Perturbation-based hard-decision nonlinearity compensation

Abstract

To provide a method and a device for compensating an input signal at a receiver of an optical fiber communication system against degradation caused by non-linear optical effects in a transmission channel.SOLUTION: Compensation is performed by, inter alia, a circuit 100 for calculating a perturbation term representing predicted optical non-linearity of a transmission channel and circuits 104, 106 for combining the perturbation term with soft data symbols obtained from an input signal stream (Figure 8). Calculation of the perturbation term requires circuits 108, 110 for converting an input stream of soft data symbols into an input stream of hard data symbols and then acting on the input stream of hard data symbols according to a model of the non-linear effects of the transmission channel.SELECTED DRAWING: Figure 8

Description

[Technical Field]

[0001] The present invention relates to devices and methods for use in coherent optical communications. [Background technology]

[0002] This section introduces aspects that may help to facilitate a better understanding of the invention. Accordingly, the statements in this section should be read in this light and not understood as admissions about what is prior art or what is not prior art.

[0003] In optical fiber communication systems, linear and nonlinear optical effects can degrade optical signals, thereby limiting system performance. Some optical fiber communication systems use digital signal processors (DSPs) to at least partially compensate for signal degradation caused by linear impairments in the optical channel.

[0004] Digital compensation of signal degradation resulting from nonlinear optical effects, particularly fiber nonlinearity, can also be useful in improving the performance of optical fiber communication systems. One potential benefit of fiber nonlinearity compensation (NLC) is that in optical fiber communication systems, such compensation can reduce the need for optical signal regeneration between a source optical data transmitter and a target optical data receiver.

[0005] Several techniques of digital compensation have been proposed to minimize or mitigate channel nonlinearities. The computational complexity of this problem has been difficult for developers in this field to overcome. Over the past few years, many algorithms have been proposed with the goal of minimizing the number of signal processing operations required to equalize the nonlinearities from the received signal. Some of these algorithms have substantially reduced computational complexity.

[0006] One approach that shows promise for practical use in coherent optical data receivers is the perturbation-based nonlinearity compensator (PNC), whose implementation involves calculating a perturbation term associated with intra-channel fiber nonlinearity and then subtracting it from the received signal.

[0007] For example, an effective implementation of PNC was proposed in European Patent Application No. 15306613.9, published on April 19, 2017 as EP 3,157,180, the entirety of which is incorporated herein by reference. As proposed therein, a nonlinear channel response is calculated using a combination of linear filters operating over several interacting symbols.

[0008] Another implementation of PNC was proposed in U.S. Patent No. 10,756,822, issued August 25, 2020. U.S. Patent No. 10,756,822 is incorporated herein by reference in its entirety. The approach proposed therein is based on the recognition that some contributions to nonlinear optical effects have frequency components much lower than the digital data symbol rate. For those contributions, low-frequency approximations are used to reduce the overall complexity of the calculations.

[0009] However, despite significant advances, PNCs can still be excessively complex for DSP implementations of at least some coherent optical fiber communication systems. Thus, there remains a need for even simpler circuits that can be implemented in ASICs for practical high-speed DSPs. [Prior art documents] [Patent documents]

[0010] [Patent Document 1] European Patent Application No. 15306613.9 [Patent Document 2] EP 3,157,180 [Patent Document 3] U.S. Patent No. 10,756,822 Summary of the Invention

[0011] The inventors have developed a new method for implementing PNC in coherent optical fiber communication systems. The new method, which the inventors call "hard-decision PNC," is based on processing hard symbols after a decision is made, instead of processing received soft symbols. This innovation significantly reduces the computational cost of computing nonlinear perturbations in PNC. Depending on the specific application scenario, there may be a slight performance penalty due to decision errors. However, this penalty can be overcome by implementing hard-decision PNC in multiple stages, where a decision on a symbol is made at the beginning of each stage. The reliability of the decision can be gradually improved with each stage.

[0012] More specifically, possible corruption of received data symbols in the input stream is corrected in the PNC by additively combining the received data symbols with perturbation terms, which are calculated from the received input stream together with system parameters. In known implementations, the correction is performed on the soft symbols using perturbation terms that are further calculated from the received soft symbols.

[0013] In this regard, a "soft symbol" is a point in the complex plane that corresponds to a received constellation symbol from the input optical channel after linear equalization, and as such, it may be affected by noise and may therefore deviate from the exact point in the complex plane where the original constellation symbol was located.

[0014] Soft symbols are subject to fiber nonlinearity and noise, among other factors, and can be corrupted, resulting in soft symbols generally not matching exactly in value with symbols from the constellation used for transmission.

