Analiza prijema SC makrodiverziti sistema sa tri grane u prisustvu Gama senke i Rajsovog fedinga
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1 INFOTEH-JAHOINA Vol., March. Analza prjema SC makrodverzt sstema sa tr rane u prsustvu Gama senke ajsovo fedna Nkola Smć, Marja Veljkovć, Mlan akć Katedra za telekomunkacje Elektronsk fakultet Nš, epublka Srbja smcnkola9@mal.com; marja.elfak@ahoo.com; rakcelfak@mal.com Neovan Stamenkovć Odsek za Informatku, Prrodno-matematčk fakultet, Unverztet u Prštn, Kosovska Mtrovca, Srbja neovanstamenkovc@mal.com Zoran Todorovć Fakultet tehnčkh nauka, Unverztet u Prštn, Kosovska Mtrovca, Srbja zorantodftn@ahoo.com Sadržaj U ovom radu data je analza makrodverzt sstema SC (Selecton Combnn) tpa koj se sastaj z tr mkrodverzt sstema MC (Maxmal ato Combnn) tpa sa prozvoljnm brojem rana na ulazu. Ulazne rane makrodverzt kombajnera su korelsane u prsustvu senke koja je modelovana Gama modelom, dok je anvelopa snala zložena utcaju fedna koj se modeluje ajsovom raspodelom. Dobjen su zraz u zatvorenom oblku za funkcju ustne verovatnoće (PDF-Probablt Denst Functon) sstema kao kumulatvnu funkcju raspodele (CDF- Cumulatve Dstrbuton Functon) na prjemu. Verovatnoća otkaza (Outae Probablt) makrodverzt sstema je razmatrana, u clju određvanja utcaja razlčth parametara sstema, poput nvoa korelsanost, reda dverztja oštrne utcaja fedna senke na performance prjema. Ključne rječ- makrodverzt prjem; ajsov fedn; Gama senka; SC kombnovanje; MC kombnovanje. I. UVOD Propaacja snala u bežčnm komunkaconm kanalma, odvja se u okruženju u kome je prsutan velk broj prepreka, od kojh mnoe mou bt pokretne. Pojave refleksje snala kao refrakcje dfrakcje na raznm objektma u propaaconom okruženju, uzrokuju prostranje snala po velkom broju razlčth putanja. Stoa je na ulazu prjemnka prsutan velk broj replka poslato snala, sa razlčtm faznm pomerajem, slabljenjem kašnjenjem, čjom se superpozcjom dobja snal vremensk promenljve ampltude. Ova pojava brze fluktuacje anvelope snala na prjemu nazva se brz fedn [,]. U bežčnm komunkaconm sstemma takodje dolaz do sporjh fluktuacja nvoa srednje snae snala. Ova pojava predstavlja spor fedn, odnosno efekat senke, a posledca je utcaja samo propaacono okruženja snala (veetacja,vsoke zrade ). Ukupn fedn u kanalu predstavlja kompleksnu kombnacju brzo sporo fedna. Performanse sstema deradrane utcajem fedna, poboljšavaju se prmenom dverzt tehnka, bez povećanja snae prenosa šrne propusno opsea []. Jedan od najefkasnjh načna za poboljšanje pouzdanost prenosa ostvaruje se prmenom tehnka prostorno dverztja. Za suzbjanje utcaja brzo fedna, u pojednačnm baznm stancama moblnh komunkaconh sstema prmenjuje se mkrodverzt sstem, koj se realzuje preko nza razdvojenh prjemnh antena. Pr tome za modelovanje prenosa snala se najčešće prmenjuje neka od sledećh raspodela: ejljeva, ajsova, Nakaam-q, Nakaam-m l Vejbulova raspodela.. Najčešće koršćene dverzt tehnke kombnovanja su : SC (Selecton Combnn), MC (Maxmal ato Combnn) EGC (Equal Gan Combnn). Selektvno kombnovanje je jedna od najjednostavnjh metoda kombnovanja realzuje se branjem rane sa najpovoljnjm odnosom snal-šum (SN, Snal to Nose ato). MC metoda je najsloženja za realzacju, al daje najbolje rezultate. Ova metoda se zasnva na kombnovanju sa maksmalnm odnosom snaa snal-šum. EGC je metoda kombnovanja sa jednakm doprnosom svh rana
