europea eviromets takig ito cosideratio a wide rage of frequecies (500MHz to 200MHz). The model is also a extesio of the Okumura Model. As a result of its prove suitability path loss predictio i urba, semi-urba, suburba ad rural areas, it is oe of the most widely used models. The model expressio is give by L = logf 13.82log B a( R ) log B logd + C (6) Where, - L = Media path loss i Decibels (db) - C=0 for medium cities ad suburba areas - C=3 for metropolita areas - f = Frequecy of Trasmissio i Megahertz (MHz)(500MHz to 200MHz) - h B = Base Statio Atea effective height i Meters (30m to 100m) - d = Lik distace i Kilometers (km) (up to 20kilometers) - h R = Mobile Statio Atea effective height i Meters (m) (1 to 10metres) - a(h R ) = Mobile statio Atea height correctio factor as described i the Hata Model for Urba Areas. - For urba areas, a(h R ) = 3.20(log10(11.75hr))2 4.97, for f > 400 MHz For sub-urba ad rural areas, a(h R ) = (1.1log(f) - 0.7)h R log(f) -0.8 V. THE COST 231 WALFISCH-IKEGAMI MODEL As described i [12], [13] the COST-Walfisch-Ikegami Model empirical propagatio model was created o the bases of the models from J. Walfisch ad F. Ikegami ad further developed by the COST 231 project. The model is suitable for path loss predictio i urba eviromets because it cosiders multiple diffractio losses over rooftops of buildigs i the vertical plae betwee the Base ad Mobile Statios. However, the model does ot take ito accout path loss due to multiple reflectios. The Model is valid for the followig parameters: - Frequecy Rage: 500 MHz to 2000 MHz - Trasmitter Height (h b ): 4m to 50 m - Lik distace: 0.02km to 5km - Mobile Statio (MS) height (h m ): 1m to 3m - Mea height of buildigs (h roof ) - Mea Street Width (w) - Mea buildig separatio (b) The Lie of Sight (LOS) path loss equatio is give by PL = logf + 26logd (7) However, whe there is No Lie of Sight (NLOS) the equatio is PL = L FS + L RTS + L MSD (8) Where, L FS is free-space path loss ad is expressed as: L FS = logf + 20logd (9) L RTS is path loss due to rooftop to street diffractio ad is expressed as: L RTS = logw + 10logf + 20 log b m + L ori (10) w w w. a j e r. o r g Page 3

4 L ori i (9) is path loss due to orietatio agle φ (i degrees), betwee icidet wave ad street, expressed as: L ori = φ for 0 φ < φ 35 for 35 φ < φ 55 for 55 φ < 90 (11) L MSD is path loss due to multi-scree diffractio, ad is expressed as: L MSD = L BSH + k a + k d logd + k f logf 9 log b (12) Where, L BSH = 18 log 1 + b roof for b > roof 0 for b roof 54 for b > roof k a = b roof for d 0.5km ad b roof b roof 0.5 for d < 0.5km ad b roof k d = 18 for b > roof b roof for b roof k f = f for medium size city ad suburba area f for metropolita area (i. e. large city) VI. MATERIALS AND METHODS Received power measuremets (P R ) were obtaied from Base Trasceiver Statios () of the mobile etwork service provider, Mobile Telecommuicatios Network (MTN), Nigeria, situated withi the metropolis of the city uder ivestigatio. The istrumet used was a Cellular Mobile Network Aalyzer (SAGEM OT 290) capable of measurig sigal stregth i decibel milliwatts (dbm). Received power (P R ) readigs were recorded withi the radiatig far field (propagatio regio) defied by the Frauhofer far field radius (R ff ), give by R ff > 2D2 λ trasmitted sigal derived from λ = c f, where D is the trasmittig atea legth i meters ad λ, the wavelegth of the, where c is the velocity of light ad f, the propagatio frequecy. For a atea legth of 2 meters, R ff at 900MHz was foud to be greater tha 24 meters. Hece, measuremets were take at a average mobile height of 1.5 meters withi the 900MHz frequecy bad at itervals of 0.05km away from the, startig with a referece distace of 0.05kilometer. Mobile Network Parameters obtaied from the Network Provider (MTN) iclude the followig: Mea Trasmitter Height, H T = 34 meters, Mea Effective Isotropic Radiated Power, EIRP = 47dBm. Path loss values (L P ) were computed from received power measuremets usig the equatio L P = EIRP P R (13) The path loss predictio capability of GRNN relative to the cosidered empirical models was determied usig two basic approaches: the first ivolves separately aalyzig each data by splittig the data ito 60% traiig, 10% validatio ad 30% testig. This is to esure that the GRNN is traied for optimum performace. The secod approach ivolves splittig the etire data obtaied from all s ito two sets: 50% traiig ad 50% testig. The geometric mea of all values at each receiver-trasmitter separatio is obtaied from the traiig set usig equatio (14), ad the used to trai the GRNN model. From the testig set, each set of data is statistically compared with the traied GRNN model ad the cosidered empirical models. GM= X 1. X 2. X 3,, X (14) w w w. a j e r. o r g Page 4

The RMSE is give by RMSE = N (M P) 2 i=1 (15) N 1 where, M is the Measured Path Loss, P the Predicted Path Loss ad N the Number of paired values.

