Patent Publication Number: US-9906309-B2

Title: System and method for determining nonlinear mitigation perturbative distortion coefficients using a received optical signal

Description:
FIELD OF THE DISCLOSURE 
     The disclosure generally relates to methods and apparatuses in fiber optic communications for mitigation of optical nonlinear effects using perturbative pre- or post-distortion. More particularly, the disclosure relates to the use of one or more coherent optical receiver in calculating perturbation in a received optical signal induced by a fiber optic link such that optical nonlinear mitigation techniques can be used to simulate a normal course of the received optical signal by determining perturbative distortion coefficients from the received optical signal, without knowledge of parameters of the fiber optic link. 
     BACKGROUND 
     In fiber optic communications, nonlinearity is a behavior of an optical signal between a transmitter and a receiver in which the optical signal received at the receiver deviates from its normal course and does not vary in direct proportion to the optical signal transmitted at the transmitter. In the art, this is known as perturbation. Examples of nonlinearities include intrachannel nonlinearities, stimulated Brillouin scattering (SBS), stimulated Raman scattering (SRS), four wave mixing (FWM), self-phase modulation (SPM), cross-phase modulation (XPM), and intermodulation. Nonlinear mitigation techniques are used to simulate the normal course of the optical signal and are key to correcting for perturbation and thereby improving capacity and performance in future optical communications. 
     Back propagation is a technique that may be used to mitigate nonlinear effects in fiber optic links in fiber optic communications. Back propagation simulates error backward down the fiber optic link to address the non-linear effects within the received optical signal. However, back propagation is very computationally intensive. 
     Optical nonlinear mitigation using perturbative pre- or post-distortion may be used to increase the reach of optical signals in fiber optic communications. The perturbation induced by the fiber optic link is typically calculated using non-linear perturbation distortion coefficients (Cm,n) and the known or recovered transmitted data. The non-linear perturbation coefficients are typically calculated using known fiber optic link parameters, such as pulse width, inverse of symbol rate, the transmission distance, dispersion map, fiber type, amplifier spacing, and fiber nonlinear parameters. 
     Optical nonlinear mitigation techniques using perturbative pre- or post-distortion algorithms have been shown to be as effective in mitigating optical nonlinear effects in a fiber link as digital back propagation. Given the non-linear perturbation distortion coefficients (Cm,n), the perturbative pre-distortion algorithm is computationally simpler than back propagation. 
     However, determining and/or measuring fiber optic link parameters used in the current systems to calculate the non-linear perturbation distortion requires human intervention which may be time consuming and expensive. Additionally, the results of the determinations and measurements may be inaccurate. Further, any change in the fiber optic link parameters requires additional determinations and measurements with the current systems. Therefore, methods and systems are needed to determine non-linear perturbation distortion coefficients automatically at the optical receiver, and ideally without knowledge and/or use of the fiber link parameters. 
     SUMMARY 
     Methods and systems are disclosed. The problem of optical nonlinear mitigation is addressed through determination of non-linear perturbation distortion coefficients Cm,n from the received optical data stream without knowledge of the fiber link parameters. 
     In one embodiment, the non-linear perturbation coefficient Cm,n used in optical non-linear mitigation algorithms executed at a coherent optical receiver can be determined by analyzing one or more representation of the received optical signal, such as an optical constellation diagram of one or more received optical data signals used in quadrature amplitude modulation and having particular combinations of amplitude and phase of the optical signal that are used to encode data. The optical constellation diagram can be of various configurations including forms known in the art as QPSK, 8-QAM, 16-QAM, 32-QAM, 64-QAM, and the like. 
     In one embodiment, the coherent optical receiver can automatically adjust the non-linear perturbation distortion coefficients Cm,n for changes in the fiber optic link periodically and/or randomly without operator intervention or updated information as to the fiber link parameters. 
     In one embodiment, a method in accordance with the present disclosure may comprise, receiving, with a processor circuit in a coherent optical receiver module, a series of electrical signals over a time period, representative of a series of optical signals received at instants of time within the time period, each of the electrical signals being indicative of a respective one of a plurality of points on an IQ plane, each of the points being spaced from one of a plurality of predetermined points in the IQ plane by a corresponding one of a plurality of distortion values; calculating, with the processor circuit, one or more perturbative coefficients based on one or more of the distortion values; and determining, with the processor circuit, data from the series of electrical signals based on the perturbative coefficient. 
     In one embodiment, the method may further comprise determining nonlinear offsets based on the perturbative coefficient and determining data from the series of electrical signals based on the nonlinear offsets. 
     In one embodiment, a coherent optical receiver module comprising one or more processor circuit may be configured to receive a series of electrical signals over a time period, representative of a series of optical signals received at instants of time within the time period, each of the electrical signals being indicative of a respective one of a plurality of points on an IQ plane, each of the points being spaced from one of a plurality of predetermined points in the IQ plane by a corresponding one of a plurality of distortion values; calculate one or more perturbative coefficients based on one or more of the distortion values; and determine data from the series of electrical signals based on the perturbative coefficient. 
