PROPAGATION MEASUREMENTS AND MULTIPATH CHANNEL MODELLING FOR LINE-OF-SIGHT LINKS AT 19.5 GHZ

Transcription

1 6 SOUTH FRICN INSTITUTE OF ELECTRICL ENGINEERS Vol.97( Jue 6 PROPGTION MESUREMENTS ND MULTIPTH CHNNEL MODELLING FOR LINE-OF-SIGHT LINKS T 9.5 GHZ K. Naicer* ad S. H. Meey** * Defece, Peace, Safety ad Security (DPSS, Coucil for Scietific ad Idustrial Research (CSIR, PO Box 395, Pretoria,, South frica ** Cetre for Radio ccess Techologies, School of Electrical, Electroic ad Computer Egieerig, Uiversity of KwaZulu-Natal, Durba,, South frica bstract: The eed for greater badwidth ad higher data rates will ievitably lead to the usage of the upper portio of the -bad i terrestrial commuicatio systems. The frequecy bad from 8 GHz to GHz has bee idetified as a suitable cadidate for short-haul lie-of sight lis. s a cosequece, a 6.73 m terrestrial LOS li cetered at 9.5 GHz has recetly bee established betwee the Howard College ad Westville campuses of the Uiversity of KwaZulu-Natal (UKZN, with the primary objective to ivestigate the effect of rai atteuatio over the li. Multipath propagatio ad the resultat frequecy selective fadig is aother major problem afflictig such LOS lis. I order to evaluate the effect of multipath propagatio over the li statistical models of the chael trasfer fuctios are required. I this paper the research ito the simulatio ad statistical modelig of the multipath propagatio for the above-metioed LOS li will be discussed. Key words: multipath propagatio modellig, multipath fadig, chael trasfer fuctio modellig, terrestrial lie-of-sight lis, path profilig, propagatio measuremets.. INTRODUCTION Durig the plaig of terrestrial lie-of-sight (LOS systems, quatitative data relatig to the fade margi, fade duratio as well as the flat ad frequecy selective characteristics of the chael are required. I order to examie the feasibility of a alterative broadbad carrier, the ecessary propagatio measuremets ad chael models are required. This paper will discuss the research ito the modelig ad measuremet of the specified terrestrial LOS li operatig at 9.5 GHz. The research aims to characterise the performace of the li by evaluatig the effects of multipath propagatio uder various meteorological coditios. LOS li was established betwee the Howard College ad Westville campuses of UKZN ad passes over both hilly ad suburba terrai. The chael respose will be examied over a MHz badwidth cetered at 9.5 GHz. I the mid 97s the Wave Propagatio Stadards Committee of the IEEE sposored several mii-reviews ito the absorptio of radio waves i the atmosphere. The wor by [] focused o the effect of oxyge ad water vapour i the atmosphere ad [] o rai atteuatio. From these mii-reviews, the followig coclusios were arrived at, Radio frequecies above 5 GHz were attractive because of their limited use at the time ad sice they could provide larger badwidths. The presece of water vapour ad oxyge i the lower atmosphere resulted i pea absorptio atteuatios ear GHz ad 6 GHz, respectively. 3 There were three regios of lesser atteuatio aroud 35 GHz, 9 GHz ad 5 GHz. However, i ear-earth coditios the atteuatio at the 9 GHz ad 5 GHz regios was eve greater tha that for the maximum loss from the GHz vapour lie. Hece these frequecies are more suitable for satellite-earth commuicatio systems. If rai losses were cosidered, the 35 GHz regio was eve more opaque tha the GHz regio. This motivates the idea of usig the upper portio of the -bad for short-haul poit-to-poit terrestrial commuicatio lis. For the majority of time, such LOS microwave lis will operate essetially error free. The trasmissio medium, which is the lower part of the atmosphere, is usually o-dispersive maig the trasmissio of high-speed digital data highly reliable. However, beig a atural medium, aomalous behaviour i the troposphere ca still occur for some fractio of time ad this ca result i multipath propagatio. The cosequece is multipath fadig cosistig of both flat ad frequecy-selective compoets ad this ca cause severe degradatios i system performace. The flat fadig compoet produces a time-variat, atteuatio that is uiform across the etire chael badwidth. Rai alog the propagatio path is oe example of a source of flat fadig. Copyright IEEE: earlier versio of this paper was first published i FRICON ', 5-7 September, Gaboroe, Botswaa.

