Harnessing oversampling in correlation-coded OTDR

Transcription

1 Haressig oversamplig i correlatio-coded OTDR Ruoli Liao, 1 Mig Tag, 1,* Ca Zhao, 1 Hao Wu, 1 Sogia Fu, 1 Demig Liu, 1 ad Perry Pig Shum 1 Wuha Natioal Laboratory for Optoelectroics (WNLO) ad Natioal Egieerig Laboratory for Next Geeratio Iteret ccess System, School of Optics ad Electroic Iformatio, Huazhog Uiversity of Sciece ad Techology, Wuha , Chia School of Electrical ad Electroics Egieerig, Nayag Techological Uiversity, , Sigapore bstract: Pulse codig is a effective method to overcome the trade-off betwee sigal-to-oise ratio (SNR) ad spatial resolutio i optical-fiber sesig systems based o optical time-domai reflectometry (OTDR) However, the codig gai has ot bee yet fully exploited We provide a comprehesive theoretical aalysis ad experimetal validatio of the samplig criteria for correlatiocoded OTDR, showig that the codig gai ca be further improved by haressig the oversamplig Moreover, the badwidth-limited feature of the photodetector ca also be utilized to select the samplig rate so that additioal SNR ehacemet is obtaied We believe this priciple could be applied to ay practical OTDR-based optical-fiber sesig techology, ad serve to update existig systems based o correlatio-coded OTDR i a straightforward maer at a relatively low cost 1 Itroductio Optical time-domai reflectometry (OTDR) is a importat distributed optical-fiber sesig techique, i which backscattered light is acquired to obtai the characteristics alog the fiber uder test However, sice the Rayleigh scatterig coefficiet is very small, the backscattered light is very weak as compared to the probig light, leadig to a poor sigal-to-oise ratio (SNR) i OTDR systems lthough icreasig the pulse width ca improve the SNR, it also deteriorates the spatial resolutio Oe solutio to this trade-off is to apply pulse codig I essece, pulse codig icreases the ijected eergy to improve the SNR, while the spatial resolutio, which is determied by the bit width, remais the same I direct detectio OTDR systems, codig schemes ca be classified ito two groups: liear combiatio codes ad correlatio codes [1] Withi the first group, the Simplex codig scheme is the most represetative ad has bee demostrated effective i various OTDR-based fiber sesig systems [ 4] The biorthogoal code is aother liear combiatio code that has proved to be useful [5] However, all codig schemes i this group suffer from the same problem, amely that ehacig the codig gai implies extedig the code legth, which results ito a remarkable icrease i measuremet time This is especially troublesome i log-rage or dyamic/istataeous measuremets O the other had, withi the secod group of codig schemes, complemetary-correlatio codes are particularly suitable for OTDR systems due to their perfect autocorrelatio property The most represetative amog them is the Golay code [6] The umber of sequeces i correlatio codes is idepedet of the code legth; hece, the umber of periods eeded to perform a complete measuremet remais costat Other correlatio codig schemes have also bee developed to further reduce measuremet time [7] or ehace codig gai [8] Iterestigly eough, as illustrated i the followig sectios, the codig gai for a correlatio codig scheme ca be further ehaced by simply choosig a appropriate aalog-to-digital coverter (DC) samplig rate after photodetectio This method does ot require ay chage i the trasmitter, which meas it ca be easily applied to existig OTDR systems with a correlatio codig scheme, thus ehacig their performace at a relatively low cost However, this techique is ot compatible with liear combiatio codes, as will be proved below I this paper, we preset a comprehesive aalysis of correlatio-coded OTDR, takig ito cosideratio the DC samplig rate ad photodetector (PD) badwidth We will prove that the codig gai ca be further improved by settig a samplig rate that is higher tha the bit rate of the iput light pulses, ie, by oversamplig Moreover, the codig gai is also affected by the PD badwidth, ad extra SNR ehacemet ca be obtaied by settig the samplig rate withi a specific rage relevat to the oise characteristics of the PD The results of the experimets performed cofirm these coclusios Theory The correlatio relatioship i OTDR The light source used i direct detectio OTDR is icoheret, so