METHOD OF COMPENSATING OPTICAL SIGNAL DISTORTIONS
DUE TO NON-LINEAR EFFECTS OF AN OPTICAL COMMUNICATIONS
SYSTEM AND COMPENSATION SYSTEM THEREFOR
TECHNICAL FIELD
The present invention relates to optical communications systems, and in particular to electrical
domain compensation of Four Wave Mixing, SPM, XPM and optical cross-talk in an optical
commimications system.
BACKGROUND OF THE INVENTION
Optical communications systems typically include a pair of network nodes connected by an
optical waveguide (i.e., fiber) link. Within each network node, communications signals are converted
into electrical signals for signal regeneration and/or routing, and converted into optical signals for
transmission through an optical link to another node. The optical link between the network nodes is
typically made up of multiple concatenated optical components, including one or more (and possibly 20
or more) optical fiber spans (e.g., of 40-150 km in length) interconnected by optical amplifiers.
In modem optical commimications networks, it is generally desirable to transmit optical signals
at high power levels in order to maintain sufficient signal to noise ratios over extended transmission
distances, and thereby obtain an acceptably low Bit Error Rate (BER) in a received optical signal.
However, conventional optical fibres comprise an optical transmission medium which exhibits
nonlinear effects at high optical power levels, resulting in degradation of the optical signal. These
nonlinear effects are generally a function of optical power, and so any increase in transmission power
level tends to increase signal degradations due to system nonlinearities. Nonlinear effects may
similarly occur within optical terminals of the system, in optical transmission media or in components
such as optical amplifiers. The optimum power level at which optical signals can be transmitted is
typically the maximum power level at which significant degradation due to nonlinearity is avoided.
Since the performance of various optical components within the system varies with operating
conditions, age, and component replacement, a safety margin is used in setting the maximum
power level. Consequently, optical communications systems typically operate at power levels
which are less than the optimum powo: level. A detailed discussion of nonlinear optical
effects is provided by Agrawal, Govind P., "Nonlinear Fiber Optics", 2"**. Ed.,
Academic Press, Inc., San thego, CA, 1995 (ISBN 0-12-045142-5).
Of particular concern in considering nonlinear processes are the effects of
phase nonlinearities, which increase as data rates and optical powor levels increase, and
which ultimately limit botii system performance and signal reach.
Phase nonlinearities are the result of complex interactions between the
optical power present in the fiber, the refiractive index of the fiber medium, the
waveloigth-division-multiplexing (WDM) chaimel spacing, the polarization states of
the signals within each of the channels, and the proximity of chaimel wavelengths to the
zero-dispersion wavelength of the fiber. Phase nonlinearities include self-phase
modulation (SPM), cross-phase modulation (XPM), and modulation-instability (MI), aU
of which are discussed in detail in Agrawal (supra), at chapters 4 and 7.
As shown in Fig. la, a conventional optical communications system may
conveniently be represented by a transmitter 2 and a receiver 6 separated by an optical
link 4. As is well known in the art, the link 4 may include multiple optical fiber spans
sqjarated by active optical devices such as, for example, optical amplifiers, channel
equalizers etc. For simplicity of illustration, these elements are not shown in the
drawings. Signal distortions due to non-linear effects, including Self Phase Modulation
(SPM), cross-phase modulation (XPM), Modulation instability (MI) and four-wave
mixing impressed on optical signals traversing the link 4 are represented (that is,
approximated) by a tlink complex nonlinear operator T[E(t)]; where T[] is the operator,
and E(t) is any optical signal. Known methods such as Voltarra Series can be used to
represent the link operator T[E(t)]. See, for Example, Voltarra and Wiener, "Theories
of Non-Linear Systems", Martin & Schetzen, John Wiley & Sons., 1980. This link
operator T[E(t)]t can be derived using known methods, such as, for example, as
discussed in detail in Agrawal (supra). T[E(t)] can encompass one-to-one non-linear
effects, in which an optical signal in one channel suffers distortions due to itself; many-
to-one non-linear effects, in which an optical signal in one channel suffers distortions
due to optical signals in two or more channels; and many-to-many non-linear effects, in
which optical signals in many charmels suffer distortions due to optical signals in many
channels. For the sake of sinq)licity, the present invention is described by reference to
embodiments that concentrate on compensation of one-to-one non-linear effects, it
being understood that the same principles may be applied to many-to-one and many-to-
many non-linear effects, without departing fix>m the scope of the present invention.
Linear Cross-talk is an artefact of the finite bandwidth of channel filters used to
demultiplex closely spaced channels of a WDM signal arriving at the receiver 6 through
the link 4. This finite bandwidth results in some optical signal power in one channel
"leaking" through the filters of adjacmt channels. Non-linear cross-talk occurs through
mechanisms such as 4-wave mixing and XPM, as discussed in detail in Agrawal
(supra)t
In operation, a coromunication signal (or bit-stream) in the form of an
electrical i]:q)ut signal x(t) 8 is convoted into a corresponding optical signal EiN(t) 10 by
a conventional Electrical-to-Optical (E/0) converter 12. The optical signal EiN(t) is then
multiplexed into a WDM signal 14 by a conventional channel multiplexer 16. As the
WDM signal 14 traverses the optical link 4, it is distorted by the complex nonlinear link
operator T[\, and arrives at the receiver 6 as adistorted WDM signal I4a. Within the
receiver 6, a received optical channel signal EouT(t)[=T[EiN(t)]] 18 is demultiplexed
fixjm the distorted WDM signal 14a by a conventional demultiplexer 20 and converted
into a corresponding electrical output signal y(t) 22 by a conventional
Optical-to-Electrical (O/E) converter 24.
Various methods have been proposed for compensating non-linearities
within an optical communications system. These systems typically operate by inserting
one or more compensators within the link 4, represented in FIG. lb by the compensation
operator C[E(t)], where C[] is the operator and E(t) is any input optical signal. The
compensation operator C[E(t)] is selected to optimize perfonnance of the link 4.
Ideally, the compensation operator C[E(t)] is equivalent to the inverse of the link
operator T[E(t)], in which case T[C[E(t)]]=E(t), and the combined effect of T[] and C[]
would be an undistorted received signal EouT(t)=T[C[EiN(t)]] that exactly corresponds
to the original optical signal EiN(t).