     In one embodiment, Forward Error Correction may be used before or after calculation of the one or more perturbative coefficients. In one embodiment, Forward Error Correction may be used before calculation of the one or more perturbative coefficients, such that training symbols are not required and live data may be used. 
     In one embodiment, an exemplary coherent optical receiver module may comprise an input port configured to receive a series of optical signals carrying data from a transmitter module via a fiber optic link having one or more optical fiber; an output port; and one or more optical receiver. The optical receiver may comprise: one or more photodiodes configured to receive the series of optical signals via the input port and translate the series of optical signals to a series of electrical signals representative of the series of optical signals carrying the data, and one or more processor circuit. The processor circuit may be configured to: receive the series of electrical signals over a time period, representative of the series of optical signals received at instants of time within the time period, each of the electrical signals being indicative of a respective one of a plurality of points on an IQ plane, each of the points being spaced from one of a plurality of predetermined points in the IQ plane by a corresponding one of a plurality of distortion values; calculate one or more perturbative coefficients based on one or more of the distortion values; and transmit, via the output port, one or more information signals indicative of the one or more perturbative coefficient to the transmitter module. The transmitter module may calculate one or more nonlinear offset values and modify the series of optical signals to preemptively mitigate the distortion before transmission of the optical signals. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate one or more implementations described herein and, together with the description, explain these implementations. In the drawings: 
         FIG. 1  is a block diagram of an exemplary coherent optical transport system in accordance with the present disclosure. 
         FIG. 2  is a block diagram of an exemplary coherent optical transmitter in accordance with the present disclosure. 
         FIG. 3  is a block diagram of an exemplary coherent optical receiver in accordance with the present disclosure. 
         FIG. 4  is an exemplary undistorted constellation diagram used in quadrature amplitude modulation and having 16 particular different combinations of amplitude and phase of the optical signal that are used to encode four-bits of data. 
         FIG. 5  is an exemplary constellation diagram of an optical signal passed through a fiber optic link and received by a coherent optical receiver in which optical nonlinear effects are present. 
         FIG. 6  is a process flow diagram of an exemplary process in accordance with the present disclosure. 
         FIG. 7  is a process flow diagram of another exemplary process in accordance with the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The following detailed description refers to the accompanying drawings. The same reference numbers in different drawings may identify the same or similar elements. 
     The mechanisms proposed in this disclosure circumvent the problems described above. Conventionally, nonlinear distortion mitigation methods are computationally intensive and/or require determination and measurement of fiber optic link parameters. In accordance with the present disclosure, systems and methods are disclosed for analyzing one or more optical signals passed through a fiber optic link and received by a coherent optical receiver in order to correct for the optical nonlinear effects of the fiber optic link without dependence on knowledge or use of fiber optic link parameters. In one aspect of the disclosure, electrical signals indicative of points on an IQ plane, each of the points being spaced from one of a plurality of predetermined points in the IQ plane by a corresponding one of a plurality of distortion values, are analyzed to calculate non-linear perturbation distortion coefficients Cm,n. The coefficients Cm,n may be used in one or more optical non-linear mitigation algorithm to calculate distortion values. The distortion values may be used to correct for optical nonlinear effects induced by the fiber optical link. 
     An exemplary embodiment may include systems and methods which may comprise receiving, with a processor circuit in a coherent optical receiver module, a series of electrical signals over a time period, representative of a series of optical signals received at instants of time within the time period, each of the electrical signals being indicative of a respective one of a plurality of points on an IQ plane, each of the points being spaced from one of a plurality of predetermined points in the IQ plane by a corresponding one of a plurality of distortion values; and calculating one or more perturbative coefficients based on one or more of the distortion values. 
     In one embodiment, the receiver processor circuit may determine data from the series of electrical signals based on the perturbative coefficients. 
     In one embodiment, the receiver processor circuit may determine nonlinear offsets based on the perturbative coefficient, and may determine data from the series of electrical signals based on the nonlinear offsets. 
     In one embodiment, the coherent optical receiver module may transmit one or more information signals indicative of the one or more perturbative coefficient to a transmitter module. The transmitter module may determine nonlinear offsets based on the perturbative coefficient and may apply the nonlinear offsets in order to modify the series of optical signals before transmission of the optical signals to the coherent optical receiver module in order to preemptively mitigate the distortion. 
     DEFINITIONS 
