AN OVERVIEW AND ANALYSIS OF BER FOR THREE DIVERSITY TECHNIQUES IN WIRELESS COMMUNICATION SYSTEMS

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1 Yugoslav Journal of Oratons Rsarch 5 5 umr, 5-69 DOI:.98YJOR37 A OVRVIW AD AALYSIS OF BR FOR THR DIVRSITY TCHIQUS I WIRLSS COUICATIO SYSTS Dragan ITIĆ Insttut for Tlcommuncatons and lctroncs, IRITL A.D. BLGRAD, Batajnč ut 3, 8 mta@rtl.com Alsandar LBL Insttut for Tlcommuncatons and lctroncs, IRITL A.D. BLGRAD, Batajnč ut 3, 8 ll@rtl.com Branmr TRKIĆ gatrnd Unvrsty Blgrad,Faculty of Comutr Scncs, Bulvar umtnost 9, 7 Blgrad, Sra trnc.ranmr@gmal.com Žaro ARKOV Insttut for Tlcommuncatons and lctroncs, IRITL A.D. BLGRAD, Batajnč ut 3, 8 Zaro.arov@rtl.com Rcvd: ovmr 3 Acctd: arch 4 Astract: Th rolm of fadng rfrs to a larg scal dtroraton rocss of wrlss communcaton channl s charactrstcs. Ths ar dscusss dffrnt tchnqus for mtgatng th fadng rolms. A soluton to th rolm s to add a fadng margn on th transmttr, ut t s not an ffctv soluton. Th othr soluton s to us an altrnatv statstcal havor of fadng channls aly th asc concts of dvrsty, whch us two or mor nuts on th rcvr to nsur th corrlaton of sgnal. So, th dvrsty tchnqu s usd to mrov systm rformanc n fadng channls. Instad of transmttng and rcvng th dsrd sgnal through on channl, w hav L cos of th dsrd sgnal transfrrd ovr dffrnt channls. Ths ar rsnts analytcal rsults of th roalty of rror for dvrsty tchnqus whch us Raylgh Fadng Channl for BSK modulaton.

2 5 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus Kywords: Dvrsty, Raylgh fadng channl, Slcton comnng, axmum rato comnng, qual gan comnng, Bt rror rat BR, Bnary has-shft yng BSK modulaton. SC: 3A7, 33, 33F5, 655, 65D8.. ITRODUCTIO In wrlss communcatons, ach wav ntracton wth th ojcts n th roagaton nvronmnt rsults n a larg numr of snt sgnal rlcas wth dffrnt attnuaton, has shft, and dlay arrvng to th rcvr nut. Th suroston of ths rlcas at th rcv sd, and th molty of transmttrs andor rcvrs, caus tm- varalty of th rcvd sgnal amltud,.. at th rcv sd sgnal thr ar amlfcaton or sgnal attnuaton. Ths hnomnon s rfrrd to, n th ltratur, as fadng [8]. Raylgh, Rc, aagam-m, aagam-q and Wull dstruton [8], [7] ar commonly usd for modlng sgnal roagaton n nvronmnts wth multl sgnal aths, whch dnd gratly on fadng hnomnon. Th alcaton of scfc modl s condtond y th scfc roagaton nvronmnt. Raylgh channl modl s usd n stuatons whr thr s no drct ln-of-sght LOS twn th transmttr and th rcvr. Ths s tycal for uran nvronmnts. Rc modl s usd n th ntr-cty aras and suuran aras, whr LOS xsts [4]. Varatons n th nstantanous strngth of th rcvd sgnal n uran aras can qut wll dscrd y aagam-m and Wull dstruton []. Shadow ffct n fadng channls nvolvs fluctuatons of th lvl of avrag sgnal owr; t s a charactrstc of largr roagaton aras. Ths fluctuatons ar usually modld y log-normal or gamma dstruton [8]. In ths ar Raylgh channl modl s slctd du to ts smlcty and frqunt us. In ordr to mrov th systm rformanc n th cas of sgnfcant fadng dffrnt mthods ar usd, ut dvrsty tchnqus ar most frquntly ald [], [3]. Dvrsty transmsson s asd on th rncl of usng multl cos of th transmttd sgnals that ar statstcally ndndnt. Th most commonly usd tchnqus of comnng sgnals aftr alcaton of dvrsty tchnqus ar: Slcton Comnng, SC, whch mans a choc of ranch wth th st sgnal-to-nos rato, axmum Rato Comnng, RC, or comnng wth a maxmum sgnal-to-nos rato, qual Gan Comnng, GC, comnng wth th qual contruton of all ranchs, Swtch and Stay Comnng, SSC, sml comnng y swtchng th sgnals, as wll as varous hyrd tchnqus of sgnal comnng. Th most commonly usd rformanc ndcators of dvrsty rcvr n fadng nvronmnts ar th man outut sgnal-to-nos rato SR or sgnal-to-ntrfrnc SIR, so as th roalty of systm falur out and t rror rat BR [8]. Snc th calculaton of rformanc ndcators s dndnt on th roalty dnsty functon DF of th rcvd sgnal, t s mortant to dtrmn th scfcty of ths functon for a consdrd roagaton nvronmnt. Cumulatv dstruton functon CDF s calculatd y ntgratng DF. CDF s usd to dtrmn roalty of systm falur for scfc thrshold lvl. In th ltratur, thr ar dffrnt modls for gnratng Raylgh fadng.

