Long-Term Cumulative Distribution Modeling of Tropospheric Scintillation for the Earth-Satellite Links in the 40/50 GHz band

Transcription

1 Lng-Term Cumulative Distributin Mdeling f Trpspheric Scintillatin fr the Earth-Satellite Links in the 4/5 GHz band M.Akhndi (1), A.Ghrbani () (1) () Electrical Engineering pt., Amirkabir University f Technlgy (Tehran Plytechnic), Tehran, 15914, Iran Abstract: In this paper, we have btained a mdel fr the dictin f scintillatin fade depth, scintillatin intensity, and cumulative distributin f its intensity, in the 4/5 GHz band. By applying a regressin analysis t the eperimental data cllected at Madrid, a new mdel is prpsed. Mrever, the dictin accuracy f the ur new mdel is evaluated using the eperimental results frm Spin d Adda, Italy. Keywrds: earth-satellite link, radiwave prpagatin, trpspheric scintillatin, fade, cumulative distributin. 1 Intrductin In rder t satisfy the grwing demand fr the lng distance cmmunicatins, during the last decades, the eplitatin f satellites fr cmmunicatin purpses has increased cnsiderably. As the C- band (4/6 GHz) is already cngested, and the Kuband (1/14 GHz) is filling up rapidly, recently, interest fcused n the utilizatin f higher bands (e.g. Ka and V bands) [1]. The perfrmance f the satellite systems perating in the Ka and V bands essentially depends n the prpagatin characteristics f the transmissin medium, i.e. trpsphere. Sme f the mst imprtant trpspheric prpagatin effects are attenuatin due t rain, deplarizatin, gas absrptin and scintillatin [,]. In general, the impact f rain n cmmunicatin systems is dminant. Scintillatin, hwever, becmes imprtant fr lw-margin systems that perating at high frequencies and lw elevatin angles. It has been bserved that, at high frequencies and fr lw elevatin angles, scintillatin may cntribute as much as rain, r mre, t the ttal fade measured. This is especially true fr lw margin systems [4]. Therefre, it is necessary t mdel the scintillatin phenmena fr earth-satellite links. This paper has been rganized as fllws; first, a review f trpspheric scintillatin thery is sented, then, current mdels already prpsed fr scintillatin fade, scintillatin enhancement and its intensity, are intrduced. Finally, accrding t the eperimental data, and applying a regressin methd, the mdels are etracted and then cmpared t elsewhere data and current eisting mdels. Thery The trpspheric turbulence yields time-varying mdificatins f the refractive inde and thus affect prpagatin f radiwaves n earth-space paths by generating randm amplitude, phase and angle f arrival fluctuatins, called scintillatin [4,5]. It is generally assumed that the fluctuatins f signal level due t scintillatin fr shrt-term perids (i.e. up t several minutes) is statinary and fllws a guassian distributin [6-8]. Hwever, fr lnger time perids the variance f fluctuatin is nt mre cnstant and fllws its wn pdf. Tw distributin fr lng-term standard deviatin r variance f scintillatin is prpsed. The first, is