2 Vol.97( Jue 6 SOUTH FRICN INSTITUTE OF ELECTRICL ENGINEERS 63 The frequecy-selective fadig compoet, o the other had, results i o-uiform atteuatio i the form of slopes or otches withi the chael badwidth. Such fadig ofte occurs durig periods of time whe there is a irregular variatio i the refractive idex of the atmosphere. I order to combat such udesirable chael pheomea, system desigers eed realistic ad readily useable models of the multipath chael resposes at their disposal. To achieve this, log term experimets eed to be implemeted. Hece, the above-metioed LOS li was recetly established. However, such experimets are few ad far betwee. Oe approach i overcomig the scarcity of experimetal measuremets is to use computer geerated trasfer fuctios ad this will be the focus of this paper. This paper is orgaized as follows. I Sectio, a brief review of the differet chael trasfer models are give. Sectio 3 provides a descriptio of the equipmet followed by path profilig i Sectio. Sectio 5 describes the modellig ad simulatio of chael trasfer fuctios. The results for the fixed delay two-ray model ad complex polyomial expasio are discussed i Sectios 6 ad 7, respectively. Cocludig remars are give i Sectio 8.. PROPGTION MESUREMENTS ND MODELING Propagatio studies for lie-of-sight lis date bac to whe FM systems were first itroduced i the early 95 s. lthough substatial research was devoted i this field, the eed for comprehesive models oly emerged with the advet of digital radios i the 97 s. Sice the several detailed models [3]-[6] have bee developed for the commo carrier bads used i digital radio systems, amely,, 6 ad GHz. Each provides a alterative approach i the statistical modellig of the multipath effects o lie-of-sight lis. τ = ( 6B where, B, is the badwidth uder cosideratio. This results i a fixed delay two-ray model. similar approach was adopted i [5], except istead of assumig a fixed delay, the four parameters of ( were reduced to three by imposig a =, thus resultig i a ormalized two-ray model. alterative approach was show i [], where the chael trasfer fuctio was modelled by the complex polyomial represetatio give by: N c (. = + ( ( = +. (3 H jb j where,. =.. c, is the frequecy measured relative to the cetre frequecy,. c. It was further show i [] that a good represetatio of the same measuremet data used i [3] is possible with a first order polyomial. I [5] it was demostrated that the parameters of the ormalized two-ray model, b,. ad τ ca be obtaied from a trasformatio of the parameters of a first order complex polyomial give by (3. The complex polyomial model ad the fixed delay tworay model will be examied i this paper ad will be discussed further i Sectios 6 ad DESCRIPTION OF EQUIPMENT 3. Trasmitter ad Receiver Statio system for moitorig the chael respose uder various meteorological coditios was istalled o the 6.73 m overlad path separatig the two campuses of the UKZN. bloc diagram of the system is provided i Figure. I [3] a measuremet-derived three-path model was established, give by the followig chael trasfer fuctio, Rohde & Schwarz FSIQ Spectrum alyser Computer Low Noise mplifier Power mplifier (. ± j( = ( H a -be.. τ Orego Scietific WMR98N Meteorological Sesors gilet E85 Sigal Geerator where, τ is the delay differece ad. is the otch frequecy of fade miimum. It is assumed that there is a egligible time delay betwee the direct LOS ray ad the d refracted ray. Subsequetly a represets the vector sum of the first two paths ad ab is the magitude of the third path. I [3], the model was further simplified by assumig a fixed delay, τ, give by, Figure : Bloc diagram of the moitorig system The trasmitter statio was setup o the roof of the Sciece Buildig at the Westville campus ad the correspodig receiver statio was established o the roof of the Electrical Egieerig Buildig located withi the Howard College campus. This provides sufficiet

