wi a et, in Bae Come Seige ee Multiple-Path Fading on Line-of-Sight Microwave Radio Systems as a Function of Path Length and Frequeney iy CL. RUTHNOEE Meow ied Mas 28, 170) rawomission over Bneosihtnieosace vo paths ia aalyend wth the a of pte Hines anprcesation ofthe ateasphevie nde of efoetin, Pe in ple onl equate edit published enperimenad {aor path deg om whi ws dee jig be opie wel te wast hg of ourh @ peti ie eating’ row mownred dota for New ecw. Ersieiein se jive foe the oorabosee gop Fromsvey seponse ne or the wow eee sey for eat fam. 1 ie we thal sf the normal Frexnhsace dries te wnietnve an aboot sin fotion wih vat sve fe etatandard eanaons of wronaeas, WT. Barnet rst Ss aan presi few Hn arth itr aion 1 exeaton on tn pate fe fst sf 2 hee Tes the ot angle fd} the je pase nce “Phe tse vf dp fea oly pathe Se predicted by this model have the once wipe a the Raaletgh ition, fouvel Su wezeureeout of atenatian tabutions on Ln ‘ope wormelly ‘Ferestral and entelite ratin syeers for enmmen eariee epics tions at fequenciee aber 10 GH Tue len propose recentiy = or tenrestil syetems the lengths of luni pate any” be n= jted fo few ilometer by the atenuarion eased by rain A sar limitation hole for satellite systen-for that pat the tansmie~ son pts which ie contained in a alemager "Yor bat: tvcesia! avd stele syste it amtieipated chat oon ‘mse can $2 scbueved if the information er be brane as Ssquenoes of wore pers BuO. E, DeLange bes show tat outs Trill curelone uf few naosecerds enn fer ecious degradation samme amt {hog oneuieon over a 22S-acile per ab a froqneney of 4 GHz; jn We cxperinerty sve crgradarion oewurred. during eunctiors of frequeney-aeeeive fading’? For le proposed systems, this result tives am iespertané qnostion—fur Li lh Tengthe of icsaeet, con pulses ofa Zew mencostonde raion be lina sithoot soering Invoteaie degredetion due 20 froquerey-sresive fading? No enswer to this question has bean fous ia tae leanne; one of the pursosee ofthis paper ie: arate it Tu plancering work an che propagation ef mierowaves, A. B, Cove ford, DeLange, W. ©. duker, an W. M. Sbplese bave showa that fevote froquency-elective Suing ox line-of-sight teanamision paths fan be explained inns of tltiplespachtrasarain,”” Theis Feaulte have been wonferl hy alhets and it ie gcoorally accepted thet the mochaniem of multple-path tansmrsson is w=pensble for noe severe srequeney-slebiew Tang. ‘a this paper, fading dhe to ulple-path traramiasion ad fading cous to eubstanare reiueion ae digessed with caspases on shore fronemision paths, [the rove used, signal power Srom the tr ‘nitter travels to the reseiver over ovo ur mote paras” Multiepathe ico eatsed ly a laser of atmeepbere above the transmitsion path ‘which has a nogative aration in the dex of reovetin, Gener the energy tewtlirg aver the separate pethe wl] tndergo snes hase shite; if che eee'wsl wignal,whien is the vector eum of the Fignole sonived fora "hese pacha, ie 2educed eubeteabie Dy below ea free-epace salu by 1his mechanism, salipe-onth facing fat “Muliple-pth fating then, # a Suaotien et che magntnde of che acento ince 0! rofaelan of the teractng layer. This ereson~ fle to aasante that theze Hew eaexinam sels of Pie gradient which ‘ocurs In esate region, Mages on this sssunyption, will he shown Ui pt Teng by omite seh abet for any pth of length TS Ta— called short pall-—aleep vankpheepath feding cannot oscur. The Tenge Ly ie eeimied for New Jersey ftom tanemission monsure- nents amide by Crwefond and Tales For example, at 80 Oz, Ly 448 km in New Jere "Expressions ane asp derived forthe eyueney seevivity, maximum eto delay, end the pts eearsnee mequinal to eliminete facing due to eabetnmdard refraction Fasting on Jong phe tn slo disoursod and i ia shown abet the path attexnaton diecbution i @ funtion of L4/ where Li the path Tengen, and iis slr yavoleah, "his agives wich Barts rele enunirumeaia vanise pd hie fe aad an extensive meneironerin ‘The correct alope of the AisleFounione of se eles ox. ong paths ie ko predict on che model Mest sevens wlusive fading eeeurs dasing loge eamemaer aighss wher tarpernture Tveriaes and sasoeiad mcleavooyioal ffste Trovinee nagaciva grwliens it che index e2 refruction oF the alm titres