Patent Description:
Modem broad-band optical communications networks, in particular those using coherent transmission and detection of optical signal, may include fiber-optic links spanning hundreds of kilometers without optical signal regeneration. Such optical communication networks typically transmit multiple wavelength-multiplexed channels over a same optical fiber and use digital signal processing at the receiver to extract transmitted signals. Performance of such long fiber-optic links may however vary over time, e.g., due to component aging, environmental effects, external interference, etc., which may occur at different locations along the link. Therefore, link monitoring techniques capable of detecting changes in relevant link parameters and estimate approximate locations of the changes along a fiber-optic link are of interest.

Prior art document <CIT> relates to deriving information concerning characteristics of individual spans of an optical network from a received optical signal which is converted into an electrical digital signal by a digital signal processor. Parameters such as per-span variations in provisioned power, local dispersion and span loss is measured and used in optimisation of the network operation. In particular, the computation of a XPM transfer function based on correlation between a first modulated signal and the phase error signal of the recovered data clock from the received second channel is performed.

Prior art document <CIT> relates to monitoring phase non-linearities of an optical communications system by generating a test signal which includes a predetermined property that is uniquely associated with at least one phase non-linearity of the optical communications system.

An aspect of the present disclosure relates to an apparatus comprising: a digital processor (DP) being configured to receive a temporal sequence of digital measurements of a first optical signal received by a coherent optical receiver (COR) from an optical fiber link and being configured to estimate a cross-correlation between the temporal sequence of digital measurements and a temporal sequence of powers of a power-modulated second optical signal for a plurality of relative time shifts between the sequences, the second and first and second optical signals having been transmitted to the optical fiber link in different frequency channels, each of the digital measurements representing a phase of the received first optical signal at a corresponding time. The DP is configured to identify a location along the optical fiber link as having a physical change in response to a magnitude of a difference between the estimated cross correlation and reference cross-correlation being greater than a fixed value for one of the relative time shifts, and to estimate the location of the physical change from the value of the one of the relative time shifts.

A related aspect of the present disclosure provides a method for monitoring an optical fiber link. The method comprises: at a digital processor (DP), receiving a temporal sequence of digital measurements of a first optical signal received by a coherent optical receiver (COR) from an optical fiber link; estimating a cross-correlation between the sequence of digital measurements and a temporal sequence of powers of a second optical signal for a plurality of relative time shifts between the sequences, the second and first and second optical signals being in different frequency channels on the optical fiber link, each of the digital measurements representing a phase of the received first optical signal; and identifying a location along the optical fiber link as having a physical change in response to determining that a difference between the estimated cross-correlation and a reference cross-correlation has a magnitude greater than a fixed value for one of the relative time shifts.

Embodiments disclosed herein will be described in greater detail with reference to the accompanying drawings which represent example embodiments thereof, in which like elements are indicated with like reference numerals, and wherein:.

In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular circuits, circuit components, techniques, etc. in order to provide a thorough understanding of the present invention. However, it will be apparent to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known methods, devices, and circuits may be omitted so as not to obscure the description of the present invention. All statements herein reciting principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof.

Note that as used herein, the terms "first", "second" and so forth are not intended to imply sequential ordering, but rather are intended to distinguish one element from another, unless explicitly stated. Similarly, sequential ordering of method steps does not imply a requirement of sequential order of their execution, unless explicitly stated. The term "connected" may encompass direct connections or indirect connections through intermediate elements, unless explicitly stated otherwise. The term "polarization channel" is used herein to refer to a transmission path of a particular polarization component of a light signal in an optical transmission system or signal processing apparatus. Different polarization components of a light signal may also be referred to as polarization tributaries, e.g., with reference to a system where they may be separately processed. The term "frequency multiplexing" and its derivatives encompass wavelength division multiplexing (WDM) and coherent frequency multiplexing of optical sub-carriers to create a unified super-channel of a higher data rate. The term "pulse" refers to an elementary waveform that is linearly modulated by one data symbol. The term "walk-off" generally refers to a difference in propagation velocities of two optical carriers. The term "carrier phase" is used herein to refer to a phase 2πf·t accumulated by a cw optical carrier over a time t, where f is an optical frequency of the optical carrier.

Furthermore, the following abbreviations and acronyms may be used in the present document:.

Embodiments described below relate to an apparatus, and a corresponding method, for monitoring changes of optical signal propagation parameters along an optical fiber link of an optical communication system. The apparatus and method employ a receiver-based technique, utilizing cross-phase modulation (XPM) between two frequency-multiplexed optical signals.

An aspect of the present disclosure provides an apparatus comprising: a digital processor (DP) being configured to receive a temporal sequence of digital measurements of a first optical signal received by a coherent optical receiver (COR) from an optical fiber link and being configured to estimate a cross-correlation between the temporal sequence of digital measurements and a temporal sequence of powers of a power-modulated second optical signal for a plurality of relative time shifts between the sequences, the first and second optical signals having been transmitted to the optical fiber link in different frequency channels, each of the digital measurements representing a phase distortion of the received first optical signal at a corresponding time. The DP is configured to identify a location along the optical fiber link as having a physical change in response to a magnitude of a difference between the estimated cross correlation and reference being greater than a fixed value for one of the relative time shifts, and to estimate the location of the physical change from the value of the one of the relative time shifts.

In some implementations, the DP may be configured to estimate that the location is at a distance, along the optical fiber line, the distance being about the value of the one of the relative time shifts times a magnitude of a difference between the propagation velocities of the first and second optical signals on the optical fiber line.

In some implementations, the DP may be configured to subtract, from phase measurements of the first optical signal at sampling times, phase decisions corresponding to said phase measurements to obtain the digital measurements. In some implementations, the phase measurements and/or the phase decisions corresponding to said measurements may be obtained from the COR.

In some implementations, the physical change includes a change of at least one of a chromatic dispersion of a segment of the optical fiber link at the location and an optical attenuation of the segment of the optical fiber link at the location.

In any of the above implementations, the apparatus may further comprise the COR. In any of the above implementations, the COR may be configured to determine the digital measurements from measures of the received first optical carrier, at least partially, digitally compensated for chromatic dispersion caused on the first optical signal in the optical fiber line. In any of the above implementations, the COR may be configured to decode for each of the digital measurements a corresponding data symbol value carried by the first optical signal.

In any of the above implementations, the apparatus may further comprise an optical transmitter. In some implementations, the optical transmitter may be configured to transmit the first and second optical signals to the optical fiber link. In some implementations, the optical transmitter may be configured to transmit the second optical signal on an optical supervisor channel and to transmit the first optical signal in the optical telecommunication C-band. In some implementations, the optical transmitter may be configured to transmit the second optical signal over different subcarriers of an optical super-channel.

In any of the above implementations, the DP is configured to estimate a cross-correlation between the temporal sequence of powers of the second optical signal and a temporal sequence of digital measurements for a first polarization component of the first optical signal for a plurality of relative time shifts between the sequence of powers and the sequence of digital measurements for the first polarization component. In some of such implementations, the DP may be further configured to estimate a cross-correlation between a temporal sequence of digital measurements for a different second polarization component of the first optical signal and the temporal sequence of powers of the second optical signal or a different temporal sequence of powers of the second optical signal.

In at least some of the above implementations the temporal sequence of digital measurements are for a first polarization component of the first optical signal, and the power values of the first temporal sequence of power values comprise a first combination of power values of two different polarization components of the power-modulated second optical signal, and the DP is configured to estimate a cross-correlation between a second temporal sequence of digital measurements of a different second polarization component of the first optical signal, and a second temporal sequence of power values comprising a different second combination of power values of the two different polarization components of the power-modulated second optical signal.