a OTDR system ca be regarded as a discrete liear time-ivariat system The OTDR respose f is defied as the backscatter respose to a optical pulse sigal, usually a rectagular pulse Whe certai codig is applied to OTDR, a umber of idetical pulses arraged accordig to the uipolar biary code sequece c are ijected ito the fiber, each of which results i the very same backscatter respose with differet time delay The total respose y is their superpositio Whe the acquisitio card records data with a samplig iterval equal to the pulse width, y is give by [6] y c, f (1) where * represets the covolutio operatio Correlatio is oe of the spread-spectrum techiques that ca provide measuremets with improved SNR without sacrificig respose resolutio It is implemeted by correlatig the detected sigal with the probe sigal Note that both covolutio ad

2 correlatio are distributive ad associative (however, covolutio is commutative whereas correlatio is ot) Thus, oe obtais, c y c c f c c f () where deotes correlatio If the autocorrelatio of the probe sigal is a delta fuctio, f ca be accurately recovered as c y f f (3) I this case, rather tha the probe sigal itself (which may be log ad eergetic), it is the autocorrelatio of the probe sigal that determies the respose resolutio However, biary sequeces with zero sidelobes are ot kow to exist Oe approach to pursue the sythesis of zero sidelobes is to sum the autocorrelatios of a group of complemetary codes For example, two L-elemet sequeces form a Golay complemetary pair, if the sum of their autocorrelatios is zero for all ozero shifts [9]: L (4) y probig the system uder test with Golay codes ad, the output sigals are expressed as y f (5) y f Correlatig these outputs with their respective probe sequeces ad summig the results, oe obtais z y y f Lf (6) Thus, we ca precisely recover f from y ad y The code words cosist of bipolar elemets, which caot be implemeted i a direct detectio scheme, so it is ecessary to trasmit the uipolar versio of these codes as the probe sequeces The costructio of uipolar codes is achieved through u 1 u 1 u 1 u 1 Trasmittig these four uipolar sequeces to the system, ad the subtractig the received sigals betwee each pair of uipolar codes, we get u f u f f y u f u f f y With (6) ad (8), the fiber respose is recovered by usig uipolar codes The effect of pulse codig i OTDR systems is evaluated through the codig gai, which is defied as the SNR improvemet with respect to covetioal averaged OTDR, whe the same measuremet time is used Whe white oise is cosidered the mai source of oise i the OTDR system, it ca be foud from [6] that the codig gai is L, where L is the legth of the Golay code The effect of oversamplig The discussio above was based o the hypothesis that the DC samplig iterval is the same as the pulse width However, this is (7) (8) ot a idispesable coditio, ad the samplig iterval ca be much shorter tha the pulse width, as log as the pulse width is a iteger multiple of the samplig iterval otherwise the correlatio process caot be correctly carried out Such multiple relatio may affect the decodig process; hece, it is ecessary to ivestigate the impact of oversamplig i correlatio-coded OTDR systems Let us assume that the pulse width is m times the samplig iterval, where m will be referred to as the oversamplig ratio This is equivalet to replicate m times each elemet i the code words If we deote the pulse width by T, the the time iterval betwee adjacet samplig poits is T/m; however, the pulse width is ot chaged Takig, for example, a bipolar Golay pair of legth ad m =, the replicatio is as follows: (9) The the result of (4) is o loger a delta fuctio, but a triagle fuctio More specifically, the sum of the autocorrelatios of a pair of m-times oversampled Golay codes with origial code legth L is a triagle fuctio with a peak value of ad a FWHM (full width at half maximum) of m: m m k kq,(10) km where m m k 1 m, m m q 1 k= k m m 0, otherwise (11) is the uit triagle fuctio, with a peak value of 1 ad a FWHM of m Obviously, this fuctio does ot deped o the code legth Figure 1 depicts the correlatio result whe m equals ad the code legth is The samplig iterval is T/m, so the FWHM of m q i the cotiuous domai is the same as the width of a sigle bit i the code sequece, which also meas they have the same eergy Fig 1 Code word of a Golay pair whe the code legth is ad m = Compariso betwee a sigle rectagular pulse (blue) ad the equivalet triagular pulse (red) Equatio (6) becomes m tri -m 0 m Red: (m=) lue: a sigle pulse z q f f (1) Note that f i (1) is the OTDR respose to a sigle rectagular pulse of width T/m, (rather tha T, as for f ) The f (tri) ca be see as the OTDR respose to the uit triagular pulse defied i (11) From (1), we see that oversamplig is equivalet to probig the