5 I performace evaluatio, the geometric mea is preferred to the arithmetic mea because it is less sesitive to extreme values [14]. The statistical performace idices used i this study are based o the Root Mea Squared Error (RMSE) ad the coefficiet of determiatio (R 2 ). The RMSE is give by RMSE = N (M P) 2 i=1 (15) N 1 where, M is the Measured Path Loss, P the Predicted Path Loss ad N the Number of paired values. R 2 = 1 The coefficiet of determiatio (R 2 ) is give by [3] N i=1 (y i y i ) 2 N i=1 (y i y i ) 2 (16) where y i is the measured path loss, y i is the predicted path loss ad y i is the mea of the measured path loss. R 2 ca take o ay value betwee 0 ad 1, but ca be egative for models without a costat, which idicates that the model is ot appropriate for the data. A value closer to 1 idicates that a greater proportio of variace is accouted for by the model. VII. RESULTS AND DISCUSSION The path loss predictio performace of the GRNN model relative the Okumura Model, the COST 231 Hata ad the COST 231 Walfisch-Ikegami models, is determied usig the two techiques described i the previous sectio. As samples, figures 2 ad 3 respectively show 1 ad 3 aalyses based o the first comparative techique. It ca be observed that the GRNN exhibits a closer predictio tha the empirical models. This fact is buttressed by the results i Table 1, which idicate that o all Base statio the GRNN outperforms the empirical models. The Geometric Mea (GM) performace across the eight s shows that the GRNN is the most accurate with a RMSE value of 4.78dB ad the highest R 2 value of This ca be attributed to the ability of eural etworks to adapt to ay eviromet give sufficiet data. The best of the empirical models is the COST 231 Hata model with a RMSE value of 10.60dB. Table 1: Splittig data ito 60% traiig, 10% validatio ad 30% testig MODEL STATS GEOM. MEAN GRNN RMSE(dB) R OKUMURA RMSE(dB) R COST 231 RMSE(dB) HATA R COST 231 WALF. RMSE(dB) R Figure 2: Aalysis of 1 Figure 3: Aalysis of 3 w w w. a j e r. o r g Page 5

The secod approach presets a similar tred with the GRNN model outperformig the empirical models. Figure 4 presets a case of traiig the GRNN model with the computed GM ad testig with data from 7.

Predictio results preseted i Table 2 idicate that based o the geometric mea of performace idicators across all s, the GRNN model is the most accurate with a RMSE value of 4.