For example, co-assigned United States Patent No. 6,124,960, entitled
Transmission System with Cross-Phase Modulation Compensation, which issued on
September 26,2000, describes a WDM transmission system carrying amplitude
modulated traffic in which significant cross-phase modulation occurs. In this case, the
compensation operator C[E(t)] is provided by "pre-chirping" each of the individual
optical channels at the transmittw (that is, u{)stream of the channel MUX) with replicas,
or low-pass filtered rq)licas of the amplitude modulation applied to each of the other
channels. Pre-chirping of a channel in this manner in]|>oses a chirp (or firequency shift)
that is approximately equal and opposite to the XPM-induced chirp of tiie fiber link.
Pre-chirping of each individual channel with a replica of the amplitude modulation
applied to that same channel may also be used in order to provide comp«isation for
self-phase modulation (SPM).
A limitation of this technique is that the pre-chirp is imposed as a discrete
step prior to MUXing each channel mto the optical fiber link 4. However, within the
link 4, XPM (and SPM) induced chirp, and the associated time-domain signal
distortions are distributed effects, in that they are a function of dispersion and link
length. Consequently, while this technique facilitates compensation of XPM and
SPM-induced firequency-domain signal distortions, it is not capable of fully
compensating the associated time-domain distortions.
In co-assigned United States Patent No. 6,067,180, entitled Equalization,
Pulse Shaping and Regeneration of Optical Signals, which issued on May 23,2000, the
compensation operator C[E(t)] is provided by optical modulators that can be used at the
receiver 6 to remove optical distortions (including SPM and XPM) firom an inbound
optical signal. A Umitation of this approach is that the optical modulators tend to be
complex, and thus expensive, and suffer high insertion losses. This latter issue reduces
the desirability of these modulators in long-haul optical network links, in which the
optical signal arriving at the receiver already have a low signal-to-noise ratio.
A technique for fully compensating effects of chromatic dispersion
(including SPM) is described in "Exact Compensation for Both Chromatic Dispersion
and Kerr Effect in a Transmission Fiber Using Optical Phase Conjugation" (Watanabe,
S., et al.. Journal of Lightwave Technology, Vol. 14, No. 3, March 1996, pp 243-248).
In this technique, the optical fiber link is divided into two fiber sections separated by an
Optical Phase Conjugator. The first section is designed as a highly dispersive medium,
in which the dispersion is designed to mirror that of the second section. As a result,
signal distortions imressed on an optical signal propagating through the first section
will be offset by those of the second section. In effect, the compensation operator
C[£(t)] is provided by the dispersion profile of the first section, and the optical phase
conjugator. Theoretically, if the dispersion profile of the first section can be made to
exactly mirror that of the second section, then the compensation operator C[E(t)] will
be the inverse of the non-linear operator T, and a substantially undistorted signal
EouKO '•'EiNCt) will appear at the receiver-end of the optical fiber link.
This technique suffers numerous disadvantages. In particular, the first span
must be designed so that the dispersion profile (along the length of the first section)
closely mirrors the dispersion profile of the second section. This means that the first
section must be uniquely designed for its corresponding second span, which
dramatically increases costs. Finthermore, known optical phase conjugators are
expensive, attenuate the optical signal, and introduce noise. Theoretically, the optical
phase conjugator may be eliminated by designing the first section such that both the
power and dispersion profiles of the first section mirror those of the second section.
However, this solution is extremely difficult to implement in the optical domain,
because mirroring of the power profile of the second section requires that the first
section be provided witli fiber spans with gain, and amplifiers with loss.
Accordingly, a cost-effective technique for mitigating the signal distortions
due to non-linear effects in a WDM optical conununications system remains highly
desirable.
SUMMARY OF THE INVENTION
An object of the present invention is to provide a method and apparatus for
at least partially compensating signal distortions due to non-linear effects in a WDM
optical conununications system.
This object is met by the features of the invention defined in the appended
independent claims. Additional optional features of the invention are defined in the
dependent claims.
Accordingly, an aspect of the present invention provides a method of compensating optical
signal distortions due to nonlinear effects of an optical communications system. According to the
present invention, a complex non-linear compensation operator is determined that is the inverse of a
link complex non-linear operator representing at least one nonlinearity-induced signal distortion
imparted to a communications signal traversing the optical communications system. An electrical input
signal is then digitally processed using the compensation operator to generate a predistorted electrical
signal. This predistorted electrical signal is then used to modulate an optical source to generate a
corresponding predistorted optical signal for transmission through the optical communications system.
In general, the compensation operator is the inverse of the optical link complex nonlinear
operator T[]. Consequently, as the predistorted optical signal propagates through the optical link, the
optical nonlinearities of the link operate on the predistorted optical signal such that the optical signal
arriving at the receiving end of the link is substantially free of non-linearity-induced distortions.
Thus the method of the invention implements compensation of optical nonlinearity-induced
signal distortions at the transmitter end of the optical link, prior to Electrical-to-Optical (E/0)
conversion of the input signal. This arrangement is particularly advantageous, because it enables
compensation to be effectively implemented independently of the type of detection (i.e., direct or
coherent) used in the receiver.
The present invention compensates nonlinearity-induced signal distortions by processing a
communications signal in the electrical domain prior to transmission through an optical link of a
communications system. This processing of the communications signal is governed in accordance with
a compensation function that is the inverse of the optical link transfer function. With this arrangement,
arbitrary nonlinearity-induced signal distortions imparted by the optical link can be compensated in
such a manner that a comparatively undistorted optical signal is obtained at the receiving end of the
optical link.

BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWING
Further features and advantages of the present invention will become
appaioit from the following detailed description, taken in combination with the
appended drawings, in which:
Figs, la and lb are block diagrams schematically illustrating operations of a
conventional optical commimications system;
FIG. 2 is a block diagram schematically illustrating principal elements and
operations of a compensation system in accordance with an embodiment of the present
invention;
FIG. 3 is a block diagram schematically illustrating principal elements and
operations of a first compensation processor usable in the embodiment of FIG. 2;
FIG. 4 is a block diagram schematically illustrating principal elements and
operations of a second compensation processor usable in the embodiment of FIG. 2;
FIGs. 5a-5c are block diagrams schematically illustrating respective
alternative embodiments of the digital filter of FIGs. 3 and 4;
FIG. 6 is a block diagram schematically illustrating principal elements and
operations of a third compensation processor usable in the embodiment of FIG. 2; and
FIG. 7 is a block diagram schematically illustrating principle elements and
operations of a compensation system in accordance with an alternative embodiment of
the present invention.
