Improved Expression for Intensity Noise in Subcarrier Multiplexed Fiber Networks

Transcription

1 53 mprved Express fr testy Nse Subcarrer Multplexed Fber Netwrks Xaver Ferad* ad Hatce Ksek SRAMT, epartmet f Electrcal ad Cmputer Egeerg Ryers Uversty, Trt, Otar, Caada Tel: ext.6077; Fax: ; E-mal: Ferad@ee.ryers.ca Abstract-The relatve testy se () plays a mprtat rle subcarrer multplexed multmeda ver fber (MOF) etwrks. The s cvetally csdered t be prprtal t the square f the mea ptcal pwer. Ths s true uder small sgal, sgle chael cdts. Nevertheless, expermets by us ad may thers have shw that the als creases wth the mdulat dex m that reflects the pwer f the stchastc mdulatg sgal s(. Accurate characterzat f the s mprtat especally MOF systems supprtg sub carrer multplexed rad sgals addt t dgtal data. Mder MOF lks ted t have large carrer t sdebad rat that ehaces. ths paper, a mathematcal express fr the s derved frm fudametal prcples that shws the depedecy f mdulat dex m ad mdulatg multmeda sgal pwer E[s (]. The ew express better explas the excess cremet f se pwer MOF systems. The sgal t se rat s aalyzed usg the ew express ad umercal evaluats are de csderg OCSS specfcats. dex Terms- Cable TV etwrks, OCSS, multmeda ver fber, ptcal mdulat, relatve testy se (), subcarrer multplexg.. NTROUCTON A ptcal fber etwrk supprtg mre tha e type f servce ca be referred as multmeda-ver-fber (MOF) system. The MOF systems have becme the backbe f ptcal access etwrks. Fr example, fber-t-the-hme (FTTH) ad, less expesve fber-t-the-curb (FTTC) systems have bee rapdly deplyed. 30 mll peple wll have FTTH by 00 Japa ly []. The tred s smlar wrldwde. MOF wll play mprtat rle these emergg FTTH ad FTTC scears addt t exstg hybrd fber caxal (HFC) etwrks ad fbertwsted par etwrks (wth SL techlgy) fr multmeda delvery. these scears, multmeda sgals such as (hgh deft r cvetal) vde, dgtal aud ad hgh-speed (tere data sgals are smultaeusly trasmtted ver ptcal fber. The vde sgal culd be ether rad frequecy (RF) aalg vde r P (teret Prtcl) dgtal vde. The P vde s smlar t teret traffc wth addtal streamg requremet. Hwever, the RF vde sgal s aalg ad subcarrer multplexg s de t trasmt multple televs chaels. Furthermre, the RF vde s a prve techlgy ad expected t ctue t play key rle the fast emergg FTTH etwrks as well []. Mrever, addt t vde, mder HFC etwrks prmses hghspeed (tere data trasmss usg cable mdems. ata-ver-cable terface Specfcats (OCSS), fr example, s the prmary prtcl adpted ths scear. OCSS perates betwee MHz rage fr dwstream trasmss f P packets. Accurate aalyss f the sgal t se rat (SNR) f MOF systems s very mprtat all these cases. A drectly mdulated ROF lk s maly subjected t sht, ad thermal se. The sht se learly creases wth the mea ptcal pwer ad s sestve t the mdulat dex m prvded the mdulatg sgal s( has zer mea. The thermal se s sgal depedet. Hwever, the s typcally assumed t crease wth the square f the mea