A related aspect of the present disclosure provides a method for monitoring an optical fiber link. The method comprises: at a DP, receiving a temporal sequence of digital measurements of a first optical signal received by a COR from an optical fiber link; estimating a cross-correlation between the sequence of digital measurements and a temporal sequence of powers of a second optical signal for a plurality of relative time shifts between the sequences, the first and second optical signals being in different frequency channels on the optical fiber link, each of the digital measurements representing a phase distortion of the received first optical signal; and identifying a location along the optical fiber link as having a physical change in response to determining that a difference between the estimated cross-correlation and a reference cross-correlation has a magnitude greater than a fixed value for one of the relative time shifts. The method includes estimating the location of the physical change from the value of the one of the relative time shifts.

The method may further include estimating a distance to the location along the optical fiber line as being about the one of the relative time shifts times a magnitude of a difference between the propagation velocities of the first and second optical signals on the optical fiber line.

Some implementations of the method may comprise subtracting, from phase measurements of the first optical signal at sampling times, phase decisions corresponding to said phase measurements to obtain the digital measurements.

In some implementations, the method may further comprise: receiving the first optical signal at the COR from the optical fiber link; and transmitting the phase measurements of the first optical signal from the COR to the DP.

In any of the above implementations, the method may comprise transmitting the first and second optical signals to the optical fiber link such that the second optical signal is on an optical supervisor channel of the optical fiber link and the first optical signal is in the optical telecommunication C-band.

In any of the above or other implementations, the method may include adding a frequency chirp to at least one of the first and second optical signals prior to transmitting thereof over the optical fiber link.

<FIG>, top panel, schematically illustrates a portion of an optical communication network in which various embodiments may be practiced. The illustrated portion includes an optical fiber link <NUM> ("the link <NUM>") connecting a coherent optical transmitter (COT) <NUM> to a coherent optical receiver (COR) <NUM>. A link monitor <NUM> is coupled to the COR <NUM> for monitoring one or more parameters related to optical signal propagation along the link <NUM>. In at least some embodiments the link monitor <NUM> preferably operates by performing measurements on signals received by the COR <NUM> from the COT <NUM>, without requiring additional measurements at any of the intermediate nodes of the link <NUM> or any changes to an optical front end of the COR <NUM>. Relevant link parameters to monitor may include, but are not limited to, optical loss along the link <NUM> and chromatic dispersion (CD) of optical fibers along the link <NUM>.

<FIG> illustrates a multi-span link, which includes a sequence of fiber-optic spans <NUM>i ("spans <NUM>") interspersed by optical amplifiers (OAs) <NUM> to compensate for the optical loss along the link <NUM>. The OAs <NUM> may be, typically but not exclusively, e.g., Erbium-doped fiber amplifiers (EDFAs). A three-span link is shown for illustration, with the fiber spans <NUM> including spans <NUM><NUM>, <NUM><NUM>, and <NUM><NUM>, but other embodiments may have the number of fiber-optic spans <NUM> varying from <NUM> to <NUM> or more.

The optical loss along the link, e.g., in the optical fibers of fiber-optic spans <NUM>, at optical connectors, etc., causes the optical signal to lose its power as it propagates along each fiber-optic span <NUM>. The middle panel of <FIG> schematically illustrates an example optical power profile <NUM>, along the link <NUM>, for an optical signal transmitted by the COT <NUM>. The optical power profile <NUM> has a saw-tooth like shape, illustrating optical signal attenuation along each of the fiber-optic spans <NUM>i, interspersed by power restorations at the OAs <NUM>.

The number and placement of the OAs <NUM> are typically determined in relation to a loss budget of the optical fiber link to provide a target optical signal to noise ratio (OSNR) at the receiver, i.e., COR <NUM>. A presence of anomalously high optical loss in the link may cause the OSNR at the receiver to deteriorate. The link monitor <NUM> may be configured to detect the presence of the anomaly high loss, and may further be configured to estimate the amount of anomalous loss and its approximate location in the link <NUM>. By way of example, the optical power profile <NUM> illustrates an L dB optical loss anomaly at a location <NUM> along the second fiber-optic span <NUM><NUM>.

Another relevant parameter of the optical fiber link <NUM> relates to CD in the optical fibers, which causes optical pulses to broaden as they propagated along the link <NUM>. The amount of broadening is determined by the total CD <NUM> (lower panel in <FIG>) accumulated by the optical signal as it propagates along the link. Although the CD-induced pulse broadening may be partially compensated for at the COR <NUM>, the total amount of CD the optical signal may be allowed to accumulate for a target system performance may also be limited by a link design budget. Furthermore, as fibers with different CD parameters induce different nonlinear effects, it is valuable to verify the installed fiber types on the field. The link monitor <NUM> may be configured to detect the presence of fiber spans with abnormally high (or abnormally low) CD, and may further be configured to estimate the amount of anomalous dispersion and/or its approximate location in the link <NUM>. By way of example, the accumulated CD profile <NUM> shown in the lower panel of <FIG> illustrates anomalously high dispersion <NUM> of the last optical fiber span <NUM><NUM>.

Embodiments described below employ a technique to monitor changes in one or more network parameters, such as e.g. optical loss or the CD along an optical fiber link, at a COR physical layer, by performing data-assisted measurements on output signals of the COR to detect inter-channel interference. The technique exploits cross-phase modulation (XPM) between two co-propagating optical signals having different group velocities in the optical fibers of the optical fiber link, e.g. due to different optical carrier frequencies of the two optical signals. The two co-propagating optical signals may correspond, for example, to two different WDM channels, or two optical sub-carriers of an optical super-channel. In at least some embodiments, XPM induced by one of the two co-propagating optical signals in the other is/are detected by digital processing of an output signal of a coherent optical receiver. In some embodiments, the digital processing is data-assisted, making use of a known power modulation pattern of the other of the two optical signals. In some embodiments, the length (duration) of the known power modulation pattern is at least equal to a maximum propagation time difference between the two optical signals in a length of the optical fiber link being monitored due to the signal walk-off between the two signals.

In the following description, the optical signal being analyzed for the XPM is referred to as the first optical signal (e.g. <NUM>, <NUM> in <FIG>, and <FIG>), with the corresponding transmission channel being referred to as the channel under test (CUT). The optical signal inducing the XPM (e.g. <NUM>, <NUM> in <FIG>, and <FIG>) may be referred to as the second optical signal or the probe (optical) signal, with the corresponding transmission channel being referred as the probe channel. In some embodiments, the CUT may be a regular communication channel, e.g. in the optical telecommunication C-band, the L-band, or the S-band, and the probe channel may be a supervisory channel of the optical communication system, which may be out-of-band. In some embodiments, both the CUT and the probe channels may be regular communication channels of the optical communication system, e.g. both in the C-band, the S-band, or the L-band. In some embodiments, the CUT and the probe channel may be supervisory channels of the optical communication system.