     If used throughout the description and the drawings, the following short terms have the following meanings unless otherwise stated: 
     DP-QPSK stands for dual-polarized quadrature phase shift keying. DP-QPSK is an optical signal modulation format that has been implemented in coherent optical systems. 
     DSP stands for digital signal processor. 
     PIC stands for photonic integrated circuit. 
     Pol Muxed DQPSK stands for polarization multiplexed differential quadrature phase-shift keying. Pol Muxed DQPSK is an optical signal modulation format. 
     PSK stands for phase-shift keying. PSK is an optical signal modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). 
     QAM stands for quadrature amplitude modulation. QAM is an optical signal modulation scheme. 
     Rx stands for Receiver, which typically refers to optical channel receivers, but can also refer to circuit receivers. 
     Tx stands for Transmitter, which typically refers to optical channel transmitters, but can also refer to circuit transmitters. 
     WDM stands for wavelength division multiplexing. In WDM, multiple optical signals, each having a different wavelength, are combined onto a single optical fiber using an optical multiplexer circuit (“multiplexer”). 
     DESCRIPTION 
     As used herein, the terms “comprises,” “comprising,” “includes,” “including,” “has,” “having” or any other variation thereof, are intended to cover a non-exclusive inclusion. For example, a process, method, article, or apparatus that comprises a list of elements is not necessarily limited to only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Further, unless expressly stated to the contrary, “or” refers to an inclusive or and not to an exclusive or. For example, a condition A or B is satisfied by anyone of the following: A is true (or present) and B is false (or not present), A is false (or not present) and B is true (or present), and both A and B are true (or present). 
     In addition, use of the “a” or “an” are employed to describe elements and components of the embodiments herein. This is done merely for convenience and to give a general sense of the inventive concept. This description should be read to include one or more and the singular also includes the plural unless it is obvious that it is meant otherwise. 
     Further, use of the term “plurality” is meant to convey “more than one” unless expressly stated to the contrary. 
     Further, the phrase “based on” is intended to mean “based, at least in part, on” unless explicitly stated otherwise. 
     Throughout this application, the term “about” is used to indicate that a value includes the inherent variation of error for the quantifying device, the method being employed to determine the value, or the variation that exists among the study subjects. For example, but not by way of limitation, when the term “about” is utilized, the designated value may vary by plus or minus twelve percent, or eleven percent, or ten percent, or nine percent, or eight percent, or seven percent, or six percent, or five percent, or four percent, or three percent, or two percent, or one percent. 
     The use of the term “at least one” or “one or more” will be understood to include one as well as any quantity more than one, including but not limited to, 1, 2, 3, 4, 5, 10, 15, 20, 30, 40, 50, 100, etc. The term “at least one” or “one or more” may extend up to 100 or 1000 or more depending on the term to which it is attached. In addition, the quantities of 100/1000 are not to be considered limiting, as lower or higher limits may also produce satisfactory results. 
     In addition, the use of the phrase “at least one of X, V, and Z” will be understood to include X alone, V alone, and Z alone, as well as any combination of X, V, and Z. 
     The use of ordinal number terminology (i.e., “first”, “second”, “third”, “fourth”, etc.) is solely for the purpose of differentiating between two or more items and, unless explicitly stated otherwise, is not meant to imply any sequence or order or importance to one item over another or any order of addition. 
     In accordance with the present disclosure, circuitry could be analog and/or digital, components, or one or more suitably programmed microprocessors and associated hardware and software, or hardwired logic. Also, certain portions of the implementations have been described as “components” or “circuitry” that performs one or more functions. The term “component” or “circuitry” may include hardware, such as a processor, an application specific integrated circuit (ASIC), or a field programmable gate array (FPGA), or a combination of hardware and software. Software includes one or more computer executable instructions that when executed by one or more component cause the component or circuitry to perform a specified function. It should be understood that the algorithms described herein are stored on one or more non-transient memory. Exemplary non-transient memory includes random access memory, read only memory, flash memory or the like. Such non-transient memory can be electrically based or optically based. Further, the messages described herein may be generated by the components and result in various physical transformations. 
     Finally, as used herein any reference to “one embodiment” or “an embodiment” means that a particular element, feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment. 
     As discussed above, current nonlinear mitigation methods are computationally intensive and/or require determination and measurement of system parameters. The present disclosure addresses these deficiencies with systems and methods for analyzing one or more electrical signal representative of one or more received optical signals in a coherent optical receiver in order to affect the performance of the optical signal system without dependence on knowledge of system parameters. 
     Referring now to the drawings,  FIG. 1  is a block diagram of an example optical network  20  in which systems and/or methods, described herein, may be implemented. 
     While  FIG. 1  shows a particular configuration of components in network  20 , in practice, network  20  may include additional components, different components, or differently arranged components than what are shown in  FIG. 1 . Also, in some instances, one of the components illustrated in  FIG. 1  may perform a function described herein as being performed by another one of the components illustrated in  FIG. 1 . 
