Optical Signal-to-Noise Ratio Estimation Using Reference Asynchronous Histograms

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 6, MARCH 15, 2009 731

Optical Signal-to-Noise Ratio Estimation UsingReference Asynchronous Histograms

Ruben S. Luís, Member, IEEE, Member, OSA, António Teixeira, Member, IEEE, and Paulo Monteiro, Member, IEEE

Abstract—This paper presents and experimentally demonstratesa novel method for the estimation of optical signal-to-noise ratio(OSNR) based on the comparison of an asynchronous histogram ofthe signal under analysis with a reference asynchronous histogram.The latter is acquired from the signal under analysis at a calibra-tion stage. The proposed method allows the use of optical amplifi-cation to increase the sensitivity of the optical monitoring system(OMS) by a factor 20 dB, when using an erbium doped fiber pream-plifier. In addition, the use of a semiconductor optical preamplifier,initially designed for nonlinear operation at 2.5 Gb/s is used in theOMS to preamplify 40-Gb/s signals, achieving a sensitivity gain of10 dB. It will be experimentally demonstrated that the proposedmethod is applicable to 40-Gb/s nonreturn to zero (NRZ) signalsarbitrarily degraded by group velocity dispersion (GVD). Further-more, accurate monitoring of the OSNR of return-to-zero (RZ)signals will also be possible using a simple RZ-to-NRZ converterbased on narrow-band optical filtering within the OMS. The pro-posed method also allows estimating of the GVD-induced OSNRpenalty between the signal under analysis and the signal at the cal-ibration stage.

Index Terms—Asynchronous amplitude histogram, opticalsignal-to-noise ratio (OSNR), optical performance monitoring,noise measurement.

I. INTRODUCTION

I N recent years, increasing efforts have been made to reducethe overall cost of optical transmission systems while si-

multaneously extend their capacity and range. This pushes thesystems requirements to a limit where optical monitoring sys-tems (OMS) become indispensable to maintain the operationalconditions within increasingly demanding margins. As such,future optical networks may no longer view OMS as supportsubsystems but rather as enabling subsystems. In fact, with theincreasing complexity of the architecture of optical networks,OMS may no longer be used only to control locally installedimpairment compensating systems but also to control remotely

Manuscript received June 18, 2007; revised May 7, 2008. Current versionpublished April 17, 2009. This work was supported in part by Nokia SiemensNetworks S. A., by Fundação para a Ciência e a Tecnologia by Grant SFRH/BDE/15542/2005, and by the CONVOCO project, from Agência de Inovação,and the E-Photon-One+ project.

R. S. Luís is with the Centre of Volcanology and Geological Risk Assessment,University of Azores, R. da Mãe de Deus, 9501-801 Ponta Delgada, Portugal,and also with Instituto de Telecomunicações, Campus Universitario de Santiago,3810 Aveiro, Portugal (e-mail: [email protected]).

P. Monteiro is the Instituto de Telecomunicações, Campus de Universitario deSantiago, 3810 Aveiro, Portugal, and with Nokia Siemens Networks, 2720-093Amadora, Portugal (e-mail: [email protected]).

A. Teixeira is with the Instituto de Telecomunicações, Campus de Santiago,3810 Aveiro, Portugal (e-mail: [email protected]).

Digital Object Identifier 10.1109/JLT.2008.926959

installed systems. In addition, the advancement of telecommuni-cations management systems using impairment constrain basedrouting [1] may allow the use of OMS to dynamically redirecttraffic through the network, according to its availability.

To understand the role of OMS in optical networks one mayconsider that optical signals are fundamentally degraded byamplified spontaneous emission (ASE) noise due to opticalamplification, crosstalk, and signal distortion due to transmis-sion in optical fibers and optical components in transmissionsystems [2]. With the rapid increase of the transmitted bit-ratesand the channel density in wavelength division multiplexed(WDM) systems, the impact of signal distortion or crosstalkon the quality of the optical signals may equal or even surpassthe currently dominant impact of ASE noise. As such, there isan urgent need for the development of OMS which effectivelydistinguish and quantify these forms of degradation. In the caseof ASE-noise, the most widespread method to infer the opticalsignal-to-noise ratio (OSNR) of optical signals is based on an-alyzing the corresponding optical spectrum [3], [4]. However,the deployment of dense WDM systems with reduced channelspacing and high bit-rates renders this approach unfeasibleas the noise floor in the optical spectrum is undistinguishablefrom the signal. In addition, the current deployment of meshedoptical network architectures using optical cross-connectorsallows for each channel within the WDM signal to presentits particular OSNR. As such, the OSNR monitoring must becarried out for each channel individually [3]. Such transmissionsystems favor the application of in-band OSNR monitoringmethods, such as the analysis of asynchronous histograms [5],[6].

OMS based on the analysis of asynchronous histograms haveattracted significant attention due to their simplicity and remark-able flexibility. Asynchronous histograms may be acquired bysampling the optical signal at an arbitrary rate in the electrical[5] or optical domain [6]. This avoids the need for clock re-covery systems, increasing the flexibility and possibly reducingthe cost of such systems. After its acquisition, an asynchronoushistogram may be used to monitor a variety of parameters si-multaneously.

Shake et al. have contributed significantly to this topic by de-veloping techniques to estimate the Q-factor, and correspondingBER, based on processing the asynchronous histograms to re-move the contribution of samples acquired during symbol tran-sitions, also referred as cross-point data [6]–[10]. This allowsan accurate estimation of the average power associated with themark and space symbols and corresponding noise variances. Inaddition, a simple variation of this technique was developed tosimultaneously monitor the impact of GVD on the Q-factor by

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732 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 6, MARCH 15, 2009

taking into account the fact that the GVD-induced distortion al-ters the difference between the average power levels associatedwith the mark and space symbols [11], [12].