3 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus 53 rformancs of Raylgh fadng channls wr analyzd n dffrnt roagaton condtons, smulatd y changng th numr of multl roagaton aths, varyng Dolr frquncy and tm dlay of fadng ath, for dffrnt modulaton tchnqus. Snc ttr rformancs ar achvd y th mlmntaton of BSK modulaton format comard wth constllatons such as QSK, 8-SK, or 4-QA, 6-QA [8], BSK modulaton format s chosn, and BR s usd as a numrcal ndcator of rformanc. In ordr to mrov th systm rformanc, dvrsty tchnqus wth SC, GC and RC comnng of sgnals at th rcv sd wr usd. Th comaratv analyss of th tchnqus ng usd s rformd. To llustrat th rsults, w analyzd th cass of on, two, thr, and sx ranchs of dvrsty, not only caus of th otntal rqurd y th smulaton rocss ut also caus th ffctv gan of furthr ncras of th numr of ranchs s vry small.. ODL OF RAYLIGH FADIG CHAL Raylgh channl modl s commonly usd to modl fadng and statstcs of sgnal, whch s transmttd n an nvronmnt whr thr s no ln of sght twn th transmttr and th rcvr. Ths modl s vry sutal for th dscrton of th rcvd sgnal statstcs n uran aras and cty aras wth tall uldngs. Raylgh dstruton dscrs th DF []: α α α x Ω Ω whr α s a random varal rrsntng th amltud of th sgnal, whl th avrag owr of ths random varal s ndcatd y Ω. Th nstantanous valu of th SR r t,, dfnd as th rato of nrgy r t scald y aramtr channl fadng, and sctral dnsty of nos owr can dscrd y th dstruton []:. x rformanc of Raylgh fadng channls wr analyzd n dffrnt roagaton condtons, whch wr smulatd y changng th numr of multl roagaton aths, varyng Dolr frquncy and tm dlay. In ach of th dvrsty ranchs, nos s modlld y Gaussan DF [8]: n µ n x, 3 π σ σ whr th man μ, varanc σ and n s th Addtv Wht Gaussan os AWG. In ach of th dvrsty ranchs, th nstantanous valu SR r t,, s modlld y th dstruton. On th rcv sd, qualzaton of th rcvd sgnal y th nown comlx channl aramtr s rformd, and slcton, n accordanc wth

4 54 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus th ruls of th slctd sgnal for comnng tchnqus RC, GC or SC, s analyzd. Aftr dcodng s don, rror roalts ar calculatd [8] as: rfc d 3. DIVRSITY TCHIQUS 4 Dvrsty tchnqus can usd to mrov systm rformanc n fadng channls. Instad of transmttng and rcvng th dsrd sgnal through on channl, L cos of th dsrd sgnal through dffrnt channls ar rcvd. Thr ar svral dffrnt tys of dvrsty tchnqus that ar commonly usd n wrlss communcaton systms [9], [3], [], [6], [7], []. 3.. Frquncy dvrsty Th frst aroach to achv dvrsty s to modulat an nformaton sgnal y dffrnt carrrs, Fgur, whr st s th quvalnt lowass of th transmttd sgnal, and W s wghtng factor. ach carrr must saratd from th othr on to achv mnmal cohrnc twn transmsson ands Δf c, so that dffrnt cos of th sgnal ar rcvd as ndndnt fadng. At th rcvr, L ndndnt fadng cos ar "otmally" comnd to gv a statstcal dcson. Otmal manulator s th maxmum rato of comnaton, whch wll dscrd latr. Frquncy Dvrsty can usd to surss frquncy slctv fadng. Fgur : Frquncy dvrsty

