An Empirical Based Path Loss model with Tree Density Effects for 1.8 GHz Mobile Communications Using Fuzzy Regression

Transcription

1 Proceedgs of the 5th WSEAS It Cof o Electrocs, Hardware, Wreless ad Optcal Commucatos, Madrd, Spa, February 15-17, 26 (pp5-57) A Emprcal Based Path Loss model wth Tree Desty Effects for 18 GHz Moble Commucatos Usg Fuzzy Regresso SUPACHAI PHAIBOON 1 ad PISIT PHOKHARATKUL 2 1 Electrcal Egeerg Departmet, Faculty of Egeer Mahdol Uversty, Salaya, Phutthamotho, Nakorprathom 7317, THAILAND 2 Computer Egeerg Departmet, Faculty of Egeer Mahdol Uversty, Salaya, Phutthamotho, Nakorprathom 7317, THAILAND Abstract: - Upper-ad lower-boud path loss models the forests are preseted ths paper We performed measuremets dfferet forest destes at a frequecy of 18 GHz wth base stato atea heght a rage of 3, 4, ad 5 m above groud whle the recevg atea heght was fxed at 18 m above groud The forest was classfed to dfferet desty areas amely, hgh-, medum-, low- desty ad grass area We proposed upper-ad-lower bouds path loss models whch deped o max ad m values of sample path loss data It does ot deped o sample sze Ths makes our models lmt path loss wth the boudary les whle the cofdece terval of stadard regresso s depeded o the sample sze Comparso betwee the fuzzy regresso model ad covetoal regresso model show that the proposed model agrees wth measured data whle the covetoal regresso model provdes over estmato Key-Words: - fuzzy regresso, moble path loss, low base stato, dfferet forest destes 1 Itroducto Forests are sgfcat features whch affect rado wave propagato rural ad suburba areas at the moble commucato bads Shadowg, scatterg, ad absorpto by trees ad other vegetato cause substatal path loss Therefore ths paper, we performed measuremets forests at a frequecy of 18 GHz to model moble path loss characterstcs Whle estmato of path loss the forest wth low base stato atea heght s ecessary for local wreless system ad mcro-cell desg, we could ot fd more accurate path loss models from covetoal emprcal methods [1]-[4] because of ucerta tree structures the forest caused by type ad desty of trees cludg tme-varyg effect wd speed It would, therefore, be extremely useful f the upper ad lower boud of path loss could be estmated Although upper ad lower boud estmatos have already bee performed for the UHF bad [5]-[6], however they were ot cluded tree desty effects wth ther fluece o wave propagato that s very hgh To solve ths problem, we propose ew upper ad lower boud formulas for propagato path loss forest usg fuzzy lear regresso The spread of the boudary les of the fuzzy models deped o maxmum ad mmum value of a gve data It does ot deped o sample sze I stadard regresso models the wdth of cofdece tervals depeds o stadard devato, sample sze, ad sgfcace level I case of small stadard devato, the wdth of cofdece tervals ofte dsable the proper estmato process The applcato of the fuzzy approach elmate ths problem Ths paper, frst presets measuremet methods ad locatos Secto 3 presets stadard regresso model Secto 4 presets modellg path loss wth fuzzy lear regresso, Secto 5 presets umercal results, Secto 6 presets comparso betwee fuzzy ad covetoal regresso models, ad fally cocluso 2 Measuremet Methods ad Locatos The measuremets have already bee doe [4] They were performed Putthamoto garde usg a fxed trasmtter ad a arrowbad(2khz) portable spectrum terfaced wth a mcrocomputer at a frequecy of 18 GHz The fxed trasmtter cossted of a etwork aalyzer (wth