Alternatively, Rasztovits et al. proposed to eliminate thecross-point data by mirroring the outer areas of the asyn-chronous histogram around the power levels correspondingto the mark and space symbols [13]. This approach was alsoused in [14] to analyze Q-factor of return-to-zero (RZ) signals,where the distinction of the mark symbols in asynchronoushistograms is less evident.

Rasztovits also proposed to reconstruct an asynchronous his-togram with a non-Gaussian noise distribution consisting of thesum of strategically centered Gaussian distributions weightedby the probability density function of the signal in the absence ofnoise, to accurately estimate the BER of distorted signals [13].This approach was further developed in [15]–[21], which pre-sented techniques based on fitting numerically estimated his-tograms to the corresponding histograms measured from thesignal under analysis. The result of the fitting allows an estima-tion of the BER. The analysis of asynchronous histograms alsoallows inferring the impact of optical impairments such as GVDand in-band crosstalk [5]. As an example, Chen et al. have pro-posed to use the cross-point data of asynchronous histograms todetermine the transition time of the signal impulses, which maybe related with the amount of accumulated GVD or polarizationmode dispersion [21], [22].

On the other hand, estimation of in-band crosstalk withsynchronous histograms was proposed by Weinert et al. in [23]and [24] and further developed in [25]. This technique usesa deconvolution method to remove the impact of ASE noisefrom the synchronous histograms, leaving only the impactof in-band crosstalk, which may be easily analyzed. Furtherdevelopments of this technique have allowed an evaluationof intersymbol interference and jitter [26]. However, its ap-plication to asynchronous histograms is not straightforwarddue to the nonuniform conditional distribution of the Gaussianand arc-sin probability density functions of ASE noise andin-band crosstalk, respectively, [27], which limit the applica-tion of deconvolution methods. This limitation may be handledby converting the asynchronously acquired samples in syn-chronous samples using their intrinsic correlation, as proposedin [28]–[30].

Alternatively, this group has proposed the evaluation ofin-band crosstalk by numerically including the impact ofin-band crosstalk on a reference histogram acquired from asimilar signal without in-band crosstalk, and fitting the resultto the corresponding histograms measured from the signalunder analysis [27]. The fitting is performed only on thesignal-to-crosstalk-ratio. Unlike previously mentioned tech-niques, this approach is nearly independent on the waveform ofthe signal by focusing only on the impact of in-band crosstalkon the asynchronous histogram. This property allows its poten-tial application to arbitrary modulation formats.

Despite the effectiveness of the aforementioned methods tomonitor the quality of optical signals using asynchronous his-tograms, the problem of directly monitoring the OSNR of an op-tical signal, regardless of other impairments and the waveformof the signal, had limited attention so far, to the authors’ knowl-

edge. The estimation of OSNR, or preferably an OSNR penalty,allows a quantification not only of the optical noise affectingthe signal under analysis but also provides a means to quantifythe impact of arbitrary optical impairments. The latter can beachieved by taking into account the changes caused in the shapeof the histogram of the signal under analysis by arbitrary opticalimpairments (e.g., chromatic dispersion or fiber nonlinearities).The measured OSNR penalty may be used as feedback for op-tical impairment compensation devices specifically designed tocompensate a given impairment (e.g., tunable dispersion com-pensator to tackle excessive accumulated dispersion) or simplyto readjust power management in the optical path in order to in-crease the OSNR of the signal, hence improving its quality. Forthis purpose, a variation of the previously mentioned crosstalkmonitoring technique to allow the estimation of the OSNR in-dependently of the distortion affecting the signal under analysiswas presented in [31]. The latter is based on using a referencehistogram of the signal under analysis in noiseless conditions toestimate the histogram of the degraded signal. However, eventhough the acquisition of a noiseless reference histogram in lab-oratorial conditions is quite simple, it is not so in the field, lim-iting the practical application of this technique.

This work proposes and experimentally validates a methodto evaluate the OSNR of a signal under analysis based on thecomparison of its measured asynchronous histogram (MAH)with the histogram of a reference signal, referred in this workas reference asynchronous histogram (RAH) with an arbitraryOSNR. This is carried out by numerically including the impactof the additional ASE noise on the RAH to match the MAHor vice-versa. By determining the amount of ASE noise thatis included to achieve the match, it is possible to estimate theOSNR penalty between the signal under analysis and the refer-ence signal. Hence, it becomes possible to determine the OSNRof the signal under analysis, assuming that the OSNR of thereference signal is previously known. An advantage of this ap-proach is that the noise generated within the OMS will havesimilar impact on the RAH and the MAH. This property willbe used to experimentally demonstrate the application of an op-tical preamplifier to improve the sensitivity of the OMS, at thecost of reducing the maximum measurable OSNR. For this pur-pose, we will use an erbium doped fiber amplifier (EDFA) and,for the first time in OMS based on analysis of asynchronoushistograms, a semiconductor optical amplifier (SOA) as opticalpreamplifiers.

In addition, the proposed method relies only on evaluatingthe impact of ASE noise on the shape of the asynchronous his-tograms, independently of the signal waveform. As such, it be-comes possible to use simplified optical processing techniquesto enhance the impact of ASE noise on the shape of the asyn-chronous histograms and, as a consequence, the accuracy of theOSNR estimation. This will be illustrated by effectively evalu-ating the OSNR of a signal with a return-to-zero (RZ) modula-tion format by first converting it to a nonreturn-to-zero (NRZ)modulation format using an optical filter with reduced band-width within the OMS.