The link-monitoring technique employed by example embodiments exploits pulse collisions under conditions of a signal walk-off, when the two optical signals propagate at different speeds, e.g. due to a frequency spacing between the two corresponding optical channels and the CD of the optical fiber. By cross-correlating a power modulation pattern of the probe optical signal with a time sequence of digtial measurements, e.g. phase distortion samples, of a corresponding segment of the first optical signal received by a coherent optical receiver, e.g., the COR <NUM>, a link monitor (e.g., <NUM>) may estimate an approximate location of a propagation-affecting change in the optical fiber link (e.g., <NUM>). The cross-correlating may be configured to detect XPM induced by a sequence of pulses of the probe optical signal upon a corresponding sequence of pulses of the first optical signal propagation time lags at the times of the XPM-inducing events, e.g., two-pulse collisions. The approximate location of different XPM-inducing events may then be estimated based on a time lag between the colliding pulses of the two optical signals and a known group velocity difference between the first and second optical signals.

<FIG> illustrates an optical communication system having at least some of the features outlined above. A coherent optical transmitter (COT) <NUM> is configured to launch two frequency-multiplexed optical signals, a first optical signal <NUM> and a second optical signal <NUM>, into an optical fiber link <NUM>, where the two optical signals co-propagate for at least some distance, with at least the first optical signal <NUM> being received by a COR <NUM> at an opposite end of the optical fiber link <NUM>. The optical fiber link <NUM>, the COT <NUM>, and the COR <NUM> may be embodiments of the optical fiber link <NUM>, the COT <NUM>, and the COR <NUM> of <FIG>, respectively.

The first and second optical signals <NUM> and <NUM> are modulated by the COT <NUM> to carry streams of digital data symbols. The second optical signal <NUM> is modulated at least in power, and is shifted in optical frequency from the first optical signal <NUM> by a frequency shift Δf<NUM>=(f<NUM>-f<NUM>), e.g. as illustrated in <FIG>; here f<NUM> is the optical carrier frequency of the first optical signal <NUM>, and f<NUM> is the optical carrier frequency of the second optical signal <NUM>. In some embodiments, the first and second optical signals <NUM> and <NUM> may be generated with respective signal generators <NUM> and <NUM>, and frequency multiplexed by a multiplexer <NUM>. In some embodiments, the signal generators <NUM> and <NUM> may each include an optical modulator coupled at its input to a coherent optical source generating light at the optical carrier frequencies f<NUM> andf<NUM>, respectively, and the multiplexer <NUM> may be a wavelength multiplexer. In some embodiments, the signal generators <NUM> and <NUM> and the multiplexer <NUM> may operate in electrical domain to output a frequency-multiplexed electrical signal, which is then modulated onto an optical carrier to form an optical super-channel, with the two carrier frequencies f<NUM> and f<NUM> being sub-carriers thereof.

The COR <NUM> is configured to perform sampling measurements on the received optical signal <NUM> for decoding therefrom the transmitter-modulated data symbols. The sampling measurements performed by the COR <NUM> may also be used by a digital processor (DP) <NUM> to monitor physical changes along the optical fiber link <NUM>. In some embodiments, the DP <NUM> may be co-located with the COR <NUM>. In some embodiments, the DP <NUM> may be implemented at least in part using a digital signal processor (DSP) of the COR <NUM>. In some embodiments, the DP <NUM> may be located remotely from the COR <NUM>, and receive digital data therefrom over a suitable communication channel.

In an example illustrated in <FIG>, the DP <NUM> is configured to receive from the COR <NUM> a stream of digital measurements <NUM> of the first optical signal <NUM> representative of a phase of the first optical signal <NUM> at sampling times. The DP <NUM> is further configured to and obtain therefrom a temporal sequence <NUM> of digital measurements <NUM>, each of which representing a phase distortion of the received first optical signal <NUM> at a corresponding sampling time. A digital measurement representative of a phase of a received optical signal may, e.g., refer to the phase sample of the received optical signal as measured by a front end of a corresponding COR, e.g. COR <NUM>, or, preferably, a processed form of such measure, e.g., to correct for carrier frequency estimation, sampling timing errors, to compensate for the CD, to remove therefrom a decoded symbol phase value, etc. The DP <NUM> is further configured to estimate, e.g. using a digital cross-correlator <NUM>, a cross-correlation <NUM> between the temporal sequence <NUM> and a temporal sequence <NUM> of power values <NUM> of the second optical signal <NUM> for a plurality of relative time shifts τn <NUM> between the sequences <NUM> and <NUM>. Temporal sequences <NUM> and <NUM> with a relative time shift <NUM> therebetween are schematically illustrated in an insert "A" in <FIG> for an example embodiment. The temporal sequence of power values <NUM> may also be referred to herein as the power modulation pattern of the second optical signal <NUM>. Each of the digital measurements <NUM> represents a phase distortion ϕi of the received first optical signal <NUM> at a corresponding, e.g. sampling, time, e.g. ti. The DP <NUM> may be further configured to identify a location along the optical fiber link <NUM> as having a physical change in response to a magnitude of the cross-correlation <NUM> being greater than a threshold.

In the illustrated embodiment, the DP <NUM> includes digital circuits implementing a link monitor <NUM>, which may be an embodiment of the link monitor <NUM> of <FIG> to monitor changes of the optical fiber link <NUM> along a length thereof where the signals <NUM> and <NUM> co-propagate. In some embodiments the link monitor <NUM> may be preceded by a phase distortion estimation (PDE) unit <NUM> as further described below. In some embodiments, the PDE unit <NUM> may be implemented within the DP <NUM>. In some embodiments, the PDE unit may be implemented at least in part inn a DSP of the COR <NUM>. The link monitor <NUM> includes a cross-correlation estimator <NUM> configured to estimate the cross-correlation <NUM> using the power modulation pattern <NUM>. The cross-correlation <NUM> for a particular relative time shift <NUM> is indicative of XPM of the first optical signal <NUM> induced by the second optical signal <NUM> at a particular portion of the optical fiber link <NUM>. The power modulation pattern <NUM> may be e.g., stored in a memory device <NUM> associated with the DP <NUM>. The link monitor <NUM> may further include a link event detector <NUM> configured to detect changes in the optical fiber link <NUM>, and estimate approximate locations of the changes, based at least in part on the cross-modulation <NUM> as a function of the relative time shift <NUM>.

<FIG> schematically illustrate the propagation of two pulses, <NUM> and <NUM>, of the first and second optical signals <NUM>, <NUM> along a length of the optical fiber link <NUM>. Pulse <NUM> represents a pulse of the first optical signal <NUM>, and pulse <NUM> represents a pulse of the second optical signal <NUM>. Here, the term "pulse" refers to an optical field for a particular symbol of a data signal carried by a corresponding optical signal, which may or may not be power-modulated. Pulse <NUM> has been transmitted by the COT <NUM> at an earlier time than pulse <NUM>, and has traveled a longer distance along the link at a time instance t<NUM> of <FIG>, but is moving at a lower velocity <NUM> than the velocity <NUM> of pulse <NUM>, due to the carrier frequency shift Δf<NUM> and the CD in the optical fiber link <NUM>, resulting in a pulse walk-off. At a time instance t<NUM>>t<NUM> illustrated in <FIG>, pulse <NUM> is caught up and "collides" with pulse <NUM>, inducing an XPM in an overlap region <NUM>. At a time instance t<NUM>>t<NUM> illustrated in <FIG>, pulse <NUM> overtakes pulse <NUM>, no longer overlapping therewith. Thus, the collision between the two pulses <NUM>, <NUM> has a final duration and occurs over a finite segment of the optical fiber link <NUM>, and the XPM induced by the collision carries a signature of that particular segment of the link.

