D T!m(7 SEP 1 o 1984 COMPONENT PART NOTICE THIS PAPER IS A COfPONENT PART OF THE FOLLOWING COMPILATION REPORT: A (TITLE): Chrcteristics of the Lower Atmosphere lfluencing Rdio Wve Propgtion- Conference Pr:cEedins of'-h Sno-iun of the Electromonetic Wve Propgtion Pnel (33rd) Held t Sptind, Norwy on 4-7 October 1983. (SOURCE): Advisory Croupo fcr Ap-os-fxe r;d flouplnpm(,nt-_ Npii'ly-ctir-5int, (Frnce). To ORDER THE COMPLETE COMPILTION REPORT USE AnAi/s nz A THE COMPONENT PART IS PROVIDED HERE TO ALLOW USERS ACCESS TO INDIVIDUALLY AUTHORED SECTIONS OF PROCEEDINGS, ANNALS, SYMPOSIA, ETC. HOWEVER, THE COMPONENT SHOULD BE CONSIDERED WITHIN THE CONTEXT OF THE OVERALL COMPILATION REPORT AND NOT AS A STAND-ALONE TECHNICAL REPORT. THE FOLLOWING COMPONENT PART NUMBERS COMPRISE THE COMPILATION REPORT: AN): TITLE: AD-PO03 885 Ice Depolriztion on Low-Angle 11 GHz Stellite 0Downlinks. AD-P003 886 The Effects of Low-Altitude Nucler Burst on (( Millimeter Wve Propgtion. AD-P003 887 Mesurements of Atmospheric Effects on Stellite 0 Links t Very Low Elevtion Angle. 0 AD-P003 888 The Effects of Meterorology on Mrine Aerosol nd Opticl nd IR Propgtion. AD-P003 889 A System to Mesure LOS (Line-of-Sight) Atmospheric CL TrnsmiLtnce t 19 GHz. AD-P003 890 A GAs FET Microwve Refrctometer for Tropospheric Studies. AD-P003 891 Prediction of Multipth Fding on Terrestril Microwve Links t Frequencies of 11 GHz nd Greter. AD-P003 892 Multipth Outge Performnce of Digitl Rdio Receivers Using Finite-Tp Adptive Equlizers. AD-P003 893 Sphericl Propgtion Models for Multipth-Propgtion Predictions. AD-P003 894 Correcting Rdio Astronomy interferometry Observtiont for Ionospheric Refrction. AD-P003 895 The Estimtion nd Correction of Refrctive Ben%'ng in the AR3-D Tcticl Rdr Systems. AD-P003 896 Effect of Multiple Scttering on the Propgtion of Light Bems in Dense Nonhomogeneous Medi. AD-P003 897 Adptive Compenstion for Atmospheric Turbulence Xfects on Optivl Propgtion. AD-P003 898 Effects of Atmospheric Turbulence on Opticl Fropo;Ation. AD-P003 899 A Rdio Interference Model for Western xurope,7 AD-P003 900 Trnshorizon Microwve Propgtion Mesuremente relted to Surfce Meteorologiol Prmeters. AD-P003 901 Troposphoio Propgtion Assessment, Thi dm1%1 do IsltI ic WlUIQ* "3 ~jl ANN%
AD#: TITLE: COMPONENT PART NOTICE (CON'T) AD-P003 902 Distortion of Nrrow Rdio Bem in Convective Medium. AD-P003 903 Anomlous Propgtion nd Rdr Coverge through Inhomogeneous Atmospheres. AD-P003 904 The Prediction of Field Strength in the Frequency - Rnge 30-1000 MHz. AD-P003 905 VINl nd UHF Propgtion in the Cndin High Arctic. AD-P003 906 Considertions Pertinent to Propgtion Prediction Methods Applied to Airborne Microwve Equipments. ~~Accession For / GRA&I DTIr TAB Unnnouoed 0 -,: Justifit ion- rtis Distribution/ Avilbility COdes ;---Avil nd/or' Specil ---------------------------------------
14-1 SPHERICAL PROPAGATION MODELS FOR MULTIPATH-PROPAGATION PREDICTIONS by L.P. Ligthrt Delft University of Technology Dept. of Electricl Engineering Mekelweg 4 2628 CD Delft Summry Multipth fding leds co limittion in the vilbility nd/or relibility of microwve links. To study the propgtion mechnism under fding conditions propgtion models.bsed on ry theory, bove sphericl erth hve been developed nd compred to the well-known plnr propgtion model bove "flttened erth". The resons for studying sphericl propgtion models re ) to void the limittion of smll elevtion ngles in plnr propgtion mcdels, b) to investigte the computed nd mesured pth dely on the microwve line of sight links, nd c) to set up n nlyticl pproch for the sphericl propgtion