Finally, the proposed method will be applied to a NRZ signaldegraded by group-velocity distortion (GVD). It will be shownthat the OSNR estimates are reasonably accurate, as long as the

LUÍS et al.: OSNR ESTIMATION 733

reference signal presents the same accumulated dispersion asthe signal under analysis. Furthermore, it will be shown that,when using a reference signal which is not degraded by GVDto obtain the RAH and use it to estimate the OSNR of a signaldegraded by GVD yields an OSNR penalty which quantifies aGVD-induced OSNR penalty of the signal under analysis.

This paper is structured as follows. To facilitate the under-standing of the proposed method, we begin in Section II.Aby presenting a short description of the previously developedOSNR estimation method using RAH without ASE-noisedegradation, presented in [31]. Section II.B presents the newmethod to allow the use of RAH degraded by ASE noise. Inaddition, the validity limits of the OSNR estimates are defined.Section III presents an experimental validation of the proposedmethod using 40-Gb/s signals. Section IV presents a summaryand the main conclusions.

II. PRINCIPLE

A. OSNR Estimation Using Reference AsynchronousHistograms

Consider the typical eye pattern of a simulated 40-Gb/s NRZsignal with raised cosine impulses and a given OSNR ,in linear units or , in logarithmic units, presented inFig. 1(a). The corresponding MAH is presented in Fig. 1(b).The histogram presents two peaks, corresponding to the markand space symbols. The peak corresponding to the mark levelpresents greater spreading than the peak corresponding to thespace level due to the impact of signal-ASE noise beat [6].The middle region of the histogram regards samples acquiredduring symbol transition intervals. All the histograms presentedin this paper will be defined within a predetermined linear setof bins, where each bin is associated with an electrical cur-rent level. Consider an estimate of the histogram shape givenby , where is the bin number. We can assume that thereceived signal in the absence of noise, is a linear superpositionof NRZ binary impulses with equal probability for the mark andspace symbols. In these conditions, the histogram of the signalin the absence of noise, , where is the bin number, can beapproximated analytically using the method described in [20].In the latter reference, the parameters that determine the shapeof are the electrical current levels of the mark and spacesymbols and the average transition time between symbols. Theinfluence of optical and electrical noise, may be included usingthe approach proposed in [13] and used in [20] by considering

proportional to a linear superposition of Gaussian pro-cesses centered in the current levels associated with the th bin,

, and weighted by , shown in (1) at the bottom of thepage, where denotes the discrete convolution and is

the estimated variance of the signal-ASE noise beat associatedwith the th current level [13]

(2)

is the estimated OSNR in linear units and is a pro-portionality constant dependent on the receiver parameters. Ex-pression (2) neglects the impact of the ASE-ASE noise beat.The term in (1) is the histogram of the noise generatedby the OMS, which may be assumed to have a known variancegiven by . Note that the OMS noise includes the electricalnoise generated by the OMS receiver, sampling noise, and quan-tization noise in the analog-to-digital converters. Using (1), theparameters of aforementioned, and the value ofcan be fitted in order to reach a match between and theMAH, using a nonlinear minimization algorithm. After a rea-sonable match is achieved, the parameters of the theoretical his-togram can be used to estimate the Q-factor [20].

The main limitation of the presented technique is that priorknowledge of the received pulse shape is required to obtain

. Nevertheless, several approximations of this shape canbe used, as long as some similarity between the actual shapeof the impulse and the theoretical model is maintained, as il-lustrated in [20]. In this reference, it is shown that using an an-alytical model or numerical simulations to compute isfeasible. Particularly in the latter case, it becomes possible to in-troduce the impact of GVD on the computation of , whichallows to quantify this parameter [20]. Nevertheless, as shownin [20], the computation time required for a reasonable estima-tion of increases significantly with its complexity, i.e.,with the number and impact of optical impairments degradingthe signal waveform, and the impact of frequency limitations ordistortions imposed by the OMS. This limits the applicability ofthis method for a generalized OMS.

An alternative approach has been proposed in [31] by re-placing in (1) by a RAH, , which is experimen-tally acquired from a reference signal in noiseless conditions.The RAH may be acquired in a calibration stage and memo-rized for later use in normal operation. Ideally, the referencesignal would be unimpaired and the RAH would be identicalto . A more realistic approach assumes that the referencesignal is affected by the OMS noise. Under such conditions, theRAH may be expressed as [17]

(3)

Assuming that the impact of the OMS noise on the signal issmall, when compared with the impact of ASE noise, we maydirectly replace by in (1). However, since the

(1)


Fig. 1. Eye pattern (a) and corresponding asynchronous histogram (b) of a simulated raised cosine NRZ signal.

Fig. 2. Schematic diagram of the fitting process to match the estimated histogram to the measured histogram.

latter already includes the impact of the OMS noise, the cor-responding term in (1) will be removed, yielding

(4)

The process used to compute (4) and estimate the OSNR ofthe signal under analysis is illustrated in Fig. 2. The referencehistogram is combined with a linear superposition of Gaussianprocesses with variance , which is computed withthe estimated OSNR . The result is the estimatedhistogram, which may be directly compared with the mea-sured histogram. The comparison measure used in this paperis the quadratic distance between the histograms, given by

. This distance is mini-mized by varying through a nonlinear minimization

method, such as the Bisectrix method. Note that using (4) to es-timate the MAH does not require knowledge of the parametersof . Instead, the fitting is performed only on the value of

. When a match between the estimated histogram andthe MAH is found, we may assume that .This results in a substantial reduction of the computation effortrequired for the implementation of the proposed method, incomparison with the approaches presented in [18], [19], and[13], where the number of fitting variables may grow rapidlywith the complexity of the histogram. However, the proposedmethod does not allow evaluating quality parameters thatdepend on the signal waveform, such as Q-factor.

