AREA COVERAGE SIMULATIONS FOR MILLIMETER POINT-TO-MULTIPOINT SYSTEMS USING STATISTICAL MODEL OF BUILDING BLOCKAGE

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1 Radoengneeng Aea Coveage Smulatons fo Mllmete Pont-to-Multpont Systems Usng Buldng Blockage 43 Vol. 11, No. 4, Decembe AREA COVERAGE SIMULATIONS FOR MILLIMETER POINT-TO-MULTIPOINT SYSTEMS USING STATISTICAL MODEL OF BUILDING BLOCKAGE Pet LÉDL, Pavel PECHAČ Dept. of Electomagnetc Feld Czech Techncal Unvesty n Pague Techncká, Paha 6 Czech Republc xledl@fel.cvut.cz, pechac@fel.cvut.cz Abstact Aea coveage smulaton esults fo LMDS o PMP systems n mllmete waveband ae pesented n ths pape. Aea coveage smulatons wee pefomed accodng to ITU-R P.141 model, whee Raylegh statstcal dstbuton wth γ = 7.95 s used to model the buldng heghts. Mophologcal data of the cty of Pague wee used to calculate a new set of values γ. The model was optmzed to local condtons. Aea coveage pedcton esults usng the new set of values γ ae also pesented. Accuacy of the model was nceased due to suggested modfcaton. Keywods LOS coveage, Buldng blockage, LMDS, PMP, Mllmete waveband 1. Intoducton Due to hgh capacty, fast deployment, and elatvely low cost, LMDS (Local Multpont Dstbuton Systems) systems have become a good altenatve to the tadtonal leased lnes o to the PMP (Pont-to-Pont) access solutons fo a last mle. Among the sevces povded by LMDS systems belong: ntenet connectvty, E1 eplacement, vdeo confeencng, voce telephony, fame elay, etc. Pont-to-Multpont stuctue (Fg. 1) of LMDS system enables multple subscbes to access the same ado platfom. LMDS utlzes the same, aleady well poven, concept of fequency euse as was ntoduced n moble cellula netwoks. The dffeence s that multple subscbes connected to the base staton ae statonay, meanng that contnuous coveage s not an essental equement. The tanspot medum utlzed n LMDS s a mcowave ado. Moe nfomaton about LMDS can be found n [1], []. Coveage analyss of LMDS s a fundamental step n the system desgn pocess. Coveage analyss s based on maketng and sales equements as well as on desgn ctea. Maketng and sales defne locatons of potental customes (coveage equements), whle RF desgn ctea detemne the numbe of stes needed n ode to meet the system equements (Lne-of-sght (LOS) coveage, capacty, elablty, BER, etc.). Snce the LOS coveage (exstence of LOS between the tansmtte and eceve) s usually equed fo LMDS system opeatng n mllmete waveband and s ndependent of the othe system equements t can be evaluated sepaately. Aea coveage s then defned as an aea whee all system equements ae met. In ths pape we wll assume that the LOS coveage s the lmtng facto, meanng that aea coveage s equal to LOS coveage. Aea coveage calculaton should be pefomed ethe wth elable undelyng 3D buldng database when avalable o could be estmated based on a statstcal model. Note that the statstcal model could become vey useful when the fst studes about the netwok stuctue and nfastuctue costs ae equed.. Aea Coveage wth 3D Database of Buldngs Avalable In case the elable 3D database of buldngs s avalable the aea coveage should be calculated wth sutable