2 54 ptcal pwer. Ths s true uder small sgal cdts. The deserves specal attet uder large mdulat cdts because t s bserved t crease wth the mdulatg RF sgal as well. A wdely used express [] gves the mea square value fr the se curret due t as = P R P B () where, P s the relatve testy se parameter typcally gve db per ut badwdth, B s the badwdth f terest, R s the detectr respsvty ad P s the mea ptcal pwer. The parameter P s geerally assumed cstat fr a gve laser dde. Nte that, accrdg t (), the testy se pwer des t chage uless P, P, B r R chages. Hwever, ur bservats ad may ther ccass ([3], [4], [5], [6] ad [7]) the s fud t be chagg wth the ptcal mdulat dex m that reflects the mdulatg sgal pwer. Wst Way, vestgated ths behavr f laser trsc ad amed a ew dyamc [4] uder drect mdulat cdts fr bth sgle ad mult mde lasers. He als bserved a threshld value fr m abve whch, a sudde jump f the level ccurs. Ths s t a majr ccer tradtally because m used t be typcally small. Hwever, wth the advet f mder ptcal sgal prcessg techques, umdulated ptcal carrer ca be suppressed resultg very hgh m [8]. Therefre ths scear, a accurate aalyss s mprtat. addt t laser trsc, there s addtal testy se the ptcal lk due t multple ptcal reflects (terfermetrc se) ad Brllu scatterg. Ths reflected als creases wth the stataeus ptcal pwer. Shbuta et. al [5] vestgated ths The P s als wdely referred as ad gve db/hz []. Hwever, we use the tat P t avd cfus. pheme ad shwed that the reflect duced learly creases wth m, the umber f cectrs ad the fber legth. They als shwed that the ttal testy se s the summat f reflected ad trsc testy ses. ths paper, we mathematcally derve a mprved express fr the varace f usg the eergy cservat thery crpratg the fluece f m a drectly mdulated MOF lk. The we aalyze the SNR perfrmace. The derved express s geeral the sese that t des t assume devce depedet parameters ad s depedet f mdulatg sgal frmat ad frequecy. t better explas the typcal behavr f uder large sgal mdulat cdts, typcally happe wth mder multmeda etwrks. t reduces t the cvetal express () fr small m.. THE FUNAMENTAL NOSE PROCESSES N MULTMEA OVER FBER LNKS ths sect, basc se that exst MOF system s aalyzed. We assume that all cectrs ad the fber are deal s that dstrt ccurs betwee the laser ad the detectr. We d t csder fber chrmatc dspers. We als assume that the recever has a electrcal amplfer fllwed by a bad-pass flter f badwdth B cetered at f c as shw Fg.. The trasfer fuct f ths uty ga bad pass flter H(f) s shw Fg. (mddle). Csderg drect testy mdulat a lear laser dde, the stataeus ptcal pwer utput P( frm the laser respse t put electrcal sgal s( s, P = [ + ms( ][ P + P( ] () Here m s the ptcal mdulat dex, P s the mea ptcal pwer, s( s the rmalzed mdulatg RF sgal s( ) ad, P( s the stataeus fluctuat term due t laser

3 55 Fg.. Blck dagram f the ptcal recever frt ed wth a deal badpass flter. relatve testy se. Neglectg fber atteuat ad dspers 3, the receved ptcal sgal at the recever s same as P(, whch prduces a detected curret (. ( s prprtal t the stataeus ptcal pwer P( s that ( = R P(. The well kw deft fr respsvty R fr a PN dde s R = = (3) P P( where s the mea value f the detectr curret. Nte that the tme varat R s the rat betwee bth the stataeus ad mea values f ( ad P(. Let the detected curret ( be fltered by a flter wth a trasfer fuct H(f) t bta a utput curret ( (Fg.). The, ( s the cvlut f ( wth the mpulse respse f the recever flter h(. ( = ( τ) h( t τ) = R P( τ) h( t τ) (4) The prcess ( s a dubly stchastc Pss prcess the presece f the relatve testy Fber atteuat wll ly scale dw P( ad ths wll have effect the fal express 3 Ths aalyss cludg fber dspers s left fr future wrk. Furthermre, typcally MOF lks used the last mle, whch are shrt ad dspers may be gred. Fg.. Spectrum f the detectr curret (f) (up) ad the frst ad secd rder frequecy respses f the recever badpass flter, S(f) s the Furer trasfrm f s(. se P(. The mea ad varace f ths dubly stchastc utput prcess are determed by the geeralzed Campbell therem as shw [9]. ( ca be re-wrtte as, ( = R [ + ms( τ)][ P + P( τ)] h( t τ) (5) the mre cveet frequecy dma, ths ca be wrtte as, ( f ) = ( f ) H( f ) = RP( f ) H( ) (6) f Fg. shws the spectrum f cmg sgal (f) (up) ad the trasfer fuct f the BPF H(f) (mddle). Typcally, the badwdth B f the recever flter s greater tha the badwdth f s(. Therefre, the flter admts the sgal, hwever, blcks the drect curret term R P. Hece, the flter utput curret, (, depeds ly the sdebads. Nte that P( s a zer mea prcess. Therefre, = RmP s( + ( ) (7) sh + t = ms + sh + (