     The network  20  may be part of a wavelength division multiplexed (WDM) optical communication system (referred to as a “WDM system”). WDM systems are systems in which multiple optical signals  22 , each having a different wavelength, are combined onto a single optical fiber. The components in an optical communication system may support communications over a number of wavelength channels. 
     As illustrated in  FIG. 1 , network  20  may include optical transmitter (Tx) module  24  (e.g., a Tx PIC) and/or optical receiver (Rx) module  26  (e.g., an Rx PIC). In some implementations, transmitter module  24  may be optically connected to receiver module  26  via link  28 , and/or optical amplifiers  30 . Link  28  may include one or more optical amplifiers  30  that amplify the optical signal  22  as the optical signal  22  is transmitted over link  28  from the transmitter module  24  to the receiver module  26 . 
     In use, the transmitter module  24  may modulate a phase of the optical signal  22  in order to convey data (via the optical signal  22 ) to the receiver module  26  where the optical signal  22  may be demodulated such that data, included in the optical signal  22 , may be recovered. A particular modulation format (e.g., phase-shift keying (PSK), quadrature amplitude modulation (QAM), demultiplex quadrature phase shift keying (QPSK), Pol Muxed DQPSK, etc.) may be used to modulate the input signal. Different modulation formats correspond to different distances that the input signal may be transmitted. Further, different modulation formats may result in different bit error rates (BERs) associated with the optical signal  22 . 
     In modulation formats, the polarization of the optical signal  22  may be used to modulate the optical signal  22 . Polarization is the direction of the electric field in the lightwave. If the electric field of the lightwave is in the Y Axis, the light is said to be vertically polarized. If the electric field of the lightwave is in the X axis, the light is said to be horizontally polarized. Additionally, the amplitude and the phase of the optical signal may be modulated. There may be an in-phase component (I) of the optical signal proportional to the cosine of the phase shift and a quadrature component (Q) proportional to the sine of the phase shift of the optical signal. 
     Transmitter module  24  may include a number of optical transmitters  32 - 1  through  32 -N (where N is greater than or equal to 1), waveguides  34 , and/or optical multiplexer  36 . Each optical transmitter  32  may receive a data channel (TxCh1 through TxChN), modulate the data channel with an optical signal, and transmit the data channel as an optical signal. In one implementation, transmitter module  24  may include 5, 10, 20, 50, 100, or some other number of optical transmitters  32 . Each optical transmitter  32  may be tuned to use an optical carrier of a designated wavelength. It may be desirable that the grid of wavelengths emitted by optical transmitters  32  conform to a known standard, such as a standard published by the Telecommunication Standardization Sector (ITU-T). 
     It will be understood that the optical transmitters  32  may be implemented in a variety of ways. For example,  FIG. 2  is one exemplary implementation of the optical transmitter  32 . The optical transmitter  32  may comprise one or more transmitter processor circuit  38 , one or more laser  39 , one or more modulator  41 , one or more semiconductor optical amplifier (SOA)  42 , and/or other components (not shown). 
     The one or more transmitter processor circuit  38  may have one or more transmitter digital signal processor (DSP)  40 , Transmitter Forward Error Correction (FEC) circuitry  43 , Symbol Map circuitry  44 , Transmitter Perturbative Pre-Compensation circuitry  45 , and digital-to-analogue converters (DAC)  46 . The transmitter processor circuit  38  may be located in any one or more components of the optical transmitter  32 , or separate from the components, and/or in any location(s) among the components. The transmitter processor circuit  38  may be in the form of one or more Application Specific Integrated Circuit (ASIC), which may contain one or more modules and/or custom modules. 
     Processed electrical outputs from the transmitter processor circuit  38  may be supplied to the modulator  41 . Processed electrical outputs from the transmitter processor circuit  38  may be supplied other circuitry in the transmitter processor circuit  38 , for example, clock and data modification circuitry. The laser  39 , modulator  41 , and/or SOA  42  may be coupled with a tuning element (e.g., a heater) (not shown) that can be used to tune the wavelength of an optical signal channel output by the laser  39 , modulator  41 , or SOA  42 . In some implementations, a single laser  39  may be shared by multiple optical transmitters  32 . 
     Other possible components in the optical transmitter  32  may include filters, circuit blocks, memory, additional modulators, splitters, couplers, multiplexers, etc., as is well known in the art. The components may be combined, used, or not used, in multiple combinations or orders. Optical transmitters are further described in U.S. Patent Publication No. 2012/0082453, the content of which is hereby incorporated by reference in its entirety herein. 
     Returning now to  FIG. 1 , waveguides  34  may include an optical link to transmit modulated outputs (referred to as “signal channels”) of optical transmitters  32 . In some implementations, each optical transmitter  32  may connect to one waveguide  34  or to multiple waveguides  34  to transmit signal channels of optical transmitters  32  to optical multiplexer  36 . In some implementations, waveguides  34  may be made from a birefringent material and/or some other material. 
     Optical multiplexer  36  may include an arrayed waveguide grating (AWG) or some other multiplexing device. In some implementations, optical multiplexer  36  may combine multiple signal channels, associated with optical transmitters  32 , into a wave division multiplexed (WDM) signal, such as optical signal  22 . Optical signals  22  may be quadrature phase shift keying (QPSK) optical signals, for example. 