3 fiber with a triagular pulse rather tha the covetioal rectagular oe These two probig pulses have the same FWHM ad eergy, which implies that the system spatial resolutio remais the same ad the correspodig OTDR resposes, ie, f ad f (tri), should have roughly the same itesity Now let us tur to the codig gai aalysis The sigal voltage at the PD is proportioal to the light itesity, so it is reasoable to use sigal voltage ad oise voltage to calculate the SNR Oly white oise is take ito cosideratio, so the oise voltage has a ormal distributio with mea value 0 ad stadard deviatio σ Hece, a oise sigal N (k) is added to each of the four received raw sigals, so Eq (8) is revised as 1 1 u f N u f N y N N u f N u f N y N N whereas, accordig to (6), Eq (1) becomes ( tri),(13) z f N N N N (14) The last two terms i (14) represet oise, ad they will be grouped together ad deoted by N (total) i the followig discussio Note that ad here have elemets due to oversamplig Sice oise is evaluated by its root-mea-square (RMS) value, our objective is to fid out the RMS of N (total) : total knk Nk knk Nk k 1 N N N N N (15) ad are made up by 1 s ad 1 s, so the RMS of N (total) is give by total DN ( ) ( total ), (16) where the operator D deotes variace Thus, the SNR of the Golay code correlatio process is give by f tri ( ) ftri ( ) SNRc (17) ( total ) I order to obtai the codig gai, it is ecessary to compare the SNRs of the Golay-coded ad sigle-pulse probe sigals uder similar measuremet coditios, ie, for the same peak power ad measuremet time Thus, we should perform four sigle-pulse measuremets ad calculate the fial result as the average This process is expected to ehace the SNR by a factor, so we have SNR p f (18) s discussed before, f ad f (tri) should have roughly the same itesity, so the codig gai is give by SNRc codig gai (19) SNR From (19), it is clear that oversamplig cotributes to a further ehacemet of the codig gai that has ot bee reported before Oversamplig actually turs a code sequece of L bits ito oe of p bits ad, from this poit of view, the codig gai coforms to the expressio for correlatio-coded OTDR without oversamplig This pheomeo occurs ot oly for the Golay code, but also for ay other complemetary-correlatio codig schemes, such as CCPONS [8] Moreover, i the case of coded-otdr based o liear combiatio codig schemes such as the Simplex code [10], as there is o correlatio i the decodig process, oversamplig does ot affect the codig gai C Noise aalysis for a badwidth-limited PD Equatio (16) is based o the assumptio that the oise sigals ( a) ( b) are ucorrelated, ie EN { m N } 0,( ab, 1,,3, 4; m ) I discrete samplig, this is true whe the PD has a ifiite badwidth, or whe the samplig rate is lower tha the PD badwidth I OTDR systems, the badwidth of the PD is ofte chose to be higher tha the bit rate of iput light pulses, but whe oversamplig is applied, the samplig rate may exceed the PD badwidth Hece, the oise should be regarded as badwidth-limited white oise, which has the followig features: a a b a a E N 0; EN Nk 0; EN Nk RN( k); a (0) E N RN(0)= ; ( a, b 1,,3,4; a b), where R N(k) is the autocorrelatio fuctio of oise From Eq (0), oise samples are ucorrelated for differet a ad b, so the four compoets i N (total) ca be separately calculated ad summed to obtai the fial result Takig eg the first compoet, sice the mea value of oise is always 0, we have D N E N 1 1 k k k k k1 k1 1 1 i j i j i j N i1 j1 i1 j1 E N N R ( ji) (1) The rage of (j i) i Eq (1) is from ( 1) to ( 1); the, we ca simplify this equatio by replacig j with (i + k): D N R ( k) 1 1 k k k1 k( 1) i1 i ik N 1 R k RN k( 1) k ( ) ( ), () where R (k) represets the autocorrelatio fuctio of Similarly, the ameded versio of Eq (16) is give by 1 ( total) N k( 1) R ( k) R ( k) R ( k) m1 m = 4 qk RN( k) k 1 (3) I Eq (3), the quatity R (k) + R (k) is the same as i Eqs (4) ad (10) For ideal white oise, the autocorrelatio fuctio R N(k) is a δ fuctio, so the secod term i Eq (3) is 0 ad Eq (3) reduces to Eq (16) Similarly, whe there is o oversamplig, Eq (3) also coicides with Eq (16) accordig to Eq (4), which meas that the badwidth-limited feature of the PD will ot exert ay extra effect i ooversamplig correlatio codig schemes However, whe the samplig rate is higher tha the badwidth of