2 Proceedgs of the 5th WSEAS It Cof o Electrocs, Hardware, Wreless ad Optcal Commucatos, Madrd, Spa, February 15-17, 26 (pp5-57) Fg1 Measuremet system 18 dbm power output) ad λ/4 om- drectoal atea wth 1x1 cm 2 groud plae (22 db ga) We also used the same type of atea for sgal stregth measuremet va a recorder as show Fg 1 The trasmttg atea heghts were vared for 3, 4, ad 5 m whle a recevg atea heght was fxed at 18 m All measuremets are vertcal polarzato Three dfferet tree destes were studed for tree loss low, medum, ad hgh tree destes I order to determe path loss ad aalyss the fast fadg provoked by movemet of the tree leaves due to wd, there are two modes for measuremets 1) The receved power was recorded for 12 s usg a 2 Hz sample rate for each measuremet pot 2) The receved power was recorded every 25 λ trackg wth wheel detector alog drect propagato path The wd speed was recorded betwee measuremets from May to August 25 It was average about 21 Kots The dstace betwee each measuremet pot was about 1 to 2 m The measuremet data was recorded from 6 local areas for path loss measuremets as follows = Tx a) Desty of 32 trees/m 2 b) Desty of 9 trees/m 2 = Rx Pot 21 Hgh desty areas There are two studed locato areas 1) Pereal trees wth a typcal heght of 17 m wth 4 m dameter truks ad 6 m dameter caopes as show Fg 1 a) The trees are geerally separated from each other by about 5 m ad have a average desty of 8 trees/5x5 m 2 The typcal leaves have dmesos of about 17 x 5 cm ad the mea desty s about 952 leaves/m 3 2) Mago trees wth typcal heght of 43 m wth 17 m dameter truks ad 3 m dameter caopes The trees are geerally separated from each other about by 5 m ad have a average desty of 72 trees/5x5 m 2 The typcal leaves have dmesos about 3 x 6 cm ad the mea desty s about 222 leaves/m c) Desty of 5 trees/m 2 Fg 2 Propagato evromet category ad measuremet locatos 22 Medum desty area The area cossts of pereal trees wth typcal heghts of 89 m wth 36 m dameter truks ad 8 m dameter caopes The trees are geerally separated from each other by about 5 m ad 7 m for row ad colum respectvely The measuremet pots average desty of trees are 52 trees/5x5 m 2 The typcal leaves have dmesos of about 14 x 7 cm ad the mea desty s about 75 leaves/m 3

3 Proceedgs of the 5th WSEAS It Cof o Electrocs, Hardware, Wreless ad Optcal Commucatos, Madrd, Spa, February 15-17, 26 (pp5-57) a r Fg3 Parameters of tree structure 23 Low desty areas There are two studed locatos, 1) Burma Padauk trees wth a heght of 65 m wth 25 m dameter truks ad 86 m dameter caopes as show Fg 2 b) The trees are geerally separated from each other by about 5 m ad 2 m for row ad colum respectvely The average desty of trees are 23 trees/5x5 m 2 The typcal leaves have dmesos of about 8 x 5 cm ad the mea desty s about 69 leaves/m 3 ad 2) Burma Padauk trees wth a heght of 62 m wth 22 m dameter truks ad 9 m dameter caopes as show Fg 2 c) The trees are geerally separated from each other about 5 m ad 2 m for row ad colum respectvely The average desty of trees are 12 trees/5x5 m 2 The typcal leaves have dmesos of about 7 x 4 cm ad the mea desty s about 714 leaves/m 3 24 Grass area Ths area cossts of flat grass wth heght of 4 m area of 3x1 m 2 There are few trees the area 3 Stadard Regresso Model A emprcal path loss model ca be wrtte the form PL(d) [db] = PL (db) 1log(d) (1) Where PL s path loss at referece dstace, s path loss expoet ad d s dstace betwee the trasmtter ad the recever Fg4 shows stadard regresso of the measuremet path loss dfferet desty areas wth dfferet trasmttg atea heght The cofdece terval the fgure s a certa rage of stadard devato [7] Summary of the path loss expoets as the parameters of tree structure Fg 3 are show Table I, where subscrpt 1, 2 ad 3 of the path loss expoet deote the case for h b = 3 m, 4 m, ad 5 m respectvely b c -1-2 Stadard regresso le -3 Cofdece tervals a) Desty of 32 trees/m 2 wth h t = 5 m -1-2 Stadard regresso le -3 Cofdece tervals b) Desty of 21 trees/m 2 wth h t = 3 m -1-2 Stadard regresso le -3 Cofdece tervals c) Desty of 9 trees/m 2 wth h t = 5 m -1-2 Stadard regresso le -3 Cofdece tervals d) Grass area wth h t = 3 m Fg4 Stadard regresso of measuremet path loss at the dfferet areas