4 56 where sh ( s the sht se curret ad ( s the testy se curret. The varace f ( gves the sht se whe P( = 0 ad, the varace f ( gves the relatve testy se whe P( 0. A. The Sht Nse Let us assume P( = 0. Uder ths assumpt, the varace f ( after the flter gves the sht se pwer. The express fr ths varace s gve by (8). The dervat f (8) s qute vlved ad gve appedx C f [9] usg a mmet geeratg fuct f the phtdde. Nte the appearace f q (8) = Rq P( τ ) h ( t τ ) (8) f we exame (8), the varace f ( depeds the sgal P( fltered thrugh a hypthetcal flter wth a mpulse respse h (. The frequecy respses f bth H(f) (mddle) ad H (f) = H(f) * H(f) (bttm) are shw Fg. Frm the trasfer fuct H (f), t s bvus that ly the C term R P passes thrugh ths flter ad bth sde bads are atteuated. Therefre, the sht se varace after the flter s gve by, = sht = qrp B = q B 0 (9) Ths express fr the varace f the sht se s wdely used the lterature. Nte that sht r quatum se depeds the receved mea ptcal sgal P, therefre des t deped the mdulat cdts prvded ( = 0. We ca physcally expla ths pheme as fllws: f the stataeus ptcal pwer P( s belw the mea level P, the there wll be less quatum se, smlarly f P( s abve P, the there wll be mre quatum se. Statstcally, f areas belw ad abve the mea level are equal that meas ( = 0. ths case, the average quatum se wll t chage due t mdulat. B. The Relatve testy Nse The relatve testy se after the badpass flter s gve by the varace f ( fr zer P(. The varace f ( s gve by the geeral express, { E[ ( )]} = E[ ] t (0) = R [ + ms( τ )][ P R [ + ms( τ )][ P + P( τ )] h( t τ ) + P( τ )] h( t τ ) Nte that P( ad s( are t crrelated ad P( s a zer mea prcess. Therefre, the expectat f the crss prduct term f the frst term f (0) s zer. That s, R [ + ms( τ )] [P P( τ )] h Hece, + R R ( t τ ) = 0 = [ ( )] ( ) R + msτ P h t τ () [ + ms ( τ )] P( τ ) h( t τ ) [ + ms ( τ )][ P + P( τ ) h( t τ ) Hwever, aga because P( = 0 ad P( ad s( are t crrelated, the last term f () becmes, R [ + ms( τ )] P h ( t τ ) ()

5 57 Ths wll be the same as the frst term f () after smplfcat. Therefre, the frst ad last terms f () are the same. Hece, = [ ( )] ( ) ( ) R + ms τ P τ h t τ (3) Equat (3) eeds careful bservat. t s terestg t te that the varace f ( des t deped P whe the put cssts f the stchastc se prcess P(. Hwever, t des deped m ad s(. Nw, let us defe a magary flter, ( τ ) = [ + ms( t τ )] h( τ ) τ h (4) = R P( τ ) h ( t τ ) (5) the frequecy dma, = R N ( f ) H ( f ) df (6) Here, N (f) s the duble sded pwer spectral desty f the relatve testy se. At frequeces f terest fr aalg ptcal trasmss ths has a cstat spectrum []. Frm (4), h ( has tw cmpets, h( + mh(s(t-τ)h( s a badpass flter wth uty ga that eclses s( ad cetered at f c. The secd term depeds s(. Therefre, frm the cservat f pwer, the pwer cfed the spectrum f H (f) s same as the average square value f the term [+ms(] fr E[s(]=0. Therefre, the se pwer due t s gve as, = R ( f ) B[ + m N (7) The duble-sded pwer spectral desty N s related t the parameter P by [] ( db / Hz) = N ( f ) / P P (8) Slvg the abve tw equats wth a kwledge that = the presece f cumulatve testy se P(, = P R P B[ + m (9) Whe s( cssts f umber f frequeces such as a subcarrer multplexed system, (9) ca be rewrtte as, = R [ + P P B m (0) where m s the mdulat depth f the sgal s (. The ttal ptcal mdulat dex m a MOF system s related t the per chael mdulat dex m by [0] m = m () f each chael has detcal mdulat dex, the () ca be smplfed as m = m. The express we btaed (9) mre accurately explas the depedecy f m ad mdulatg sgal pwer. Whe m = 0, the express (9) reduces t the wdely used express fr the (statc) gve (). Typcally m 40 % ad s( <. Hwever, whe these quattes are hgh, ths term s t eglgble.. THE SGNAL TO NOSE RATO Csderg the express derved (9), the sgal t se rat als wll be slghtly dfferet frm cvetal assumpts. Frm (3) = RP [ + ms( ] = = [ + ms( ] p [ + ms( ] The sgal pwer s = m (.