     As further shown in  FIG. 1 , receiver module  26  may include optical demultiplexer  50 , waveguides  52 , and/or optical receivers  54 - 1  through  54 -O (where O is greater than or equal to 1). In some implementations, optical demultiplexer  50  may include an AWG or some other device. Optical demultiplexer  50  may supply multiple signal channels based on a received WDM signal (e.g., optical signal  22 ). The optical receiver module  26  may be used to demultiplex quadrature phase shift keying (QPSK) optical signals  22 . 
     As shown in  FIG. 1 , optical demultiplexer  50  may supply signal channels to optical receivers  54  via waveguides  52 . Waveguides  52  may include optical links to transmit outputs of optical demultiplexer  50  to optical receivers  54 . In some implementations, each optical receiver  54  may receive outputs via a single waveguide  52  or via multiple waveguides  52 . In some implementations, waveguides  52  may be birefringent (e.g., based on the width of waveguides  52 ). 
     Optical receivers  54  may each operate to convert an input optical signal  22  to an electrical signal  60  that represents the transmitted data. In some implementations, optical receivers  54  may each include one or more photodetectors and/or related devices to receive respective input optical signals  22  outputted by optical demultiplexer  50  and a local oscillator  72 , convert the signals to a photocurrent, and provide a voltage output to function as the electrical signal  60  representation of the original input optical signal  22 . Optical receivers  54  may be implemented in other ways, as is well known in the art. Exemplary optical receiver modules  26  and optical receivers  54  are further described in U.S. patent application Ser. No. 12/052,541, titled “Coherent Optical Receiver”. 
     For example,  FIG. 3  illustrates a block diagram of an exemplary optical receiver  54  consistent with the present disclosure. Optical receiver  54  may comprise one or more local oscillator (LO)  72 , a polarization and phase diversity hybrid circuit  74  receiving the optical signal  22  and the input from the local oscillator (LO)  72 , one or more balanced photo-diodes (BDP)  76  that produce the electrical signals  60  representative of the optical signal  22 , and one or more receiver processor circuit  80 . 
     The one or more receiver processor circuit  80 , may comprise one or more analogue-to-digital converter (ADC)  81  receiving the electrical signals  60  from the balanced photo-diodes  76 , one or more receiver digital signal processor (DSP)  82 , Receiver Perturbative Post-Compensation circuitry  84 , and Receiver Forward Error Correction (FEC) circuitry  86 . The Receiver Forward Error Correction circuitry  86  may apply corrections to the data, as is well known in the art. The one or more receiver processor circuit  80  and/or the one or more receiver DSP  82  may be located on one or more components of the optical receiver  54  or separately from the components, and/or in any location(s) among the components. The receiver processor circuit  80  may be in the form of an Application Specific Integrated Circuit (ASIC), which may contain one or more modules and/or custom modules. 
     The one or more receiver DSP  82  receives and processes the electrical signals  60  with multi-input-multiple-output (MIMO) circuitry, as described, for example, in U.S. patent application Ser. No. 12/052,541, titled “Coherent Optical Receiver”, the entire content of which is incorporated herein by reference in its entirety. Processed electrical outputs from receiver DSP  82  may be supplied other circuitry in the receiver processor circuit  80 , such as the Receiver Perturbative Post-Compensation circuitry  84  and the Receiver Forward Error Correction (FEC) circuitry  86 . 
     Various components of the optical receiver module  26  may be provided or integrated, in one example, on a common substrate. Further integration is achieved by incorporating various optical demultiplexer designs that are relatively compact and conserve space on the surface of the substrate. 
     In use, the optical signal  22  may be subjected to optical non-linear effects between the transmitter module  24  and the receiver DSP  82  of the receiver processor circuit  80  such that the optical signal  22  received does not accurately convey the carried data in the form that the optical signal  22  was transmitted. The effects of optical nonlinear effects can be mitigated by applying perturbative distortion algorithms to determine the nonlinear offset (which may be referred to as a distortion offset and/or Δu). Optical nonlinear mitigation using perturbative pre- or post-distortion may be used to compensate for the optical non-linear effects and increase the reach of optical signals in fiber optic communications. 
     The amount of perturbation may be calculated using coefficients (Cm,n) in the algorithms and the known or recovered transmitted data. The coefficients Cm,n may be calculated, in accordance with the present disclosure, by use of analysis of one or more incoming optical signal  22  at the receiver module  26 . In one aspect of the present disclosure, analysis of the one or more incoming optical signal  22  utilizes analysis of points on an IQ plane, such as in a constellation diagram  100 , based on electrical signals  60  indicative of the optical signals  22 . 
     Turning now to  FIG. 4 , the receiver DSP  82  of the optical receiver  54  may create the constellation diagram  100  based on the received electrical signals  60  representative of the optical signal  22 . The constellation diagram  100 , also referred to as a constellation map, an optical constellation, and/or simply a constellation, is a representation of the optical signal  22 , where the optical signal  22  is modulated by a digital modulation scheme (such as quadrature amplitude modulation, phase-shift keying, etc.). The constellation diagram  100  displays the representation of the optical signal  22  as a two-dimensional scatter diagram in the complex IQ plane at symbol sampling instants. The constellation diagram  100  may be graphed with “Q” as the y axis and “I” as the x axis. In a more abstract sense, the constellation  100  represents the possible symbols that may be selected by a given modulation scheme as points in the complex plane. The symbols are representative of data bits transmitted in the optical signal  22  at any one time. 