2 gamma distributin and is apprpriate fr mderate scintillatin intensities [9,1]. The secnd, is lgnrmal distributin and is prper fr vigrus scintillatin intensities [7,11]. Mst f the mdels try t relate the parameters f these distributins t the link and meterlgical parameters (e.g. beacn frequency, elevatin angle, humidity, temperature). In rder t calculate, theriticaly, the signal fadings (negative fluctuatins arund the mean signal level) and enhancements (psitive fluctuatins arund the mean signal level) due t scintillatin, we must use the fllwing cnditinal integral equatin [7]: χ p( χ > χ ) = p( χ ) p( ) d dχ (1) χ where χ is a threshld value and p( χ ) is the cnditinal pdf f χ fr given. Different mdels that already prpsed fr scintillatin fade and enhancement, derived frm (1) and eperimental results. Current Mdels In this sectin, the current mdels prpsed fr scintillatin intensity, fade and enhancement are sented..1 Karasawa mdel Based n the eperimental results at Yamaguchi, Japan, at an elevatin angle f 6.5, frequencies f 11.5 and 14. GHz, during the year 198, Karasawa sented a dictin mdel fr signal standard deviatin due t scintillatin ( scintillatin intensity) as fllwing [9]: =.8 n f g( ) / sin θ () where: n = N wet () and N wet is the wet term f grund refractivity inde, f is the beacn frequency (GHz), θ is the elevatin angle f slant path, and g( ) is given by: 1..7( ) 1. g( ) =.5.( ) 1. <. (4).1. < χ χ where λ is the wavelength in m, D e is the effective antenna diameter ( D e = D η, and η is radiatin efficiency f antenna), and z is the distance f the turbulent part f the path, given by: h z = (5) sin θ + h / a e + sinθ Accrding t (1), and assuming a guassian distributin fr shrt-term fluctuatins f signal level and a gamma distributin fr scintillatin intensity, Karasawa btained the fllwing essin fr the scintillatin enhancement: y =.67) (.6 lg p.8 lg p 1.5 lg (.1% p 5%) (6) As the bserved scintillatin fade is larger than its enhancement, and guassian distributin results in symmetrical essins fr fade and enhancement, Karasawa fit a curve t the eperimental data and prpsed fllwing essin fr scintillatin fade: y = (.6 lg p +.7 lg p 1.7 lg p + ) p + (.1% p 5%) (7) Karasawa mdel was tested in several sites and fund t be valid fr 7 t 14 GHz frequency range and elevatin angles frm 4 t.. ITU-R mdel The Internatinal Telecmmunicatin Unin- Radicmmunicatin sectr, ITU-R, prpsed a mdel that is mstly derived frm the Karasawa mdel. They sent the fllwing mdel fr dictin f scintillatin intensity [1]: 4 = ( N wet ). (8) 7 /1 1. f g( ) / sin θ and g( )` is given by [15]: g( D ) =.867( and e + 1) /1 5 / sin[ arctan ] fr =.584k / z. << 1 (9) 5 / 6

3 ITU-R apply the (7) fr scintillatin fade and did nt prpse any mdel fr scintillatin enhancement. This mdel is applicable fr frequencies between 7- t -GHz and elevatin angles frm 4 t.. Ortgies mdels By analyzing the eperimental data derived frm Olympus satellite measurements at Darmstadt, Germany, using the beacns at 1.5,, and GHz, Ortgies sented tw mdel fr dictin f scintillatin distributin parameters. He cnsidered a lg-nrmal pdf fr lng-term distributin f scintillatin intensity with parameters f µ and s which are mean amd standard deviatin f ln, respectively. Ortgies fund that the parameter s is independent f link and meterlgical parameters and is apprimately 1.1. Hwever, he sented tw mdel fr dictin f µ. The first, links µ t wet term f refractivity inde, N wet, and called Ortgies-N mdel and given by [1]: µ = ln( g ( D ).sin( θ ). f ) e N wet (1) While, the secnd, relate µ t T ( C) and called Ortgies-T mdel and is as fllwing [14]: µ = ln( g( ).sin( θ ). f ) T (11) Ortgies assumed a nrmal pdf fr the shrt-term distributin f signal level flucuatins and a lgnrmal pdf fr the lng-term distributin f scintillatin intensity, and applied the cnditinal integral (1) fr calculating the cumulative distributin f signal amplitude. At last, the fllwing simplified integral equatin btained fr the lng-term cdf f scintillatin amplitude ( by using the ERFC(.) functin definitin ): p( X X ) = 1 π. s. Erfc( X (ln µ ) ) ep(. s ) d (1) Accrding t eperimental results frm different sites, Ortgies mdels fund t be reliable fr elevatin angles frm 6.5 t and frequencies f 8 t GHz..4 Otung mdel Based n the scintillatin measurements btained at Sparshlts, U.K, ver a ne-year perid using the Olympus satellite GHz beacn, Otung prpsed a mdel fr scintillatin variables (e.g. intensity, fade and enhancement) [1]. The Otung mdel fr scintillatin is very similar t ITU-R mdel and nly the elevatin dependence term is 11/1 1. sin( θ ) instead f sin( θ ). Fr scintillatin fade and enhancement, Otung fit curves t the eperimental data and fund the fllwing relatin fr them. The scintillatin fading is given by: a ep{ p 4 [.4 +. p].ln( p)} and the signal enhancement is as fllwing: + a.17 (1) ep{.59 p [.7.4 ].ln( p )} (14) Otung mdel is valid fr / GHz frequency range and elevatin angles higher than 1. 4 Analysis and Results 4.1 Scintillatin intensity dictin mdel By frequency dependence analysis fr 4/5 GHz band, accrding t the eperimental results at Spin d Adda, Italy, using the Italsat beacns at 9.6 and 49.5 GHz, Van de Kamp fund the epnent f frequency scaling factr f scintillatin intensity equal t.86 [16]. Fr elevatin angle and meterlgical dependency, 11 / 1 we utilize the theretical term f sin( θ ). Therfre, the mdel that we apply t dict the scintillatin intensity is: 4 5 = ( ). (15).86 11/1 f.sin( θ ). g( ) Nw, we use the eperimental results btained at Madrid, Spain, ver a ne-year perid, using the Italsat satellite beacn at 49.5 GHz, with an elevatin angle f 4. The diameter f receiving antenna is 1. m. 4. CDF f the scintillatin fluctuatins We have used the essin η( p ) fr the frmulatin f curve fitting in which is the