4 Proceedgs of the 5th WSEAS It Cof o Electrocs, Hardware, Wreless ad Optcal Commucatos, Madrd, Spa, February 15-17, 26 (pp5-57) Table 1 Summary of the path loss expoets as parameters of tree structure Areas Number of tree / m 2 Tree structure leave leaves Path loss expoets dmeso a b c r (m 2 /m 3 ) Hgh desty x x Medumdesty x Low desty x x Grass Modellg Path Loss Wth Fuzzy Lear Regresso I ths secto, we troduce fuzzy regresso to expad the covetoal lear regresso model to represet possble regos of path loss data 41 Fuzzy regresso model I fuzzy regresso model [8], the parameter (1) are replaced wth fuzzy umbers as show (2) to cover a wde rage of data PL(dB) = A (db) A1 log(d) (2) The parameter A, A1, are determed that the observed data are ecompassed by the fuzzy regresso model The varable PL(dB) s also fuzzy umber, whch has a rego of data covered a varyg degree of possblty Fg 5 show the tragular fuzzy set represetg the fuzzy umber A wth three crsp parameters, amely a, c, c ( c, c ) Here, a s the most lkely value of the regresso parameter, whereas c ad c are possble maxmum spread from a to the hgher ad lower values of the parameter, respectvely We use the expresso A ( a, c, c ) to represet such a tragular = fuzzy umber I the modelg process, the mea value of the fuzzy umber s smple determed by covetoal regresso The spread parameters c ad c are determed by optmzato a Fg 5 The tragular fuzzy set represetg the fuzzy umber 42 Rage Optmzato To determe the remag parameters for the fuzzy umbers ( c ad c ) we apply lear programmg to ft the model to the gve data The optmzato process s formulated as follows: Mmze: { c c 1 log( d )} (3) d = 1 subject to a log(1) c c1 log(2) PL(2) ad a 1 a a log( ) c c log( ) PL( ) 1 1 a a 1 log(1) c c1 log(2) PL(2) a a log( ) c c log( ) PL( ) 1 1 c, c, c1, c1 (4) where s the total umber of measured data pots The parameters a are determed by the method of lear regresso The parameters c ad c are determed as the optmal soluto of the LP problem (3) (4) The FLR models for propagato path loss are preseted form PL db) = [ a, c, c ] [ a, c, c ]log( ) (5) ( d

5 Proceedgs of the 5th WSEAS It Cof o Electrocs, Hardware, Wreless ad Optcal Commucatos, Madrd, Spa, February 15-17, 26 (pp5-57) Where d = dstace betwee trasmtter ad recever The optmzato s amed at fttg the model wth as arrow a rage as possble, whle coverg all the data cosdered wth the rego 43 Fuzzy parameters modfcato Because of outler data, the resultat rage of fuzzy model may appear large boudary A method to arrow dow the boudary s α cuts of the fuzzy umbers (2) to modfy ther rage By usg a sgle parameter α ( α 1), A ad A 1 are modfed as A A = a, c (1 α), c (1 α) 1 = a1, c1 (1 α), c1 (1 α) (6) At α =, the orgal fuzzy regresso model are obtaed whle the value of α crease toward 1, the model become the covetoal regresso 5 Numercal Results By solvg ths LP problem of measured data ad usg α cuts, the followg FLR models are obtaed: 51 Hgh desty area wth desty of 32 tree/m 2 Path loss models for trasmtter heght of 3 m, 4 m, ad 5 m are wrtte (7), (8) ad (9) respectvely PLht_3 = [5,2,1][33,6,]log(d); d 1 m (7) PLht_4 = [55,2, 5][33,,2]log(d); d 1 m (8) PLht_5 = [56,26,13][36,,1]log(d); d 1 m (9) 52 Medum desty area wth desty of 21 tree/m 2 Path loss models for trasmtter heght of 3 m ad 4 m are wrtte (1) ad (11) respectvely PLmt_3 = [51,24,13][35,,1]log(d); d 1 m (1) PLmt_4 = [45,25,1][44,,2]log(d);d 1 m (11) 53 Low desty areas wth desty of 9 tree/m 2 Path loss models for trasmtter heght of 3 m, 4 m, ad 5 m are wrtte (12), (13) ad (14) respectvely PLlt_3 = [55,18,1][23,,]log(d); d 1 m (12) PLlt_4 = [62,15,1][18,,]log(d); d 1 m (13) PLlt_5 = [63,17,9][23,3,]log(d); d 1m (14) 54 Grass area Path loss models for trasmtter heght of 3 m, 4 m, ad 5 m are wrtte (15), (16) ad (17) respectvely PLgt_3 = [58,1,1][21,4,]log(d); d 1 m (15) PLgt_4 = [59, 9, 6][17,,]log(d); d 1 m (16) PLgt_5 = [58, 8, 6][2,1, 2]log(d); d 1m (17) Path loss dstace characterstcs wth fuzzy regresso are show Fg 6-9 for hgh desty area, medum desty area, low desty area ad grass area respectvely Estmated path loss bouds are show by dot les the fgures The ceter les or sold les are the same as covetoal regresso whle spreadg of the upper- ad lowerles are depeded o max ad m values of data These spreadg are geerally creased wth desty of trees Ths s because of fluece of mult-path compoets cludg leave movemet from wd I case of the medum desty area of 21 trees/m 2, the spreadg of the upper- ad lower- les are wder tha case of the hgh desty area of 32 trees/m 2 Ths s because there are low sde trees the medum desty area that ther leaves make a lot of scatterg ad atteuato as show Fg 7 ad table 1 Whle case of hgh desty area, the trees are hgh sde therefore the scatterg ad atteuato are geerally occurred va oly truk ad brach of trees We determed the α cut to eradcate the outlers at lower boud for Fg 6 c), Fg 7 a), b), ad Fg 8 a), b) The α cut values are a rage of 2 to 5