3 6 SOUTH FRICN INSTITUTE OF ELECTRICL ENGINEERS Vol.97( Jue 6 clearace for the LOS li, which passes over both hilly ad suburba terrai. 3. teae ad Cablig Valulie WR/R parabolic ateae of diameter.6 m are used at both the receivig ad trasmittig statios. The multibad ateae ca operate withi the GHz ad GHz bads ad provide a gai of 38.6 dbi ad a 3 db beamwidth of.9 degrees at 9.5 GHz. The cablig cosists of FSJ-5 superflexible coaxial cables of legth 6 m at the trasmitter ad 5.5 m at the receiver. 3.3 Trasmitter The gilet E85 sigal geerator is used to provide the source sigal. It ca supply a output power of 35 dbm to +3 dbm ad ca operate up to GHz. It ca also provide both M ad FM modulatio schemes. To provide a sigal from - mw to the parabolic atea, a preamplifier is used. The gilet 838 power amplifier is used ad it ca operate from GHz to 6.5 GHz ad provide a gai of 7 db. The followig modes of operatio are thus possible: Fixed frequecy, umodulated cotiuous wave (CW, Narrowbad Sweep (5 MHz, 3 Broadbad Sweep ( MHz, M Modulatio 5 FM Modulatio. To date, CW (fixed frequecy sigals have bee trasmitted ad recorded for calibratio ad setup, as well as to examie the effects of rai o the sigal stregth. few arrowbad sweeps ad broadbad sweeps have bee tae ad oce sufficiet datasets have bee recorded the chaels trasfer fuctio will be modelled as described i Sectio 5. Modulated sigals ca be used later to determie the delay spread. 3. Receiver other gilet 838 power amplifier is used to provide additioal gai before feedig the sigal ito the Rohde & Schwarz FSIQ Spectrum alyzer. Here the resolutio badwidth (RBW, video badwidth (VBW ad frequecy spa ca be selected to provide a desired sweep time. The data will be logged periodically oto a computer. I additio, the followig meteorological coditios are also logged usig the Orego Scietific WMR98N Wireless professioal weather statio: Outdoor Temperature (- C to 6 C Raifall Rate ( to 9999 mm/h 3 Relative Outdoor Humidity (% to 98% Outdoor Dew Poit Temperature (- C to 6 C 5 Outdoor Pressure (795 to 5 mbar 6 Wid Speed ( to 56 m/s ad 7 Wid Directio ( to 359. The Path Profile. PTH PROFILING The measuremets will iitially be tae over a period of oe year examiig the effects of the varyig meteorological coditios. The li passes over both hilly (ear Westville ad suburba (ear Cato Maor terrai. aerial map of the li is provided i Fig.. Due to the high directive gai of the parabolic ateas used at each of LOS statios, accurate poitig is required. The azimuth details are obtaied usig the latitude ad logitude coordiates of each statio (see Figure. The distace betwee the two base statios is 6.73 m. Figure : aerial photograph of the LOS terrestrial li The azimuth required at the Westville trasmitter statio is 38.3 ad the azimuth at the Howard College receiver statio is 8.3. These azimuth agles are measured clocwise from the referece of the magetic south. The various terrestrial li parameters such as altitude ad ateae heights are give i Table. The path profile is show i Figure 3 ad cotais a adjustmet to accout for the vegetatio ad buildigs alog the lie-of-sight.. Path Clearace Westville (Trasmitter E Howard College (Receiver E ccordig to ITU recommedatios [9], diffractio fadig ca be reduced if the ateae heights are sufficietly high so that eve i the worst case of refractio, there is still sufficiet clearace above ay path obstacles. Fresel ellipsoids ca be used to estimate the diffractio ad reflectios alog the path. The radius of the first Fresel ellipsoid is give by:

4 Vol.97( Jue 6 SOUTH FRICN INSTITUTE OF ELECTRICL ENGINEERS 65 F = 7.3 d d fd ( where F deotes the radius of the first Fresel ellipsoid (m, f fis is the frequecy (GHz, d is is the path legth (m ad d ad d the the distace from from either either statio statio (m. (m. The path clearace from the the first first Fresel ellipsoid ad ad the LOS the LOS path path are are also also show i i Figure factor or effective radius factor smaller tha oe ca be used to examie the clearace for the worst case of of ray bedig. Height above sea level i m Howard College (Receiver <== Distace i m ==> (Trasmitter Westville Figure 3: The path profile for the 6.73 m LOS li betwee the Howard College ad Westville campuses TBLE TERRESTRIL LINK PRMETERS Parameter Path legth Height of trasmittig atea above the groud ltitude of trasmitter statio Height of receivig atea above the groud ltitude of receive statio Carrier frequecy Badwidth uder ivestigatio Trasmitter power Trasmittig/receiver atea gai Trasmittig/receiver atea beamwidth Free space loss Total cablig ad coector losses Clear air atteuatio Receiver badwidth Descriptio 6.73 m m 78 m m 5 m 9.5 GHz MHz - mw 38.6 dbi.9 degrees 35 db db db Hz - GHz. How do the multipath model parameters vary for these higher frequecy rages? 3. re the models extedable to larger badwidths?. How applicable are these models to other LOS lis? Computer simulatios ca provide a vital tool i aswerig these questios ad i the modellig of multipath chaels. Oce simulated chael trasfer fuctios have bee geerated, they ca be statistically aalysed ad mathematically modelled as discussed i Sectio. The statistical variability of the model parameters ca the be examied for various simulated chael trasfer fuctios. I [7] the statistical behaviour of multipath chaels was examied ad a method of simulatig chael trasfer fuctios was the developed. The chael trasfer fuctios were geerated by causig several simulated rays to iterfere with oe aother. These simulated rays were depedet o several iput parameters, amely, the umber of iterferig rays, N, the ray amplitudes, a, ray delays, τ, ad the ray phases, φ. I [7], three differet approaches of geeratig the trasfer fuctios were examied. I each case, the chael trasfer fuctios were the statistically aalyzed ad mathematically modelled usig the ormalized two-ray model. The results were the compared to measured results from the PCEM experimet, amely.5 GHz. simulatio approach based o [7] was adopted for the 9.5 GHz LOS li. The simulated trasfer fuctios were the modelled usig the two approaches metioed i Sectio, amely the fixed delay two-ray model ad complex polyomial expasio model. The statistical parameters of each model were the examied, as i [] ad [], the results of which are discussed i Sectios 6 ad The Simulatio Iput Parameters The simulatio procedure discussed i [7] cosists of allowig N rays to iterfere with oe aother, resultig i the trasfer fuctio H, give by, ( = = N j( π fτ φ a e (5 H f 5. MODELING ND SIMULTION OF THE MULTIPTH CHNNEL TRNSFER FUNCTION where N is the umber of rays, a, τ ad amplitude, delay ad phase shift of the respectively. φ is the th ray, The fudametal aim of this research is to model the effects of the atmosphere o terrestrial lie-of-sight lis operatig i the upper portio of the -bad. The ey questios that eed to be aswered are: The ext step is to determie the reduced trasfer fuctio, which is the ratio of the actual trasfer fuctio to a o fade or flat trasfer fuctio. This flat referece level is desigated as, which is give by,. Do existig multipath models [3] ad [] still hold for the frequecy rage uder examiatio?