2 U ovom radu razmatra se ajsov fedn, koj se prmenjuje kod prenosa snala u prradskm medjuradskm zonama. Ova vrsta fedna odnos se na brze slučajne fluktuacje anvelope prjemno snala u slučaju kada zmeđu predajne prjemne antene postoj lnja optčke vdljvost (os-ne of Sht). Značajnu prmenu ajsov model fedna ma kod modelovanja kanala kod sateltskh komunkaconh sstema [4], de se korst za preczan model moblno sateltsko kanala kada je kanal slobodan l u zauzeću [5, 6]. Efekat senke se najčešće modeluje lo-normalnom l ama raspodelom. U ovom radu se na makro nvou razmatra utcaj Gama senke [7]. Makrodverzt sstem se prmenjuje za otklanjanje utcaja sporo fedna, pr čemu se prmenjuje tehnka smultano kombnovanja snala sa zlaza z mkrodverzt sstema veće broja prostorno raspoređenh baznh stanca [8]. Bće zložena analza makrodverzt sstema SC (Selecton Combnn) tpa koj se sastaj z tr mkrodverzt sstema MC (Maxmal ato Combnn) tpa sa prozvoljnm brojem rana na ulazu. Odredće se zraz u zatvorenom oblku za funkcju ustne verovatnoće (PDF-Probablt Denst Functon) sstema kao kumulatvnu funkcju raspodele (CDF- Cumulatve Dstrbuton Functon) na prjemu, a zatm na osnovu njh će bt određene neke mere performans sstema, kao utcaj razlčth parametara sstema, poput nvoa korelsanost, reda dverztja oštrne utcaja fedna senke na performance prjema. II. MODE SISTEMA azmatramo bežčn komunkacon sstem koj se sastoj z tr mkrodverzt sstema sa prozvoljnm brojem rana. Dverzt sstem na mkro nvou su MC tpa podvrnut su utcaju ajsovo fedna dok je makrodverzt sstem SC tpa. Smatramo da su rane na makro nvou podvrnute utcaju Gama senke. ezultujuć snal na zlazu MC kombajnera sa rana -te bazne stance (=,,) je: = r j de je r j anvelopa snala j-te rane dverzt sstema -te bazne stance. Pretpostavljajuć da su anvelope statstčk nezavsne u prenosnom medjumu sa domnantnom os komponentom, možemo opsat pomoću ajsove raspodele [9]: de je ( K ) K ( / ) exp p = K () ( K ) ( ) K K I, =,,. K K = A predstavlja ajsov faktor defnsan kao σ () odnos snae domnantne komponente snala rasejane snae. U prethodnom zrazu srednju snau snala po ran bazne stance dok I n (x) predstavlja modfkovanu Beselovu funkcju prve vrste n-to reda []. Smatrajuć da je korelacja zmeđu rana na mkro nvou tolko mala da je zanemarljva uz pretpostavku da su slučajne promenljve podjednako raspodeljene, združena ustna verovatnoće srednjh snaa svh snala na ulazu je []: p... (... ) exp Ic = ρ ( ρ) = c ρ ( ρ) ( ρ), c c ( ) ( ) c ρ ( c ) = = de je ρ koefcjent korelacje zmeđu rana na makro nvou, c predstavlja oštrnu utcaja Gama senke a su promenljve snae na ulazu mkro kombajnera. Nakon procesranja snala na mkro makro nvou funkcja ustne verovatnoće (PDF) se defnše sa []: p d d p d d p ( ) = d d p ( / ) p ( ) ( / ) p ( ) ( / ) p ( ) d d d dok se kumulatvna funkcja ustne raspodele snala (CDF) defnše kao []:: F d d F d d F ( ) = d d F ( / ) p ( ) ( / ) p ( ) d ( / ) p ( ) d d () (4) (5) - 4 -