PC tool. Example of such a database s shown n Fg. 1. Ths s usually ecommended soluton and othe methods should only be used when 3D database s not avalable o s too expensve fo the gven aea. 3. Coveage Based on Statstcal Model 3.1 ITU-R model In ITU-R P.141 [3] statstcal model the pobablty of exstence of LOS ay between tansmtte and eceve poston s gven by combnaton of the pobabltes that each ooftop of the buldng lyng n the popagaton path s below the heght of the ay connectng the tansmtte

2 44 Aea Coveage Smulatons fo Mllmete Pont-to-Multpont Systems Usng Buldng Blockage Radoengneeng Vol. 11, No. 4, Decembe and eceve at the pont whee the ay cosses the buldng (Fg. ). The model assumes that the tean s flat o of a constant slope ove the aea of nteest. Fo the puposes of ths pape t was always assumed that the tean s flat. Note that n pactce the tean must always be consdeed. whee h htx d( htx hx ) x = s the LOS heght n the place of -th buldng and γ the paamete. One may dentfy that (4) s a CDF of Raylegh statstcal dstbuton. Snce t has been obseved that buldng heghts dstbuton of Malven cty n UK s close to Raylegh one, t s ecommended n the ITU-R model. The esult of ITU-R model s shown n Fg. 3, paametes used n the model whee obtaned fom measuement of one town n UK and ae gven n Tab. 1. α β γ Tab. 1 Paametes fom Malven town (UK) Fg. 1 3D Buldng database of Chcago (sceenshot fom EDX SgnalPo plannng tool, Tx Rx The esults (Fg. 3) ae gven n the fom of LOS pobablty n a gven dstance fom the base staton (adus of a cell). The temnal antenna heght was assumed to be h = 7.5 m and the base staton antenna heght was assumed to be h t = 5 m, 1 m, 15 m, m, 5 m and 3 m. In ode to confm the accuacy of ITU-R model and to evaluate the lmtatons and the poblems, whch mght appea due to ITU-R model usage, seveal smulatons wee pefomed and the esults wee publshed n [4]. htx hlos hx 1 9 modeled cumulatve coveage (ITU-R P.141), h = 7.5m los x Fg. ITU-R P.141 model geomety The pobablty that the LOS exsts s calculated as follows P b ( LOS ) = P( buldng heght < ) b= 1 _ (1) whee b s the numbe of buldngs cossed. The estmaton of b s based on assumpton that the buldngs ae evenly spaced between the tansmtte and eceve. The ato of land coveed by the buldngs to total land aea (α) as well as the mean numbe of buldngs pe unt aea (β) aea s taken nto account when evaluatng b h los b = floo( αβ ) () x whee x s the lnk length (Fg. ). Snce t s assumed that the buldngs ae evenly sepaated between the tansmtte and eceve, the -th buldng dstance fom the tansmtte s gven as d whee δ = ( + 1 ) {,1, K, ( b 1) } = x b δ (3) s the buldng sepaaton. The pobablty that the buldng heght s below the LOS heght s gven by h γ P = 1 e (4) coveage [%] ht = 3m ht = 5m ht = m ht = 15m ht = 1m 1 ht = 5m adus [km] Fg. 3 Aea coveage accodng to the ITU-R model 3. ITU-R model Tunng fo Local Condtons Because the paametes obseved n the ITU-R model ae based on a measuement n sngle town n UK t s necessay to fnd the key paametes n equatons () and (4) (.e. α,β, and γ) fo local ctes as well, n ode to use the model n local condtons. In ths secton we wll optmze the ITU-R statstcal model fo local condtons n tems of evaluaton the key paamete γ needed. The othe paametes (α, β) could ethe be estmated fom a good knowledge of the gven aea o should be obtaned fom elable D map (e.g. mltay maps). Fo the optmzaton puposes we used 3D mophologcal data of the aea of Pague. The used data had aleady been pe-pocessed, meanng that the eal data we obtaned wee n the fom of