4 the PD the situatio we are mostly iterested i it is ot evidet whether the secod term (which i the followig discussio will be called extra term, for coveiece) i Eq (3) will be positive or egative If it is egative, the Eq (3) implies that a extra SNR ehacemet ca be obtaied Next, we will prove that it is possible to achieve this by choosig a proper samplig rate -T (c) R ( k) R ( k) R ( k) R ( k) R ( k) R ( k) 0 T -T 0 N -T 0 p1 p p3 Fig Estimatio of σ (total) Sum of the autocorrelatios of ad utocorrelatio of oise (c) Their product The poits p1, p, ad p3 are the first three zero-crossigs The spectrum of oise is determied by the frequecy respose of the PD, which is usually a lowpass filter For coveiece, a rectagular widow is adopted as a ideal lowpass filter to represet the oise spectrum, so the autocorrelatio of oise is a sic fuctio, as show i Fig This assumptio does ot affect our coclusios O the other had, we have already demostrated that the sum of the autocorrelatios of the Golay codes is a triagle fuctio; see Fig The product of these autocorrelatios is displayed i Fig (c), where the first three zerocrossig poits are idicated For a ideal lowpass filter, p1, p, ad p3 are 1/, 1/, ad 3/, respectively, where the badwidth is the equivalet oise badwidth of the PD, usually larger tha the frequecy respose badwidth For a real PD, p1 is also 1/, but the other two poits may ot follow the same multiple relatioship This curve is defied i the cotiuous time domai, so the result of Eq (3) is obtaied by samplig it ad summig up all the samples Our primary cocer is whether the extra term i Eq (3) is positive or egative s we kow, the zero-crossig poits of the sic fuctio have good periodicity Further, the oscillatio of this fuctio atteuates quickly, a atteuatio further accelerated by the triagular widow Whe the samplig iterval is set at a valley of the curve i Fig (c), the extra term will be egative, resultig i a higher codig gai tha the theoretical value This extra SNR ehacemet will be maximum if the samplig iterval is set betwee p1 ad p, especially at (p1+p)/ However, for the same reaso, if the samplig iterval is set betwee p ad p3, the badwidth-limited character of the PD will reduce the SNR ehacemet Sice the curve atteuates rapidly, cotiuig to icrease the samplig iterval will make the extra term approach zero, correspodig to the case i which the samplig rate is withi the badwidth of the PD, so the oise ca be see as ideal white oise O the other had, whe the samplig iterval is smaller tha p1, the extra SNR ehacemet will be smaller Whe the N T T samplig iterval is sufficietly small, ie, the oversamplig ratio m is sufficietly large, the sum i Eq (3) will approach a itegral Note that a oversamplig ratio m meas that the time iterval betwee adjacet samplig poits is T/m, so we have 1 m1 m N k N k( 1) k( m1) m 1 m T C qk RN( k) T k( m1) m T R ( k) R ( k) R ( k) q R ( k) (4) gai, the sum i Eq (4) approaches a itegral whe m is sufficietly large The value of such itegral depeds oly o the autocorrelatio fuctio of the PD oise ad thus ca be regarded as a costat, deoted by C The the codig gai is give by ftri ( ) 4 C / T LT codig gai (5) f C Equatio (5) implies the codig gai will evetually reach a upper limit whe icreasig the samplig rate I coclusio, the samplig rate should be set betwee 1/p1 ad 1/p i order to get extra SNR ehacemet by utilizig the badwidth-limit feature of the PD For the real PDs that we tested, p1 was 1/, while p ad p3 were roughly 3/ ad 5/, respectively, so the samplig rate should be chose betwee /3 ad The actual value also depeds o the pulse width of the iput light, sice m must be a iteger However, a samplig rate betwee /5 ad /3 will reduce the SNR ehacemet Excessive oversamplig will ot cotribute to codig gai aymore lthough oversamplig has o effect i liear combiatio codig schemes like the Simplex code, they