5 66 SOUTH FRICN INSTITUTE OF ELECTRICL ENGINEERS Vol.97( Jue 6 N a = (6 where, N is the mea umber of rays ad a deotes mea value of the amplitudes. The values for the simulated parameters were the geerated accordig to the distributio fuctios suggested by [7]. I the first case the iput parameters were assumed to be urelated. The secod case cosidered depedece o the ray agle-of-arrival (O ad i the third case the iterferig rays were divided ito three distict groups, amely the atmospheric refracted group, the direct group ad the groud-reflected group. For each case, these respective distributio fuctios were the used to geerate the ray umber, N, ad thereafter N values for the amplitude, delay ad phases of the rays. These iput parameters were the used to geerate the trasfer fuctio sampled at MHz steps over the frequecy rage from 9. GHz to 9.6 GHz. The trasfer fuctio was the trasformed, with respect to the cetre frequecy of 9.5 GHz, ad ormalised usig the referece level,. This process was repeated util reduced trasfer fuctios were obtaied for each case. Whe actual chael measuremets are tae, the chael will be swept at MHz itervals over the MHZ badwidth. Each power measuremet will be recorded i db ad refereced to the average power level of that frequecy at mid-day. The resultat data from each sweep will thus give a reduced trasfer fuctio of the chael. Next, a occurrece criterio is applied to the reduced trasfer fuctios, so as to retai oly those trasfer fuctios whose atteuatio at ay frequecy i the badwidth cosidered is greater tha some threshold, T. atteuatio threshold of ad T = db was used. The trasfer fuctios meetig these criterios are the modelled usig the fixed delay two-ray model ad the the complex polyomial expasio. 5. Case : Urelated Iput Parameters I the first approach, it is assumed that the amplitudes, delays ad phases are mutually idepedet ad urelated to the ray umber, N. s discussed i [7], N, follows a modified biomial distributio ad rage from to rays. The ray amplitudes, a, are give by, a ( π = arccos( x (7 where, x is a [,] uiformly distributed radom variable. The referece level,, was subsequetly calculated to be equal to.777. The ray phase shifts, φ, follow a uiform distributio over the rage [,π ]. The ray delays, τ, are give by: τ = γ l( x (8 where γ =.5s, as i [7]. The distributio fuctios for the simulated parameters are show i Figure. Figure : Distributio fuctios of simulated parameters (Case : Urelated iput parameters 5. Case : Depedece o O I this approach, the cocept of ray O is itroduced alog with the depedece of the ray amplitudes ad delays o this parameter. The ray phase shifts, φ, ad N, are still assumed to be idepedet ad are still determied as discussed i the first case. The O, α, is give by, α α arcsi( x π max = (9 where α ad α max are i radias ad x is a [,] uiformly distributed radom variable. Typical values for αmax ca rage from. to. I this case α max =.5 is assumed. The ray amplitudes, a, are the give by, a Ray umber distributio α.5 mplitude distributio = ( The referece level,, was calculated to be equal to 3.85 ad a is foud to be.868. To geerate the ray delay it is assumed that the simulated ray is reflected at a poit i the middle of the hop legth, D, ad that the reflected ray forms a agle, α, with respect to the direct ray..5.5 The ray delays, τ, are ow subsequetly give by,.5.5 Delay distributio (γ =.5.

6 Vol.97( Jue 6 SOUTH FRICN INSTITUTE OF ELECTRICL ENGINEERS 67 Dα τ = ( c where c is the speed of light ad D = 6.73 m. The distributio fuctios for the above metioed simulated parameters are show i Figure O tmospheric Refracted Group mplitude O distributio (α = mplitude distributio (α =.5.. O Groud-reflected Group mplitude Delay distributio (α =.5 Figure 5: Distributio fuctios of simulated parameters (Case : Depedece o O Figure 6: Distributio fuctios of simulated parameters (Case 3: Ray Groups TBLE NUMBER OF TRNSFER FUCTIONS RETINED FTER TTENUTION CRITERI RE PPLIED TTENUTION T = db CSE : UNRELTED CSE : O DEPENDENCE CSE 3 : RY GROUPS Case 3: Ray Groups I the last approach, the iterferig rays are divided ito the three categories as discussed previously. The distributio fuctios are modified for each group. For the atmospheric refracted group N, rages from to rays accordig to a biomial distributio. The O, α, is give by a half-sie distributio, as discussed i the secod case, with α max =. ad a offset of.5. The direct group cosists of a sigle ray hece, N = with α =. The groud-reflected group comprises of to 5 rays, geerated