COMPLEX SIMULATION MODEL OF MOBILE FADING CHANNEL

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1 Advaes i Eletrial ad Eletroi Egieerig 194 COMPLEX SIMULATION MODEL OF MOBILE FADING CHANNEL Toáš Marek, Vladiír Pšeák, Vladiír Wieser Elektrotehiká fakulta ŽU v Žilie, Siees PSE, s.r.o Veký diel, Žilia, tel.: , ail: wieser@fel.ut.sk, arek@fel.ut.sk, vladiir.pseak@siees.o Suary I the obile ouiatio eviroet the obile hael is the ai liitig obstale to reah the best perforae of wireless syste. Modelig of the radio hael osists of two basi fadig ehaiss - Log-ter fadig ad Short-ter fadig. The otributio deals with siulatio of oplex obile radio hael, whih is the hael with all fadig opoets. Siulatio odel is based o Clarke-Gas theoretial odel for fadig hael ad is developed i MATLAB eviroet. Siulatio results have show very good oiidee with theory. This odel was developed for hybrid adaptatio 3G uplik siulator (desribed i this issue) durig the researh projet VEGA - 1/0140/ INTRODUCTION The eviroet of obile ouiatio etworks is haraterized by differet orphology, e.g. the ope outaieerig or flat area, suburbs with low buildigs, tow eter with high-rise adiistratio buildigs [4]. Two basi types of fadig ifluee the sigal trasferred through obile hael: 1. Log-ter fadig idued by two ehaiss: Path-loss ad shadow fadig.. Short-ter fadig idued also by two ehaiss: Multipath propagatio ad Doppler spread. These partiular fadigs are illustrated i Fig.1. Reeived sigal power Reeived sigal Path-loss Distae fro trasitter Shadow fadig Short-ter fadig Fig.1. Log-ter ad short-ter fadig. Let s defie the reeived sigal as ( t) = L x( t τ) y, (1) where τ is the ea ultipath delay, x(t) is the trasitted wavefor, L is the geeral loss o the trasitted path ad its value depeds o three ifluees: Distae betwee trasitter ad reeiver path loss L PL, Shadowig betwee trasitter ad reeiver shadowig loss L SL, Short-ter sigal flutuatios short-ter fadig loss L STL. So, L a be expressed as jφ L = LPL LSL LSTL e, () where Φ is the sigal phase.. COMPLEX SIMULATION MODEL For purposes of obile etwork siulatios we have realized the oplex siulatio odel of obile hael i MATLAB eviroet. Our oplex siulatio odel osists of three parts log-ter sigal variatios (path loss ad shadow loss) ad short-ter fadig (e.g. Rayleigh fadig). The log-ter effets are odeled by ultiplyig bloks i the fig.7. We have used two ETSI path loss odels [3]: Path Loss Model for Outdoor to Idoor ad Pedestria Test Eviroet, where the path loss L PL is expressed by L PL ( R) + 30log ( ) 49 [ db] L PL = 40log10 10 f +, (3) = 40 1 where R is the base statio obile statio separatio (k), f is the arrier frequey for UMTS appliatio (000 MHz). The odel is valid for o-lie-of-sight (NLOS) oditios ad desribes worse ase propagatio. Log-oral shadow fadig stadard deviatio of 10 db a be expeted. This odel we have used oly for pedestria eviroet. Path Loss Model for Vehiular Test Eviroet is appliable for the test searios i urba ad suburba areas outside the high rise buildigs where these are of early uifor height. 3 ( 4 10 hb ) log( R) 18log( hb ) ( f ) + 80 [ db] + 1log +, (4) where R is the base statio obile statio separatio (k), f is the sae as above, h b is the base statio atea height, easured fro the average rooftop level. For sipliity we have fixed base statio atea height at 15 ad the forula beoes: ( ) [ db] L PL = 18,1 + 37,6 log R. (5)