<FIG> illustrate example pulse collision regions <NUM> and <NUM> for two different frequency shifts Δf<NUM> between the first and second optical signals <NUM> and <NUM> (the CUT and the probe channel), Δf<NUM>= 2Δf = <NUM> in <FIG> and Δf<NUM>= 3Δf = <NUM> in <FIG>; here Δf denotes e.g., a frequency spacing between adjacent channels of the frequency-multiplexed optical signal for an example embodiment. In the illustrated example, the symbol rate in both channels is <NUM> Gbd, the optical fiber link <NUM> employs a single-mode fiber (SMF) with a dispersion coefficient of <NUM> ps/nm/km. The horizontal axis corresponds to a walk-off time between the two optical signals in units of symbol intervals. For instance, in the embodiment of <FIG>, with Δf<NUM> = <NUM>, the collision region <NUM> of an i-th pulse <NUM> of the first optical signal <NUM> with the k=(i+<NUM>)-th pulse <NUM> of the second, or probe, optical signal <NUM>, extends between about <NUM> and <NUM> of the optical fiber link. In the embodiment of <FIG>, with Δf<NUM> = <NUM>, the collision region <NUM> for these two pulses is proportionally narrower and extends between about <NUM> and <NUM>. Here the pulse counts i and k are synchronized so that i=<NUM> and k=<NUM> indicate approximately the same transmission time, e.g. within about half of a symbol interval.

Referring back to <FIG>, the COR <NUM> is configured to output a stream of digital measurements <NUM> comprising phase information for the first optical signal <NUM>. In some embodiments, the digital measurements <NUM> may be complex-valued signal samples. In some embodiments, the digital measurements <NUM> may be measurements of a phase of the first optical signal <NUM> relative to its carrier phase 2πf<NUM>t. In some embodiments, the digital measurements <NUM> may be phase distortion samples as described below. In some embodiments, the PDE unit <NUM> may be provided to process the digital measurements <NUM> to remove therefrom corresponding symbol phase decisions <NUM>. The cross-correlation <NUM> comprises information about XPM-induced content of the digital measurements <NUM> induced in the first optical signal <NUM> by collisions with pulses of the second optical signal <NUM>. The cross-correlation <NUM>, as a function of the relative time shift τn, may be referred to herein as the XPM pattern and may be described e.g., by a cross-correlation function c(n) or a cross-correlation vector {cn}, where n is an integer counter of the relative time shift τn. The cross-correlation <NUM> comprises signatures of different segments of the optical fiber link <NUM>, which locations along the link may be mapped to the relative time shifts τn. The cross-correlation <NUM> may further comprise an estimate of a pulse collision tensor Xkkii, as described below.

In some embodiments, the cross-correlation <NUM> may be analyzed, e.g., by a link event detector <NUM>, to relate the relative time shifts τn, or the corresponding integer shifts n, to propagation time lags between the signals <NUM>, <NUM> as the signals co-propagate along the length of the optical fiber link, as further described below. The link event detector <NUM> may be configured to detect a physical change in the optical fiber link <NUM>, and estimate approximate location of the changes based at least in part on a value of the cross-correlation <NUM> for the corresponding propagation time lag. In an embodiment, the link event detector is configured to generate a threshold crossing alert (TCA) when the cross-correlation <NUM>, or a change thereof relative a reference, is greater in magnitude than a fixed value.

The power modulation pattern <NUM> represents pulse power modulation for a segment of the second optical signal <NUM>. In an example embodiment, the first and second optical signals <NUM>, <NUM> are optical carriers modulated at the COT <NUM> with streams of digital data symbols ai and bk, respectively, where i and k are the symbol counters in the respective streams. The first optical signal <NUM> may use any modulation format, including but not limited to PSK, e.g., QPSK, BPSK, M-PSK, QAM, and PAM. The second optical signal <NUM> may use any modulation format in which symbol power varies, i.e., excluding pure PSK formats.

The power modulation pattern <NUM> may be e.g. a temporal sequence {pk} of power values ("powers") pk =|bk|<NUM> for a K-long sequence {bk} of digital data symbols bk of the second optical signal <NUM>, where K is the number of symbols in the sequence. In some embodiments, the power values, or "powers", pk may be relative to an average, or DC, value thereof <|bk|<NUM>> for the sequence, e.g. pk = (|bk|<NUM> - <|bk|<NUM>>), so that <pk> = <NUM>. In one embodiment, the sequence {bk} may be a pre-determined probe sequence for which the sequence of symbol power values {pk} is stored at the DP <NUM> or externally to the COR <NUM>. For example, the sequence {bk} may include pilot symbols of a supervisory channel. In other embodiments, the sequence of symbol power values {pk} may be reconstructed by the COR <NUM> from the received second optical signal <NUM>, e.g. using FEC-assisted detection, or operating at a high OSNR for the second optical signal.

In some embodiments, e.g. when the first and second optical signals are polarization multiplexed, the power modulation pattern <NUM> may be e.g. a sequence of power values pkx,y combining power values of corresponding k-th symbols in X- and Y- polarization tributaries of the probe optical signal <NUM>, as described below.

In some embodiments, the cross-correlation estimator <NUM> computes the cross-correlation function {cn} <NUM> between the sequence <NUM> of symbol power values {pk} <NUM> for the second optical signal <NUM> and a sequence <NUM> of phase samples {ϕk} <NUM> obtained by the COR <NUM> or DP <NUM> for a co-propagating segment of the first optical signal <NUM>, in accordance with equation (<NUM>): <MAT> Here E{. } denotes statistical expectation, which may include averaging over a plurality of measurements.

In an embodiment, the sequences of the phase samples {ϕi} and the power values {pk} are of the same length K, i.e., with integer indices i, k = <NUM>,. , K-<NUM> indicating consecutive sampling times for the first (<NUM>) and second (<NUM>) optical signals, respectively, e.g. one per respective symbol interval. Estimating the cross-correlation cn may include averaging over pairs of the phase samples and power values, {ϕi, pi-n}, with the same "symbol lag" n therebetween, e.g. in accordance with equation (<NUM>): <MAT> where a is a normalization constant. The sequence {pk} in equation (<NUM>) may be circularly extended, e.g. so that p-n= PK-<NUM>-n for n><NUM>.

The operations in the right-hand side (RHS) of equation (<NUM>) or equation (<NUM>) may include, for example, computing the quantities cn by first computing the cross power spectral density (cPSD) for the sequences {pk} and {ϕi} , followed by an inverse discrete. Fourier transform of a resulting periodogram, e.g., as illustrated in <FIG>.

In some embodiments, the phase samples ϕi in equations (<NUM>) and (<NUM>) may be phase distortion samples, which may be obtained by removing a transmitter-generated phase modulation from phase measurements of the received first optical signal <NUM>. In some embodiments, the transmitter-generated phase modulation component may be determined based on hard symbol phase decisions <NUM> on the complex-valued signal samples si = ri·exp(j·ψi), and the phase samples ϕi are generated by removing the symbol phase decisions <NUM> from the complex-valued signal samples si. Here ri denotes the carrier amplitude samples. The complex-valued signal samples si are typically generated by the COR <NUM> by, e.g., sampling the in-phase and quadrature components of the received first optical signal <NUM> in the baseband.

Referring again to <FIG>, in some embodiments the PDE unit <NUM> may be provided to remove the phase modulation component from the digital measurements <NUM>. In some embodiments, the digital measurements <NUM> may be in the form of a stream of phase measurements ψi, and the PDE unit <NUM> may be configured to subtract therefrom the phase ψdi of the hard symbol decisions <NUM>, e.g. in accordance with equation (<NUM>) <MAT> where di denotes a hard decision on a complex signal sample si, and the arg(. ) function is the argument of the complex number.