5 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus Tm dvrsty Anothr aroach to achv dvrsty s to transmt th dsrd sgnal n dffrnt tm rods,.., ach symol s transmttd tms, Fgur, whr st s th quvalnt lowass of th transmttd sgnal, and W s wghtng factor. Th ntrvals twn th transmsson of th sam symol should dtrmnd n such a way to achv th last cohrnc of tm ntrvals Δt c so that dffrnt cos of th sam symols undrgo ndndnt fadng. Th otmal comnaton can otand y th maxmum rato of comnatons. W notc that sndng th sam symol tms s as alyng th, rtton cod. In fact, non-trval codng can also usd. rror control codng wth ntrlacng can an ffctv way to comat tm slctv fast fadng. Fgur : Tm dvrsty 3.3. Sac dvrsty Th thrd mthod to achv dvrsty s to us antnnas to rcv cos of transfrrd sgnal, Fgur 3. Fgur 3: Sac dvrsty

6 56 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus Th antnnas should locatd far nough from ach othr to achv that rcvd cos of th sgnal hav ndndnt fadng. Unl frquncy dvrsty and tm dvrsty, t s not ncssary to hav addtonal rocssng at th nd of transmsson. It s not ncssary to rsrv addtonal transmsson and or addtonal transmsson tm. Thrfor, thr ar hyscal lmtatons for usng sac dvrsty. Somtms, svral transmsson antnnas ar also usd to snd svral cos of transmttd sgnal. Sac dvrsty can usd to comat aganst oth tys of fadng, frquncy fadng and tm fadng. 4. DIVRSITY COBIIG THODS Th da of dvrsty s to comn svral cos of th transfrrd sgnal assng ndndnt fadng n ordr to ncras total rcvng owr. Dffrnt tys of dvrsty rovd dffrnt mthods of comnng. In ths ar, w rvw som common mthods of dvrsty comnng. For slow flat fadng channl, th quvalnt low-ass rcvd sgnal for th ranch can wrttn as: jθ r t A s t + z t,,,, -, j whr st s quvalnt to low-ass transmttd sgnal, A θ th fadng attnuaton for th ranch, z t s Addtv Wht Gaussan nos, AWG. rlcas of transfrrd sgnal ar otand from ranchs: [ r t r t r t ] r,, Slcton Comnng, SC SC s th smlst and most commonly usd mthod for comnng sgnals n Dvrsty systm, whch s asd on choosng th ranch wth th most favoural SR, Fgur 4. SC rcvr stmats th currnt valu of SR n all ranchs and slcts th on wth th most favoural SR [6], [7], []. Comnng th oututs, t s otand jθ y t A s t + z t, wth A max{a, A,, A - }. Rcvd SR can wrttn as follows: A Γ max { Γ, Γ,..., Γ } Wth uncorrlatd ranchs, th CDF for..d ndndnt and dntcally dstrutd ranch s: Γ Γ Γ [ ]..

7 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus 57 Fgur 4: Slcton Comnng Th followng xaml s gvn for th Raylgh Fadng Channl. roalty s xrssd y quaton 5, and s rsntd n Fgur 5, for,, 3, 6 s th numr of antnnas: Γ, σ. 5 Fgur 5: Slcton Comnng n Raylgh Fadng Channl for th cas of rcvng antnnas 4... Outag roalty n Slcton Comnng In ordr to analyz th roalty of t rror BR, lt us frst fnd th roalty of falur for th th on th rcvng antnna [5], []. roalty of falur s