It will be noted that throughout the appended drawings, like features are
identified by like reference numerals.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
The present invention provides a method and system for compensation of
non-linear and cross channel efTects in an optical communications system. For the
purposes of the present invention, "non-linear and cross-channel effects" shall be
understood to refer to signal distortions due to phase non-linearities, such as Self Phase

Modulation (SPM), cross-phase modulation (XPM), Modulation instability (MI) and
four-wave mixing. "Cross-channel effects" shall be understood to refer to signal
distortions due to optical cross-talk. Fig. 2 is a block diagram schematically illustrating
principal elements and operations of a condensation system in accordance with the
method of the present invention.
In accordance with the present invention, signal distortions due to the link
complex non-linear operator T[E(t)] are at least partially compensated by deriving a
con4)ensation operator C[E(t)] that optimizes the performance of the link 4, and then
piedistorting the ii^ut signal x(t), in the electrical domain, iising the detemiined
compensation operator C[E(t)]. Because the link operator T[E(t)] is complex, the
con^>ensation operator C[E(t)] will also be complex.
In order to provide compoisation for one-to-one, many-to-one, and many-to-
many non-linear effects in a wavelength division multiplexed (WDM) system, it is
convenient to consider all of the channel signals together using vector notation. Thus all
of the channel input signals can be referenced collectively as an input vector

where x(t,Ci)0 is the input signal for the ith WDM channel. Similar notation can be used
across the entire link 4. Thus, for example, the WDM signal can be represented as a
vector:

where is the optical chaimel signal for the ith WDM channel. Following this
notation for referencing all of the chaimels together, the link complex non-linear
operator T[E(t)] and the compensation operator C[E(t)] will both be matrix operators.
Many-to-one and many-to-many effects can then be readily approximated by computing
appropriate values for each element of the link complex non-linear operator T[E(t)], and
the compensation operator C[E(t)] can, for example, be deiived by calculating the
inverse of the link complex non-linear operator T[E(t)]. In order to simplify the
description of the present invention, the following description will focus on a single
channel. In this case, vector and matrix notation can be avoided, and the channel
identifier omitted, for the sake of brevity. Those of ordinary skill in the art will
appreciate that this description applies directly to the case of one-to-one non-linear
effects (e.g. self-phase modulation), and can be readily extended to cover many-to-one
and many-to-many non-linear effects by reverting to vector and matrix notation and
methods to treat all of the channels togetho:.
As shown in FIG. 2, a compensation processor 26 uses the compensation
operator C[E(t)] to process each channel input signal x(t)8, thereby producing a
corresponding predistorted electrical input signal x^(t) 28. The predistorted iiq)ut signal
x'(t) 28 is tibien converted into a corresponding predistorted optical signal E^iN(t) 10a by
the E/0 converter 12, multiplexed into a WDM signal 14 and transmitted through the
optical link4 to the received. Matiiematically, the predistorted optical signal
E'iN(t) 10a can be related to the (undistorted) channel optical signal £iN(t) 10 generated
by the E/O converter 12 in the conventional system of FIG. 1 as E]ff(t) = C[Ej^(t)].
Within the receiver 6, a conventional demultiplexer 20 DEMUXs the
incoming optical signal E^oirKt) 18a firom the WDM signal 14 traversing the link 4.
The Optical-to-electrical (0/E) converter 24 then converts the optical signal
E'ouT(t) 18a into a corresponding output signal y*(t) 22a. As may be seen in Fig. 2, the
received optical signal E^oirKt) 18a is the predistorted optical signal E'iN(t,Wi) 10a
modified by the link non-linear operator T[E(t)], thus:
^ot/r (0 = T[Em(t)] = r[C[^^(0]] (Eq. 1)
As may be appreciated, when the distortions introduced by the compensation operator
C[E(t)] exactly counterbalance those introduced by the link non-linear operator T[E(t)],
the received optical signal E'ourCt) 18a "seen" by the 0/E converter 24 will be
substantially identical to the original (undistorted) optical signal EiN(t) 10 (FIGs. la
and lb).
If desired, the link non-linear operator T[E(t)] may include non-linear effects
of the multiplexer 16 and demultiplexers 20 (such as cross-talk), as well as non-
linearities of the E/O and 0/E converters 12 and 24. In this case the compensation
operator C[E(t)] will also provide effective compensation of these effects as well.
Thus the present invention provides a technique for compensating distortions
impressed upon an optical signal traversing the link 4, by predistorting the origmal input
signal x(t) 8, in the electrical domain, prior to E/0 conversion and transmission through
the optical link 4. Because distortion compoisation is accomplished in the electrical
domain, a substantially arbitrary compmsation operator C[E(t)] can be implemented,
thereby facilitating effective compensation of even comparatively severe non-linear and
cross-channel effects.
As may be ^>preciated, the compensation operator C[E(t)] can be formulated
in various ways. Typically, the compensation operator C[E(t)] will be formulated as the
inverse of the link operator T[E(t)], such thatT[C[E(t)]] «€(t). hi this case, the
compensation operator C[E(t)] will contain the same terms as the link operator T[E(t)],
and "determination" of the compensation operator C[E(t)] in order to faciUtate electrical
domain predistortion of the iiq)ut signal x(t) 8, becomes a matter of determining
magnitudes of each term of C[E(t)].
It may be noted that extreme non-linear and cross-channel effects can be
imagined for which a practical solution for the compensation operator C[E(t)] will not
be possible. Furthermore, it should be appreciated that the extent or degree of
compensation will be inherently limited by the formulation of the compensation
operator C[E(t)] implemented in the compensation processor 26. For example, consider
a case in which the compensation operator C[E(t)] is formulated to only compensate
SPM. While parameters of this compensation operator C[E(t)] can be determined such
that SPM is exactly compensated, signal distortions due to other effects of the link (such
as XPM, MI, four-wave mixing and cross-talk) will remain imcompensated.