accordig to a modified biomial distributio as discussed i the first case. The O, α, is agai give by a half-sie distributio, as discussed i the secod case, with α max =.6 ad a offset of -.. For all groups the ray delays ad ray phase shifts are give as discussed i the secod case. Thus i the third case, the total umber of rays rages from 3 ad rays. The referece level,, was subsequetly calculated to be equal to 3.6. The distributio fuctios for the above metioed simulated parameters are show i Figure 6. For each of the simulatio cases, trasfer fuctios were geerated. Table cotais the umber of trasfer fuctios retaied after the atteuatio threshold criteria of ad T = db were applied. These trasfer fuctios, which were the, modelled usig the fixed delay two-ray model i Sectio 6 ad the complex polyomial expasio i Sectio THE FIXED DELY TWO-RY MODEL The fixed delay two-ray model was itroduced by [3] to model a 6. MHz badwidth at 6 GHz. The dataset icluded 5 scas of the chael badwidth, with each sca recordig the power measuremets at frequecies separated. MHz apart. This model will ow be applied to the two simulated datasets for ad T = db. ( Y = Y ω for =,,, ( 6 ( ω = π for =,,, (3 model for the voltage trasfer fuctio, H ( ω, give by ( is the obtaied by estimatig Y with, ( Yˆ = H ω = α βcos( ω ω τ ( where α ad β ca be related to a ad b of ( as follows, ( b α = a + β = a b (5

7 SOUTH FRICN INSTITUTE OF ELECTRICL ENGINEERS The value for the fixed delay, τ, is obtaied from (, usig a MHz badwidth, givig τ =.833 s. The remaiig three parameters of the model were the solved for by miimizig the weighted mea-square error betwee the estimated power, Y, ad the observed power, Yˆ [3] which is give by: Vol.97( Jue 6 The scatter diagrams of the parameters BET for case (urelated parameters Figure 8. The upper curve limit is the correspodig to the costrait α > β. The limit is effect atteuatio threshold. (6 STNDRD DEVITIONS OF THE PRMETERS OF THE FIXED DELY TWO-RY MODEL TTENUTION CSE : O DEPENDENCE CSE : UNRELTED Parameter with the costrait, α > β. If α < β the the solutio yields complex-values for a ad b. Real values ca still be acquired for these trasfer fuctios by movig ω away from the iitial optimum value ad re-optimizig. The datasets for each simulatio case were modelled as discussed with the costrait, α > β. If α < β the the solutio yields complex-values for a ad b. Real values ca still be acquired for these trasfer fuctios by movig ω away from the iitial optimum value ad reoptimizig. The datasets for each simulatio case were modelled as discussed above. Table 3 cotais the percetage of trasfer fuctios that result i complexvalued solutios. These trasfer fuctios have either little shape or a steep slope across the badwidth. TBLE 3 PERCENTGE OF DTSET WITH COMPLEX-VLUED T = db 6.7 %.3 % 3. %. %.7 % 3. % The parameter is fade level or loss term ad B relates to the relative otch depth. The parameter Γ is a useful idicatio of the shape of the gai curve give that β ( β α is effectively the ratio of the radius of curvature to the level of the otch. It is apparet that the choice of threshold has a greater effect o the mea values as opposed to the stadard deviatio. lso the parameter BET seems to be less affected. Histograms for these parameters are give i Figure 7. The shape of the distributio fuctios are smooth ad may be expressed as covetioal statistical distributios, such as ormal ad gamma laws. The choice of threshold clearly has a widowig effect o the distributio fuctios. T = db Mea Stadard Deviatio.69 = log a LPH = log α BET = log β Γ = log ª β ( β α ¼º = log a B = log b LPH = log α BET = log β Γ = log ª β ( β α º¼ = log a B = log b LPH = log α BET = log β Γ = log ª β ( β α º¼ T = db 5 LPH 5 LPH BET Parameters a ad b relate to the shape ad scale of the multipath fade. These parameters are expressed logarithmically, with the mea ad stadard deviatio give i Table. Stadard Deviatio BET Mea B = log b SOLUTIONS FOR LL THREE CSES ND NTENNUTION TTENUTION CSE : UNRELTED CSE : O DEPENDENCE CSE 3 : RY GROUPS LPH ad are give i straight lie lower curved TBLE EFFECT OF ON THE MEN VLUES ND (Y α + β cos(ω ω τ Y E= Y CSE 3 : RY GROUPS Figure 8: The scatter diagrams of LPH ad BET for case (urelated iput parameters Future wor will ecompass the modellig of measured chael trasfer fuctios from the LOS li, usig the above metioed model. The ext step would be to determie what parameter values result i a desired error rate. The outage time for that give error rate ca the be determied.