6 58 The sgal t se rat f multmeda fber ptc lk csderg majr se prcesses s gve belw. se SNR = m P se t P = qb + 4F K T B / R + P B[ + m B L () Sht, ad thermal se terms vlved the express are gve. Thermal se has a cstat varace ad depeds the recever resstace ly. The varace f the sht se s learly prprtal t mea ptcal pwer the fber. Althugh the stataeus ptcal pwer the fber fluctuates due t RF testy mdulat, the mea ptcal pwer des t chage uless the C bas curret s chaged. Therefre, the sht se des t chage wth mdulatg sgal pwer ad cstat fr a gve mdulat depth m. Hwever, the chages wth RF sgal level. Ths s see frm the express (7). Ths s als lgcal because, the s prprtal t the square f the ptcal pwer. Sce, the stataeus ptcal pwer the fber fluctuates at rad frequecy, the square f t creases wth RF sgal level depedg m. The fllwg addtal pts are bserved frm the express fr sgal t se rat: ) The hgher the badwdth B f s(, the lwer the SNR because, the wder se badwdth the ptcal lk cllects mre se. ) The hgher mdulat dex m yelds better SNR. Ths s because mre pwer s ctaed the sde bads cmpared t the umdulated carrer f the thermal se at the recever amplfer s made small eugh due t a mprved desg, the () becmes, SNR = qb + P m B + m Frm (3) we further deduce that, ) the sht se lmted case, (3) m SNR= (4) qb That s, SNR creases wth the mdulatg RF sgal pwer whch s sdebads. ) the lmted case, SNR m = P [ + m B (5) Uder ths cdt, the SNR creases wth m (RF pwer) frst. Hwever, whe the RF pwer s large eugh, the SNR saturates. V. NUMERCAL EVALUATON AN SCUSSONS We assume that fr the sgle mde laser the specfed P s -40 db/hz. Zer fber atteuat s assumed. E[s (] s take as uty, assumg rmalzed base bad square pulses. We csder that the recever s a PN dde wth respsvty R f 0.9 A/W. The lad resstace s 50 Ω the recever amplfer has a se fgure F t f 3 db. B s 6 MHz, the badwdth allcated by each data-carryg chael a OCSS system. Fg.3, the pwer btaed by the cvetal () ad the mprved (0) expresss are pltted. The mdulat dex m s 0.8 ad s. Ths fgure demstrates the

7 Cvetal Express mprved Express 75 cvetal mprved Relatve testy Nse() Pwer [dbm] SNR [db] Mea Optcal Pwer(P) [dbm] Fg. 3. Relatve testy se pwer versus mea ptcal pwer, =, B=6 MHz Relatve testy Nse Pwer [dbm] Cvetal Express mprved Express Mdulat dex m Fg. 4. The relatve testy se pwer usg the cvetal express ad the mprved express, =, B= 6 MHz addtal se pwer yelded by the ew express. As expected, bth cases, se pwer s drectly prprtal t the square f P. Fg. 4 shws the smulated pwer usg the cvetal express () ad, the derved express (0). The mea ptcal pwer P s assumed t be mw the fber ad ly a sgle chael s trasmtted the etre OCSS perat bad. As see the fgure, the s depedet f m accrdg t () whereas wth (0), se pwer creases wth m. At m=, se pwer creases by 3 db. Fg. 5 llustrates the sgal t se rat (SNR) at the recever the lmted case (5). ths fgure, smlar tred as Fg. 4 s bserved. At Mdulat dex, m Fg. 5 SNR curves btaed by the cvetal ad the mprved expresss the lmted case, =, B= 6 MHz lw m values, the behavr f cvetal ad the mprved SNR plts are dstgushable. Hwever, wth the crease m, there s csderable dfferece. The SNR s reduced by 3 db at m=. Fally, let us lk at the verall SNR express gve by (), whch csders all three sht, ad thermal se. Fg. 6 shws the SNR f a sgle chael the presece f varyg umber f adjacet chaels. Nte that the smulat, each chael has detcal mdulat dex m ad the ttal m s 0.8. The se wth the badwdth (6 MHz) f the sgle chael creases as mre umber f chaels s laded t the fber ptc lk. Therefre, the SNR perfrmace f e chael drps wth umber f adjacet chael. Ths s a mprtat pheme that may expla the perfrmace degradat eve befre learty start t appear. V.EXPERMENTAL VERFCATON We als setup a expermet shw Fg. 7 t bserve the mpact f ther chaels the desred chael a subcarrer multplexed MOF system. Ths s de by recrdg errr vectr magtude (EVM). BPSK mdulated RF sgal (850 MHz) carryg data at 5 Mb/s s added wth a secd RF sgal at 750 MHz at a RF pwer