may also be affected by the badwidth-limited feature of the PD, depedig o the decodig process However, the coclusios cocerig codig gai may be differet [10] 3 Experimets Experimets were performed to verify the theoretical aalysis, usig the setup show i Fig 3 We employed a broadbad amplified spotaeous emissio (SE) light source, operatig at 1559 m ad with a 3 d spectral width of 1 m The output power of cotiuous-wave (CW) light was set at 16 dm To modulate the CW light, it was used a acoustic optical modulator (OM), which was cotrolled by a arbitrary fuctio geerator (FG) that geerated the code sequeces or sigle pulses The backscattered light was coverted ito a electrical sigal by a 150 MHz highly sesitive photodetector (PD) Fially, the electrical sigal was received i the oscilloscope ad processed by a computer The badwidth of the OM was 10 MHz, so the bit width or sigle pulse width could be o shorter tha 100 s The maximum samplig rate of the oscilloscope was 0 gigasamples per secod (GS/s), ad the samplig rate could oly be selected from a set of preset values To esure that the oversamplig ratios were iteger, i the followig two experimets we chose 00 s ad 100 s for the bit width ad sigle pulse width, respectively ll the fibers uder test were stadard sigle-mode fibers (SMFs)

5 LS CW light OM code trigger 1 FG OSC PD 3 km SMF km SMF flage plate 38km SMF Fig 3 Experimetal setup for coded OTDR LS, amplified spotaeous emissio light source; OM, acoustic-optic modulator; FG, arbitrary fuctio geerator; OSC, oscilloscope; PD, photodetector maximum code legth could ot be over 048 bits, as the Golay code legth must be a power of [9] The osigal sectio of the OTDR curve was used for calculatig oise ad further obtaiig the codig gai through (6) The samplig rate raged from 10 MS/s to 5 GS/s, correspodig to a oversamplig ratio from 1 to 50 Golay sequeces with code legth ragig from 3 to 048 were ijected ito the fiber, ad each of the backscattered sigals was acquired at the differet samplig rates metioed above Provig the triagular pulse pheomeo 0m Fig 4 Compariso betwee the itesities of the Golay-coded OTDR (blue) ad Simplex-coded OTDR (red) respose sigals The goal of the first experimet was to prove that the equivalet probig pulse i correlatio-coded OTDR with oversamplig is a triagular pulse Sice the reflectio peak i a OTDR curve should have the same shape as the probig pulse, we chose for our tests two km SMFs coected by a flage plate carefully screwed to geerate a small reflectio i the juctio To reach a high eough SNR, the Simplex code was used to obtai a sigle pulse OTDR respose The legth of the Simplex ad Golay codes was 55 ad 048, respectively The pulse width was 00 s, ad the samplig rate was 50 MS/s i both cases, so that the oversamplig ratio was 10 The results for the itesity as a fuctio of the positio i the fiber system are show i Fig 4 The two curves are almost idetical, provig that the decodig process exactly recovered the OTDR respose Moreover, the shapes of the two reflectio peaks are also i agreemet with our aalytical results Codig gai verificatio The secod experimet was coducted to verify the codig gai aalysis Sice the sigal itesity is costatly chagig alog the fiber while the RMS of oise remais costat, the codig gai is obtaied as follows: Sc N N c p codig gai, (6) S N N p p c where S c ad S p are the sigal itesities ad N c ad N p the oise itesities i the Golay-coded ad sigle-pulse cases s has bee explaied, S c ad S p ca be regarded as equivalet, so we oly have to calculate the RMS oise i both cases Sice implemetig the Golay code takes 4 measuremets, the oise of the sigle-pulse measuremet N p should be recorded 4 times ad averaged for the compariso to be fair The fiber legth i this case was 38 km, cosumig 38 μs i a period of 500 μs We chose 100 s for the bit width, so the Fig 5 Compariso betwee the itesities of the sigle-pulse OTDR (blue) ad 048 bit Golay-coded OTDR (red & yellow, for two differet oversamplig ratios) respose sigals The sigle pulse result was averaged, while the coded results were ot Fig 5 shows a compariso betwee the itesities of the siglepulse ad Golay-coded OTDR respose sigals The blue curve gives the average sigle-pulse OTDR results calculated from measuremets We see that the sigal ca hardly be distiguished from the massive