The approximation proposed by (4) is valid for the caseswhere the contribution of the ASE noise to the MAH is sub-stantially larger than the contribution of the OMS noise, i.e.,

, where is the


Fig. 3. Experimental comparison between the measured asynchronoushistogram and the corresponding theoretical estimate obtained using (4) for�� =22 dB.

variance of the signal-ASE noise beat of the signal under anal-ysis. This condition may be expressed as

(5)

which basically implies that the proposed approximation is onlyvalid above a given power level. This power level is condi-tioned by the variance of the noise generated by the OMS andthe OSNR that is to be measured and is in agreement with thegeneral conditions predicted in [4]. To illustrate the implica-tions of condition (5), Fig. 3 presents a comparison betweenan experimental asynchronous histogram of a NRZ signal with

dB, measured within a resolution bandwidth of0.1 nm, and the corresponding estimated histogram. The RAHwas obtained by acquiring an histogram of the same signal withan OSNR of 28 dB, which in this work represents a noise-less signal. The value of was adjusted to find the bestmatch between the estimated histogram and the MAH using theNelder-simplex nonlinear minimization algorithm. As shown inFig. 3, the region of the estimated amplitude histogram corre-sponding to low current levels near the space symbol presentssignificant error since condition (5) is not observed. The regioncorresponding to the mark symbol verifies condition (5) and iswell approximated. As such, to avoid the error for low elec-trical current levels, the histograms used in our analysis will betruncated bellow the level corresponding to the average signalpower, as shown in Fig. 3.

B. OSNR Estimation Using ASE-Degraded ReferenceAsynchronous Histograms

The main drawback of the method described in Section II.Ais the requirement of a noiseless reference signal. The corre-sponding RAH may be easily acquired in laboratory conditionsbut would be difficult to obtain in a field installation. Therefore,we propose an adaptation by using a RAH with finite OSNR.The reference signal then becomes characterized by an OSNRgiven by , in linear units, or , in logarithmicunits, which corresponds to a signal-ASE noise beat variancegiven by . The initial value of

may be measured at a calibration stage, using externalequipments when installing the OMS in the field. Alternatively,the output of the network planning may be used to estimatethis value. Subsequent histogram acquisitions will reflect the

changes of OSNR of the signal under analysis. Further updatesof the RAH and corresponding may be required whenthe traffic on the network is rearranged. However, these updatesmay be performed without the support of external equipmentsimply acquiring a RAH of the new signal and using the pre-vious RAH and corresponding to estimate the newvalue of .

Consider the case where , i.e., thesignal under analysis presents a higher degradation than thereference signal. As such, the method described in Section II.Amay be used to include the impact of additional noise onthe RAH to approximate the MAH. In this case, the matchbetween the MAH and the estimated histogram will be foundwhen the estimated variance of the signal-ASE beat noise,initially defined by (2), reflects the difference between thecorresponding noise variances of the signal under analysis andthe reference signal, i.e.,

. Finally, assuming that when amatch between the MAH and the estimated histogram is foundwe have , yields:

(6)

which replaces expression (2) for the implementation of thenovel method. Note that, if is known from the calibra-tion stage, the only unknown variable is . On the otherhand, one could consider and as unknownvariables and find the best combination of both which wouldmatch the estimated histogram to the MAH. However, this isoutside the scope of this work and will be addressed elsewhere.

Expressions (4) and (6) correspond to an adaptation of themethod described in Section II-A to handle ASE noise-degradedRAH when the signal under analysis presents a higher degrada-tion than the reference signal and will be referred in this paper asmethod A. Similar to the case presented in Section II.A, the va-lidity of the approximation used in (6) requires that the varianceof the signal-ASE noise beat affecting the signal under analysisis higher than the variance of the noise affecting the referencesignal added to the variance of the OMS noise, assuming thatthe latter may be approximately described by a Gaussian distri-bution. This is represented by the condition

(7)

Note that for very high , the contribution of theASE noise affecting the reference signal at the OMS inputmay be neglected in comparison with the contribution of theOMS noise. As such, the validity condition may be written as

. This implies that the range of methodA depends directly on the power at the OMS input. However,when reducing the impact of the OMS noise becomesnegligible and the validity condition may be written simply as

. Note that the latter is independent of thepower at the OMS input, suggesting that reducingincreases the sensitivity of the OMS at the cost of reducing themaximum measurable OSNR.

Consider now the case when the signal under analysis is lessdegraded than the reference signal, i.e., .When using method , the nonlinear minimization algorithm


will diverge to an arbitrarily high value of , corre-sponding to the lowest possible value of[see (6)]. As such, the condition of failure of method Amay be identified when the distance between the esti-mated and reference histograms, defined in this paper as

, converges to zero. Al-though it is not possible to calculate an estimate of the MAHby including the impact of ASE noise in the RAH, as proposedfor method A, it is possible to do the opposite. In the aforemen-tioned conditions, the signal under analysis is less degraded byASE noise than the reference signal. Hence we may calculatean estimate of the RAH by including the impact of ASE noisein the MAH. The amount of ASE noise that has to be includedto find a match will allow an estimation of the . Thismethod will be referred here as method B. In this case, (4)becomes

(8)

where represents the MAH. In addition, considering thatthe roles of the reference signal and the signal under analysis areswapped, (6) will become

(9)

Expressions (8) and (9) allow estimating the OSNR of the signalunder analysis when it is lower than the OSNR of the referencesignal. Similarly to (7), the validity of the approximation usedto estimate the RAH is given by

(10)

Note that for high , the impact of the ASE noise de-grading the signal under analysis is negligible in (10), and thevalidity condition becomes . This im-plies that the maximum is conditioned by the powerat the OMS input. Furthermore, it indicates that the reachableOSNR range may be increased by reducing . For low

, the OMS noise is negligible and the validity conditionsimply becomes .

The remaining problem with the proposed methods is the bi-nary decision between using method A or . Sinceis usually unknown, it may not be compared with inorder to select the appropriate method. As such, we propose toinitially use method A and test its condition of failure, definedabove. If the value of converges to zero, one may assumethat . As such, a new calculation will be re-quired, using method B.