8 EVM vs. umber f chaels Ttal SNR [db] f e chael EVM [% rms] Number f chaels, Fg. 6. SNR f a sgle chael (6 MHz) whe varyg umber f adjacet chaels c-exst the OCSS system umber f chaels, Fg. 8. Average errr vectr magtude (EVM) versus umber f chaels behavr f average EVM ( % rms) f the 850 MHz chael wth the ttal umber f chaels.the ttal RF pwer was kept wth the lear reg f the laser dde t avd lear dstrt ad crss talk. The EVM f the desred chael ca be see t crease as mre chaels are added t the system valdatg the thery. V. CONCLUSONS Fg. 7. The blck dagram f a expermetal setup used measurg the EVM f a sgle chael a multchael ver fber system cmber. The cmbed mcrwave sgal s drectly mdulated usg a dstrbuted-feedback (FB) lw se laser (Fber-Spa AC3T-.5-.3). The ptcal sgal trasmtted thrugh a very shrt sgle mde fber s detected by a fber ptc recever (Fber-Spa AC3R-.5-.3). The recever s a hgh speed, lw dstrt GaAs PN dde pht detectr. Fllwg the detect, the RF sgal at 850 MHz s fed t a Sy Wreless Cmmucats Aalyzer (WCA380). The, the EVM that reflects the se the lk s measured. The RF pwer f the sgal at 750 MHz s creased t emulate multple RF chaels the system. At each pwer level 0 readgs were take ad a average EVM was btaed. Fg. 8 shws the ths paper, we derved a mprved express fr the that reflects the cremet f the wth mdulat dex m (7) ad aalyzed the sgal t se rat perfrmace f a multmeda ver fber system. Nte that the ew express s mathematcally derved frm the fudametal prcples ad t shws gd agreemet wth expermetal measuremets de by us ad may thers ([4], [5], [6] ad [7]). Smulats cmplyg wth the OCSS stadard cfrm that the depedece f pwer the mdulat dex cat be gred strg mdulat cases. Furthermre, a MOF system, the se ctrbut f c-exstg chaels has sgfcat affect the SNR ad EVM f a chael f terest. REFERENCES [] Hrmch Shhara, Bradbad access Japa: Rapdly grwg FTTH market, EEE Cmmucat Magaze, vl. 43,. 9, pp.7 78, 005.

9 6 [] Jh M. Ser, Optcal Fber Cmmucats: Prcples ad Practce, Number TK S46. Pretce Hall, edt, 99. G. L. [3] Xaver Ferad ad Abu Sesay, Characterstcs f drectly mdulated ROF lks fr wreless access, Prceedgs f the CaadaCferece Electrcal ad Cmputer Egeerg. May 004, vl. 4, vl. 7,., pp , Nvember 989 [4] W.. Way, Subcarrer multplexed lghtwave system desg csderats fr subscrber lp applcats, Jural f Lghtwave Techlgy, vl. 7,., pp , Nvember 989. [5] Makt Shbuta, Wataru m, ad Katsum Emura, Reflect duced degradats ptcal fber feeder fr mcr cellular mble rad systems, ECE trasacts electrcs, vl. E76-C,., pp. 87 9, February 993. [6] X. Lu, C. B. Su, R. B. Lauer, G. J. Mesleer, ad L. W. Ulbrcht, Aalyss f relatve testy se semcductr lasers ad ts effect subcarrer multplexed systems, Jural f Lghtwave Techlgy, vl.,. 7, pp , July 99. [7] K. Y. Lau ad H. Bluvelt, Effect f lw frequecy testy se hgh-frequecy drect mdulat f semcductr ject lasers, Appled Physcs Letter, vl. 5, pp. 694, 988. [8] Xja Gu, Yfeg He, Hatce Ksek, ad Xaver Ferad, Trasmss effcecy mprvemet mcrwave fber-ptc lk usg subpcmeter ptc badpass flter, Prceedgs f SPE, Phtc Nrth, September 005. [9] Gra Earss, Prcples f Lghtwave Cmmucats, Number TK E.36. Jh Wley ad Ss, West Sussex, Eglad, 995. [0] Gerd Keser, Optcal Fber Cmmucats, Number TK K44. McGraw-Hll, 3 edt, 000.