backgroud oise The red ad yellow curves represet the results of 048 bit Golay-coded OTDR with oversamplig ratios of 10 ad 100, respectively, without averagig The SNR for the red curve is already better tha for the blue curve, ad that for the yellow curve is eve better Note that both coded results take 4 periods, or ms, to complete oe measuremet, while the sigle pulse result takes periods, or 5 s, to acquire all data, ad its SNR is still worse tha i the coded cases Implemetig a averagig method i the codig scheme could serve to ehace the SNR eve further Fig 6 Measured codig gai versus code legth for differet samplig rates The curves represet theoretical values, while the crosses correspod to the experimetal results Figure 6 shows the measured codig gai versus code legth for differet samplig rates It is apparet that the measured results (represeted by the crosses) agree perfectly with the theoretical curves Note that for a samplig rate of 10 MS/s there is o

6 oversamplig, so Fig 6 also proves that oversamplig cotributes to the SNR ehacemet However, if we cotiue icreasig the samplig rate, the experimetal codig gai will diverge from the theoretical curve, as show i Fig 7 The values of the zero-crossigs p1 ad p for the PD used were measured to be 185 ad 59 s, respectively, as ca be see i Fig 7 This meas that the equivalet oise badwidth was about 70 MHz ad that the best samplig rate sectio i order to obtai extra SNR ehacemet was from 180 to 540 MS/s Obviously, the experimetal results just agree with our coclusios Whe the samplig rate was over 1 GS/s, the codig gai did ot icrease ay more To make our aalysis more covicig, we used aother PD to repeat the experimet, ad the results are show i Fig 8 This PD had a 300 MHz badwidth, while its p1, p ad p3 values were measured to be 09, 6, ad 47 s, respectively, as ca be see i Fig 8 Thus, the equivalet oise badwidth was about 550 MHz, ad the preferred samplig rate sectio raged from 370 to 1100 MS/s, while the egative samplig rate sectio (where the SNR is ot ehaced, but reduced) wet from 0 to 370 MS/s Ideed, for this PD, whe samplig rate is 50 MS/s, the codig gai will be lower tha theoretical value, as show i Fig 8 The experimetal results from these two PDs provide sufficiet ad covicig verificatio of our theoretical aalysis p1 p p3 Code Gai (d) autocorrelatio p1 p p3 Fig 7 Measured codig gai versus samplig rate whe the samplig rate becomes larger tha the badwidth of the 150 MHz PD The curves represet theoretical values, while the crosses correspod to the experimetal results utocorrelatio fuctio of the PD oise Fig 8 Measured codig gai versus samplig rate whe the samplig rate becomes larger tha the badwidth of aother 300 MHz PD The curves represet theoretical values, while the crosses correspod to the experimetal results utocorrelatio fuctio of this PD oise 4 Coclusio We have made a thorough ivestigatio of the samplig criteria for correlatio-coded OTDR Oversamplig has bee prove to further improve the codig gai without extedig the measuremet time, while it also turs the received OTDR curve ito a triagular pulse respose istead of the covetioal, rectagular oe However, the codig gai is ot always improved with the icrease of the samplig rate due to the badwidth-limited feature of the PD Oe ca take advatage of this feature to obtai extra SNR ehacemet by choosig the samplig rate betwee /3 ad To cotiue icreasig the samplig rate would make o sese sice the codig gai would reach a limit value Whe the bit width of Golay codes is fixed, larger PD badwidth ca support larger oversamplig ratio, resultig i better codig gai improvemet Therefore, large badwidth PD is preferred i correlatio-coded OTDR to fully utilize oversamplig Sice oversamplig does ot require ay chage i the optical trasmittig ed, it ca be coveietly applied to the existig systems lthough the Golay code was take as a example for our purposes, the samplig criteria proposed i this paper is also valid for other correlatio codig schemes, such as the CCPONS code [8] Moreover, this priciple ca also serve to sigificatly improve the performace of other fiber sesig systems based o direct detectio OTDR, such as OTD ad ROTDR Fudig Natioal Natural Sciece Foudatio of Chia ( , ); 863 High Techology Pla of Chia ( );

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