In some embodiments, the digital measurements <NUM> may be in the form of a stream of the complex signal samples si, and unit <NUM> may be configured to first generate a sequence of complex distortion samples ui therefrom, e.g. in accordance with ui = si·exp(-j·ψdi), where ψdi = arg(di) is a hard symbol phase decision. The phase distortion sample ϕi may then be estimated as the phase, arg(ui), of the complex distortion sample ui. In some embodiments, unit <NUM> may be configured to estimate the phase distortion sample ϕi as the ratio yi/xi, where xi and yi are the real and imaginary parts of the complex distortion sample ui. In some embodiments, unit <NUM> may be configured to first generate the phase measurements ψi from the complex signal samples si, and then estimate the phase distortion samples ϕi, e.g. based on equation (<NUM>).

A value of the cross-correlation cn <NUM> for a particular n represents a scaled estimate of an average XPM of the first optical signal <NUM> due to collisions with pulses of the second optical signal <NUM> shifted by n symbol intervals. The symbol lag n may be mapped to a location of the XPM-causing collision event relative to a reference location along the optical fiber link, e.g. the coordinate where the probe optical signal <NUM> enters in the optical link <NUM> to co-propagate with the first optical signal <NUM>. The value cn may thus comprise a signature of the optical fiber link at a specific location along the link defined by the symbol lag n. In an embodiment, the distance D from a reference location to a cn anomaly detected for a particular symbol lag n may be estimated to be about the value of the relative phase time shift τn=T*n, times a magnitude |Δvg| of a difference Δvg between the propagation velocities of the first and second optical signals <NUM>, <NUM> on the optical fiber line: D ≅ T·n·|Δvg|, where T is the symbol interval and Δvg is the group velocity difference between the two optical signals <NUM>, <NUM> in the optical fiber link <NUM>.

In some embodiments, the DP <NUM> is configured to synchronize the temporal sequences {pk} and {ϕi} so that, e.g., the counters k = <NUM> and i=<NUM> correspond to symbols or pulses of the two optical signals <NUM>, <NUM> transmitted through a reference location along the optical fiber link <NUM> at approximately the same time, e.g. within half a symbol period from each other. The symbol lag n is then a function of the propagation time difference between the colliding pulses of the two optical signals from the reference location to the location of the pulse collision, and therefore is directly indicative of the pulse collision location along the optical fiber link.

In the example embodiment illustrated in <FIG>, both optical signals <NUM> and <NUM> are transmitted by the same COT <NUM>, and the reference location may correspond, e.g. to an end of the optical fiber link <NUM> coupled to the COT <NUM>. In some embodiments, the reference location may be e.g. a location of an intermediate OA. In some embodiments, the second optical signal <NUM> may be transmitted by a different COT, and may enter the optical fiber link <NUM> at a different location therealong, e.g. using a wavelength multiplexer (MUX) or a wavelength selective switch (not shown); in such embodiments, the reference location may be, e.g. where the second optical signal <NUM> enters the optical fiber link <NUM>, or at a first OA thereafter.

In some embodiments, e.g. when the first and second optical signals <NUM>, <NUM> are transmitted by a same COT as illustrated in <FIG>, the synchronization of the sequences may be pilot-assisted; e.g. the COT <NUM> may transmit one or more known pilot symbols in the CUT that synchronously with transmitting, e.g., a forward end of the power-modulation pattern <NUM> in the probe channel. In such embodiments, the COR <NUM> or the DP <NUM> may be configured to detect the one or more known pilot symbols, to suitably determine the forward end of the temporal sequence <NUM> of the digital measurements <NUM> to be correlated with the power modulation pattern <NUM>. In some embodiments, the DP <NUM> may be configured to synchronize a test temporal sequence of the digital measurements <NUM> to a stored power modulation pattern <NUM> based on a magnitude of the cross-correlation cn, e.g. by detecting peaks in cn as a function of n, which may indicate location of OAs along the optical fiber link <NUM>, and assigning n=<NUM> to cn at the first peak. Once the two temporal sequences are synchronized, i.e. one of the digital measurements <NUM> that aligns at the transmission with the first one of the power values pk, i.e. pk=<NUM>, is determined, a new temporal sequence <NUM> of the digital measurements <NUM>, which suitably aligns with the stored power modulation pattern <NUM> and has the desired length K, maybe selected, and used to compute an update cross-correlation cn.

In an embodiment, the length K of the stored power modulation pattern <NUM>, e.g. of the form of the probe sequence {pk}, may be selected to be large enough, i.e. i.e. K ≥ τ·RB, to accommodate a maximum time lag τ = L/Δvg, i.e. the propagation time difference between the first and second optical signals <NUM>, <NUM> in a length L of the optical fiber link <NUM> being monitored; here Δvg is the group delay difference between the first and second optical signals, and RB is the largest symbol rate of the two channels.

In some embodiments, computing the cross-correlation <NUM> may include averaging over a plurality of temporal sequences <NUM> of digital measurements <NUM>, cross-correlating each with a corresponding power modulation pattern {pk} of the second (probe) optical signal. This may include, e.g., averaging over a plurality of cPSD periodograms to obtain a single cPSD periodogram. In an example embodiment, the plurality of sequences <NUM> of phase distortion samples may be detected for different segments of the first optical signal, each transmitted approximately simultaneously with, e.g., a sequences of pilot symbols of a probe optical signal, e.g., in a supervisory channel.

<FIG> illustrates a functional block diagram of the link monitor <NUM> for an example embodiment. The cross-correlation estimator <NUM> includes a cPSD computing unit <NUM> followed by an IFFT computing unit <NUM> to estimate the cross-correlation <NUM> between the sequence of symbol power values {pk} and a sequence <NUM> of the phase distortion samples {ϕn}. The cPSD computing unit <NUM> computes an estimate of the cPSD <NUM> for the two sequences <NUM> and <NUM>, e.g., using the Welch's method known in the art. In an embodiment, the cPSD computing unit <NUM> may perform a sequence of signal processing operations including i) dividing the pair of sequences <NUM> and <NUM> into a plurality of equal-size blocks, which may overlap, each of the blocks containing corresponding segments of the two sequences <NUM> and <NUM>, ii) for each block, applying a window function to each segment, computing a pair of periodograms for the pair of segments, e.g., using a discrete Fourier transform, and performing an element-by-element multiplication of the two periodograms, and iii) averaging the resulting single-block product periodograms over all blocks. This process produces the cPSD estimate <NUM>, which is then provided to the IFFT unit <NUM> to perform an IFFT operation to compute the cross-correlation function {cn}.

The XPM cross-correlation vector <NUM> is passed to a comparator unit <NUM>, which may perform at least some of the functions of the link event detector <NUM>. The comparator unit <NUM> compares the cross-correlation vector {cn} to a stored reference cross-correlation vector <NUM>, which represents the cross-correlation <NUM> obtained for a reference, e.g., non-perturbed, state of the optical fiber link <NUM>. In some embodiments the comparator <NUM> may, for example, compute an element-by-element difference between the estimated cross-correlations <NUM> and the reference cross-correlations <NUM>, and then detect elements of the difference matrix or vector exceeding in value corresponding threshold values to estimate an approximate location of a link event. In some embodiments, a machine learning algorithm may potentially be used to determine whether the detected anomaly relates to e.g. a change in optical loss or a change in CD.