III. EXPERIMENTAL VALIDATION

A. Experimental Setup

Consider the experimental setup presented in Fig. 4. A pseu-dorandom binary sequence of symbols at 40 Gb/s isused to modulate the intensity of a continuous waveform signal,generating a NRZ signal. An additional pulse carver driven bya 20-GHz clock signal may be used to convert the NRZ marksymbols in RZ impulses with a full-width at half-maximum of

Fig. 4. Experimental setup.

12.5 ps. The optical signal is combined in a 50:50 coupler withASE noise generated by a set of two erbium doped fiber ampli-fiers (EDFA) connected in series with a 100-GHz optical filter.A variable optical attenuator (VOA) is used to set the noisepower and control the OSNR at the output of the coupler. Asample of the degraded signal is sent to an optical spectrum ana-lyzer to accurately determine the OSNR with a resolution band-width of 0.1 nm. The remaining signal power is fed to a VOAused to control the power at the input of the OMS. Alternatively,a lump of standard single-mode fiber (SSMF) may be placedprior to the VOA to introduce GVD on the signal under anal-ysis. The monitoring system will consist of an unsynchronizeddigital oscilloscope equipped with an optical front-end with abandwidth of 65 GHz to obtain the asynchronous amplitude his-tograms. In addition, the signal at the OMS input may be ampli-fied using an EDFA, with a noise figure of approximately 6 dB,or a semiconductor optical amplifier (SOA) with a noise figureof 9 dB, and filtered prior to the digital oscilloscope using 0.6 or0.35 nm optical filters. The latter filter will be used to performNRZ-to-RZ conversion. Each histogram will be obtained by ac-quiring asynchronous samples of the signal.

To estimate the OSNR, the OMS must first be calibrated for aknown reference OSNR. This will be carried out by setting thesignal under analysis with the required reference OSNR and ac-quiring the RAH. Normal operation of the proposed system willbe carried out by setting the desired OSNR on the signal underanalysis and acquiring the MAH. The latter will be comparedwith the RAH to estimate the corresponding OSNR.

B. OSNR Monitoring of NRZ Signals Without OpticalPreamplification

We begin by validating the OSNR estimation method usingNRZ signals. The reference signal will be obtained in nearlynoiseless conditions, with an OSNR of 28 dB. GVD-induceddistortion and preamplification or filtering within the OMS willnot be considered at this point. Note that the bandwidth of theASE noise at the OMS input has been previously limited at the


Fig. 5. Asynchronous histograms of the reference signal considering an OSNR of 28 dB (dashed line) and the signal under analysis with OSNR values of 14, 20,and 30 dB for (a) power at the OMS input of 0 dBm and (b) power at the OMS input of -5 dBm. Optical amplification or filtering in the OMS is not considered inthis case.

Fig. 6. Dependence of the estimated OSNR on OSNR for OSNR =28 dB ( ), OSNR =22 dB (�) and OSNR =16 dB (�). Optical amplificationor filtering in the OMS is not considered in this case. The insets present the eye diagram of the signal under analysis for OSNR values of 16 and 30 dB. (a) Powerat the OMS input of 0 dBm. (b) Power at the OMS input of -5 dBm.

noise generator. Fig. 5(a) and (b) present examples of the mea-sured histograms for , 20, and 30 dB, as wellas the reference histogram with dB. Averagepowers at the input of the OMS of 0 dBm and dBm havebeen considered. In the first case, the impact of ASE noise isclearly distinguishable on the shape of all presented histograms,particularly in the region of the histograms corresponding to themark level. When the power at the OMS input is reduced todBm [see Fig. 5(b)], the impact of the electrical noise, generatedat the oscilloscope receiver, and the quantization noise, resultingfrom the limited resolution of the analog-to-digital converterof the oscilloscope, becomes evident from the broadening ofthe peaks of the mark and space symbols, and the spikes ofthe histograms, respectively. In these conditions, the histogramobtained for dB is indistinguishable fromthe reference histogram with dB. Fig. 6(a)and (b) presents the dependence of on ,considering average powers of 0 and dBm at the input of theOMS, respectively, for , 22, and 28 dB. Theresults presented for dB were estimated usingonly method A, thus are limited to .For and 22 dB, the estimates were obtainedusing method A for and method Bfor . The selection between methodA and was performed automatically using the technique de-

scribed in Section II-B. Analyzing only the results obtained fordB it is shown, in Fig. 6(a), that

follows accurately in all the considered range withestimation errors below 1 dB. In the case of Fig. 6(b) with

dB, becomes independent offor values higher than 24 dB due to the impact

of the OMS noise. For values of above this limit,the impact of ASE noise will not be reflected in the MAHdue to the OMS noise. This shows that the minimum powerat the input of the OMS is conditioned by the power of theoscilloscope noise, as indicated by (7). However, the range ofthe OMS with low input powers may be increased by reducingthe OSNR of the reference signal and using also method B,as indicated in Section II-B. To demonstrate this, consider thedependence of on shown in Fig. 6(a)and (b) for and 22 dB. Fig. 6(b) showsthat, with or 22 dB, the estimated OSNRfollows the real OSNR values with errors bellow 1 dB on theconsidered range. The advantage of reducing the referenceOSNR is not verified in Fig. 6(a) with a power at the OMSinput of 0 dBm. In this case, the maximum measurable OSNRwith dB becomes limited to 27 dB with errorsbellow 1 dB. With dB, this limit is extendedabove 30 dB with no significant improvement in comparisonwith the case of dB.