Accordingly, for the purposes of the present disclosure, references to "compensation of
non-linear and cross-chaimel effects" should be understood to refer to those effects that
are accounted for by the chosen formulation of the compensation operator C[E(t)].
Similarly, references to a "substantially undistorted optical signal" being obtained at a
receiving end of ttie link 4, as a result of non-linear and cross-channel effects of the
link 4 operating on the predistorted optical signal E^iN(t) 10a, should be understood to
mean that the received optical signal E^ourCt) 18a is substantially free of signal
distortions due to those effects that are compensated by the specific formulation of the
compensation operator C[E(t)] being used in that embodiment.
Various methods may be used to determine the compensation operator
C[E(t)]. In the example of Fig. 2, the WDM signal 14 and optical signal E'ouKO 18a at
or near the receiver 6 is monitored (at 30) in order to detect signal quality parameters
indicative of non-linear and cross-channel effects of the optical link 4. In preferred
embodiments, the signal quality parameters comprise direct measurements of SPM,
XPM, MI, foinr-wave mixing and cross-talk across the wavelengdi band of interest
Methods of measuring SPM, XPM, MI, four-wave mixing and cross-talk are known in
the art Methods for measuring these parameters in installed networks are disclosed in,
for exanq)le. United States Patrat Nos. 6,128,111 (Roberts et al.), and co-assigned and
co-pending US patoit application No. 10/xxx,xxx, entitled Monitoring Phase
Non-Linearities In An Optical Communications System. Thus, for example, XPM
between a pair of chaimels can be measured by laimching a probe signal through a jQrst
channel, while a data signal ED(t) is simultaneously transmitted through the other
channel. As the two signals co-propagate through the link 4, XPM betwe^i channels A
and N generates a test signal which is received, by the receiving node 4b, through
channel N. Correlation between the received probe and test signals enables computation
of an XPM transfer function, which models XPM-induced signal distortions impressed
on signal traffic traversing the link.
In many cases, SPM can be described as a function of XPM, because the
mechanisms involved in producing both XPM and SPM are related. Consequently, for
any particular optical communications system, a look-up table can be defined for
estimating SPM from the detected XPM. The data used to populate the look-up table
may, for example, be based on experimental data obtained during the set-up and
commissioning of the optical commimications system. If desired, the look-up table data
may be updated, e.g., using fresh experimental data obtained during maintenance of the
optical communications system to accommodate migration of the optical component
performance.
Alternatively, a data signal arriving at the receiving node can be monitored
to detect variations in signal noise with dispersion. This provides a direct indication of
total XPM- and SPM-induced signal distortions, but does not enable these effects to be
separated.
Some optical networidng equipment utilize high-speed Aaalog-to-Digital
Converters (ADCs) to convert recdved data traffic into corresponding digital signals for
data recoveiry and system management The sample rate of these ADCs can be chosen
to satisfy Nyquist's theorem for the received signal traffic, which means that the
complete received signal waveform can be recovered fix>m the digital data stream
produced by the ADC. Conventional data recovery circuits, such as digital equalizers
and Forward Error Correction circuits can then be used to recover data bits fix>m the
digital data stream. With this arrangement, it is possible to store sample data in fho
form of a sequential series of digital samples of the digital data stream produced by the
ADC. This sample data can be correlated with the corresponding data bits recovered by
the receiver's data recovery circuits. Comparison between the signal waveform (as
represented by the stored ADC output) and the corresponding recovered data bits
provides a direct measure of signal distortions, and can be used to directly compute the
complex transfer function due to dispersion and SPM. Comparison between the signal
waveforms (as represented by the respective stored ADC outputs) of adjacent channels
provides a direct indication of cross-channel effects, such as crosstalk.
The above-noted methods can be used, either alone or in combination, to
evaluate phase non-linearities and cross-channel effects within the link 4. This
information can then be used to determine the compensation operator C[E(t)], using
known methods.
Other signal quality parameters such as, for example, the bit error rate,
signal-to-noise S/N ratio, variance of the signal dispersion or eye closure may be used as
proxies for the non-linear and cross-channel efifects. Any of the signal quality
parameters may be detected based on an optical signal obtained by tapping the WDM
signal 14 within optical link 4 (as shown at 32), the demultiplexed optical channel signal
E'ouT(t) (at 34), and/or by analysis of the output signal yl(t) 22a generated by the E/0
converter 24 (as shown at 36). A compensation operator C[E(t)] which optimizes the
detected parameters can then be determined (at 38) deterministically and/or adaptively,
using known techniques.
Other methods may be used to determine the compensation operator C[E(t)].
For example. United States Patent No. 6,124,960 (Garth at al) teaches a method of
coxoputing the transfer function due to XPM between any pair of wavelengths in a
WDM system. This XPM transfer function can be used to determine ^propiiate
component values of the compensation operator C[E(t)] to compensate XPM.
Alternatively, the compensation operator C[E(t)] could be confuted by
simulating the optical performance of a hypothetical mirror image of the optical link 4,
using known methods of computing optical fiber nonlinear propagation, such as
split-step Fourier. In this case, the link 4 is described by y(z) = fP{z), where y is the
coefficient of non-linearity and P(z) is the power profile along the link. Define z=L/2 as
the beginning of the link 4 and z=L as the end of the link. A hypothetical mirror image
of the link 4 is then defined for 0 SS: ^L/2 and has the property that /(z) = y{L - z). The
predistorted signal x'(t) is then calculated using mid-span spectral inversion, that is, by
propagating the input signal x(t) from 2r=0 to 7r=U2 using tiie pulse propagation
equation, and then phase conjugating the result. The parameters needed for this
computation are the fiber losses, fiber types, signal power levels, EDFA or Raman
amplification, and dispersion for each fiber span and amplifier of the link 4. These
values could be measured before (or during) system installation, or may be measured by
the system using, for example, the methods of United States Patent No. 5,513,029 to
measure power levels; United States Patent No. 6,252,692 to measure dispersion. United
States Patent Application No. 09/481,691 to determine the fiber type. United States
Patent Application No. 09/852,777 to measure distributed Raman amplification, and
United States Patent Application No. 09/975,985 to measure the PDL.