6 The secod approach presets a similar tred with the GRNN model outperformig the empirical models. Figure 4 presets a case of traiig the GRNN model with the computed GM ad testig with data from 7. Likewise, figure 5 shows a GM traiig ad 8 testig pairig. It ca be observed from both figures 4 ad 5 that GRNN plot is more coverget with the test data tha the empirical models. Predictio results preseted i Table 2 idicate that based o the geometric mea of performace idicators across all s, the GRNN model is the most accurate with a RMSE value of 4.28dB, while the differece i performace betwee the Okumura ad the COST 231 Hata models is egligible. Fig.4 : Traiig with GM, Testig with 7 Fig.5: Traiig with GM, Testig with 8 Table 2: Traiig with GM of Traiig Set ad Testig with data from Testig Set MODEL STATS. GM/ 5 GM/ 6 GM/ 7 GM/ 8 GEOM. MEAN GRNN RMSE(dB) R OKUMURA RMSE(dB) R COST 231 RMSE(dB) HATA R COST 231 RMSE(dB) WALF. R The geometric mea performace of the two approaches shows that the GRNN is the most accurate with a RMSE value of 4.52dB ad a impressive R 2 value of 0.9. The best of the empirical models is the COST 231 Hata with RMSE ad R 2 values of 10.85dB ad 0.6 respectively. This is a typical example of a terrai where the iadequacies of empirical modes are exposed as the results further buttress the fact that empirical models are ot always accurate outside the terrais for which they were formulated. O the other had, the much greater accuracy of the GRNN ca be attributed to the ability of eural etworks to adapt to ay eviromet give sufficiet data. VIII. CONCLUSION This study cosiders the applicatio of a Geeralized Regressio Neural Network (GR-NN) model for radio propagatio modelig of the city of Jos, Nigeria. Measuremets obtaied at 900 MHz from Base Trasceiver Statios were aalyzed for path loss predictio usig two distict approaches. Results idicate that the GRNN has a combied RMSE value of 4.52dB. This is a sigificat improvemet o the widely used empirical models Okumura, COST 231 Hata ad COST 231 Walfisch-Ikegami. The COST 231 Hata model is the most accurate of the three empirical models with a RMSE value of 10.85dB. REFERENCES [1]. Akpado K.A., Oguejiofor O.S., Abe A., Ejiofor A. C. Pathloss Predictio for a typical mobile commuicatio system i Nigeria usig empirical models. IRACST Iteratioal Joural of Computer Networks ad Wireless Commuicatios (IJCNWC), ISSN: Vol.3, No Pp [2]. Östli, E., Zeperick, H.J., ad Suzuki, H. Macrocell Path loss Predictio Usig Artificial Neural Networks: IEEE Trasactios o Vehicular Techology, vol. 59, No. 6, 2010, pp [3]. Abraham U. U., Okereke O. U. ad Omizegba E. E. Macrocell path loss predictio usig artificial itelligece techiques: Iteratioal Joural of Electroics, 2013, pp w w w. a j e r. o r g Page 6

7 [4]. Joseph M. M, Callistus O. M, ad Gabriel A. I. (2014). Applicatio of Artificial Neural Network For Path Loss Predictio I Urba Macrocellular Eviromet. America Joural of Egieerig Research-ISSN: , 2014,pp [5]. Callistus O. M, Joseph M. M, ad Gabriel A. I. Performace Evaluatio of Geeralized Regressio Neural Network Path loss Predictio Model i Macrocellular Eviromet. Joural of Multidiscipliary Egieerig Sciece ad Techology (JMEST) ISSN: , 2015, pp [6]. Specht D.F.A. A geeral regressio eural etwork. IEEE Trasactios o Neural Networks. 2, 1991, [7]. Leszek R. Geeralized Regressio Neural Networks i Time-Varyig Eviromet. IEEE Trasactios o Neural Networks, Vol. 15, No. 3, 2004, pp [8]. Su G., Hoff S. J., Zelle B. C., Nelso M. A. Developmet ad Compariso of Backpropagatio ad Geeralized Regressio Neural Network Models to Predict Diural ad Seasoal Gas ad PM 10 Cocetratios ad Emissios from Swie Buildigs. America Society of Agricultural ad Biological Egieers ISSN Vol. 51(2):2008, pp [9]. Yuvraj S. Compariso of Okumura, Hata ad COST-231 Models o the Basis of Path Loss ad Sigal Stregth. Iteratioal Joural of Computer Applicatios. ( ) Volume 59 No.11, 2012, pp [10]. Obot A, Simeo O., Afolaya J. Comparative Aalysis of Path Loss Predictio Models for Urba Macrocellular Eviromets. Nigeria Joural of Techology Vol. 30, No. 3, 2011, pp [11]. Purima K. S. Comparative Aalysis of Propagatio Path loss Models with Field Measured Data. Iteratioal Joural of Egieerig Sciece ad Techology Vol. 2(6), 2010, pp [12]. Hemat K.S., Satosh S., Sajeev S. Ehaced Cost231 W.I. Propagatio Model i Wireless Network. Iteratioal Joural of Computer Applicatios ( )Volume 19 No.6, 2011, pp [13]. Chhaya D. Comparative Study of Radio Chael Propagatio ad Modelig for 4G Wireless Systems. Iteratioal Joural of Egieerig ad Advaced Techology (IJEAT) ISSN: , Volume-2, Issue-5, 2013, pp [14]. Nicholas C. (2002). Computer Architecture,. (The Mc-Graw Hill Compaies, p. 5.) w w w. a j e r. o r g Page 7

Department of Mathematics, S.R.K.R. Engineering College, Bhimavaram, A.P., India 2

Department of Mathematics, S.R.K.R. Engineering College, Bhimavaram, A.P., India 2 Skewess Corrected Cotrol charts for two Iverted Models R. Subba Rao* 1, Pushpa Latha Mamidi 2, M.S. Ravi Kumar 3 1 Departmet of Mathematics, S.R.K.R. Egieerig College, Bhimavaram, A.P., Idia 2 Departmet