8 Vol.97( Jue 6 SOUTH FRICN INSTITUTE OF ELECTRICL ENGINEERS Case : Urelated Parameters T = db B LPH BET Γ.5 Case : O depedece T = db T = db B LPH BET Γ Case 3 : Ray Groups B..5 LPH BET Γ THE COMPLEX POLYNOMIL EXPNSION METHOD I this method the power gai trasfer fuctios are fit to th a M order polyomial give by, M H (. = D +. D + +. D (7 c The coefficiets of this polyomial are the used to solve for the parameters of the polyomial expasio, give i (3. It was show i [5], that a polyomial of order M = is sufficiet to model observed fadig resposes. Secod order polyomials were thus fit to each of the simulated trasfer fuctios. The coefficiets of the polyomial fits, amely, D, D ad D, ca the be used to determie., give by, ( D D D. = (8 The coefficiets of the complex polyomial expasio, ca the be solved as follows: = D B = D ±. ;. = = ± B + B B 8. ;. < ;.= = + ;. < B B = B (9 It ca be see that a optimum solutio ( = ad B = is possible oly if. =. For the case. <, a suboptimal solutio is obtaied by eglectig ad B ad usig the resultig trucated polyomial. Table 5 cotais the percetage of trasfer fuctios that result i suboptimal solutios. The mea ad stadard deviatio for the relevat parameters are give i Table 6 TBLE 5 PERCENTGE OF DTSET WITH SUBOPTIML SOLUTIONS FOR LL THREE CSES ND NTENNUTION TTENUTION M T = db CSE : UNRELTED 5.9 %.3 % CSE : O DEPENDENCE 53.9 % 37. % CSE 3 : RY GROUPS 5.8 % 65.7 % Figure 7: Histograms of the parameters of the fixed tworay model for atteuatio thresholds, T = db (left ad (right Oce agai, the choice of threshold has a greater effect o the mea values of the parameters, as oppose to the stadard deviatio. lso the parameter seems to be

9 7 SOUTH FRICN INSTITUTE OF ELECTRICL ENGINEERS Vol.97( Jue 6 less affected. The mea ad stadard deviatio for the optimum ad suboptimum cases are give i Table 7. TBLE 6 EFFECT OF ON THE MEN VLUES ND STNDRD DEVITIONS OF THE PRMETERS OF THE COMPLEX POLYNOMIL EXPNSION MODEL CSE : UNRELTED CSE : O DEPENDENCE CSE 3 : RY GROUPS TTENUTION PRMETER Mea Stadard Deviatio Mea T = db Stadard Deviatio (MHz B (MHz a = log (MHz B (MHz a = log (MHz B (MHz a = log Optimal Cases (59.7%...6 x x - Optimal Cases (6.8%.. Case : Urelated parameters.5.5 Suboptimal Cases (.3% x - B. Case : O Depedece x - Suboptimal Cases (37.%.. TBLE 7 THE MEN VLUES ND STNDRD DEVITIONS OF THE PRMETERS OF THE COMPLEX POLYNOMIL EXPNSION MODEL FOR T = DB CSE CSE CSE 3 PRMETER OPTIMUM CSE = B = ( Mea Stadard Deviatio SUBOPTIML CSE = B ( Mea Stadard Deviatio (MHz B (MHz (MHz B (MHz (MHz B (MHz The histograms for these parameters are give i Figure 9. The shape of the distributio fuctios are agai smooth ad may be expressed as covetioal statistical distributios. I the suboptimal cases, the values for ad B are of the order. This justifies the assumptio = B ad the subsequet usage of the trucated sigle order polyomial. The histograms of the parameters ( MHz ad B ( MHz for case (urelated parameters are give i Figure. The complex polyomial represetatio of the chael trasfer fuctios is particularly advatageous whe lower order polyomials are applicable. The model suggests the form of a adaptive equaliser respose, Hc ( ω, which is highly effective agaist multipath fadig, whe >. However, if <, the result is a.5. x x Optimal Cases (3.3%.... x x x x - Figure 9: Histograms of the parameters of the polyomial model for optimal cases (left ad suboptimal cases (right, with T = db reductio of the amplitude distortio at the expese of icreased delay distortio. Future wor will ecompass the modellig of measured chael trasfer fuctios from the LOS li, with the complex polyomial expasio method. B Case 3 : Ray Groups Suboptimal Cases (65.7%.... x - B x -