<FIG> illustrates a block diagram of a dual-polarization COR <NUM>, which is coupled to a DP <NUM> implementing a link monitor <NUM> according to an embodiment. The DP <NUM> and the link monitor <NUM> may be embodiments of the DP <NUM> and the link monitor <NUM> described above. The COR <NUM> is configured to receive a light signal <NUM> from an optical fiber link, e.g. link <NUM> of <FIG>. The light signal <NUM> may include first and second optical signals <NUM>, <NUM>, which may be embodiments of the first and second optical signals <NUM>, <NUM> described above with reference to <FIG> and have corresponding optical carrier frequencies f<NUM> andf<NUM>.

The first and second optical signals <NUM>, <NUM> may be each polarization-multiplexed at a corresponding remote COT to comprise two polarization tributaries, hereinafter referred to as X and Y, carrying corresponding modulation signals at the respective first or second optical carrier frequency f<NUM> or f<NUM>. In some embodiments the input light signal <NUM> may be absent of the second light signal <NUM>, e.g. if the second light signal has been de-multiplexed prior to the COR <NUM> or dropped at an intermediate node of the optical fiber link.

The light signal <NUM> is provided to an optical-to-electrical (OE) converter <NUM>, which is coupled to a DSP <NUM>. The OE <NUM> implements a polarization-diversity homodyne-detection or intradyne-detection of the first optical signal <NUM> to output electrical signals <NUM> separately for two orthogonal polarizations of the received first light signal <NUM>. The DSP <NUM> is configured to de-convolve the modulations of the X- and Y-polarizations of the first optical signal <NUM> from the electrical signals <NUM>, and to generate streams of complex signal samples 633X and 633Y for the X- and Y- polarization tributaries of the first optical signal <NUM>, respectively. The complex signal samples 633X and 633Y may be generally referred to hereinafter as signal samples <NUM>, or the digital measurements <NUM>. The signal samples <NUM> comprise a phase component representing the carrier phase modulation of the corresponding polarization tributaries of the first optical signal <NUM>, distorted by the propagation in the optical fiber link. The signal samples <NUM> are provided to decision gates <NUM> for generating hard symbol decisions thereon, which comprise (hard) symbol phase decisions.

In some embodiments, the streams of signal samples 633X and 633Y are provided to corresponding PDE units <NUM> to extract phase samples 637X and 637Y therefrom, which may be generally referred to as phase samples <NUM>. In some embodiments the phase samples <NUM> are phase distortion samples, with corresponding hard symbol phase decisions removed, to represent accumulated carrier phase distortions of the corresponding polarization tributaries of the first optical signal <NUM> due to the propagation in the optical fiber link, including the non-linear XPMs due to the pulse collision interactions with the second optical signal <NUM> as the two optical signals co-propagate along the optical fiber link. One or both of the streams of the phase samples 637X, 637Y may then be provided to the link monitor <NUM> for computing the cross-correlation function(s) with one or more power modulation patterns of the second optical signals <NUM> as described above and estimating the XPMs induced in the first optical signal <NUM> by the second optical signal <NUM> during their co-propagation in the fiber optical link.

In an example embodiment shown in <FIG>, the OE converter <NUM> comprises a polarization beam splitter (PBS) <NUM> configured to decompose the light signal <NUM> into two orthogonally polarized components. Light of each of the two polarization components is then provided to a corresponding optical hybrid <NUM> wherein it is mixed with a correspondingly polarized local oscillator (LO) light from a laser source <NUM>. In an embodiment, laser source <NUM> is configured to emit coherent light at optical frequency approximately equal to the carrier frequency f<NUM> of the first optical signal <NUM>. Each of the optical hybrids <NUM> operates to output four mixed optical signal in which portions of the light signal <NUM> are coherently mixed with portions of the LO light with a <NUM>° phase shift increment. The four mixed optical signals from each optical hybrid <NUM> are detected by corresponding two balanced photodetectors (PDs) <NUM>, to provide electrical signals <NUM> corresponding to the in-phase (I) and quadrature (Q) modulation signal components for each of the respective polarization components of the received light. The electrical signals <NUM> from the balanced photodetectors <NUM> are provided to analog-to-digital converters (ADCs) <NUM>. The ADCs <NUM> sample the corresponding electrical signals <NUM> at a suitable sampling frequency to produce digital electrical signals <NUM> comprising phase modulation and distortion information for the first optical signal <NUM>. In some embodiments, the electrical signals <NUM> may be amplified and optionally filtered prior to the sampling.

In an example embodiment, the DSP <NUM> operates to perform: (i) signal equalization; (ii) clock recovery; and (iii) carrier- and data-recovery (CDR) processing. In the illustrated embodiment, the DSP <NUM> includes chromatic dispersion compensation (CDC) modules <NUM>, followed by digital clock recovery circuitry (CRC) <NUM>, which is in turn followed by polarization de-multiplexing circuitry (p-DMUX) <NUM>, and carrier phase estimation (CPE) modules <NUM>. The CDC modules <NUM> are configured to at least reduce, or substantially cancel, the detrimental effects of CD in the optical fiber link upon the first optical signal <NUM>, such as e.g. inter-symbol interference (ISI) due to the group delay dispersion and the resulting pulse broadening. The CRC <NUM> may operate to recover a symbol clock used at the remote COT and to synchronize thereto various digital data streams in DSP <NUM>, e.g. for controlling the rate and phase of a clock signal applied to ADCs <NUM>. The p-DMUX <NUM> is configured to perform MIMO processing to de-convolve modulation signals of the X and Y polarization tributaries of the first optical signal <NUM> from the streams of digital samples received for the two polarization outputs of the PBS <NUM>. The CPE modules <NUM> operate at the outputs of the p-DMUX <NUM> to generate the streams of digital measurements 633X, 633Y, e.g. in the form of streams of complex samples of the received signal for each polarization tributary. Decision gates <NUM> perform hard decisions on the complex samples <NUM> to generate hard decisions <NUM>, which may be complex-valued. The complex samples 633X, 633Y are provided to respective PDE units <NUM>, each of which may be an embodiment of unit <NUM> described above with reference to <FIG>, and is configured to generate respective phase samples 637X or 637Y. In one embodiment, the PDE units <NUM> also receive the hard decisions 635X, 635Y and is configured to remove hard symbol phase decisions from corresponding phase measurements as described above, so that phase samples 637X and 637Y represent phase distortion samples for the X and Y polarization tributaries of the first optical signal, respectively.

In an illustrative embodiment, a remote COT may modulate an optical carrier of the first optical signal <NUM> with complex symbols Ak · exp(jθk). An optical filed Ek for each symbol at the COR <NUM> may be approximately described as Ek = rk exp[j(θk + βk + αk)], where βk =<NUM>πf<NUM>tk is the carrier phase for the k-th transmitted symbol, and αk denotes the phase distortion of the k-th symbol due to e.g. ASE noise, transmission nonlinearity, laser phase noise, etc. Each CPE module <NUM> of COR <NUM> may generate an estimate <MAT> of the carrier phase βk and may output complex samples <MAT>, with phase measurements <MAT>. Here αrk denotes phase distortions accumulated by the signal along the transmission path up to and including the decision gates <NUM>, including ASE noise, nonlinearity distortions including the XPM in the optical link, laser phase noise, other phase distortions due to e.g. transponder imperfections, imperfect compensation of CD, GAWBS, thermal photodiode noise, IQ imbalance, the mismatch "noise" due to imperfect phase recovery, the mismatch "noise" due to errors in symbol decision. The decision gate <NUM> generates the phase decision <MAT> of the sample k, <MAT>. In an embodiment, the PDE unit <NUM> may generate phase samples <NUM> e.g. as phase distortion estimates <MAT>; this may include estimating a "distortion field" with complex samples <MAT>.