Fig. 7. Dependence of the estimated OSNR on OSNR for OSNR =28 dB ( ), OSNR =22 dB ( �) and OSNR =16 dB (�). An EDFA is usedwithin the OMS for pre-amplification. The insets present the eye diagram of the signal under analysis for OSNR values of 16 and 30 dB. (a) Power at the OMSinput of -20 dBm. (b) Power at the OMS input of -25 dBm.

C. OSNR Monitoring of NRZ Signals With OpticalPreamplification

Experimental validation of the proposed method for averagepower at the OMS input below dBm was not possiblewithout optical preamplification, due to the impact of the OMSnoise. Therefore, we include an EDFA as preamplifier operatingin a constant output power mode within the OMS to increaseits sensitivity, as presented in Fig. 4. The 0.6-nm filter in theOMS was also included to limit the preamplifier noise. Thisallowed the acquisition of valid asynchronous histograms withan average power at the OMS input as low as dBm. Notethat the proposed method is only sensitive to the OSNR penaltybetween the RAH and the MAH. As such, the ASE noise gen-erated by the preamplifier will not invalidate the measurementas long as the noise generated by the EDFA is considered in theRAH. Fig. 7(a) and (b) presents the dependence ofon the , assuming , 22, and 28 dB,and considering average powers of and dBm at theinput of the OMS, respectively. In the case ofdB, the OSNR estimates follow a similar behavior as observedfor similar and higher powers in Fig. 6(a) and (b).Note that, in the case of an average power at the OMS input of

dBm, is independent on , for valuesabove 24 dB. This limitation is due to the noise generated bythe digital oscilloscope and also due to the noise generatedby the preamplifier, which masks the impact of ASE-noise onthe signal under analysis. However, it occurs for an averagepower at the OMS input 20 dB below the corresponding casewithout an optical preamplifier, demonstrating its advantage.When is reduced to 22 and 16 dB, we verify thatthe maximum measurable OSNR is limited to 24 and 26 dB,respectively, for errors below 1 dB and for both consideredvalues of power at the OMS input. Further experiments haveshown that these limitations may be overcome by increasingthe power at the OMS input.

We have also considered the use of a SOA as a preampli-fier in the OMS. The smaller dimensions and simple integrationof SOAs may be an advantage in comparison with the applica-tion of an EDFA in an OMS. In the case of our experiment, wehave considered an SOA initially designed for a nonlinear ap-plication with 2.5 Gb/s signals, which is clearly insufficient for

amplification of the 40-Gb/s signal under analysis without sig-nificant distortion. Fig. 8(a) presents the typical asynchronoushistograms for , 20, and 30 dB, obtained whenusing the SOA preamplifier. As shown, the peak correspondingto the mark symbol is significantly broadened in comparisonwith Fig. 5(a) and (b). This results from the overshoot generatedby the SOA, which is also observable from the eye diagram insetFig. 8(a). Fig. 8(b) presents the dependence of theas a function of the for , 22, and28 dB, considering an average power of dBm at the inputof the OMS. Lower power levels at the OMS input were notachievable due to the limited gain of the SOA, which in suchconditions is unable to yield an average power at the input of theoscilloscope above the minimum limit of dBm, presented inSection III-B. As shown in all considered cases, the maximummeasurable OSNR is limited to 24 dB for an estimation errorbelow 1 dB. Similarly to the case of the EDFA preamplifier,this limitation results from the additional ASE noise introducedby the SOA. However, it may be noted that the signal distortioninduced by the SOA does not impact significantly on the max-imum measurable OSNR.

D. OSNR Estimates of RZ Signals

Fig. 9(a) presents the asynchronous histograms acquired froman RZ signal with OSNR values of 14, 20, and 30 dB. An EDFApreamplifier was used to increase the OMS sensitivity. Unlikethe asynchronous histograms of a NRZ signal, the asynchronoushistograms of the RZ signal do not allow a clear distinction be-tween the mark and space symbols. This results from the lim-ited duty-cycle of the RZ signal, which yields a low proba-bility for a sample to be acquired during a mark symbol. Sincethe latter are the most affected by ASE noise, it also becomesdifficult to distinguish between histograms acquired from sig-nals with different OSNR, as shown in Fig. 9(a). Several tech-niques have been proposed to handle this limitation. Shake et al.have proposed to eliminate the samples in the central area ofthe histogram, thus exposing the mark symbol [6], [7], and [9].Alternatively, Weinert et al. have proposed to mirror the his-togram area above the maximum of the mark symbol to create abell-shaped histogram, similar to what could be obtained from asynchronous sampling system [13] and [14]. In both cases, the


Fig. 8. Impact of a SOA pre-amplifier on the asynchronous histograms (a) and dependence of the estimated OSNR on OSNRSIG (b) for various OSNRREF andOSNRSIG values and an input power at the OMS input of -15 dBm. The inset presents the eye diagram of the signal at the oscilloscope input for OSNRSIG=30dB. : OSNRR=28 dB; �: 22 dB; and �: 16 dB.

Fig. 9. Examples to asynchronous histograms of (a) an RZ signal and (b) the NRZ signal resulting from the RZ-to-NRZ conversion, for OSNR values of 14, 20,and 30 dB.