It should be noted that the fimctional step of determining the compensation
operator C[E(t)] (at 38) can be implemented by any suitable combination of hardware
and software, which may be co-located with the receiver 6, the transmitter 2, or any
other location. In embodiments in which the detected parameters comprise direct
measurement of non-linearities, or calculation of an associated transfer function, the
compensation operator C[E(t)] can be calculated to minimize (and preferably eliminate)
the total non-linearity-induced signal distortion. Where bit error rate and/or eye closure
are used as proxies, then the compensation operator C[E(t)] would be calculated to
optimize these respective values.
As mentioiied above, because the link operator T[E(t)] is complex, the
coinpensation operator will also be compile. In this case, the E/O converter 12 must be
designed in such a manner that differential phase delays can be impressed onto an
outgoing optical signal, in addition to amplitude information of the ii^ut signal x(t) 8.
Various known E/O converters are capable of providing this functionality. In the
embodiment of FIG. 3, the E/O converter 12 is provided as a tuned optical source 40
such as a nairow band laser coupled to a 2-Dimensional optical modulator 42. With this
arrangement, the 2-D modulator 42 can be driven to modulate the amplitude and phase
delay of the optical source 40 ou^ut to generate the predistorted optical signal EV(t)
10a. Various known 2-D optical modulators capable of providing this functionality are
known in the art, such as, for example, Mach-Zehnder modulators.
In general, the design of the compensation processor 26 will be driven by the
formulation of the compensation operator C[E(t)] and the requirement that the
predistorted signal x\t) 28 must be formatted to provide suitable control signals for the
E/O converter 12. In the embodiment of FIG. 3 the 2-D modulator 42 is controlled by a
respective pair of orthogonal Oe table 62 contains at least one digital value
representing a corresponding instantaneous analog level of the respective componmt
(44, 46) of the predistorted signal x\t) 28, which has been previously calculated for a
unique set of N bits. Accordingly, as the (serial) irput signal x(t) 8 is latched through
the serial-to-parallel converter 64, a stream of successive digital values 52 of the
predistorted signal 28 are ou^ut from the look-up table 62.' This stream of digital
values 52 can then be converted into the corresponding analog signal component 44,46
using the digital-to-analog converter 54. The analog predistorted signal x*(t) 28 can
then be converted into the corresponding predistorted optical signal E*iN(t) 10a by
optical converter 12, as described above.
Because phase nonlineaiities cause time domain distortions of the optical
input signal E(N(t), the instantaneous level of the analog predistorted input signal
x^(t) 28 at a particular instant (t) will necessarily be a function of the analog waveform
of the ii^ut signal x(t) within a time window that brackets the instant in question. The
width of the time window, measured in symbols, will generally be a function of the
maximum dispersion for which compensation is to be provided; the bandwidth of the
optical signal; and the symbol interval of the optical signal.
Following the discussion above, it will be seen that each value stored in the
look-up table 62 can readily be calculated (at 66) by applying the calculated
compensation operator C[E(t)] to each one of the 2*^ possible N-bit sequences. For each
N-bit sequence, the calculated look-up table value would then be stored in the RAM
look-up table 62 register that is indexed by the N-bit sequence in question. This process
will result in the look-up table 62 being loaded with pre-calculated values of the
predistorted signal 28 which will be accessed, in sequence, as successive bits of the
input data signal x(t) are latched through the serial-to-parallel converter 64.
In order to enable accurate generation of the analog signal component 44,46
by the DAC 54, the rate at which digital values 52 are output from the RAM LUT 62
should preferably satisfy Nyquist's Theorem for the iapvA signal x(t) 8, including the
effects of spectral regrowth. This will normally require that the RAM LUT 62 output
more than one digital value 52 of the predistorted signal 28 compon^t for each symbol
of the input signal x(t). Thus; for example, digital values 52 can be latched out of the
RAM LUT 62 at a clock speed that is two or more times the data-rate of the input signal
x(t) 8. This can readily be accomplished by calculating (at 66) the required set of digital
values for each N-bit sequence, and storing the resulting set of digital values in the
appropriate register. Consequently, as each bit of the iiq>ut signal x(t) is latched through
the SPC 64, all of the digital values calculated for each unique N-bit sequence will be
ou^ut, in the appropriate sequence, from the RAM LUT 62.
As mentioned above, in the embodiment of FIG. 5a, N=8, meaning that the
system can compensate time domain distortions spanning at most 8 s>anbols. For
long-haul optical links, distortion compoisation spanning a far greater number of
symbols (e.g., up to 76, or more) may be required. In principle, the RAM LUT 62 and
SPC 64 can be expanded as required to span any desired number of symbols. However,
as N increases, the size of the R AM LUT grows exponentially (since a RAM contains
2^ registers) with the result that manufacturing costs of the RAM LUT 62 begin to
impose serious penalties. These limitations can be avoided by using a linearizing
approximation and dividing the RAM LUT 62 into a series of two or more smaller
RAMs 68, as shown in FIG. 5b. In this case, each RAM 68 stores a respective portion
of the desired numerical value(s) 52 of the predistorted signal component x'(t) 28. The
outputs from each RAM 68 are digitally summed (at 70), in a conventional manner, to
produce a numerical value 52 that is an acceptable qjproximation of the "ideal" value
generated by the singular RAM LUT 62 of FIG. FIG. 5a. This arrangement enables the
digital filter 50 to provide effective distortion compensation spanning virtually any
desired number of symbols, simply by providing a suitable number of RAMs 68.
For many practical optical link topologies, signal variations due to non-linear
effects are concentrated within the center portion of the compensation window. Toward
the extreme ends of the compensation window, signal walk-off tends to randomize
variations due to non-linear effects, such that these variations tend to become
indistinguishable from linear noise. This provides an opportunity for reducing the size
and complexity of the RAM LUT 50.