     Data is transmitted by a sequence of the symbols over time, where each symbol is represented as a point  102  at a location on the constellation  100 . When the symbols are transmitted, the symbols conform to points  102  on the expected the IQ plane of the constellation  100 . Upon reception of the electrical signals  60  representative of the optical signal  22 , the receiver DSP  82  examines the received symbol, which may have been corrupted and therefore may not conform to the expected predetermined point  102  on IQ plane of the constellation  100 . The receiver module  26  may select, as an estimate of the symbol that was actually transmitted, the point  102  on the constellation diagram  100  which is closest (in a Euclidean distance sense) to that of the received symbol point  102 . 
     For example,  FIG. 4  depicts an exemplary 16-QAM constellation  100  exhibiting the correct rotation and no in-phase or quadrature-phase inversion errors. The 16 points  102  (numbered  102 - 1  through  102 - 16 ) of the overall constellation diagram  100  have been arbitrarily indicated as shown. It will be understood, however, that at any instant in time, a symbol may be represented on the constellation as one of the points  102 - 1 - 102 - 16 . 
     Various embodiments may utilize many different modulation techniques for the optical signal  22 , which determines the ideal pattern of predetermined points in the IQ plane of the constellation  100 . Nonexclusive examples of modulation schemes for the optical signals  22  include rectangular QAM, regular or irregular star-QAM, circular QAM, phase shift keying (PSK), amplitude shift keying (ASK), and orthogonal frequency-division multiplexing (OFDM). The different modulation techniques used may comprise smaller constellation diagrams  100  (e.g., 8-QAM) or larger constellation diagrams  100  (e.g., 256-QAM) than the exemplary sized constellation diagrams  100  discussed herein. Additionally, the different modulation techniques used may utilize differential encoding or non-differential encoding techniques. Other modifications will be known to those skilled in the art and informed by the teachings of the present invention. The type of system and number of light transmissions dictates how many points  102  are seen in the constellation  100  representing a particular instant, for example, as 4 points, 8 points, or 16 points. 
     For the optical receiver module  26  to provide valid data through the correct symbol-to-binary demapping, the constellation  100  processed by the optical receiver  54  must exhibit a correct rotation and have no in-phase or quadrature-phase inversion errors associated with it. 
     If the optical network  20  were perfect, without nonlinearity, the received points  102  would be perfectly centered on a grid, exactly as transmitted, at predetermined points. With nonlinearities, however, the received points  102  don&#39;t lie on grid exactly—the offset from the grid, that is, the space from the predetermined points, is represented as a distortion value “Δu” (also known as an offset Δu) at the receiver module  26 . The offset Δu represents the nonlinear shift, not Amplified Spontaneous Emission (ASE) shift. 
     The still-encoded sample stream provided by the receiver DSP  82  to subsequent demodulation/processing elements (not shown in the various figures) is corrected to conform to the requirements of the constellation  100  (i.e. the predetermined points in the IQ plane), either immediately after the receiver DSP  82 , or at another suitable stage within the processing chain, e.g., at a pre-FEC stage, an FEC stage, or at an OTN deframing stage. 
     Referring now to  FIG. 5 , an exemplary constellation diagram  100 , is shown of the optical signal  22 , passed through the fiber optic link  28  and received by the coherent optical receiver  54 , in which optical nonlinear effects are present. The constellation  100  depicts a received symbol illustrated as representative point  102 - 17  in the IQ plane. The shift between where the symbol would be expected, for example, at predetermined point  102 - 1 , and the received point  102 - 17  occurs due to pattern-dependent nonlinearities. Therefore, point  102 - 17  would appear to be in different locations in the IQ plane of the constellation diagram  100  depending on the pattern. Vector  104 , from the predicted predetermined point  102 - 1  to the received symbol point  102 - 17 , corresponds to an offset Δu (that is, a distortion value) for a point in time. 
     If the nonlinear offset can be determined, the nonlinear distortion may be mitigated. Calculations to determine nonlinear offset to mitigate the nonlinear distortion may be run in a processor circuit, such as the receiver DSP  82  or the Receiver Perturbative Post-Compensation circuitry  84  of the receiver processor circuit  80 , or the transmitter DSP  40  or the Transmitter Perturbative Pre-Compensation circuitry  45  of the transmitter processor circuit  38 . 
     Algorithms to calculate nonlinear offset, which may be averaged, smoothed, or otherwise modified to reduce noise factors, may utilize perturbative coefficients Cm,n. The perturbative coefficients Cm,n used in the calculations of the offsets may be determined either inside the receiver DSP  82  or outside the receiver DSP  82  or elsewhere in the receiver module  26 . Computation of the coefficients Cm,n is not on the main data path. In one embodiment, an averaging circuit may be used. A single averager (or one per polarization, or one each for xx, yx, yy, and xy) on the receiver processor circuit  80  may be used. 
     The following algorithms may be calculated by the receiver processor circuit  80  to determine the coefficients Cm,n using special averaging techniques applied to determinations of the incoming data, utilizing the points  102  and distortion values Δu on the IQ plane of constellations  100 : 
     