3 de je: F ( ) = p ( / ) / (6) d kumulatvna verovatnoća snala na zlazu z MC prjemnka. Zamenom zraza () () u (4), uzmajuć zbo jednostavnost da je K =K =K =K, = = =, ρ = ρ = ρ = ρ c = c = c = c 4 =c, dobjamo analtčk oblk funkcje ustne verovatnoće snala na zlazu sstema: p ( ) exp( K) ()( c j ) j! ( s c) ( w c) w!(s w c) (w c) ( s w c ) ( w c ) ( K ) ( K) ρ s w ( ρ) = 6 s= w= = t= (6 j s t w) ( ρ) ( ) ρ (-4-- j-s-t- w) (4 j s t w)) s c w t-j- (- j- ( s t w)) ( ρ)( K ) ( ) ρ K s c w t-j- de je K v () modfkovana Beselova funkcja drue vrste a x Pochamerova funkcja []. ( ) n Kumulatvnu ustnu raspodele snala na zlazu sstema dobjamo nakon zamene zraza (), () (6) u (5). Zamenom zrara, smatrajuć da je sstem smetrčan dobja se: j s! t (7) ρ K s c j w e z s c j w e z ρ o K ( ) ( ) ρ Verovatnoća otkaza (Outae probablt, OP, P out ) je standardna mera performans bežčnh sstema koj rad preko fedn kanala. Verovatnoća otkaza, P out se defnše kao verovatnoća da postnut nvo snala na prjemu bude manj od vrednost praa γ dovoljno za zadovoljavajuć prjem. Verovatnoća otkaza pomoću funkcje kumulatvne raspodele može bt određena: ( ς γ) ς ( ) ς ( γ) P = P < = p t dt = P out III. NUMEIČKI EZUTATI Funkcja ustne verovatnoće zlazno snala prkazana je na Sl. za razlčte vrednost parametara sstema. γ (8) (9) F ( ) [ ( )] ( 5 e j s w z K ) ( K) j ( j ) ( j ) ( ) ( e j s w z ) ρ ( ) ( 5 e j s w z ) ()( c s c) s ( w c) ( ρ) = 6 e = s= w= e= z= s w ρ exp( K)! j w! j! ( s w c)( w c)( s w c ) e ( w c ) z Slka. Funkcja ustne verovatnoće na zlazu dverzt sstema Na Sl. je prkazana verovatnoća otkaza sstema kada na svakom mkrodverzr kombajneru mamo po dve ulazne rane u zavsnost od koefcjenta korelacje na mkro nvou razlčth parametara fedna
4 odnosno 4 antene, dobjaju se vrednost verovatnoće otkaza reda -, odnosno -4 pr vrednost /=5 db respektvno. IV. ZAKJUČAK U ovom radu prkazan su karakterstke prjema selektvno makrodverzt sstema u prsustvu ajsovo fedna na ulaznm ranama mkrodverzt sstema kada je sstem zložen utcaju Gama senke. azmatran je utcaj razlčth parametara sstema na ponašanje njeovh performans prjema. ZAHVANICA Ovaj rad je fnansran od strane Mnstarstva za prosvetu nauku tehnološk razvoj Vlade epublke Srbje u okvru projekta T 9. Slka. Verovatnoća otkaza (Outae probablt) sstema u zavsnost od koefcjenta korelacje parametara fedna Posmatrajuć Sl. jasno se može uočt da sa povećanjem koefcjenta korelacje ρ zmeđu rana na makro nvou dolaz do povećavanja verovatnoće otkaza sstema, tj. do pooršanja performans. Pored toa može se uočt da sa povećavanjem parametra c, tj. smanjenjem oštrne senke kao sa povećanjem parametra K ajsovo fedna dolaz do smanjenja verovatnoće otkaza, pa samm tm do poboljšanja performans čtavo sstema. Kako je očekvano, sstem ma bolje perforrmanse za slučaj većh snaa snala na ulazu u MC prjemnk, međutm evdentno je da tada verovatnoća otkaza ma relatvno vsoke vrednost. Na Sl. prkazana je verovatnoća otkaza sstema u zavsnost od broja ulaznh rana na mkro nvou. Slka. Verovatnoća otkaza (Outae probablt) sstema u zavsnost od broja ulaznh rana na mkro nvou Sa Sl. se uočava da sa povećanjem broja ulaznh rana na mkro nvou dolaz do značajno smanjenja verovatnoće otkaza sstema. U slučaju kada na ulazu mkro kombajnera postoje, ITEATUA [] Stuber, G. Prncples of Moble Communcaton. Boston, Kluwer Academc Publshers;. [] Smon, MK., & Aloun, M-S. Dtal Communcaton over fadn channels. New York, Wle,. [] Neasmth, EA., & Beauleu, NC. New esults n selecton dverst. IEEE Trans Commun 998, 46, [4] Wtrsal, K., Km, Y.H., & Prasad,. A new method to measure parameters of frequenc-selectve rado channels usn power measurements. IEEE Trans. Commun., vol. 49, pp , Oct.. [5] Corazza, G. E., & Vatalaro, F. A statstcal model for land moble satellte channels and ts applcaton to no eostatonar orbt sstems. IEEE Transactons on Vehcular Technolo, vol. 4, no., part, pp , 994. [6] Wakana, H. A propaaton model for land moble satellte communcatons. In Proceedns of IEEE Antennas and Propaaton Socet Internatonal Smposum, vol., pp , ondon, Ont, Canada, June 99. [7] A. Cvetkovć, M. Stefanovć, N.Sekulovć, D. Mlć, D. Stefanovć, Z.Popovć, Second-order statstcs of dual SC macrodverst sstem over channels affected b Nakaam-m fadn and correlated amma shadown, Electrcal evew vol. 87, no. 6, pp , Jun.. [8] D. Stefanovć, S. Panć, P. Spalevć, Second Order Statstcs of SC Macrodverst Sstem Operatn over Gamma Shadowed Nakaam-m fadn channels, Internatonal Journal of Electroncs and Communcatons (AEU), Volume 65, Issue 5, Ma, Paes 4-48 [9] J. Zhan and V. Aalo, Effect of macrodverst on averae-error probabltes n a can fadn channel wth correlated lonormal shadown," IEEE Trans. Commun., vol. 49, no., pp. 4-8, Jan.. [] I. Gradshten, & I, zhk. (98). Tables of Interals, Seres, and products. Academc Press, New York, 98. [] N. Sekulovc, M. Stefanovc, Performance Analss of Sstem wth Mcro- and Macrodverst ecepton n Correlated Gamma Shadowed can Fadn Channels, Wreless Personal Communcatons, (), vol. 65 no., pp [] S. Panć, et al, "Second order statstcs of selecton macro-dverst sstem operatn over Gamma shadowed k-μ fadn channels", EUASIP Journal on Wreless Communcatons and Networkn, vol, no. 5, pp
5 ABSTACT In ths paper an analss of selecton combnn (SC) macrodverst sstem whch conssts of three maxmal rato combnn (MC) mcrodverst sstems wth an arbtrar number of branches at the entrance wll be presented. At macrolevel nput branches are correlated n the presence of shadown modeled b Gamma lon-term model, whle snal anvelope s exposed to shortterm fadn modeled b can model. Closed form results are obtaned for the Probablt Denst Functon (PDF) and Cumulatve dstrbuton functon (CDF) at the recepton. Outae Probablt (OP) of macrodverst sstem was observed, n order to determne the nfluence of dfferent parameters such are correlaton level, dverst order and fadn and shadown severt on recepton performances. Analss of the SC macrodverst recepton n the presence of Gamma shadowed can fadn Nkola Smć, Marja Veljkovć, Mlan akć, Neovan Stamenkovć, Zoran Todorovć - 4 -
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