Accordingly, the embodiment of FIG. 5b may be modified by replacing the
RAMs 68b and 68c at the extreme ends of the SPC 64 (e.g., receivmg the first and
last 32 bits) with linear addition trees 72, as shown in FIG. 5c. The HAM 68a lying at
the center of ttie SPC 64 (e.g., to receive the middle 12 bits) is retained, and therefore
enables accurate compensation of non-linear effects in the center portion of the
compensation window. Preferably, the size of the central RAM 68a is maximized. The
respective outputs of the linear addition trees 72 are digitally summed (at 74), and then
digitally added to the output of the center RAM 68a (at 76) to yield a numerical
value 52 that is an acceptable approximation of the "ideal" level of the predistorted
signal 28.
FIG. 6 illustrates principal elements of an alternative embodiment of the
compensation processor 26. This embodiment relies on the fact that the optical
performance of a span of the optical link 4, can be mathematically approximated using
cascaded functions that collectively define a respective span operator Ti[]. Using this
approximation, phase non-linearities of an individual span (i) can be modeled using an
operator Ti[] in the form of non-linear function cascaded with a linear filter function. A
typical non-linear Slter function usable for this purpose is:
where F is a constant; and l^a is the effective length of the non-linearity in the fiber. A
simple linear filter function that may be used is the loss and dispersion of the span. A
simple linear filter function that may be used is:

where G is the gain/loss of the span, and TF(t) is a linear transversal filter which
approximates the dispersion of the span. As will be appreciated, various other known
linear and non-linear functions may be used to approximate the performance of the
span, in a mamier well known in the art.
Using the above mathematical approximations for each span of the link 4,
the compensation processor 26 can be constructed by cascading linear and non-linear
filters to mathematically mirror the cascaded non-linear and linear fimctions of the link
4. Thus each span of the link 4 is represented by a corresponding linear/non-linear filter
pair, which implements the corresponding span compensation operator Q[]. The linear
and non-linear filters are arranged in reverse order, relative to the functions used to
approximate the span, and each filter in^leoients the inverse of its corresponding
fimction, as may be seen in FIG. 6. In this case, Leff of each span is known in advance,
so tiiat, for a span operator Ti[] formed by the non-linear and linear fimctions described
above, derivation of the corresponding span compensation operator Q[] comprises
calculation of the constants FLeff, G, and TF(t) for the span.
In the embodiments described above with reference to FIGs. 1-6, the
compensation processor 26 is located in the transmitter 2, and implements compensation
of phase non-linearities by predistorting the input signal x(t) in the electrical domain,
prior to E/0 conversion and transmission through the link. As may be appreciated,
directly analogous techidques may be used to implement electrical domain
compensation in the receiver 6. FIG. 7 is a block diagram schematically illustrating a
receiver including a compensation processor in accordance with the present invention.
The receiver of FIG. 7 utilizes a four-dimensional coherent receiver capable
of detecting and receiving an incoming optical signal with an arbitrary polarization.
Thus, a polarization beam splitter 78 separates the inbound optical signal EouKt) into
orthogonal polarization modes (denoted as H and V), each of which is sub-divided into
a respective pair of components (denoted as HI, H2, V2 and V2). If desired, however, a
polarization controller (not shown) can be used upstream of the polarization beam
splitter 78, in order to align the polarization of the inbound optical signal EotrKt) to a
principal axis of the polarization beam splitter 78. Respective optical couplers 80 then
mix the optical components H1,H2,V1,V2 with a respective local oscillator signal 82,
and the combined lightwave 84 detected by a conventional photodetector 86. The
resultant Intermediate Frequency (IF) signal 88 is then filtered by a conventional band-
pass filter 90, to generate a corresponding received signal component 92.
As may be seen in FIG. 7, the receiver 6a generates a received signal EouT(t)
in the form of a respective pair 94 of received signal components 92 for each
polarization mode H,V. Each signal pair 94 provides orthogonal (e.g., quadrature)
components of the respective polarization mode H and V, and therefore provides
sufficient infonnation for the reconstruction of the respective polarization mode H and
V of the received signal EouKt). Taken together, the two received signal pairs 94
contain sufficient infonnation for complete reconstruction of the received signal
EouKO, including amplitude, phase, and polarization dependent content
The compensation processor 26 comprises a respective Analog-to Digital
A/D converter 96 for sampling each signal component 92 at the Nyquist frequency
(including spectral regrowth). A digital filter 98 then processes the digital signal
components to generate the (substantially undistorted) output signal y(t) 22. Either of
the methods described above with reference to FIGs. 4 and 6 may be used to Lmplement
the digital filter 98. For the method of FIG. 6, the linear and non-linear filter blocks
need to be suitably reordered, in order to properly mirror the span 4. It is theoretically
possible to design the digital filter 98 to implement the non-linear Schrbdinger equation
and performing a (hypothetical) mid-span spectral inversion. By recalculating the
Schrodinger equation for each successive bit of the output signal y(t) 22, signal
distortions due to phase non-Unearities can be compensated.
The embodiment(s) of the invention described above is(are) intended to be
exemplary only. The scope of the invention is therefore intended to be limited solely by
the scope of the appended claims.
WE CLAIM :
1. A method of compensating optical signal distortions due to nonlinear effects of an optical
communications system, the method comprising steps of:
determining a complex non-linear compensation operator C[(E(t)] that is the inverse of a link
complex non-linear operator T[E(t)] representing at least one nonlinearity-induced signal
distortion imparted to a communications signal E(t) traversing the optical
communications system ;
digitally processing an electrical input signal x(t) using the compensation operator C[(E(t)] to
generate a predistorted electrical signal; and
modulating an optical source using the predistorted electrical signal to generate a
corresponding predistorted optical signal for transmission through the optical
communications system.
2. A method as claimed in claim 1, wherein the step of dete^rmining a compensation operator
comprises steps of:
measuring a performance parameter related to the nonlinearity-induced signal distortion ; and
calculating respective values of each parameter of the compensation operator that optimizes
the measured performance parameter.
3. A method as claimed in claim 2, wherein the step of measuring the performance parameter
comprises a step of measuring at least one of:
cross-phase modulation;
self phase modulation;
modulation instability ; and
cross-talk.
4. A method as claimed in claim 1, wherein the step of digitally processing the electrical input
signal comprises a step of digitally filtering the electrical input signal using either one of:
a Finite Impulse Response (FIR) filter; and
a Look-Up-Table (LUT).