4 dicted scintillatin intensity and η ( p ) is a cubic plynmial in lg( p ). Figure 1 shws the eperimental cumulative data f scintillatin fade and enhancement at 49.5 GHz and their least-square fit curves. In the case f annual cdf f scintillatin intensity, thse quality parameters are respectively,.9977 and.14. Figure :. Annual cdf f scintillatin intensity data and its curve fitting at 49.5 GHz Figure 1:. Annual cdf f scintillatin fade and enhancement data and their curve fit at 49.5 GHz S, the essin fr signal fading is: a +.67) (.51lg( p) +.9 lg( p) And the scintillatin enhancement is: + a (.4lg( p) +.lg( p) 1.78 lg( p) (16) 1.8lg( p) +.6) (17) 4.4 Wrst mnth CDF f the scintillatin intensity Figure shws the eperimental data f the cumulative prbability f wrth mnth scintillatin intensity and the least-square fit curve. Fr the cdf f scintillatin fade, R-square statistics and rms errr are.996 and.995,respectively. Fr the cdf f scintillatin enhancement, thse are, respectively,.994 and Annual CDF f the scintillatin intensity Figure shws the data f cumulative distributin f scintillatin standard deviatin at 49.5 GHz and the best fitting curve. S, the relatin fr CDF f scintillatin intensity becmes as fllwing: a = (.6 lg( p) +.1lg( p) 1. lg( p) pr +.) (18) Figure :. Wrst mnth cdf f scintillatin intensity and its curve fiting at 49.5 GHz,at Madrid site, Spain The wrst mnth distributin is the synthetic peak envelpe f mnthly cumulative distributin btained by selecting at each time percentage the maimum value f the scintillatin intensity eceeded in 1 mnth. Therefre, The essin fr wrst mnth cdf is btained as:

5 wm = (.5lg( p) +.7lg( p) 1.9 lg( p) +.5) (19) Fr wrst mnth cdf f scintillatin intensity, the R-square statistics and rms errr are.99 and.1476, respectively. Thus, fr all the btainrd essins fr cumulative distributin f scintillatin variables, R-square statistics is apprimately.999 and the rms errr is lwer than.15, and this shws the accuracy f the fitting prcess. percentages between 1% t 5% and fades frm - db t.-db, which is shwn in Figure 5. 5 Cmparisin In this sectin, we will cmpare ur prpsed mdel fr scintillatin fade depth with current mdels and available elsewhere eperimental data btained at Spini d Adda, Italy, using the beacn f 9.6 GHz. The elevatin angle f the slant path is 7.8, and the recieving antenna has a diameter f.5 meters and.64 radiatin efficiency. The cmparisin between eperimental fade data at 4 GHz, prpsed mdel and currernt mdels are shwn in Figure 4. Figure 5: A windw f Figure 4 As it is clearly seen, all f the current mdels underestimate the measured fade in the practical range f higher than 1%, while the new prpsed mdel is in gd agreement with data. Als, accrding t Figure 5 we can say that, amng the current esiting mdels, the Ortgies-T mdel dicts the scintillatin fade better than thers and ITU-R and Otung mdel have a similar behaviur. 6 Cnclusin Figure 4: Cmparisin between new prpsed mdel fr scintillatin fade and eperimental data and ther current mdels at 4 GHz As it is clearly seen, fr time percentages lwer than 1%, the mdels f Karasawa and ITU-R underestimate the measurement results, while anther mdels verestimate the data. The mdels f Ortgie-T and Ortgies-N have a better perfrmance in this range f time percentages. In rder t have a mre bvius bservatin, we cnsider a windw f Figure 4 in the range f time New mdels fr the lng-term cumulative distributin f signal fluctuatins due t scintillatin in the V-band, are sented. We btained mdels fr annual cdf f scintillain fadings, enhancements, and intensity. Meanwhile, wrst mnth cdf f scintillatin intensity is als btained. Fr etracting these mdels, we used the eperimental data gathered at Madrid statin, using the beacn 49.5 GHz, with elevatin angle f 4 and the antenna f 1. meters diameter, and then, applied a regressin analysis t these data. T shw the accuracy f the prpsed mdel, we cmpared ur mdel with the measurements results at 4 GHz and bserved its gd perfrmance in cmparisin with ther current mdels. Fr the time percentage higher than 1%, all the current mdels understimated the eperimental fade, and amng them, nly the rtgies-t mdel is fund t be better than thers. Therefre, at higher frequencies, it is suggested t utilize the new