6 Proceedgs of the 5th WSEAS It Cof o Electrocs, Hardware, Wreless ad Optcal Commucatos, Madrd, Spa, February 15-17, 26 (pp5-57) a) ht = 3 m Upper- ad Lower- boud a) ht = 3 m b) ht = 4 m Path loss (db) Dstace (m) b) ht = 4 m c) ht = 5 m Fg6 Fuzzy regresso of measuremet path loss the desty area of 32 trees/m 2 wth dfferet trasmtter atea heght Fg7 Fuzzy regresso of measuremet path loss the desty area of 21 trees/m 2 wth dfferet trasmtter atea heght 6 Comparso Betwee Fuzzy ad Covetoal Regresso Models To check our proposed model, we performed path loss measuremet aother hgh ad low desty area wth desty of 28 trees/m 2 ad 5 trees/m 2 respectvely The fuzzy models (7)-(9) ad (12)-(14) were appled for hgh ad low desty area respectvely Fg 1 shows a comparso betwee the fuzzy ad covetoal regresso model for hgh desty area at trasmttg atea heght of 3 m The upper- ad lower- boud of the fuzzy models agree wth measured path loss whle those of the covetoal regresso models are over estmato at ther upper-ad lower- bouds Summary of comparsos are show Table 2

7 Proceedgs of the 5th WSEAS It Cof o Electrocs, Hardware, Wreless ad Optcal Commucatos, Madrd, Spa, February 15-17, 26 (pp5-57) a) ht = 3 m a) ht = 3 m b) ht = 4 m b) ht = 4 m c) ht = 5 m Fg8 Fuzzy regresso of measuremet path loss the desty area of 9 trees/m 2 wth dfferet trasmtter atea heght c) ht = 5 m Fg9 Fuzzy regresso of measuremet path loss the grass area wth dfferet trasmtter atea heght

8 Proceedgs of the 5th WSEAS It Cof o Electrocs, Hardware, Wreless ad Optcal Commucatos, Madrd, Spa, February 15-17, 26 (pp5-57) Pathloss ( db ) Pathloss ( db ) a) fuzzy regresso Cofdetal terval b) stadard regresso Fg 1 Comparso betwee fuzzy ad stadard regresso for hgh desty area wth h t = 3 m Table 2 Summary of comparso % path loss error betwee fuzzy regresso ad covetoal regresso Methods Desty area Number of Atea heght (m) trees/m covetoal hgh low fuzzy hgh low Cocluso Propagato path loss dfferet forest destes at a frequecy of 18 GHz have bee modeled usg fuzzy lear regresso The forest was classfed to dfferet desty areas amely, hgh-, medum-, low- desty ad grass area The spread of the boudary les of the fuzzy models deped o maxmum ad mmum value of a gve data It does ot deped o sample sze Ths makes the proposed model lmt path loss data wth the boudary les The proposed models agree wth the measured data at the trasmttg heght rage of 3 to 5 m ad the recevg atea heght of 18 m Ackowledgmet Ths work was supported by a medum research grat (Roud 6/24) from Mahdol Uversty, Thalad Refereces: [1] Wessber, M A, A Ital Crtcal Summary of Predctg the Atteuato of Rado Waves By Trees ESD-TR EMC Aalyss Ceter, Aapols MD [2] ITU, Radowave Propagato Effects o Next Geerato Terrestral Telecommucato Servces COST235, falreport, 1996 [3] J C R D Bello, G L Squera, ad H L Berto, Theoretcal Aalyss ad Measuremet Results of Vegetato Effects o Path Loss for Moble Cellular Commucato Systems IEEE TrasVehTechol,Vol49, No 4 July, 2, pp [4] S Phaboo, ad S Somkurpach Moble Path Loss Characterstcs for Low Base Stato Atea Heght Dfferet Forest Destes 1 st Iteratoal Symposum o Wreless Pervasve Computg (ISWPC 26), Phuket, Thalad, Ja 16-18,26 [5] H Masu, T Kobayash, M Akake, Mcrowave path loss modelg urba leof-sght evromets, IEEE J Select Areas Commu, Vol2,pp , August 22 [6] L B Mlste, D L Schllg, R L Pckholtz, V Erceg, MKullback, E G Kateraks, D S Fshma, W H Bederma, ad D C Salero, O the feasblty of a CDMA overlay for persoal commucatos,ieee JSelect Areas Commu, Vol1,pp , May 1992 [7] F Saleh, Cellular Moble Systems Egeerg, Artech House Publshers, Bosto Lodo,1996 [8] H Taaka, S Uejma, ad K Asa, Lear regresso aalyss wth fuzzy model, IEEE TrasSyst, Ma,Cyber, Vol SMC-12, pp 93-97, Jue 1982