Figure 1 ilustrales sine prohla of the sex of eefsue- on whieh ca pelsce ero et three trarasson oathe between frsueai-te= wl feces: to essa pale se saan As is ‘boul, exo sellin i asamaed va elitage oa in Ue veal tfeneneon, fro wees eye, the posron of fhe clewate negative rude inde ices 0° rsracing. oe gine, ay basen tease ig 1-Ratacon doe inde 2A7R ome mau EM sEOARAON. SERN, HRETANEUED RL ellen eeoiver as shown in Hig. 1, ane senses ener ray, launched ‘upmard wt small avg, 0 ta be rotated into the miver The staypdtos ef cho’ gracienea in the irdex of wofrackan re scusllen] only shee saps whieh arn Inanezed we stl! snow to Ube Frizantal cay e evfsacted int the ruciver, Pur eT ang tse boom abun kif sin gradient in che inde ef refraction is cnt the reacted ray fol ews te ate of «role wita radius HZ, where™ 1 fa gyn HB. © ae WEE e Tha bight adore oasth ie 2 wfc} i the index of reaction, mnt Nip) = nt) 10 To digi in te index ef reaction ows to We wal wr ruta a} apd JE 20 Snead of frecpeoey* “Tee mlde of Mg. 1 ie gle appresimatin tothe cota! verse thong inthe Snccx of rece ‘on wi cert on Iraramiaion path "Pn ne ot ard Bee te tpl becaue ie doe chat tan aed of 4 odel—the rele pail eS agree wh he ‘esc rvaniied in eaeponding cep {51 Bilas one, to, or fiver shee tag es peta by the tne abe all of cvs coutinninn of ys Tne en cheese? Far ns more dlrete vay vo tetas ) Bregaane-eyoop mourns, high eertafoe have Bren ayprocratod hy agers tna nee xn ns ang reve ine Sener ent epoxinesed oy thee dieian sual tie “esate tee wns i Uv Delt, eka, and inde of vera to ofthe erating "an Tis) Dacell ae decevived he dependence of sttemution dst butions ex pach long aid avelagh Kous aeteuomets RD Paty nor naps the eam seule peli. by ths oda (ie The corre, spe of deepfading asibtios on ong paths fc aap sil Fron hin re 21 Powe Sift Along 0 ay Cano Cove ‘Tae geomers cer 4 angle sefuoting Inyo bx show in Fig, {The Aline” vey ba radius Ny and ax ancl of dayartune @ LiKe. A ces ray ‘eave the tensniter wt aces @y wd ull the ae uf Acipee with rads y uri the xy etches Fei 2). Abe pi thy slg of she inde of efretionebaczee wd is Ue rel Za => = 2, tye my Tollaws an exe of & citele with zaézae 1 When the ray aumtrencranr api any nto ini the rein = Z,,thagan follows an ave of a stele vith vadige Ry asd aPrvee aC tho eraevee at the angle %y shove the Ivinotal ai "The chase silty ebaecs he ranted rma i given Br ant fn 2) i Tho indo of ration, fe the Fmipapne wavelgth, a sala the element of length song the ay ‘The integral in (21 tke optic erat of the rey, TE i possible zor a refeuted siy oo ae ubove tbe refeting lave sad stil exek the rveiver. Ty inelso Lsenat oto (he yoomery of Fig 2 0 derive the phuse sift along a relimewad ey. There 120 thre rooms lo ene Tie. 2 Sindslves mation wil» ig above the easing aye 2980 aM went evsows PRHNLOML SORA, SETHE 71 Region 1 In the rogon below 2.» = %y — wus; snd a paint on the roy ven ny 2 = dg > Maes 9 — woe Oh, O47 6 y, Bbatating for Fin and nosing thet dave = —my = —1/Ry Hany mE mere, KRENEK. B) Te element of Ith aes the ee i his we egion In the rsiruting lover, » — 1 — auf — amie — toa the ray is iver by += 2; + (cory ~ cos 81,025 Fig. Bs 6, = ne By + (2s — Zell. Suetiating for coe fy in 2, ‘nna asi Unt dale va, mide cob tot, MELE. ‘tho retrening lpr, ds = Rat Region 11 hoor the retsaoting layer, © — wy — ot — me — Fi) — fly ~ tsb anda pei on th ray is given by # = 3 — Fleas — serena Hig. 200s 8, = 060 (By — Za for coe dyin fur 2 nw and ting Uae Ty —ocey +008, OSYSA. 1 a thie rexiou d= Rath ‘inte made fe omitted fom (21, (8, ae (8). By ating Hew soars ite 2) the corn: Jengeh ofthe reread rag cua he wlio coe €F 008 Be care ewe Kaley 2 [im = wr + coe O6Rs dy 2s me 848) = A) — in 5 2g + 28 08 | 2x Feo 884 — ei a =F) in 8, 0 cuvmirs nec wana aI Dniy share saps wie rweh the wereiver age of interest, Por a ray to be rebarted inte the recuiver fue rary af Fig. 2 zequires the the dllsing to vlatons be sti Resin, — (Re — Ribin sin 8) = 1”, “ osnsnss C ‘Tho tauseh ankle fo atl the sles & and My ane rested to the hight, hy ofthe rfeaeting layer above the path ax and ite verfieal ‘hikes, v, by the following equetions haz. Ba My 2, ~ Rese 8 = Roos an 4 priveia, do, @ so Be