3 Radoengneeng Aea Coveage Smulatons fo Mllmete Pont-to-Multpont Systems Usng Buldng Blockage 45 Vol. 11, No. 4, Decembe occuences of buldngs of specfc heght class n a gven aea. The mentoned buldng heght classes ae defned n Tab.. Heght class Buldng heghts [m] Class I < 1 Class II 1 Class III 3 Class IV > 3 Tab. Buldng classes fo ITU-R model tunng Occuences wee always gven pe facton of the total geogaphcal aea. Each facton coesponds to fve squae klometes (Fg. 4 each squae fo whch data wee avalable s labeled wth captal lette and numbe). E1 E E3 D1 D D3 D4 D5 D6 E4 E5 E6 In ths case two paametes must be optmzed (γ, a). In ode to use the ITU-R model the equaton (4) must be eplaced wth (6). Obtaned esults ae gven n Tab. 4, see also Fg. 6 fo compason wth Fg. 5. Map squae A B B B5 1.8 C 1.48 C C C C6 1.4 D 11. D D D D E E4 1.8 E γ Tab. 3 Optmzed values fo ITU-R model used n local condtons C1 C C3 C4 C5 C6 8 Buldng heghts dstbuton n B4 aea B1 B B3 B4 B5 B6 7 measued dstbuton 6 A1 A A3 A4 A5 A6 # of occuences [-] optmzed dstbuton (γ = 1.55) Fg. 4 Geogaphcal locaton of 3D data The optmzaton was based on a andom numbe geneato bult n MatLab. The heghts geneated accodng to the Raylegh dstbuton wth paamete γ wee ftted nto the pevously mentoned heght classes. The optmzed γ was the one fo whch the esultant dstbuton causes the smallest eo wth espect to the measuement (see Fg. 5). The eo was defned n tems of cumulatve dffeence eo = 4 ( N _ measued N _ geneated ) = 1 (5) whee N_measued and N_geneated ae numbe of occuences of -th heght class of dstbuton n a gven tal. The defnton of Raylegh dstbuton gven by equaton (4) was used dung optmzaton meanng that values obtaned (Tab. 3) could dectly be used n the ITU-R model. Because the accuacy was found to be vey poo, t has been decded to use moe geneal defnton of Raylegh statstcal dstbuton gven n [5] P 1 exp ( h a) = γ. (6) 1 Fg Buldng heght [m] Measued vs. geneated sample dstbuton (Raylegh) 3.3 Toleance Analyss In ode to nvestgate the senstvty of computed coveage pobablty (Fg. 3) to the changes of paametes γ and a obtaned n the optmzaton pocess (Tab. 4), toleance analyss was pefomed. Output of the toleance analyss expesses the dffeence between coveage pobablty computed wth unvesal paametes and coveage pobablty computed wth optmzed paametes fo gven map squae (fom Tab. 4). Unvesal paametes ae the paametes optmzed fo the whole aea of Pague and ae gven n Tab. 5. In the next step we nvestgated the nfluence of unvesal paamete on cumulatve dffeence (5). It was obseved that the ncease of cumulatve dffeence due to usage of unvesal (thus non-optmal) values fom Tab. 5 compaed to usage of optmal values fom Tab. 4 fo selected map squae vaes fom 4 % to 35 %.