model without numericl difficulties nd co "puting-time intensive procedures. In this pper computtionl results of the models re shown, including n ccurcy nlysis, nd the use of sphericl propgtion models is illustrted for surfce duct lyers bove wter. 1. Introduction Multipth propgtion cn cuse lrge vritions in the received signl level. ko prevent multipth fding on terrestril microwve rdio links two diversity techniques re frequently used: - frequency-diversity, - height-diversity. Another possibilit' for multipth fding reduction is derived from the ngle of rrivl dependency of incoming rys t the receiver ntenn. This third diversity technique looks promising wnen use is mde of electroniclly controlled limited scn ntenns (Ref. 1). Hybrid reflector ntenns for multipth fding reduction hve determined the Germn nd the Dutch contribution to the COST 204 project (Europen Co-2pertion in the fielo of Scientific nd Technicl Reserch-Commission of the Europen Communities). The project is entitled "Phsed Arry Antenns nd their Novel Applictions" (Ref. 2). In The Netherlnds the Dr. Neher Lbortory of the Dutch PTT nd the Microwve Lbortory of the Delft University of Technology hve collborted on reserch progrm to investigte the possibilities of using limited scn ntenns on digitl microwve line of sight links. To come up with ntenn specifictions for fding reduction, group dely requirements in two ry propgtion models hve been considered. Firstly, the plnr propgtion model hs been used. This model pproximtes smll elevtion ngles nd cn be found by n "erth flttening" coordinte trnsformtion to preserve reltive curvture between rys nd the erth. Becuse ccurte time dely informtion is needed for specifying the wnted ntenn chrcteristics sphericl models hve lso been investigted. In Section 2 some ttention is pid to ry prmeters in plnr nd sphericl models, ssuming constnt refrctive index grdient over given height segment. In Section 3 results cf time dely computtions for both models nd of the ccurcy nlysis for the sphericl model re shown. In Section 4 modified logrithmic refrcti-:e index profile is ssumed in order to study the propgtion mechnism through surfce ducts bove wter under different sphericl model conditions. 2. Ry prmeters for plnr nd sphericl models In the model with plnr erth (Figure 1) the verticl refrctive index profile m is ssumed to be dependent on z only nd is chrcterized by the trnsformtion dn(r) dm(z) - =B" -I dr dz R R where n = refrctive index in the sphericl model with erth rdiuu R nd with ssumed rdil dependency r
14-2 n = refrctive index in the plnr model B" = refrctive index grdient per meter in the plnr model L Se 2 -'ry pth T m R Z=Z2 ZL P I p P t h 0 D Z=Z I Figure 1. Plnr propgtion model Figure 2. Ry prmeters in plnr propgtion model Segmenttion is crried out in such wy tht B" = constnt per segment p (Figure 2). The ry prmeters re functions of the refrctive index profile nd 8. In the plnr model the ry prmeters per segment become - h p = height difference of the ry = segment thickness - d P9 = horizontl distnce of the ry long the erth surfce - spp = pth length of the ry t- P = pth dely of the ry p If ry reches mximum or minimum height within the segment n extr segment is introduced bsed on these heights. The whole rdio pth is described by summing the ry prmeters. The ppel of the plnr model is tht nlyticl formuls of the of the ry prmeters cn be given. -- -,~ p segment to Figure 3. Sphericl propgtion model Figure 4. Ry prmeters in sphericl propgtion model In the model with sphericl erth (Figure 3) the refrctive index profile is chrcterized by the trnsformtion dn(r) dn (rf) 1 1 B' 1 1 dr drf R R f R Rf where N = refrctive index in the sphericl model with rbitrry fictive rdius Rf B' = efrctive index grdient per meter in the sphericl model Segmenttion is illustrted in Figure 4 where B' = constnt per segment p. The ry prmeters in the sphericl model become - h sph = segment thickness - d sph = Rf. = horizontl distnce of the ry long the erth surfce - s P sph = pth length of the ry p