2 195 Coplex siulatio odel of obile fadig hael Log-oral shadow fadig with 10dB stadard deviatio is assued i both urba ad suburba areas. The short-ter effet is odeled by hael ipulse respose odel based o a tapped-delay lie odel. The uber of taps, the tie delay relative to the first tap, the average power relative to the strogest tap, ad the Doppler spetru of eah tap haraterize the odel. Beause the easureets i outdoor eviroet showed that rs delay spread σ a vary over a order of agitude [3] ad this delay spread variability aot be aptured usig a sigle tapped delay lie, up to two ultipath haels are defied for eah test eviroet. Chael A is the low delay spread ase that ours frequetly, hael B is the edia delay spread ase that also ours frequetly. Tap Tab.1 Pedestria Test Eviroet Paraeters. Delay (s) Chael A Power (db) Chael B Delay (s) Power (db) Tab. Vehiular Test Eviroet Paraeters (High atea). Tap Delay (s) Chael A Power (db) Delay (s) Chael B Power (db) For siulatio of short-ter fadig we assue the odel developed by Clarke [1] whih is based o fixed trasitter with vertially polarized atea ad obile reeiver with field oprised of N plae waves with arbitrary arrier phases, arbitrary aziuthal agles of arrival ad eah havig equal average aplitude. Every wave reeived by the obile udergoes a Doppler shift due to the otio of the reeiver ad arrives at the reeiver at the sae tie. That is, o exess delay due to ultipath is assued for ay of waves (flat fadig). Doppler shift for -th wave arrivig at a agle α is give by f v = os α, (6) λ where v is the veloity of obile ad λ is the wavelegth of the iidet wave. The vertially polarized waves arrivig at the obile have E ad H field opoets. The E field a be expressed i a i-phase ad quadrature for where ad ( t) os( πf t) T ( t) si( πf t) E = T T T s N ( t) = E C ( πf t + Φ ) 0 = 1 N s, (7) os (8) ( t) = E C ( πf t + Φ ) 0 = 1 si. (9) Both T (t) ad T s (t) are Gaussia rado proesses whih are deoted as T ad T s, respetively. These are uorrelated zero-ea Gaussia rado variables with a equal variae T s z = = T = E E, (10) 0 where the overbar deotes the eseble average. The evelope of the reeived E-field, E z (t), is give by E ( t) = T ( t) + T ( t) r( t) z s =. (11) Sie T ad T s are Gaussia rado variables it a be show that the rado reeived sigal evelope r has a Rayleigh distributio give by r r exp 0 r p ( r) = σ σ. (1) 0 r < 0 Gas developed a spetru aalysis for Clarke s odel. The reeived power fro agle dα (i the ase of isotropi atea) is deoted p(α)dα ad the atea gai (fro that agle) G(α). Tha the total reeived power (beause of the great uber of travelig paths, N ) is give by π 0 P r = G( α) p( α) dα. (13) Fro Gas s aalysis iplies that the spetru is etered o the arrier frequey f ad is zero outside liits of f ± f, where f is the axiu Doppler shift. Eah of the arrivig waves has its ow arrier frequey, whih is slightly offset fro the eter frequey. The resultat value of the reeived sigal power spetral desity a be expressed by