8 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus 58 th roalty that th rato of t nrgy to nos dros low a gvn thrshold. roalty of falur, th on th antnna rcton, s: < s s out d, ] [, whr s: s dfnd thrshold for th rato of t nrgy to nos. In th cas that w hav rcvng antnnas, and f assumd that th channl for ach antnna s ndndnt, th jont roalty s th roduct of th ndvdual roalts s s s s out s < < < < ] [ ] [ ]... [ ] [. ot that th aov gvn quaton dfns th roalty that th ffctv rato of t nrgy to nos for rcvng antnnas lt's ta lal s lss than th thrshold s. Ths s actually cumulatv dstruton functon CDF of. roalty dnsty functon DF s thn otand as th drvatv of th CDF: out d d. 6 Wth slctv Dvrsty, w hav sn that th ffctv SR s mrovd, ut t s not mrovd lnarly wth th numr of rcv antnnas; th mrovmnt s rducd whn th numr of antnnas s ncrasd, Fgur Bt rror Rat wth Slcton Comnng If th calculaton of BR wth AWG, [8], as a functon of t nrgy to nos,, thn th BR for BSK wth AWG can dfnd as: rfc. Consdrng that th ffctv rato of t nrgy to nos for th slctv dvrsty s gvn y, th total BR s ntgral of th condtonal BR ntgratd ovr all ossl valus of, whch can xrssd as:

9 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus 59 d rfc d rfc. 7 Ths quaton s rducd to +, quaton.4 n Scton.3. [6]. In Fgur 6, w rsnt th BR for BSK n Raylgh channl wth Slcton Dvrsty. It can sn that th mrovmnt of th two rcvng antnnas wth rsct to th on rcvng antnna s aout 6dB for BR -4. Fgur 6: BR lot for BSK n Raylgh channl wth Slcton Dvrsty for th cas of rcvng antnnas 4.. axmal Rato Comnng, RC RC s th otmal lnar tchnqu of sgnal comnaton n th Dvrsty systm, whch rovds th st statstcal rsults n lmtng th mact of fadng. Th sgnal n ach of Dvrsty ranchs s, for summarzng, multld y th matchng wghtng factor, thus quatng hass of all sgnals, and th ranchs wth mor

10 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus 6 favoral SR ar tan wth gratr contruton, Fgur 7. Ths nsurs that th sgnal wth mor owr has gratr contruton n th rcvd sum of sgnals. Thrfor, t s ncssary to hav masurmnt of SR n all ranchs, and that s why ths tchnqu s xnsv for ractcal mlmntaton [4], [8]. Fgur 7: axmal Rato Comnng Comnd outut s xrssd y: t r w t y. Wghtng factors ar chosn n such a way that channl gan s conjugat must stmatd: t z A t s A t y j + θ. Th SR of th comnd sgnal s: Γ Γ A. For Raylgh Fadng channl, th outag roalty s gvn y 8 and s shown n Fgur 8, for,, 3, 6 s th numr of antnnas: Γ!. 8

11 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus 6 Fgur 8: axmal Rato Comnng n Raylgh fadng Channl for th cas of rcvng antnnas 4... ffctv o wth axmal Rato Comnng In th rsnc of channl h, th currnt rato of nrgy and nos for th th rcvng antnna s: h. Tang nto consdraton that w qualzd all channls and mard thm y h, th ffctv rato of t nrgy to nos, for rcvng antnnas, s: h Th ffctv rato of t nrgy to nos n th cas rcvng antnnas s tms gratr than th rlatonsh of nrgy to nos n th cas of on antnna, as rsntd latr n Fgur 3..

12 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus Bt rror Rat wth axmal Rato Comnng If w consdr th ch-squar random varal [8], t s wll nown that f h s Raylgh dstruton of th random varal, thn h s th ch-squar random varal wth two dgrs of frdom. Thn th DF for s: Hnc, th ffctv rato of t nrgy to nos,, s th sum of random varals, whr th DF of s th ch-squard random varal wth dgrs of frdom. DF of s:.,! 9 If w dsgnat th rlaton of t nrgy to nos as, BR for BSK wth AWG s xrssd as: rfc. If th dsgnat y, th ffcnt rato of t nrgy to nos for th RC, thn usng 9 and, th total BR s ntgral, for th condtonal BR, calculatd ovr all ossl valus of, as rsntd n : dy rfc dy rfc! λ λ. quaton s rducd to +, whr s +, quaton. and.3 n scton.3. [6]. BR for BSK n Raylgh channl wth axmal Rato Comnng s rsntd n Fgur 9. From ths fgur, t can sn that th mrovmnt for th two rcvng antnnas, comard to on rcvng antnna, s aout 3dB for BR -3.