14-3 - tsph P pth dely' of the ry Different nlyticl pproximtions for the ry prmeters hve been derived for B' > -N(rf)/rf, B' < -N(rf)/rf nd for the rys which rech mximum heights. Per segment nlyticl expressions cn be obtined by mking pproximtions in the ry theory, especilly of the term I = r f2'n 2 (r f) C 2 Using Snell's lw for sphericl lyered medium the ry pth constnt C becomes C = N(rf). rf * sine For B' < -N(rf)/rf the term I yields I l(r m 2 -r f 2 ) -- K I rm is the mximum rf vlue the ry would rech if the refrctive index grdient B' = constnt were extended fp to bove. This mens r m r The fctor Kp is chosen so tht for r m > r 2 (2 r2) K r 2 2 N 2 (r2 ) C 2 S( m 2 ff 2- nd for r = r 2 = -N2 Kp =-N2(r) B'. N(r r For B' > -N'rf)/rf the term I yields 2 I = V1 -(r _r + K" p f 1 p K' nd K" re chosen so tht the pproximtion is optiml for rf = r 1 ; K' nd K" become p p P p K' p Pp N 2l) +B'. N(r 1 ).r I V" N2r2 ). r 1 - C 2 3. Pth dely computtions nd ccurcy nlysis To mke comprisons between plnr nd sphericl models computer progrms hve been developed. The input prmeters in the progrms re - link geometry (i.e. ntenn heights, distnce between ntenns, erth rdius) - refrctive index profiles linerized in given number of segments - elevtion ngles of trnsmitted rys For n incoming ry t the perture of the receiver ntenn the results re - pth length nd pth dely T - ngle of rrivl - mplitude nd phse In cse the elevtion ngles of trnsmitted nd received rys re within I degree the min difterences between the models re mostly found in pth dely nd mplitude computtions. Therefore, in this.ection results of pth dely computtions re compred for the sphericl model with R = R nd the plnir model. f For simplicity constnt refrctive index grdient B' nd thus constnt B" hs been ssumed owr the tmospheric height region of interest. For the sphericl model this height region is subdivided into,eg-
14-4 ments with constnt thickness of 10 meters. The ntenn heights t trnsmitter nd receiver equls 100 m bove the erth. Three different B' (nd B") vlues re considered:. B' = -5 * 107 [ 1 ],0 B" -3.4" 10* 7 [m- I b. BI =-.78* 10-7 [m - 11,, =.78* 10-7 [m - 1 ] c. B' 1 * 10-7 [M - ]., B" = 2.6 * 10-7 Im - 1] c c In these three cses the ngle of rrivl dependency of the distnce D is pproximted by '. D = 106. [kin] in degrees mldegrees] b'. D, - 420. km] c'. D c -135. [km] The pth dely computtions AT = T totl-t0 for both mc lels re shown in Figures 5-7 where: - T tot = totl pth dely time from trnsmitting to receivirg ntenn - T = dely time of ry propgting t the erth's surfce with refrctive index t erth 00 n o = 1.0002 nd B' = -/R -10-5 -5 AT[ns] Figure 5. Pth dely s function of, for The figures give indiction of lrger B' = -5.0 *10-7 [M -I (solid line), nd AT vlues in the sphericl model. By wy of B" = -3.4 * (dottd line) -2-2 [degrees] o.[degrees] Ax I- - - I Figure 6. Pth dely s function of Ot, for Figure 7. Pth dely s function of, for BI -. 78 *10-7 m 1 (solid line), nd B' - = 1.0 *10-7 [m - I (solid line), nd B" -.78 * 10-7 m I (dotted line) B" = 2.6 * 10 " Em - I] (dotted line) I exmple, differences in AT up to 2.5 ns re found for ngles less thn 0.3 degrees nd distnces less thn 40 km.