6 prpsed mdel fr the dictin f scintillatin fade in designing the earth-satellite links. Acknwledgements This wrk was supprted by Iran Telecmmunicatins Research Center, ITRC. The authrs wuld like t thank them fr their supprt. References [1] M. M. J. L. van de Kamp, Climatic radiwave prpagatin mdels fr the design f satellite cmmunicatin systems, Ph.D. dissertatin, Technical University Eindhven, The Netherlands, [] D. V. Rgers, L. J. Ipplit, Jr., and F. Davarian, System requirements fr Ka-band prpagatin effects n earth-satellite links, Prc. IEEE, vl. 85, pp , June [] C. E. Mayer, B. E. Jaeger, R. K. Crane, and X. Wang, Ka-band scintillatins: Measurements and mdel dictins, Prc. IEEE, vl.85, pp , June [4] Vanhenacker, D., G. Brussard, F. Haidara, G. Ortgies, A. Parabni, T. Pratt, C.Riva, J.Tervnen, S. Tuw, H.Vasseur. Chapter V Atmspheric Scintillatin, OPEX Secnd Wrkshp f the OLYMPUS Prpagatin Eperimenters, Eurpean Space Agency, Nrdwijk Netherlands, pp , Nvember [5] B. R. Arbesser-Rastburg and A. Parabni, Eurpean research n Ka-band slant-path prpagatin, Prc. IEEE, vl. 85, pp , June [6] Karasawa, Y., M. Yamada and J. E. Allnutt, A New Predictin Methd fr Trpspheric Scintillatin n Earth-Space Paths, IEEE Trans. Antennas Prpagat., pp , [7] Mulsley, T. J. and E. Vilar, Eperimental and Theretical Statistics f Micrwave Amplitude Scintillatins n Satellite Dwn-Links, IEEE Trans. Antennas Prpagat., pp , 198. satellite link, Electrn. Lett., pp , [9] Karasawa, Y., K. Yasukawa and M. Yamada, Trpspheric Scintillatin in the 11/14- GHz Bands n Earth-Space Paths with Lw Elevatin Angles, IEEE Trans. Antennas Prpagat., pp , [1]I.E. Otung, Predictin f Trpspheric Amplitude Scintillatin n a Satellite Link, IEEE trans. n Antennas & Prpagatin, Vl. 44, N. 1, pp , cember [11]G. Ortgies, Prbability density functin f amplitude scintillatins, Electrn. Lett., pp , [1] ITU-R, Rec. PN. 618-, Prpagatin data and dictin methds required fr earthspace telecmmunicatins systems PN Series Vl., pp. 9-4, [1] G. Ortgies, Predictin f Slant-Path Amplitude Scintillatins frm Meterlgical Parameters, Prceedings f 199 Internatinal Sympsium n Radi Prpagatin, Beijing, pp. 18-1, 199. [14]G. Ortgies, Frequency dependence f slantpath amplitude scintillatins, Prc. f the th Meeting f Italsat prpagatin eperiment (OPEX), Darmstadt (Germany), pp , 199. [15]Haddn, J. and E. Vilar, Scattering Induced Micrwave Scintillatins frm Clear Air and Rain n Earth Space Paths and the Influence f Antenna Aperture, IEEE Trans.Antennas Prpagat., pp , [16]Van de Kamp, et al, Frequency pendence f Amplitude Scintillatin, IEEE Trans. Antennas Prpagat., pp , [17]E.Gimnet, N.Duchin, J.Lemrtn, "TEST OF STATISTICAL PREDICTION MODELS FOR CLEAR-AIR SCINTILLATION", COST 55 Wrkshp, First Internatinal Wrkshp n Radiwave Prpagatin Mdelling fr SatCm Services at Ku-band and abve, Vl.4, ESTEC, Nrdwijk, The Netherlands, Octber [8] Otung, I. E. and B. G. Evans, Shrt term distributin f amplitude scintillatin n a