       
         
           
             
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                     ⁢ 
                     
                       A 
                       
                         
                           m 
                           + 
                           n 
                         
                         , 
                         p 
                       
                       * 
                     
                     ⁢ 
                     
                       A 
                       
                         m 
                         , 
                         x 
                       
                     
                   
                 
               
             
           
         
       
     
     where p can be either the x or y polarization, and 
     where m denotes moving forward in time, and 
     where n denotes moving backward in time, and 
     where the range of n and m is typically in the range of +/−10 or +/−20, and 
     where T is the number of samples averaged, and 
     where t is Δu at a particular point of time, and 
     where Δu in the equation is the difference due to nonlinear interactions of an actual location of the point  102  compared to an expected predetermined location of the point  102  in the IQ plane of the constellation diagram  100 , at a point in time, represented by:
 
Δ u   t,x =SoftOut t,x −Decision t,x  
 
     where SoftOut represents the location on the grid of the constellation  100  of the point  102  as received (for example point  102 - 17 ), and 
     where Decision represents the chosen expected point (for example, points  102 - 1 - 102 - 16 ) on the grid to which the point  102  as received should conform. 
     In the equations, the symbol sequence is denoted as A n , where “A” is a complex number of the data on the I/Q complex plane below, and n is the position in time relative to the current symbol. “A” may be the data pattern. The Decisions can also be used for “A”. In one embodiment, the Decisions can be taken after the FEC circuit  43  applies forward error correction to the data. In one embodiment, “A&#39;s” could also be based on SoftOut without Decision. 
     From the first equation, Δu can be calculated for each symbol in time (t), given the “A&#39;s” (symbols at other times), and the coefficients Cm,n. The offset Δu may be calculated in the receiver processor circuit  80 , such as the receiver DSP  82 , and/or the transmitter processor circuit  38 , such as the transmitter DSP  40 . If the Δu is calculated in the receiver processor circuit  80 , such as in the Receiver Perturbative Post-Compensation circuitry  84 , the “A” may be the SoftOut. If the Δu is calculated in the transmitter processor circuit  38 , such as the Transmitter Perturbative Pre-Compensation circuitry  45 , the “A&#39;s” may be the actual symbols. 
     The receiver processor circuit  80  (for example, firmware of the receiver DSP  82 ) may build a coefficient Cm,n matrix by sequencing through the (p, m, n) combinations using the following equations under the following circumstances for the different polarizations x, y: 
     
       
         
           
             
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     where β is a scaling factor, where: 
     
       
         
           
             
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     The coefficient Cm,n may also be determined using a Least Means Squares algorithm or any mathematical method to iteratively near the actual values of the coefficient Cm,n based on samples over time, to adjust the coefficients Cm,n to minimize the perturbative error. 
     The coefficient Cm,n values may then be used to calculate, for example, in the receiver processor circuit  80  and/or the transmitter processor circuit  38 , the offset Δu using known equations for the offset Δu (for example, Equation 10 detailed in  Multiplier - Free Intrachannel Nonlinearity Compensating Algorithm Operating at Symbol Rate , Zhenning Tao, et al., Journal of Lightwave Technology, Vol. 29, No. 17, p. 2572, Sep. 1, 2011.), such as the following:
 
Δ u   x =Σ m,n   P   0   3/2 ( A   n,x   A*   m+n,x   A   m,x   +A   n,y   A*   m+n,y   A   m,x ) C   m,n  
 