14-5 To verify the convergence in the ccurcy of the numericl computtions for the sphericl model AT computtions hve been mde for specific ngles nd the number of segments (segment thicknesses which hve been chosen re 10, 5, 1, nd 0.25 meters) hs been incresed. In Figures 8 nd 9 the ccurcies re given elevtion ngle [degrees] elevtion ngle [degrees] x x -10 10 - X X X 1 5 x-.1-2 -3 -.4 d[m] II d[m] X,, \ /1X/ X X XXX I -I x m - 0, K -1 -.5 0.05-1ns Figure 8. Error e(t) in AT computtions s function Figure 9. Error e(t) in AT computtions s function of segment thickness d for of segment thickness d for s s B' =-5.0 * 10-7 (m - ] B' = 1.0 * 10-7 m - 1] for B' =-5. 10-7 [m - I nd B' = 10-7 [m-]. The point of convergence in the origin hs been obtined by extrpoltion of the curve for segment thickness of 1 m nd thickness of 0.25 m. From these results it cn be seen tht for segment thicknesses less thn 10 meters the ccurcy lies within 1 ns, which is less thn the differences between the sphericl nd the plnr model. 4. The modified logrithmic refrctive index profile An ppliction of the theory is given for refrctive index profile chrcteristic of duct bove wter. This model hs been chosen becuse strong grdients nd thus strong convergence or divergence of the rys cn be expected just bove the wter surfce. At the sme time there is the possibility to investigte whether simple reltionship exists between the mplitude of incoming rys nd their dely time. For the microwve link the following is selected: / / // - distnce between trnsmitter nd receiver = 40 km 3d / / - ntenn heights = 80 m 2d -2 d The modified logrithmic refrctive index profile dm bove flttoned erth is given by (Figure 10). M(z) = C 2 liz - z I - (d + z) (n/z--7-)] + M 1 where d =duct height (5-50 meters) z = roughness prmeter t the erth's surfce M Mz (10 3m) z, = height where Figure 10. Modified logrithmic refrctive index heightere M(z M/z ) C= 1 h nd C chrcterizes dp/dz t high ltitudes 2 profile bove plnr erth >3) (z > 3d)
,14.-6 6 t[ns]1-2 1.5- -.5 [degrees) r.5-0 - 010203040 0 10 20 30 40 50 0 10 20 30 40 50 () (b) (c) Figure 11. Computtionl results s function of duct height e. Moc.l 1: k = I, M t = 325; ) time dely difference 6T; b) reltive mplitude of the indirect ry; c) ngles of rrivl -2-15- - c.degrees) r 1. 6-[ns 1.0- -3-1.0- -.2-0 10 20 30 40 S0 0 10 20 30 40 50 0 10 20 30 40 50 d[m] d [m] - d [m () (b) (c) Figure 12. Computtionl results s function of duct height d. Model 2: k = 4/3, M 1 = 325; ) time dely difference 6T; b) reltive mplitude of the indirect ry; c) ngles of rrivl *1
14-7 The refrctive index n bove the sphericl erth is determined by: M(z) = (n - 1 + T-) 106. dm/dz = (dn/dz + l/r) 106 For fictive erth rdius R = kr it it found tht: f R= dm/dz = 10 C for z > 3d f (dn/dz + /R) ~ kr 2 Is] -2 1.5-1 ii -. 6-. [ (degrees) -1L -2-.5- -3- -111 ' 1 ' I0' 0 ' l l l i l 0 0 10 20 3040 50 0 10 20 3040 50 0 1020 30 4050 - dm] - d [m]- rn () (b (c) NFigure 13. Computtionl results s function of duct height d; Model 3: k = 2, M 1 = 325; ) time dely difference 6 T; b) reltive mplitude of the indirect ry; c) ngles of rrivl This mens tht k determine:. the modelconditions for high ltitudes. The computtions with 1 meter segmenttion nd for k = 1, 4/3 (stndrd lmnosphere bove the duct) nd k = 2, re presented in Figures 11, 12 nd 13. In these figures 6T is the dely time difference nd r is the reltive mplitude fctor of the two rys in this two-wy propgtion model. A dominnt k-dependency on 6T nd cler correltion between 6T nd c re found s function of the duct height, while no simple reltionship exists between 6T nd r. From Section 3 it is knov'n tht the pproprite sphericl model hs to be used for ccurte ST computtions. Conclusions In this pper it is proposed tht for pth dely computtions in multipth fding conditions sphericl models be used. In the sphericl model nlyticl formuls for the ry prmeters hve been used, ssuming constnt refrctive index grdients per segment. By doing so the compting time cn be reduced considerbly reltive to numericl solutions of the differentil equtions. The ccurcy nlysis shows strong convergence in pth dely results by decresing segment thicknesses. The exmple of two-wy sphericl model bsed on surfce duct lyers bove wter indictes strong reltionship between time dely differences nd ngles of rrivl combined with dominnt dependency of the model on the time dely computtions.