handling of the histograms is directed at isolating the mark sym-bols rather than enhancing the impact of ASE noise for easiermeasurement. As such, these techniques may be inappropriatefor the estimation of OSNR. Fig. 10 illustrates the approach pro-posed in this work by converting the RZ signal to an NRZ signal.This is carried out by filtering the RZ signal within the OMSwith an optical filter with a bandwidth of 0.35 nm. As show inthe eye diagrams inset Fig. 10, the outcome of the optical filteris a low quality NRZ signal, which may be used for the OSNRestimates. Note that the presented setup requires a preamplifierto compensate the high insertion loss of the optical filter, hencethe use of the EDFA in the OMS. Fig. 9(b) presents the asyn-chronous histograms of the RZ-to-NRZ converted signal for thesame OSNR values used for Fig. 9(a). As shown, the histogramspresent clearly distinguishable space and mark symbols. Fur-thermore the mark symbol clearly reflects the impact of the ASEnoise, as can be seen by the broadening of the mark symbol withthe decrease of the OSNR, as originally intended. Fig. 11(a)and (b) present a comparison of without and withRZ-to-NRZ conversion, respectively, assuming an OMS inputpower of dBm and , 22, and 28 dB. Inthe case of Fig. 11(a), the nonlinear minimization algorithm isunable to accurately estimate due to the weak de-pendence between the OSNR of the signal under analysis and

the histogram shape. After RZ-to-NRZ conversion, the anal-ysis becomes similar to that of a NRZ signal, as reported inSection III-B and III-C. In this case, the OSNR estimates arewithin a 1–dB error margin up to dB for

dB and 28 dB, and up todB for dB.

E. OSNR Estimates of GVD-Degraded NRZ Signals

Consider the application of the proposed method to GVD-de-graded signals. This results from the fact that the OMS maybe placed in arbitrary points of the network. Hence, there isthe possibility that the signal under analysis presents nonzeroaccumulated dispersion. As such, the asynchronous histogramof such signals will reflect the distortion of the nonzero ac-cumulated dispersion. To illustrate these changes, Fig. 12(a)presents the asynchronous histogram of the 40–Gb/s NRZsignal affected by 102 ps/nm of accumulated dispersion, cor-responding to transmission through 6 km of SSMF. The eyediagram inset Fig. 12(a) illustrates the GVD-induced degrada-tion of the 40–Gb/s NRZ signal. As shown, the impact of GVDon the asynchronous histograms is particularly evident for

dB. In this case, one may notice the distortionof the mark and space symbols presented as additional peaks.As such, the changes of the asynchronous histogram can be


Fig. 10. RZ to NRZ conversion scheme using a narrow optical filter for analysis of the asynchronous histogram of the signal. The insets present the eye diagramsof the RZ signal before the filter and the NRZ signal after the optical filter.

Fig. 11. Dependence of the estimated OSNR on OSNR�� for an (a) unfiltered and (b) filtered RZ signal with OSNR��=28 dB (\square),OSNR��=22 dB(� ) and OSNR��=16 dB (�). An EDFA is used as optical amplifier to achieve a power at the OMS input of -20 dBm.

Fig. 12. Impact of GVD on (a) the asynchronous histograms and (b) dependence of the estimated OSNR on OSNR�� for various OSNR and OSNR��values and an input power at the OMS input of -15 dBm. The inset presents the eye diagrams of the signal at the oscilloscope input for OSNR��=30 dB.? OSNR =28 dB; �: OSNR =22 dB; and �: OSNR =16 dB.

used to estimate the impact of accumulated dispersion, asproposed by [5], [11], [12], [18], and [26]. However, for lowerOSNR values, the impact of GVD becomes less evident due tothe dominant ASE-induced degradation of the signal. In thesecases, the GVD-impact will be masked by the ASE noise andbecomes indistinguishable.

Fig. 12(b) presents the dependence of on, for , 22, and 28 dB, considering an

average power of dBm at the input of the OMS and intro-

ducing an accumulated dispersion of 102 ps/nm on the signal.An EDFA was used as preamplifier to allow a reduced power atthe OMS input and it is assumed that the accumulated disper-sion of the MAH is identical to that of the RAH. As shown, theOSNR estimates have the similar behavior as shown previouslyin Fig. 7 for signals unaffected by GVD. This indicates that theaccumulated dispersion has negligible impact on the OSNRestimation method as long as this impact is identical in theRAH and the MAH. To verify this property, Fig. 13 presents


Fig. 13. Dependence of the estimated OSNR on the accumulated dis-persion of the measured and reference signals. : OSNR��=26 dBand OSNR��=22 dB; �: OSNR��=20 dB and OSNR��=16 dB;

: OSNR��=28 dB and OSNRREF=14 dB.

Fig. 14. OSNR estimates of an NRZ signal using a RAH with OSNR =22 dB and a power at the OMS input of -5 dBm. : Estimates using MAH withnull accumulated dispersion; : Estimates using MAH with an accumulateddispersion of 102 ps/nm.

the dependence of on the accumulated dispersionfor several values of and . As shown inall considered cases, the estimated OSNR varies negligiblywith the accumulated dispersion, validating the application ofthe proposed method for GVD-degraded signals.

The case presented in Fig. 13 assumes that the optical pathof the signals propagated through the optical network remainsunchanged from the moment that the RAH is acquired to themoment that a MAH is acquired, which is acceptable for circuitswitched static networks. However, recent deployment of com-mercial systems using optical cross-connects allows operatorsto rapidly alter the paths of the optical signals and consequently,of their accumulated dispersion. As such, a realistic approachrequires assuming that the accumulated dispersion of the RAHand MAHs will differ along time. For this purpose, we maynote that the impact of GVD on the histogram shape will be in-terpreted by the nonlinear minimization algorithm as additionalASE, which allows associating it with an OSNR penalty. Underthese conditions, the application of the proposed method toMAH with different GVD-degradation than the correspondingRAH will result in an underestimation or overestimation of theOSNR, which reflects the GVD-induced OSNR penalty. Thisis illustrated in Fig. 14 where a RAH withdB without GVD induced degradation is used to estimate theOSNR of the same signal with an accumulated dispersion of102 ps/nm. As shown for dB, the OSNR esti-mate shows a GVD-induced OSNR penalty of approximately

Fig. 15. Dependence of the OSNR estimates of an NRZ signal on theaccumulated dispersion of the signal under analysis, using reference sig-nals with null accumulated dispersion. �: OSNR =OSNR =24 dB;

: OSNR =OSNR =20 dB; : OSNR =OSNR =16 dB.