4 46 Aea Coveage Smulatons fo Mllmete Pont-to-Multpont Systems Usng Buldng Blockage Radoengneeng Vol. 11, No. 4, Decembe # of occuences [-] Buldng heghts dstbuton n B4 aea optmzed dstbuton (γ = 7.; a = 8.4) measued dstbuton The paamete γ fo ITU-R P.141 model was deved fo local condtons - vaous pats of the cty of Pague. The enhancement of the model was poposed usng addtonal paamete a. The model paametes wee deved fo the modfed model as well Buldng heght [m] Fg. 6 Measued vs. geneated sample dstbuton (Raylegh) In the last step we nvestgated the senstvty of coveage pobablty to nceased cumulatve dffeence. Fo the base staton antenna heght t was assumed that h t = 35 m and fo temnal antenna heght t was assumed that h = 8 m, h = 1 m, h = 16 m, and h = m. One can see n Fgs. 7 1, that usage of unvesal paametes could lead to sgnfcant dffeences n computed coveage pobablty, but on the contay vey small dffeences wee obseved as well. Ths means that key paametes selecton fo ITU-R model must be done caefully and usage of unvesal paametes should be avoded. Fg. 7 Coveage pedcton fo B3 aea wth unvesal and optmzed key paametes used 4. Concluson It can be concluded that the aea coveage pobablty calculated by ITU-R P.141 model s too senstve to key paametes (a, γ) that should always be vey caefully selected. Because the optmzed values (Tab. 4) wee gven fo each map squae, thus fo the dffeent buldng chaactestcs, the engnee can select the values fom Tab. 4 such that the buldng dstbuton n the coespondng map squae (Fg. 4) s the most smla to the aea of nteest. Note that tean was assumed to be flat n ths case. In the eal plannng pocess the tean must also be ncluded. Map squae γ a A B B B C C C C C D D D D D E E E Tab. 4 Optmzed values fo ITU-R model used n local condtons Fg. 8 Coveage eo fo B3 aea when unvesal and optmzed key paametes used Map squae γ a A3 E Tab. 5 Unvesal values fo ITU-R model optmzed fo Pague Fg. 9 Coveage pedcton fo D6 aea wth unvesal and optmzed key paametes used

5 Radoengneeng Aea Coveage Smulatons fo Mllmete Pont-to-Multpont Systems Usng Buldng Blockage 47 Vol. 11, No. 4, Decembe Refeences [1] Clak M. P. Weless Access Netwoks, Fxed Weless Access and WLL Netwoks Desgn and Opeaton. John Wley & Sons, Ltd,. [] Smth C. LMDS. McGaw-Hll,. [3] ITU-R P.141 Popagaton data and pedcton methods equed fo desgn of teestal boadband mllmetc ado access systems opeatng n a fequency ange about -5 GHz. ITU, Geneva,. [4] Pechač P., Lédl P., Mazánek M. Sgnal popagaton aspects fo local multpont dstbuton system (LMDS) opeatng n mllmete waveband. Radoelektonka, Padubce, 1. [5] Peebles P. Z. Pobablty, Random Vaables and Random Sgnal Pncples. McGaw-Hll, 198. Fg. 1 Coveage eo fo D6 aea when unvesal and optmzed key paametes used Acknowledgements Ths wok has been suppoted by the Gant Agency of the Czech Republc gant No. 1/1/9 Pefomance and Relablty of Advanced Telecommuncaton Systems Usng Mllmete Wavelengths n the Czech Republc and by the eseach pogam No Reseach n the Aea of Infomaton Technologes and Communcatons. About Authos... Pet LÉDL gaduated at the Czech Techncal Unvesty n Pague n 1. He s wth the Depatment of Electomagnetc Feld as a post gaduate student. Hs eseach nteests have been manly n the feld of the electomagnetc waves popagaton and moble netwoks. Pavel PECHAČ gaduated at the Czech Techncal Unvesty n Pague n He eceved hs Ph.D. n Radoelectoncs n 1999 at the Depatment of Electomagnetc Feld. He s wth the depatment as an assocate pofesso. Hs eseach nteests have been manly n the feld of the electomagnetc waves popagaton pedcton. The 1th CONFERENCE ON MICROWAVE TECHNIQUE COMITE 3 IEEE Czechoslovaka Secton and ts MTT/AP/ED and CAS/COM/SP Chaptes Unvesty of Padubce Septembe 3-4, 3, Padubce, The Czech Republc CONFERENCE TOPICS 1. Mcowave mateals 7. Electomagnetc compatblty and packagng. Passve and actve mcowave ccuts 8. Radas and emote sensng 3. Mcowave acoustcs and optoelectoncs 9. Communcatons and navgaton 4. Antennas and popagaton 1. Moble communcatons 5. Smulaton, modelng and CAD of mcowave devces 11. Industal and bomedcal applcatons 6. Mcowave measuements 1. Sgnal pocessng n ada and communcatons M. Mlan Pavel tel. (+4) Unvesty of Padubce fax: (+4) Studentská 95 e-mal: mlan.pavel@upce.cz 53 1 Padubce Czech Republc