10 Vol.97( Jue 6 SOUTH FRICN INSTITUTE OF ELECTRICL ENGINEERS 7. x -7 T = db.5 - B x -7 Figure : Histograms of the secod order parameters, ( MHz ad B ( MHz for suboptimal cases, for case with T = db.. 8. CONCLUSION Comprehesive chael models ad chael measuremets are of great value i system plaig. Such owledge ad data provide a essetial tool i optimizig chael usage. There exists tremedous potetial for the use of millimetre-waves i terrestrial lis, due to the better spectral availability ad higher badwidths that are possible. This exposes the eed to perform accurate chael measuremets ad develop chael models at these frequecies. To achieve this goal, log term experimets eed to be implemeted hece a LOS li was established betwee the Howard College ad Westville campuses of the Uiversity of KwaZulu-Natal (UKZN. However, such experimets are few ad far betwee ad to overcome this scarcity of available measuremets, oe ca use computer geerated chael trasfer fuctios. I this paper the simulatio ad statistical modellig of the above-metioed LOS li is discussed. Three differet simulatio approaches were adopted to geerate chael trasfer fuctios. For each approach, the chael trasfers were modelled usig the fixed delay two-ray model ad the complex polyomial expasio method. The relevat parameters of the models were the statistically aalysed. Future wor will ecompass the recordig of the sigal stregth ad delay spread of the li over a period of year. These measuremets will the be modelled as discussed i this paper. The resultat chael fadig models ca the be used to predict the outage time for the LOS li REFERENCES [].W. Straito, The bsorptio ad Reradiatio of Radio Waves by Oxyge ad Water Vapor i the tmosphere, IEEE Tras. o teas ad Propagatio, vol. 3, o. 5, pp , July 975. [] R.K Crae, tteuatio due to Rai, IEEE Tras. o teas ad Propagatio, vol. 3, o. 5, pp , Sept [3] W. D. Rummler, New Selective Fadig Model : pplicatio to Propagatio Data Bell System Techical Joural, vol. 58, o. 5, pp. 37 7, May/ Jue 979. [] L. J. Greestei ad B.. Czeaj, New Selective Fadig Model : pplicatio to Propagatio Data Bell System Techical Joural, vol. 59, o. 7, pp. 97 5, September 98. [5] J. Lavergat, M. Sylvai ad J. Bic, Method to Predict Multipath Effects o a Lie-of-Sight Li, IEEE Tras. o Comm., vol. 38, o., pp. 8 8, October 99. [6] L. J. Greestei ad M Shafi, Microwave Digital Radio. New Yor: IEEE Press, 988. [7] J. Lavergat ad P. Golé, Statistical Behaviour of a simulated microwave multipath chael., IEEE Tras. o teas ad Propagatio, Vol. 39, No., pp , December 99. [8] M. Sylvai ad J. Lavergat, Modellig the trasfer fuctio i medium badwidth radio chaels durig multipath propagatio,. Télécummu., vol., o. -, pp , 985. [9] ITU-R P.53-; Propagatio Data ad Predictio Methods Required for the Desig of Terrestrial Lieof-Sight Systems. [] K. Naicer ad S.H. Meey, Propagatio measuremets ad modelig for terrestrial lie-ofsight lis at 9.5 GHz, i Proc. frico, Gaboroe, Botswaa, September 5-7, [] K. Naicer ad S.H. Meey, Multipath chael modelig for terrestrial lie-of-sight lis at 9.5 GHz., i Proc. STNC Stellebosch, South frica, September 6-8,.