7.4 dB. This penalty increases linearly with dueto the decrease of the ASE noise-impact on the asynchronoushistograms. To further illustrate the principle of the GVD-in-duced OSNR penalty, Fig. 15 presents the dependence of

on the accumulated dispersion of the signal underanalysis, assuming , which take thevalues of 14, 20, and 26 dB. As shown in Fig. 15, the valuesof decrease with the accumulated dispersion for allcases, reflecting the penalty due to the GVD-induced distortionof the asynchronous histograms. Furthermore, as the valueof accumulated dispersion exceeds 68 ps/nm, correspondingto 4 km of SSMF, the impact of GVD on the shape of theasynchronous histograms becomes dominant over the impactof ASE noise. As a consequence, the values ofconverge, regardless of the value of , reflecting thepenalty of the dominant impairment, which in this case is GVD.

Note that the GVD-induced OSNR penalty may only be di-rectly related with the actual BER of the signal if the receiverused to detect it presents the same optical and electrical charac-teristics as the OMS. Since this is generally not the case, it maystill be used as a reference.

IV. SUMMARY AND CONCLUSION

This paper presented and experimentally demonstrated anovel method for the estimation of OSNR of NRZ and RZsignals using asynchronous amplitude histograms. The newmethod is based on the comparison of asynchronous histogramsacquired from the signal under analysis with a reference asyn-chronous histogram, obtained from the same signal in acalibration stage. Through this comparison, it becomes possibleto estimate the OSNR of the signal under analysis, regardless ofthe OSNR that affected the reference asynchronous histogramat the calibration stage, as long as the waveform of the signalis maintained.

It has been shown that the maximum measurable OSNR de-creases with the power at the input of the optical monitoringsystem and the variance of the noise generated in the OMS.However, this limitation may be overcome by lowering the valueof the reference OSNR. Furthermore, the proposed method al-lows the use of optical preamplification to increase the sensi-tivity of the optical monitoring system by as much as 10 and 20dB, when using a SOA or an EDFA preamplifier, respectively.


This is achieved at the cost of limiting the maximum measur-able OSNR to values as low as 24 dB.

Since the new method is based on the comparison of his-tograms of signals with the same waveform but with distinctvalues of OSNR, it may be applied, in principle, to arbitrarymodulation formats. This work has experimentally demon-strated its application to 40-Gb/s NRZ signals with and withoutGVD-induced degradation, and also 40-Gb/s RZ signals. Inthe latter case, the RZ signal was converted in a NRZ signalwithin the OMS by narrowband filtering, to enhance the impactof ASE noise on the shape of the acquired histograms. Allconsidered cases presented negligible changes of sensitivity ormaximum measurable OSNR.

Finally, the impact of GVD-induced changes on the shapeof the measured histograms with respect to the reference his-tograms was analyzed. It was shown that the proposed methodinterprets these variations as additional noise, underestimatingthe OSNR. Therefore, the reduction of the OSNR estimates maybe seen as a GVD-induced OSNR penalty, thus reflecting an ac-tual penalty between the signal under analysis and the referencesignal.

ACKNOWLEDGMENT

The authors would like to thank the extensive support byDr. D. Fonseca and R. Meleiro of the Nokia Siemens NetworksOptics Research Group, Portugal.

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Ruben S. Luís (M’02) was born in Azores, Portugal,in 1977. He received the degree in electrical engi-neering and computers in 2000 and the M.Sc. degreein 2003 from the Instituto Superior Técnico, LisbonTechnical University, Portugal, and the Ph.D. degreein 2007 in electrical engineering from the Universityof Aveiro, Portugal.

He has been with the Optical Architecture group inNokia Siemens Networks S.A. where he lead workedtowards the development of optical network planningtools. He is currently with the Centre of Volcanology

and Geological Risk Assessment, University of Azores. He is also a researcherat Instituto de Telecomunicações.

Dr. Luís is a member of OSA.

António Teixeira (S’98–M’01) was born in Portugalon November 17, 1970. He received the Licenciaturadegree in electronics engineering and telecommuni-cations, in July 1994 and the Ph.D. degree in elec-trical engineering in 1999, all from the University ofAveiro, Portugal.

He is currently an Assistant Professor at the De-partment of Electronics, Telecommunications and In-formatics of the University of Aveiro and researcherat the Institute of Telecommunications. His researchinterests include DWDM optical networks and sub-

systems, passive optical networks, fiber bragg gratings and radio over fiber tech-nologies. He is/was involved in several FP6, FP7, and national projects.

Paulo Monteiro was born in Coimbra, Portugal, in1964. He received the diploma and Ph.D. degrees inelectronics and telecommunications from the Univer-sity of Aveiro, Portugal, and the M.Sc. degree fromthe University of Wales, U.K.

He is a research manager with Nokia SiemensNetworks Portugal and an Associate Professor withthe University of Aveiro where he has been teachingcourses of telecommunications. He is also a re-searcher with the Instituto de Telecomunicações. Hismain research interests include high speed optical

communications for access and core networks. He has authored/coauthoredmore than 15 patent applications and over 200 refereed papers and conferencecontributions.

Dr. Monteiro has acted as a reviewer for the IEEE JOURNAL OF LIGHTWAVE

TECHNOLOGY, the IEE ELECTRONICS LETTERS; ETRI Journal, the OSA Journalof Optical Networking (JON); and SPIE Optical Engineering. He has partic-ipated in several national and European projects and his currently the projectcoordinator of the large-scale integrating project “Fibre Optic Networks forDistributed, Extendible Heterogeneous Radio Architectures and Service Pro-visioning”—FUTON.

Optical Signal-to-Noise Ratio Estimation Using Reference Asynchronous Histograms

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