The link monitor <NUM> may operate e.g., as described above with reference to <FIG> and the optical signals <NUM> and <NUM>. In some embodiments, the link monitor <NUM> may correlate a segment of any one of the streams of phase samples <NUM> with a corresponding sequence of power values {pk} for a co-propagating sequence of symbols of the second optical signal <NUM>.

In embodiments where the first and second optical signals <NUM> and <NUM> are commonly polarization multiplexed at a same COT, the symbol power values pkx to correlate with the (noise) phase samples 637x of the X polarization tributary may be computed as <MAT> while the symbol power values pky to correlate with the noise phase samples 637yx of the Y polarization tributary may be computed as <MAT> where bkx and bky are the amplitudes of the k-th symbol interval for the X and Y tributaries of the second optical signal <NUM>, respectively. In embodiments where the second optical signal <NUM> is polarization multiplexed at a different COT independently of the first optical signal <NUM>, the DP <NUM> (e.g. the link monitor <NUM>), may cross-correlate sequences of phase samples 637X and 637Y of the X and Y polarization tributaries of the first optical signal <NUM> with a same sequence of power values {pk} of the second optical signal <NUM>, e.g. with pk=<NUM>|bkx|<NUM>+<NUM>]bky|<NUM>.

Embodiments described above exploit XPMs induced by nonlinear interactions between two frequency-multiplexed optical signals co-propagating in an optical fiber. An XPM induced upon a pulse (data symbol) of a CUT signal, e.g. <NUM> or <NUM>, by its collision with a pulse (data symbol) of a second optical signal, e.g. <NUM> or <NUM>, may be approximately described using an approximate analytical framework presented in, e.g., in <NPL>.

In a first-order perturbative approximation, non-linear Kerr interactions add a non-linear interference (NLI) contribution to a signal detected by a coherent. optical receiver, such as e.g. the COR <NUM> or <NUM>. In embodiments without polarization multiplexing, the NLI contribution to the i-th sample detected by the COT for the CUT after recovering the linear impairments accumulated during propagation and sampling, e.g. as described above with reference to <FIG>, can in some approximation be described by the following discrete-time model describing four-pulse collisions: <MAT> where the summation is from -∞ to ∞, and Xkmni is defined by the following equation (<NUM>) and is hereafter referred to as the collision tensor: <MAT> Here ni is the NLI impairing the CUT digital symbol ai at discrete-time symbol i, bk is the k-th digital symbol in the interfering channel, y is a coefficient characterizing the strength of the Kerr nonlinearity in the optical fiber, f(z) is a nominal loss profile of an optical path of the signals along a propagation coordinate z, p(z,t) is the supporting pulse shape of the digital modulated signals at coordinate z, accounting for pulse distortions due to the CD accumulated up to that coordinate and at time t, τ(z) is the channel walk-off, i.e., the delay between the interfering channel and the CUT arising from the different group velocities of the two signals in the optical fibers. The discrete-time indexes (k,m,n,i) label the four pulses under Kerr interaction, i.e., the four pulses undergoing collision during propagation.

Equation (<NUM>) may be generalized for embodiments with polarization multiplexing, e.g. as described above with reference to <FIG>. Data symbols carried by a polarization multiplexed optical signal may be described by a two-element vector, the two elements of which being the corresponding data symbols transmitted over the X and Y polarizations: <MAT> where akx and aky are the corresponding k-th symbols transmitted in the CUT over the X- and Y-polarizations, respectively, and bkx and bky are the corresponding k-th symbols transmitted in the interfering channel over the X- and Y-polarizations, respectively. With this notation, the NLI contribution to the i-th sample of the CUT signals detected by a COR, e.g. the COR <NUM>, after recovering the linear impairments accumulated during propagation and sampling, e.g. signals 635X and 635Y of the COR <NUM> of <FIG>, can be approximately described by the following equation (<NUM>): <MAT> where the superscript "H" indicates transpose conjugate and I is the identity 2x2 matrix. Equation (<NUM>) suggests that in the absence of polarization-mode dispersion, which is typically small in modern SMF, the NLI due to collisions of polarization multiplexed pulses is still weighted by the same tensor Xkmni.

In some approximation, embodiments described above with reference to <FIG> may be viewed as exploiting two-pulse collisions, corresponding to (k=m) and (n=i) in equations (<NUM>), (<NUM>), and (<NUM>). The NLI ni induced by two-pulse collisions contributes to the quadrature (Q) signal component and thus to the collision-induced XPM. The collision tensor Xkkii for the two-pulse collisions satisfies the following equation (<NUM>): <MAT> describes relative strengths of the XPMs induced in the CUT at a plurality of locations along the link, with each element bearing the signature of a collision region of the two pulses.

In an example embodiment absent of polarization multiplexing, equation (<NUM>) for the NLI caused by two-pulse collisions may be rewritten for an XPM contribution φi into the phase of the i-th symbol of the CUT: <MAT> where <MAT> is the symbol power of the k-th interfering pulse. In this embodiment, the XPM cross-correlation cn computed according to equation (<NUM>), i.e. by cross-correlating the sequence of phase distortion samples ϕi detected for the first optical signal with a corresponding sequence of the symbol powers {pk} of the second optical signal, is approximately proportional to a square of a product of the symbol power <MAT> of the interfering pulse, and the collision tensor Xkkii, with i=k-n: <MAT> where A and B are constant independent of n, and Xn = Xkkii , i = (k-n). In some embodiments pk=(|bk|<NUM>-<|bk|<NUM>>), and B = <NUM>. Accordingly, the estimation of the cross-correlation cn, e.g. as described above, may also provide an estimate of the two-pulse collision tensor Xkkii. In an embodiment where the two optical signals are polarization multiplexed, an estimate of the two-pulse collision tensor Xkkii may be obtained by computing the cross-correlation of the sequence of phase distortion samples ϕi obtained for the first optical signal in one of the two X- or Y-polarization channels with the symbol power sequences defined e.g. by equations (4A) and (4B), as described above.

As an illustration, <FIG> shows an example of the two-pulse collision tensor for a computer-simulated <NUM>-span SMF link, with the interfering channel spaced <NUM> (solid line) or (-<NUM>) GHz (dashed line) from the CUT, and a symbol rate of <NUM> Gbaud. As can be seen from <FIG>, in this example each pulse of the CUT may experience on the order of <NUM> NLI-inducing collisions with pulses of the interfering channel. The collisions occur at different locations along the optical fiber link, see e.g. <FIG>, with the collision tensor Xkkii carrying signatures of those locations.

<FIG> shows a flowchart of a method <NUM> for monitoring changes in light propagation properties of an optical fiber link along a length thereof, according to an aspect of the present disclosure. In <FIG>, each block represents one or more operations that may be performed by various elements or modules of the example systems and apparatuses described herein with reference to <FIG>, <FIG>, and <FIG>.