[0015] The mapping of soft symbols to constellation symbols, resulting in the output of "hard symbols," is performed by a hard-decision processor. The range of possible values ​​for soft symbols is much larger than the range of hard symbols, which are limited to discrete constellation points. Therefore, it typically takes significantly more bits to represent soft symbols with sufficient precision than it takes to represent hard symbols.

[0016] In our new scheme, the perturbation terms are calculated from hard symbols rather than soft symbols, which requires fewer bits to represent, reducing the computational complexity.

[0017] As noted above, hard decisions made before computing the perturbation terms can conceivably introduce decision errors that can degrade receiver performance. As further noted above, the inventors believe that a multi-stage approach can overcome this drawback. In a first stage of the multi-stage approach, input soft symbols are subjected to hard decisions, perturbation terms are computed from the resulting hard symbols and a first subset of nonlinear contributions, and new soft symbols are computed using the computed perturbation terms.

[0018] In each subsequent stage, a new set of perturbation terms is calculated as described above, but using a subset of the nonlinear contributions that is independent from the subset used in the previous stage or stages. "Independent" subsets mean subsets that have no common elements. The perturbation calculations become progressively more refined as they progress through multiple stages.

[0019] Accordingly, the present disclosure relates in one aspect to a method that may be performed in each of one or more stages in a digital signal processor for a coherent optical receiver, the method including obtaining an input stream of soft data symbols, generating a stream of perturbation terms that represent optical nonlinearities of an optical transmission channel, and compensating, using the perturbation terms, each of the soft data symbols in the input stream of soft data symbols for the optical nonlinearity.

[0020] To generate a stream of perturbation terms, an input stream of soft data symbols is transformed into an input stream of hard data symbols, and the method operates on the input stream of hard data symbols to produce the perturbation terms. Operating on the input stream of hard data symbols includes forming weighting coefficients. For each of the perturbation terms, operating on the input stream of hard data symbols further includes forming a weighted sum of the hard data symbols using the weighting coefficients.

[0021] The input stream of soft data symbols for a first of the one or more stages is produced from a stream of measurements of an optical signal received by an optical receiver.

[0022] In an embodiment, using the perturbation term for compensation may include subtracting the perturbation term from each of the soft data symbols to produce a compensated version of the soft data symbol.

[0023] In an embodiment, the method may be performed in a series of stages, where at each stage after the first stage in the series, obtaining an input stream of soft data symbols includes obtaining compensated soft data symbols generated by a previous stage in the series.

[0024] In an additional embodiment to any of the above embodiments, each weighting factor is formed at least in part by performing a convolution between a set of channel coefficients and a set of multiplicative products of hard data symbols, the channel coefficients being complex numbers that characterize nonlinear effects of the optical transmission channel. Each respective convolution may be performed numerically in the time domain. Alternatively, each convolution may correspond to a respective linear filter, and each respective convolution may be performed numerically by evaluating the corresponding linear filter in the frequency domain.

[0025] In an additional embodiment to any of the above embodiments, the method may be performed in a series of two or more stages, where in each stage, a weighted sum of a set of N terms is formed from the input stream of hard data symbols for that stage in generating each perturbation term, where N is a predetermined positive integer, and the respective sets of N terms used in different stages are independent of each other.

[0026] In an embodiment in addition to any of the above embodiments, the last of the one or more stages may direct a stream of compensated soft data symbols to a decoder, where the directed stream is decoded.

[0027] In an embodiment, using the perturbation terms to compensate the soft data symbols may include forwarding at least some of the perturbation terms to a soft-decision FEC decoder, and performing soft-decision compensation of at least some of the soft data symbols in the FEC decoder using the forwarded perturbation terms.

[0028] In a second aspect, the present disclosure relates to an apparatus including a digital signal processor including one or more PNC stages for performing perturbation-based optical nonlinearity compensation of measurements of an optical data signal in an optical receiver. Each PNC stage includes circuitry configured to convert a stream of soft data symbols into a stream of hard data symbols. Each PNC stage further includes PNC circuitry configured to generate a stream of perturbation terms from the hard data symbols. Each PNC circuit is configured to generate individual ones of the perturbation terms as a weighted sum of the hard data symbols. The digital signal processor further includes at least one circuitry configured to compensate individual ones of the soft data symbols using corresponding ones of the perturbation terms.

[0029] In an embodiment, the digital signal processor may include a series of PNC stages, each configured to subtract a respective perturbation term from a respective soft data symbol to generate a corrected soft data symbol. The PNC circuitry in each PNC stage except the last PNC stage in the series is configured to output the corrected soft data symbols therefrom to the next PNC stage in the series, which is configured to output the corrected soft data symbols therefrom to a decoder.