13 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus 63 Fgur 9: BR lot for BSK n Raylgh channl wth axmal Rato Comnng for th cas of rcvng antnnas 4.3. qual Gan Comnng, GC Whn alyng GC tchnqu of comnng sgnals, has-changs of sgnals n all dvrsty ranchs ar comnsatd, and thn sgnals ar summd, Fgur. Unl th RC tchnqu, all summands hav th sam wghtng factor, so t s not rqurd to masur and stmat SR n all dvrsty ranchs. That s why ths tchnqu s smlr and char for ractcal mlmntaton. Slghtly wors rformancs comarng to RC tchnqus mlmntaton ar th rc of smlr and char ractcal mlmntaton [7], [], []. Fgur : qual Gan Comnng Th avrag mrovmnt of SR for GC s tycally aout db wors than for RC mlmntaton, ut t s stll much ttr than wthout dvrsty. ach ranch of th sgnal s rotatd y jθ, thn all ranchs of sgnals ar summd.

14 64 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus Comnd outut s xrssd as: jθ jθ y t r t A s t + z t For Raylgh Fadng channl, th outut roalty s gvn y 3 and s rsntd n Fgur for th cas of rcvng antnnas,,, 3, 6: Γ A 3 Fgur : qual Gan Comnng for th cas of rcvng antnnas ffctv wth qual Gan Comnng In th rsnc of channl h, [5], [], th currnt rato of t nrgy to nos at th rcvng antnna s: h. For convnnt notaton, lt's dfn as h.

15 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus 65 ffctv for GC s channl owr accumulatd ovr all rcvng antnnas,..: y h h + h, h h Th frst trm n 4 s a ch-squard random varal [8] wth dgrs of frdom, and has a man valu of Hnc, th frst art s rducd to h. σ h h 4 5 Th scond art n 4 s th roduct of two Raylgh random varals. Th man valu of th Raylgh random varal, σh s σ h h h π π π π. Hnc, th scond art s,. 6 Smlfd, f w rlac 5 and 6 nto 4, th ffctv for GC s of th form: π π [ + ] [ + ]. 4 4 Fgur rsnts th rato of th ffctv t nrgy to th nos n th cas rcvng antnnas Bt rror Rat wth qual Gan Comnng Calculaton of th BR for GC s rsntd n [5]. Th currnt valu of th SR r t n th cas of GC tchnqus n a Dvrsty systm wth two ranchs can dscrd y th dstruton []:

16 66 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus x o + π x o o 4 o o o + Q o, 7 whr Q s a Q-functon [] whch dfns th roalty that th Gaussan random varal has a valu gratr than a dfnd thrshold valu. Aftr dmodulaton, rror roalty s calculatd and, asd on 4 and 7 for th cas, t s: + + BR for BSK n Raylgh channl wth qual Gan Comnng for th cas of rcvng antnnas s rsntd n Fgur. Fgur : BR lot for Rcv Dvrsty wth qual Gan Comnng for th cas of rcvng antnnas

17 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus COARISO OF TH THR TCHIQUS, SC, RC AD GC Hr, w comar th tchnqus for slctv comnng SC, maxmal rato sgnal-to-nos owr comnng RC and comnng wth an qual contruton of all ranchs GC n trms of comlxty and mrovmnt of th SR. In Fgur 3 s rsntd an mrovmnt of th SR as th functon of th numr of lmnts numr of usd antnnas,, 3 and 6 antnnas for thr tchnqus SC, RC and GC. Fgur 3: SR gan wth Slcton Dvrsty, axmal Rato Comnng and qual Gan Comnng In Fgur 4, comarng for Raylgh Fadng channl, th outut roalty s gvn y 5 for SC, 8 for RC and 3 for GC for th cas of rcvng antnnas,,, 3, 6. As xctd, th st mrovmnt s achvd for th tchnqu for comnng wth maxmal rato of owr sgnal-to-nos RC, and th worst s th tchnqu of slctv comnng SC. It s mortant to notc that th mrovmnt n th cas of GC s comaral to RC. Consdrng th ncssary rsourcs for th mlmntaton, SC s th smlst, snc th tchnqu rqurs only a masurmnt of th SR at ach lmnt, not has or amltud,.. th tchnqu dos not hav to cohrnt. Both tchnqus, RC and GC, on th othr hand, rqur nformaton aout th has. RC tchnqu rqurs mor rcs masurmnt than GC. RC mrovs rformanc y aout.6db comard wth GC, for th BR%.