In an embodiment, the method starts with a step <NUM> wherein a DP (e.g. <NUM> or <NUM>) obtains a temporal sequence of digital measurements (e.g. <NUM>, or <NUM>) of a first optical signal (e.g. <NUM> or <NUM>) received by the COR from an optical fiber link (e.g. <NUM> or <NUM>). At step <NUM>, the DP estimates a cross-correlation (e.g. <NUM>) between the sequence of digital measurements and a temporal sequence of power values of a second optical signal for a plurality of relative time shifts (e.g. <NUM>) between the sequences, the second and first and second optical signals being in different frequency channels on the optical fiber link, each of the digital measurements representing a phase distortion ϕi of the received first optical signal at a corresponding time instance ti, e.g. a sampling time. At step <NUM>, the DP identifies a location along the optical fiber link as having a physical change in response to determining that a difference between the estimated cross correlation and a reference cross-correlation has a magnitude greater than a fixed value for one of the relative time shifts.

According to the method, the first optical signal co-propagated with a second optical signal along a length of the optical fiber link, the second optical signal being power-modulated and shifted in optical frequency from the first optical signal. In an embodiment, the first optical signal may be processed, e.g. at step <NUM>, to output streams of phase distortion samples for the first optical signal. In some embodiments the processing at step <NUM> may be performed at least in part by a DSP of a COR, e.g. the DSP <NUM> of COR <NUM>. In some embodiments the processing at step <NUM> may be performed in part off-line by a separate DP, e.g. the DP <NUM> or <NUM>, which may be either co-located with the COR or remote from the COR. Furthermore, embodiments may be envisioned in which an approximate removal of the transmitter-related phase modulation component from the phase sampling measurements may be performed by the DSP of the COR without an explicit subtraction of phase decisions, e.g. for QPSK signals.

The processing at step <NUM> may include using a cross-correlation estimator, e.g. <NUM>, to determine a pattern of XPMs of the first optical signal by the second optical signal, e.g. in the form of the cross-correlation cn. In some embodiments, the cross-correlation may be analyzed as a function of the symbol lag index n, between the first and second signals along the length of the optical fiber link. In some embodiments, the processing at step <NUM> may further include computing a cPSD periodogram followed by an IFFT processing, e.g. as described above with reference to <FIG>.

In some embodiments, step <NUM> may include subtracting Cn from a reference CnRef (i.e., calculated for the line without anomalies) to compute an (anomaly) indicator vector Δn=[Cn-CnRef]. Some embodiments may include identifying time lags τn for which the corresponding anomaly indicator Δn is outside of a pre-determined range (-Δ1n, Δ2n) of normal operation. In some embodiments, peaks (i.e., local maxima) of the anomaly indicator calculated in step <NUM> are identified, e.g., using a suitable peak detection algorithm and/or threshold crossing method. The time lags τn corresponding to these peaks are then mapped into the detected positions of the anomalies along the length of the optical fiber link based on the time lag index n thereof, e.g. as described above. In other embodiments, the anomaly indicator vector may be provided to an artificial intelligence algorithm which is trained to distinguish between anomalies of different types and/or detects anomaly amplitudes.

Some features of the cross-correlation method described above may be qualitatively illustrated with reference to <FIG>, which shows an application of the method to detect a CD anomaly for a numerical model of an optical fiber link. In the simulations, the optical fiber link had <NUM> spans of SMF optical fibers, each span being <NUM> long; the optical fibers had an attenuation of <NUM> dB/km and a nonlinear coefficient of <NUM><NUM>/W/km. The transmission of <NUM> WDM channels, spaced <NUM>, modulated with 16QAM at <NUM> Gbaud each, was simulated using the split-step Fourier method. The vertical axis shows the difference between the tensor Xkkii, as estimated using the cross-correlation processing described above, and its value without the dispersion anomaly, according to the simulations. The horizontal axis shows the distance from the beginning of the link, expressed in terms of the propagation time lag, in symbol intervals, between the colliding pulses of the CUT and the probe channel; the further away from the beginning of the link, the proportionally larger is the propagation time lag. The dispersion anomaly is represented by having an NZDSF fiber with a different dispersion coefficient, i.e., <NUM> ps/nm/km, in a single fiber span of the <NUM>-span SMF link. The CUT is the central, i.e., <NUM>th, of the <NUM> WDM channels simulated, the second (probe) channel is the 12th WDM channel, corresponding to Δf<NUM> = <NUM>. The cross-correlation of the phase distortion signal, coherently detected and sampled at the end of optical fiber link using the data processing described above with reference to <FIG>, and a power modulation pattern of the probe channel signal, was computed using averaging over <NUM> randomly seeded signal blocks of <NUM> symbols each. The noise floor visible in <FIG> can be reduced by increasing the number of observation blocks. The different peaks in <FIG> correspond to different positions of the anomalous fiber in the link.

The spatial resolution of the method depends on the frequency spacing between the CUT and probe channels, and on the amount of the CD accumulated by the colliding pulses. For a set value of the frequency spacing Δf<NUM>, the spatial resolution of the method is better at the beginning of the optical fiber link, i.e. at smaller distances from the source COT, because of the smaller CD-induced broadening of the pulses, and correspondingly smaller length of the collision region; this is illustrated e.g. by the narrower peaks in <FIG> near the beginning of the link.

To increase the spatial resolution, some embodiments of the method <NUM> may exploit optical signals traveling both in the forward and in the backward direction along the same optical fiber link, such that the anomaly detection is performed at the two link-end of the CUT connection. In this way, the spatial resolution of the method may be suitably high at both ends of the link. In some embodiments of the method <NUM>, one or both of the first and second optical signals may be dispersion pre-compensated before entering the optical fiber link, e.g. at the COT <NUM> or <NUM>, e.g. by adding a suitable amount of frequency chirp to the signal. The dispersion pre-compensation may be done either in the electrical domain, e.g. by adding a linear frequency chirp to the modulation signal using an electrical-domain dispersion pre-compensator, or in optical domain, e.g. by using a suitable length of dispersion compensation fiber. In some embodiments, the amount of the dispersion pre-compensation may be selected so that the CD accumulated by the optical signal is zero at a given coordinate of the optical fiber link, as illustrated in <FIG>.

The example embodiments described above are not intended to be limiting, and many variations will become apparent to a skilled reader having the benefit of the present disclosure. For example, the data rates in the CUT and probe channels may be different. Furthermore in the description above, for purposes of explanation and not limitation, specific details are set forth such as particular architectures, interfaces, techniques, etc. in order to provide a thorough understanding of the present invention. In some instances, detailed descriptions of well-known devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail. Thus, for example, it will be appreciated by those skilled in the art that block diagrams herein can represent conceptual views of illustrative circuitry embodying the principles of the technology. All statements herein reciting principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof.

Claim 1:
An apparatus comprising:
a digital processor, DP, (<NUM>) being configured to obtain a temporal sequence of digital measurements (<NUM>) of a first optical signal (<NUM>) and a temporal sequence of powers of a power-modulated second optical signal, both received by a coherent optical receiver, COR, (<NUM>) from an optical fiber link (<NUM>) and being configured to estimate a cross-correlation between the temporal sequence of digital measurements and the temporal sequence of powers of the power-modulated second optical signal for a plurality of relative time shifts between the sequences, the first and second optical signals having been transmitted to the COR via the optical fiber link in different frequency channels, each of the digital measurements representing a phase distortion of the received first optical signal at a corresponding time; and
wherein the DP is configured to identify a location along the optical fiber link as having a physical change in response to a magnitude of a difference between the estimated cross correlation and a reference cross-correlation being greater than a fixed value for one of the relative time shifts; and
wherein the DP is configured to estimate the location of the physical change from the value of the one of the relative time shifts.