5. A method as claimed in claim 4, wherein the step of digitally processing the electrical input
signal comprises a step of digitally filtering the electrical input signal through a respective pair of
cascaded digital filter blocks associated with each span of the optical communications system.
6. A method as claimed in claim 4, wherein the step of digitally filtering the electrical input signal
comprises steps of:
calculating successive numerical values of the predistorted signal, based on the electrical input
signal and the compensation operator ; and
converting each successive numerical value into a corresponding analog value of the
predistorted signal.
7. A method as claimed in claim 6, wherein the predistorted signal is represented by two or more
orthogonal components, and the step of calculating successive numerical values of the predistorted
signal comprises a step of calculating successive corresponding values of each component.
8. A method as claimed in claim 6, wherein the electrical input signal comprises a substantially
undistorted binary signal, and wherein the step of calculating successive numerical values of the
predistorted signal comprises steps of:
calculating a respective numerical value of the predistorted signal corresponding to each one
of a set of predetermined N-bit sequences ;
storing each calculated numerical value in a look-up table; and
extracting a plurality of successive numerical values of the predistorted signal from the
look-up table using the binary signal.
9. A method as claimed in claim 8, wherein the set of predetermined N-bit sequences encompasses
all possible sequences of N-bits.
10. A method as claimed in claim 8, wherein the step of extracting a plurality of successive
numerical values of the predistorted signal comprises steps of:
converting the binary signal into a series of N-bit words ;
using each N-bit word as an index value to access a respective register of the look-up table.
11. A method as claimed in claim 10, wherein the step of extracting a plurality of successive
numerical values of the predistorted signal comprises a step of extracting at least one numerical value
of the predistorted signal for each N-bit word.
12. A method as claimed in claim 8, wherein the number (N) of bits within each sequence is based
on at least one of:
an expected maximum dispersion of the optical communications system; and
an expected response time of the look-up table.
13. A method as claimed in claim 8, wherein the steps of calculating respective numerical values of
the predistorted signal and storing the calculated numerical values in a look-up table are repeated at
predetermined intervals.
14. A compensation system for compensating optical signal distortions due to nonlinear effects of
an optical communications system, the compensation system comprising :
a processor adapted to determine a complex non-linear compensation operator C[E(t)] that is
the inverse of a link complex non-linear operator T[E(t)] representing at least one
nonlinearity-induced signal distortion imparted to a communications signal E(t)
traversing the optical communications system ;
a compensation processor for modifying an electrical input signal x(t) using the compensation
operator C[(E(t)] to generate a predistorted electrical signal; and
an optical modulator for modulating an optical source using the predistorted electrical signal to
generate a corresponding predistorted optical signal for transmission through the optical
communications system.
15. A system as claimed in claim 14, wherein the processor is implemented remote from the
compensation processor.
16. A system as claimed in claim 14, wherein the processor comprises :
a detector for measuring a performance parameter related to the nonlinearity-induced signal
distortions ; and
a calculation engine for calculating respective values of one or more parameters of the
compensation operator that optimizes the measured performance parameter.
17. A system as claimed in claim 16, wherein the detector is adapted to measure at least one of:
cross-phase modulation;
self phase modulation;
modulation instability; and
cross-talk.
18. A system as claimed in claim 14, wherein the compensation processor comprises :
a digital filter for filtering the electrical input signal using the compensation operator to
generate a series of successive numerical values of the predistorted signal; and
a digital-to-analog converter for converting each successive numerical value into a
corresponding analog value of the predistorted signal.
19. A system as claimed in claim 18, wherein the digital filter comprises a respective pair of
cascaded digital filter blocks associated with each span of the optical communications system.
20. A system as claimed in claim 18, wherein the digital filter comprises at least one of:
a Finite Impulse Response (FIR) filter ; and
a look-up-table.
21. A system as claimed in claim 20, wherein the look-up table comprises :
a serial to parallel converter (SPC) for converting the electrical input signal into a series of
successive N-bit words ; and
a Random Access Memory (RAM) coupled to receive each N-bit word from the SPC, the
RAM being adapted to store a plurality of numerical values of the predistorted signal,
and output a selected one numerical value based on the N-bit word from the SPC.
22. A system as claimed in claim 21, wherein the RAM comprises :
a plurality of parallel RAMs ; and
a digital ADDER for digitally summing the output of each RAM to generate each successive
numerical values of the predistorted signal.
23. A system as claimed in claim 20, wherein the look-up table comprises :
a serial to parallel converter (SPC) for converting the electrical input signal into a series of
successive N-bit words ;
a Random Access Memory (RAM) coupled to receive a center portion of each N-bit word
from the SPC, the RAM being adapted to store a plurality of numerical values of the
predistorted signal, and output a selected one numerical value based on the received
center portion of the N-bit word ;
a respective linear adder tree for digitally summing each end portion of the N-bit word from
the SPC ;
a first digital ADDER for digitally summing the output of each linear adder tree ; and
a second digital ADDER for digitally summing the output of the first digital ADDER and the
RAM to generate each successive numerical value of the predistorted signal.
24. A system as claimed in claim 20, wherein the predistorted signal is represented by two or more
orthogonal components, and the look-up-table comprises a respective look-up-table for generating each
component.
25. A system as claimed in claim 20, wherein at least one numerical value of the predistorted signal
is extracted from the look-up-table for each N-bit word.
26. A system as claimed in claim 20, wherein the number (N) of bits within each N-bit word is
based on any one or more of:
an expected maximum dispersion of the optical communications system; and
an expected response time of the look-up-table.
27. A distortion compensator for compensating optical signal distortions due to nonlinear effects of
an optical communications system, the distortion compensator comprising :
a compensation processor for modifying an electrical input signal using a predetermined
complex non-linear compensation operator C[(E(t)] to generate a predistorted electrical
signal, the compensation operator C[E(t)] being the inverse of a link complex non-linear
operator T[E(t)] representing one or more nonlinearity-induced signal distortions
imparted to a communications signal E(t) as it traverses an optical link of the optical
communications system, such that modulation of an optical source using the predistorted
electrical signal generates a corresponding predistorted optical signal for transmission
through the optical link of the optical communications system to yield a substantially
undistorted optical signal at a receiver end of the optical link.