ent Te und from (8), (10), we) 1) in terns af the pathlength, gradient ef Ube indes of rofreron, and the Heit and thicker of the misiting Iayer. Theee values of fy ant hy a then be substituted ines 7) to detoesine the optics length of i refrartist ray, Dur purpae i bela earved, however, hy seialzing the solution. By = Ry ore 8) — Ry ome 6, ard ay san Phos Shit Along 0 Ray—Bperiol Case The wo'st en3e of inerfesin, tl, he langect iforence in phase toveven “he fives ane reine ml rays, opeite ben the le Tthiel enough tnt no ray hie rower Ue evcever ses above tho Inger. This ean be demersinatet yy the asuel mettods snd che proof ff not rep oed bere ‘The ret of this paper will be emncerned primarily with the worst cage inerietence, fr whieh fe = When Hy — 0, (8) and (Q) ern fin 0, — (Ry ~ Rosin 8 ~ L/2, and ay usses a3 ‘The Limite ws the launch enale, Je, wre Touré by setitutang 113) into (12) yO, S sin 9, H/AR. ay We inroduoe a normalizing paruniclee# such that te i, 1sks 1 = Beno then. trom (14), TEKS RVR 15) Now, 2082 iy wc. evaERO avenstear JonRNAL, ahr eHE Mh _afiey, be) wd LB). a as a) Man ,1(ue=ny ‘ wena 6G «y Wich (14), (18), ond (161 sna recalling thst option feng af the eta say a ed en be atten ‘The index of refraction so ¢ Mra Pap b= wt Seer aim [eat] a8 ‘or LER SRR ‘The intrierenes berween the dine wl rete rays wil he datere sxined from (18), Vin, however, we need expressions ‘ar che dee tin: Angle ane the clatanoe © ray ease above the oath a3 Sunol af the bight ofthe refracing ayer an The Reloion Betcsen the Angle of Deportce athe Sleigh of the Refaeting Layer ‘The civtunve of the miracting lover shove the path axis ic 2 2, ~ By. From Dig. 1, = Bend, e088. 1s souvenian! to oxpmes k interme of the maximum distanee, Ry ‘thet the direre ray ies above the path axis, hy = Rall — 80} Subesisting from (16) and nating that a * 2/2 ay eo 24 Th Disance« Hey Hite abow the Path ‘rom Fig, 1, We meximum estanee, thet 9 ray Hes abawe the pall axis is senneanit rams 2388 Ri — ew LL Substitatiag ftom (16), (29), sad 20), a dye eo air) ea 8 The Optical Fength ofthe Divot Roy 1 8, — 0 the zetrsetng [aver i i high to affect census. In this nao, lanamiaion 4s norcal wal a single ray, nunched et sn Engle « = sine! L/2R. , wall eee le toviver. This ie the dizeeb ey fri ite optien hgh i ven 9p eetting 3 = Me = Dandy = a= Set Ty2Ry = L/Aly + 1/85/28) in 7). sae Y @ ‘The ime of vefesetion ni, © 1 and (22) eam be weston ‘ee e 2 Dhree Paik Tomson he height afte rctactine layer abowe the pet axis, fe sein ght that refraris’ ray aes abaes =e oath gx, snd he phnee hile, gn elong he reiraced rays ano shown in Fig, 3 a2 fonecioe of bb for Re/le 4, The absoisea ie spproxantely propartinal cot lange of departure of ray neue Siz sal wd = (Roi) sin ‘The eurves in Fig, were computed from (18), (20), ant (21) “From Eig. 8 it can be ston that aither ope, two, ot hme rays can rea the seeeiver depending op the beat of che reeneting lye; evera) exannples are shown in Fig. 4a Big. the ner eight 420 hy. Tn adsiton to the dev my, wo wave are rofzacte inl Lhe receiver, As tae lager beh lkerraes a verbal sepurasin eles The te trance aye erasers ay indizccet in Figure th “When the azighi e-sh layer equals tas eight of he der. esp, 1 = bp av the roe rage eier ith eno rleacod cays byw c4ys real ie receiver Ang Sn, she she layer height ie es hn bly one ny. refracted fom the ine, rena ee resizer as shown i Figure 4 The citcl ray exists whe che height ofthe lever eques or exceeds Jing that when hp. Ae sore iy Riguve de, the diet ray tnd one uibnta ray evince when b= fy This vers when fo the refeuetoe ray 284 ree meen astm TRowMTEAD sOcAL, sueTineRES “srt 1 has been known by many peuple for a long time, andi int Lovely vious, Ue if w pace skort enough ae. ceep facing all cor. Aparcitle ne cnantiative annyae ot short path Be been putlisl:herefoee, we presal x deGnision of exboce pat, emdaten tf short poli eral New feney Ze eoveralfreqcenece of inte fend an enalysé of Urnwinikos uver shot! pals, st Denn of Short Pt ‘The largess plane citleroes between mays securs whe A/hy Te this cue the dzeet ray and ane refracted ray eoinee, vein the umber of says to two. "The eomesponding vive af xtc at yy ER att - Sa ein