Acknowledgements Mny thnks re due to the Dutch P r, Dr. Neher Lbortory, for hving mde this study possible. References (1) K.P. Dombek: "Minderung von Mehrwegeschwund durch dptive Schwenkung der Antennechrckteristik", NTG-Fchtgung, "Richtfunk" Mnchen 1980, NTG-Fchberichte Bnd 70, VDE-Verlg, GmbH, Berlin, ~pp. 133-138 (2) L.P.i tk.p. Dombek, G.Do, V. Sntom: "COST-204 review on limited scn rrys", prr presented t the joint ESA/COST 204 Phsed-Arry Antenn Workshop, held t ESTEC, Noordwijk, The ~Netherlnds, 13 June 1983, ESA SP-204, pp. 15-21 DISCUSSION M.P.M. Hll (U.K.): Your Figures 1-4 show rther simple cse where both trnsmitter nd receiver re -situted t height bove which the refrctive index decreses shrply with height, nd below which it increses shrply with height. Could you plese comment on how the min conclusions of your pper would be different for more generl ducting geometry in which the terminl height would not be t this region of refrctive index chnge, nd where the curvture of ech ry would chnge significntly with height nd even chnge direction long its pth? L.P. Ligthrt (The Netherlnds): In the sphericl model, rbitrry refrctive index profiles my be used nd ntenn heights my vry. Mximum time differences A T occur in the cse you mentioned nd re shown in Figures 1-4. The min conclusion remins, s cn be seen from Figures 11-13 in which modified logrithmic refrctive index profile bsbeen tken. U. Buse (Germny): At which frequency rnge re your models v!id? L.P.Ligthrt (The Netherlnds): At 4 nd 6 GHz. *dimensions S. Rotherm (U.K.): The use of flt erth with n erth flttening trnsformtion nd modified refrctive index should give the sme nswer s sphericl erth nd the ordinry refrctive index. In two (cylindricl geometry) the erth flttening trnsformtion cn be mde exct. L.P. Ligthrt 'The Netherlnds): The erth flttening trnsformtion yields modified refrctive index, which gives pproximte results. In the limit of smll elevtion ngles, exct results re obtined. In comprison between plner nd sphericl propgtion models, differences hve been found only in the pth dely. L. Boithis (Frnce): Vous ne tenez ps compte des vritions horizontles de l'indice de refrction. Les erreurs introduite insi ne sont-elles ps supdrieures b celles que vous envisgez de corriger? L.P. igthrt (The Netherlnds): Horizontl vritions in the refrctive index cn influence the numericl results. Therefore experimentl verifiction of the models is needed. *it T.A.Th. Spoelstr (The Netherlnds): This is comment. The necessity to use plnr or sphericl erth pproximtion in the model depends on the ccurcy one needs. In rdio stronomy, correltion of signls from telescopes t distnces of few hundred meters mke sphericl pproximtion mndtory. Furthermore should be vlid for ll elevtion ngles. N. Amity (U.S.): Roughly, wht improvement cn you expect to obtin by using ngulr diversity? L.P. Ligthrt (The Netherlnds): Deep fdings cn be reduced between 5 to 10 db by using ngulr diversity. The effects on group dely depends on dely time differences.