28. A distortion compensator as claimed in claim 27, wherein the predetermined compensation
operator is calculated to at least partially compensate optical signal distortions due to nonlinear effects
of the optical communications system.
29. A distortion compensator as claimed in claim 27, wherein the compensation processor
comprises :
a digital filter for filtering the electrical input signal using the compensation operator to
generate a series of successive numerical values of the predistorted signal; and
a digital-to-analog converter for converting each successive numerical value into a
corresponding analog value of the predistorted signal.
30. A distortion compensator as claimed in claim 29, wherein the digital filter comprises a
respective pair of cascaded digital filter blocks associated with each span of the optical
communications system.
31. A distortion compensator as claimed in claim 29, wherein the digital filter comprises either one
of:
a Finite Impulse Response (FIR) filter ; and
a look-up-table.
32. A distortion compensator as claimed in claim 31, wherein the look-up table comprises :
a serial to parallel converter (SPC) for converting the electrical input signal into a series of
successive N-bit words ; and
a Random Access Memory (RAM) coupled to receive each N-bit word from the SPC, the
RAM being adapted to store a plurality of numerical values of the predistorted signal,
and output a selected one numerical value based on the N-bit word from the SPC.
33. A distortion compensator as claimed in claim 32, wherein the RAM comprises :
a plurality of parallel RAMs ; and
a digital ADDER for digitally summing the output of each RAM to generate each successive
numerical values of the predistorted signal.
34. A distortion compensator as claimed in claim 31, wherein the look-up table comprises :
a serial to parallel converter (SPC) for converting the electrical input signal into a series of
successive N-bit words ;
a Random Access Memory (RAM) coupled to receive a center portion of each N-bit word
from the SPC, the RAM being adapted to store a plurality of numerical values of the
predistorted signal, and output a selected one numerical value based on the received
center portion of the N-bit word ;
a respective linear adder tree for digitally summing each end portion of the N-bit word from
the SPC ;
a first digital ADDER for digitally summing the output of each linear adder tree ; and
a second digital ADDER for digitally summing the output of the first digital ADDER and the
RAM to generate each successive numerical value of the predistorted signal.
35. A distortion compensator as claimed in claim 31, wherein the predistorted signal is represented
by two or more orthogonal components, and the look-up-table comprises a respective look-up-table for
generating each component.
36. A distortion compensator as claimed in claim 31, wherein at least one numerical value of the
predistorted signal is extracted from the look-up-table for each N-bit word.
37. A distortion compensator as claimed in claim 31, wherein the number (N) of bits within each N-
bit word is based on any one or more of:
an expected maximum dispersion of the optical communications system; and
an expected response time of the look-up-table.
38. A method of compensating optical signal distortions due to nonlinear effects of an optical
communications system, the method comprising steps of:
determining a complex non-linear compensation operator C[(E(t)] that is the inverse of a link
complex non-linear operator T[E(t)] representing at least one nonlinearity-induced signal
distortion imparted to a communications signal E(t) traversing an optical link of the
optical communications system ;
detecting a distorted optical signal received through the optical link, to generate a
corresponding distorted electrical signal; and
modifying the distorted electrical signal using the compensation operator C[E(t)] to generate a
substantially undistorted electrical output signal.
39. A method as claimed in claim 38, wherein the step of determining a compensation operator
comprises steps of:
measuring a performance parameter related to the at least one nonlinearity-induced signal
distortion ; and
calculating respective values of each parameter of the compensation operator that optimizes
the measured performance parameter.
40. A method as claimed in claim 39, wherein the step of measuring the performance parameter
comprises a step of measuring at least one of:
cross-phase modulation;
self phase modulation;
modulation instability; and
cross-talk.
41. A method as claimed in claim 38, wherein the step of modifying the distorted electrical signal
comprises a step of digitally filtering the distorted electrical signal using at least one of:
a Fast Fourier Transform (FFT) filter ;
a Finite Impulse Response (FIR) filter ;
a Infinite Impulse Response (IIR) filter ; and
a Look-Up-Table (LUT).
42. A method as claimed in claim 41, wherein the step of modifying the distorted electrical signal
comprises a step of digitally filtering the distorted electrical signal through a respective pair of cascaded
digital filter blocks associated with each span of the optical link.
43. A method as claimed in claim 41, wherein the step of digitally filtering the distorted electrical
signal comprises steps of:
converting the distorted electrical signal into a corresponding N-bit digital distorted signal; and
calculating successive numerical values of the substantially undistorted output signal, based on
the digital distorted signal and the compensation function.
44. A method as claimed in claim 43, wherein the step of calculating successive numerical values of
the substantially undistorted output signal comprises steps of:
calculating a respective numerical value of the substantially undistorted output signal for each
one of a set of predetermined N-bit words ;
storing each calculated numerical value in a look-up table ; and
extracting a plurality of successive numerical values of the substantially undistorted output
signal from the look-up table using the digital distorted signal.
45. A method as claimed in claim 44, wherein the set of predetermined N-bit words encompasses
all possible sequences of N-bits.
46. A method as claimed in claim 44, wherein the step of extracting a plurality of successive
numerical values of the of the substantially undistorted output signal comprises a step of using each N-
bit word of the digital distorted signal as an index to access a respective register of the look-up table.
47. A method as claimed in claim 46, wherein the step of extracting a plurality of successive
numerical values of the predistorted signal comprises a step of extracting at least one numerical value
of the predistorted signal for each N-bit word.

The present invention provides a method of compensating optical signal distortions due to nonlinear effects of an optical communications system, the method comprising steps of: determining a complex non-linear compensation operator C[(E(t)] that is the inverse of a link complex non-linear operator T[E(t)] representing at least one nonlinearity-induced signal distortion imparted to a communications signal E(t) traversing the optical communications system ; digitally processing an electrical input
signal x(t) (8) using the compensation operator C[(E(t)] to generate a predistorted electrical signal (28) ; and modulating an optical source using the predistorted electrical signal (28) to generate a corresponding predistorted optical signal (10A) for transmission through the optical communications system. A compensation system for implementing the above method is also disclosed.