18 68 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus Fgur 4: Comarng Slcton Dvrsty SC, SC, SC3, SC6, axmal Rato Comnng RC, RC, RC3, RC6 and qual Gan Comnng GC, GC, GC3, GC6 6. COCLUSIO Otmzaton of th xstng and th dvlomnt of nw modls of roagaton n fadng channls, so as th alcaton of varous tchnqus to mrov th rformanc n cas of fadng xstnc, ar of grat mortanc n lannng and dvlong wrlss communcaton systms. Ths ar analyzs th charactrstcs of th Raylgh channl. In ordr to mrov systm rformanc, dvrsty tchnqu was ald wth dffrnt tchnqus of sgnal comnng at th rcv sd. Charactrstcs hav n nvstgatd n th cas of rcvr, whch mlmnts dvrsty tchnqus wth on, two, thr, and sx ranchs, usng SC, GC and RC tchnqus of sgnal comnng, usng th BSK wth cohrnt dtcton of sgnal. As a masur of rformanc, w hav chosn BR, and concludd that th st rformanc s achvd y alyng th tchnqus of RC. Slghtly wors rformanc s achvd y usng th tchnqu of GC, and th worst, y usng SC tchnqus. Ths s consstnt wth th analytcal rsults. Acnowldgmnts. Ths wor s artally suortd y th nstry of Scnc and Tchnologcal Dvlomnt of th Rulc of Sra wthn th rojct TR37.

19 D.tć, t al. An Ovrvw and Analyss of BR for Thr Dvrsty Tchnqus 69 RFRCS [] DR. Kamlo Fhar, Wrlss Dgtal Communcatons-odulaton & Srad Sctrum Alcatons, rntc Hall Inda, 4. [] Godara L.C., Handoo of Antnnas for Wrlss Communcatons, CRC rss,. [3] Hafth Houran, An Ovrvw of dvrsty tchnqus n wrlss communcaton systms, S ostgraduat cours n rado communcaton, 45. [4] Jas Jr.W.C., crowav ol Communcaton, Wly, w Yor, 974. [5] Janaswamy R., Radowav roagaton and Smart Antnnas for Wrlss Communcatons, Kluwr Acadmc ulshrs,. [6] John R. Barry, dward A. L, and Davd G. ssrschmtt, Dgtal Communcaton, Thrd dton, 3. [7] L W.Y.C., ol Cllular Communcatons, cgraw-hll Boo Co., w Yor, 989. [8] roas J., Dgtal Communcatons, Thrd dton, cgraw-hll, 999. [9] Raaort D., Wrlss Communcatons rncls and ractc, agl hood Clffs, J: rntc Hall 996. [] Smon.K., and Aloun.S., Dgtal Communcatons ovr Fadng Channls, nd d., John Wly& Sons, w Yor, Y, USA, 5. [] Smon.K., and Aloun.S., A Unfd Aroach to th rformanc Analyss of Dgtal Communcaton ovr gnralzd Fadng Channls, roc. I, [] Smon.K., and Aloun.S., Dgtal Communcaton Ovr Fadng Channls: A Unfd Aroach to rformanc Analyss, Wly, w Yor. [3] Stur G.L., rncls of ol Communcatons, nd d, Kluwr Acadmc ulshrs,. [4] Thomas. Covr, and Joy A. Thomas, lmnts of Informaton Thory, nd dton, Wly- Intrscnc, 6. [5] Zhang Q.T., roalty of rror for qual-gan comnrs ovr Raylgh channls: som closd-form solutons, Communcatons, I Transactons on [6] Wllam C.Y. L, ol Communcatons Dsgn fundamntals, Wly Srs n Tlcommuncatons, Scond dton, 993. [7] Wllam C.Y. L, ol Communcatons ngnrng-thory and Alcatons, Scond dton, Tata c-graw Hll ulshng Comany lmtd, w Dlh, 8. [8] Wntrs J.H., Otmum comnng n dgtal mol rado wth cochannl ntrfrnc, I Trans. Vh. Tchnol., VT

2. Grundlegende Verfahren zur Übertragung digitaler Signale (Zusammenfassung) Informationstechnik Universität Ulm

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