3 Advaes i Eletrial ad Eletroi Egieerig 196 S ( f ) = G( α) p( α). (14) f f f 1 f For the ase of a vertial λ/4 atea ad a uifor distributio p(α) = 1/(π) over 0 to π, the output spetru is give by 1,5 S E z ( f ) =. (15) f f πf 1 f I equatio (15) the power spetral desity at f = f ± f is ifiite, i.e., Doppler opoets arrivig at exatly 0 ad 180 have a ifiite power spetral desity. Fig. shows the power spetral desity (Doppler spetru) of the resultig RF sigal for the value f = 100 Hz (MATLAB siulatio). 3. SIMULATION OF CLARKE-GANS MODEL Siulatio ethod uses the oept of i-phase ad quadrature odulatio paths to produe a siulated sigal with eeded spetral ad teporal harateristis. Two idepedet Gaussia low pass oise soures are used to produe two odulatio paths. Suig two idepedet Gaussia rado variables, whih are orthogoal, fors eah Gaussia soure. SEz(f) f - f Fig.. Doppler spetru for f = 100 Hz. f f + f With the spetral filter defied by (15) to shape the rado sigals i the frequey doai, we a produe the aurate tie doai wavefors of Doppler fadig by usig a IFFT (Iverse Fast Fourier Trasfor). Sith s algorith [] is to be used to realize this siulatio: 1. Speify the uber of spetral poits N for Doppler filter represetatio ( f ) S z E ad the axiu Doppler frequey shift f.. Copute the frequey spaig betwee adjaet spetral lies f = f /(N-1). This defies the duratio of fadig T = 1/ f. 3. Geerate oplex Gaussia rado variables for eah of the N/ positive frequey opoets of the oise soure. 4. Costrut the egative frequey opoets of the oise soure by ojugatig positive frequey values ad assigig these at egative frequey values. 5. Multiply the i-phase ad quadrature oise soures by fadig spetru ( f ) SE z. 6. Perfor a IFFT o the resultig frequey doai sigal ad opute the su of the squares of eah sigal. Take the square root of the su to obtai N poit tie series of a siulated Rayleigh fadig sigal. Several Rayleigh fadig siulators with variable gais ad tie delays are used to produe frequey seletive fadig. I our siulatio of obile fadig hael we have used odified Sith s algorith for short-ter fadig siulatio (oe brah): 1. We have speified the uber of spetral poits to N =16.. I eah brah it is used the Gaussia oise geerator with low frequey to obtai rado sigal aplitudes (i tie doai). 3. The followig FFT blok trasfors sigal to frequey doai so we get deaded spetral lies with the rado aplitude i positive ad egative frequeies. 4. The odified Doppler filter is tha applied (at edge poits the value of ifiitive is replaed by value of 1). 5. The ext poits are exatly the sae as i Sith s algorith, i.e. IFFT ad oputatio of a absolute value fro both brahes. The Rayleigh fadig siulator for oe brah of ultipath fadig hael is i Fig.3. Several Rayleigh fadig siulators have bee used i ojutio with variable gais ad tie delays (Tables 1, ) to produe frequey seletive fadig effets. This is show i Fig.7.

4 197 Coplex siulatio odel of obile fadig hael Fig.3. Rayleigh fadig siulator for oe brah of ultipath fadig hael. 4. SIMULATION RESULTS Our siulatio results are show i fig.4 6. We have preseted here oly B haels, beause of their ore daagig effet o trasitted sigal. Chaels have bee odeled with the sae iitial seed of paraeters. To opare these wavefors we have prologed siulatio to se. Fro both fig. 6 ad 7 short ter fadig ad shadowig fadig are visible, ad the great satterig property of the vehiular hael is obvious. Loss (db) Tie (s) Fig.4. Short ter fadig for Pedestria B hael Loss (db) Tie (s) Fig.5. Short ter fadig for Vehiular B hael

5 Advaes i Eletrial ad Eletroi Egieerig 198 Fig.6. Short ter fadig for Vehiular B hael (seget of 50s) Rayleigh 1 Rayleigh Rayleigh 3 Rayleigh 4 Fig. 7. Rayleigh fadig siulator for four brahes of ultipath fadig hael. 5. CONCLUSION Coplex fadig hael for two eviroets (pedestria ad vehiular) has bee odeled. Model osists i three ai fadig ehaiss, i.e. log-ter fadig, idued by two ehaiss: path-loss fadig ad shadow fadig ad short-ter fadig, idued also by two ehaiss: ultipath propagatio ad Doppler spread. As theoretial odel for short-ter fadig we have hose the Clarke-Gas odel prepared for oputer siulatio by Sith. Our oplex fadig odel akes possible to siulate all three fadig ehaiss i oe MATLAB -file. Siulatio has show very good oiidee with the theoretial odel.

6 199 Coplex siulatio odel of obile fadig hael REFERENCES [1] Clarke, R.H.: A Statistial Theory of Mobileradio Reeptio. I: Bell Systes Tehial Joural, Vol. 47, 1968, s [] Sith, J.I.: A Coputer Geerated Multipath Fadig Siulatio for Mobile Radio. IEEE Trasatios o Vehiular Tehology, Vol.VT-4, No.3, August 1975, s [3] Tehial Report ETSI: UMTS: Seletio Proedures for the Choie of Radio Trasissio Tehologies of the UMTS. TR V3..0 ( ), s [4] Doboš,.: Measureet of Radio Lik Paraeters. Vyžiadaá predáška predeseá 1. Júla 001 a Uiverzite Reggio Di Calabria (3h).