Δ u   y =Σ m,n   P   0   3/2 ( A   n,y   A*   m+n,y   A   m,y   +A   n,x   A*   m+n,x   A   m,y ) C   m,n  
 
     where P 0  is the pulse peak power at the launch point, and 
     A* represents the complex conjugate of A. 
     In one embodiment, the offsets Δu may then be applied to the electrical signals  60  by the optical receiver  54  to conform the symbols to the points  102  of the constellation  100  to mitigate the nonlinearities affecting the optical signals  22  and to retrieve the data from the electrical signals  60 . In one implementation, the receiver processor circuit  80  applies the offsets Δu before the Receiver Forward Error Correction circuitry  86  processes the data and/or applies corrections. 
     In one embodiment, the data patterns (“A”) used in the calculations to determine the perturbative coefficients Cm,n may be taken after the FEC corrections, which may make the calculations for Cm,n more accurate. Taking the data patterns “A” after the FEC corrections means that training symbols are not required, and the method may be used with live data. 
     Alternatively, or additionally, the receiver module  26  may transmit signals indicative of the perturbative coefficients Cm,n to the transmitter module  24 . The Transmitter Perturbative Pre-Compensation circuitry  45  may then calculate the offsets Δu. The transmitter module  24  may then preemptively apply the offsets Δu in an opposite direction of the measured distortion to the optical signals  22  before transmission such that the nonlinear distortions are mitigated. In one implementation, the transmitter processor circuit  38  applies the offsets Δu in, before the Transmitter Forward Error Correction circuitry  43  processes the data. 
     The coefficients Cm,n and offsets Δu may be calculated in situ with live traffic incoming to the receiver module  26 , thus allowing for changing conditions in the network  20 . Additionally, calculating the coefficients Cm,n and offsets Δu as described does not require training symbols. 
       FIG. 6  is a process flow diagram of an exemplary process  200  in accordance with the present disclosure. In step  202 , the receiver processor circuit  80  of the optical receiver module  26  receives a series of the electrical signals  60  over a time period. The electrical signals  60  are representative of a series of the optical signals  22  received at instants of time within the time period. The optical signals  22  contain data in a form of the constellation  100 , such that a particular point  102  in the grid of the constellation  100  is represented for a particular instant in time. The electrical signals have distortion and representative points  102  at locations within the constellation  100 . In step  204 , the receiver processor circuit  80 , analyzes the location of the representative points  102  within the constellation  100  relative to a predetermined pattern of points  102 . 
     In step  206 , the receiver processor circuit  80 , calculates one or more perturbative coefficient based on the analysis. The perturbative coefficient Cm,n may be calculated outside of the main data path. In step  208 , the receiver processor circuit  81 , such as the Receiver Perturbative Post-Compensation circuitry  84  and/or the receiver DSP  82 , may determine offsets Δu utilizing the perturbative coefficient(s) Cm,n. 
     In step  210 , the receiver processor circuit  80 , determines the data from the series of electrical signals  60  using the perturbative coefficient(s) to interpret the distortion in the plurality of points  102  in the constellation  100 . In one implementation, the receiver processor circuit  80  applies the offsets Δu before the Receiver Forward Error Correction circuitry  86  processes the data. 
       FIG. 7  is a process flow diagram of an exemplary process  250  in accordance with the present disclosure. In process  250 , steps  202  through  206  are identical to steps  202  through  206  described in relation to  FIG. 6 . In step  252 , however, the receiver module  26  transmits one or more information signals indicative of the coefficients Cm,n to the transmitter module  24 . In step  254 , the transmitter module  24  receives the information signals and calculates the offset values Δu. In step  256 , the transmitter module  24  applies the offset values Δu preemptively before transmission of the optical signal  22  to preemptively mitigate the nonlinear distortion in the optical signal  22 , so the optical signal  22  when received at the coherent optical receiver module  26  will conform to requirements of the constellation  100 . In one implementation, the transmitter module  24  may apply the offset values Δu after the Transmitter Forward Error Correction circuitry  43  processes the data and/or applies corrections. 
     CONCLUSION 
     Conventionally, nonlinear distortion mitigation methods are computationally intensive and/or require determination and measurement of system parameters. In accordance with the present disclosure, systems and methods are disclosed for analyzing the incoming optical signal carrying a data stream in a coherent optical receiver in order to affect the performance of the optical signal network without dependence on knowledge of system parameters. 
     The foregoing description provides illustration and description, but is not intended to be exhaustive or to limit the inventive concepts to the precise form disclosed. Modifications and variations are possible in light of the above teachings or may be acquired from practice of the methodologies set forth in the present disclosure. 
     Further, while implementations have been described in the context of an optical network, this need not be the case. These implementations may apply to other types of networks having nonlinear distortions. 
     Even though particular combinations of features are recited in the claims and/or disclosed in the specification, these combinations are not intended to limit the disclosure. In fact, many of these features may be combined in ways not specifically recited in the claims and/or disclosed in the specification. Although each dependent claim listed below may directly depend on only one other claim, the disclosure includes each dependent claim in combination with every other claim in the claim set. 
     No element, act, or instruction used in the present application should be construed as critical or essential to the invention unless explicitly described as such outside of the preferred embodiment.