[0030] In an apparatus embodiment in addition to any of the above embodiments, the PNC circuitry in each PNC stage may be adapted to perform a convolution between a set of channel coefficients and a set of multiplicative products of hard data symbols to generate weighting coefficients, the channel coefficients representing nonlinear effects of the optical transmission channel. In some embodiments, the PNC circuitry in each PNC stage may be adapted to perform the convolution numerically by evaluating a corresponding linear filter in the frequency domain.

[0031] In an apparatus embodiment in addition to any of the above embodiments, the digital signal processor may include two or more series of PNC stages, wherein the PNC circuitry in each PNC stage is configured to form each of its respective weighted sums from a set of N terms selected from the stream of hard data symbols, where N is a predetermined positive integer, and the sets of N terms used by each PNC stage are independent of each other.

[0032] In an embodiment, the digital signal processor may further include a soft-decision FEC decoder, wherein the PNC circuit of the last stage of the one or more PNC stages is configured to output the stream of soft data symbols and the stream of perturbation terms to the soft-decision FEC decoder, and the soft-decision FEC decoder is configured to perform soft-decision compensation on the output soft data symbols using the output perturbation terms. [Brief explanation of the drawings]

[0033] [Figure 1] 1 is a diagram illustrating a schematic of an optical fiber communication system; [Figure 2] FIG. 1 is a block diagram illustrating a coherent optical data transmitter in which some pre-compensation of nonlinear optical effects is performed digitally in a DSP. [Figure 3] FIG. 1 is a block diagram illustrating a coherent optical data receiver that digitally implements post-compensation of some of the nonlinear optical effects in a DSP. [Figure 4] FIG. 1 is a block diagram of a PNC equalizer circuit that can perform nonlinear processing by operating on an input signal stream to produce a stream of perturbation terms, correct symbol components of the input signal stream by combining the symbol components of the input signal stream with the respective perturbation terms, and output a corrected signal stream. [Figure 5] FIG. 1 is a simplified block diagram of a PNC implementation using FFT processing according to principles described herein. [Figure 6]1 is a simplified block diagram of an architecture for PNC equalization with reduced computational complexity. [Figure 7] 1 is a simplified block diagram of a soft-decision PNC scheme according to principles described herein; [Figure 8] 1 is a simplified block diagram of a new scheme for hard-decision PNC according to principles described herein; [Figure 9] FIG. 1 is a simplified block diagram of a hard-decision PNC scheme in a multi-stage implementation according to principles described herein. [Figure 10] FIG. 1 is a block diagram showing the architecture for a coherent optical receiver represented as an optical front end and a DSP chain. [Figure 11] 1 is a simplified block diagram of an example scheme for soft decision compensation according to principles described herein; [Figure 12] FIG. 1 is a simplified block diagram of an optical receiver architecture showing the processing of multiple wavelength channels. [Figure 13] 1 is a flow chart summarizing a method according to some of the principles described herein. [Figure 14] 1 is a flow diagram summarizing an alternative method according to some of the principles described herein. DETAILED DESCRIPTION OF THE INVENTION

[0034] This Detailed Description and its accompanying drawings are intended merely to illustrate the principles of the present invention. Based on this specification, one skilled in the art will be able to devise various configurations which, although not explicitly described or shown herein, embody the present invention and fall within the scope of the claims. Moreover, statements herein reciting principles, aspects, and embodiments are intended to encompass equivalents thereof.

[0035] FIG. 1 illustrates an optical fiber communication system 10 including an optical data transmitter 12, an optical data receiver 14, and an optical fiber line 16. The optical fiber line 16 forms an all-optical communication channel between the optical data transmitter 12 and the optical data receiver 14. The optical fiber line 16 comprises one or more optical fiber spans, typically single-mode optical fiber spans (FS) as shown, that are connected all-optically at optical nodes (ONs). The optical data transmitter 12, or the optical data receiver 14, or the transmitter 12 and the receiver 14, each include a digital signal processor (DSP) configured to evaluate corrections to the transmitted optical signal and digitally compensate for intra-channel and / or inter-channel signal impairments that are attributable, at least in part, to nonlinear optical effects in the optical fiber line 16.

[0036] 2 illustrates an exemplary embodiment 12' of the optical data transmitter 12 of FIG. 1. As shown, the transmitter 12' is configured to impose a respective data modulation on each of two orthogonal polarizations of an optical carrier, conventionally referred to as the x-polarization and the y-polarization, respectively. The transmitter 12' may also digitally pre-compensate the optical signal, at least in part, for nonlinear optical effects occurring, for example, in the optical fiber line 16 of FIG. 1.

[0037] The optical data transmitter 12' can transmit an independent signal on each of multiple optical carriers having different wavelengths. In other words, the optical data transmitter 12' can transmit on multiple wavelength channels. However, for simplicity of explanation, the optical data transmitter 12' is described herein without explicit reference to more than a single wavelength channel.

[0038] As shown, the optical data transmitter 12 ′ includes a light source 22 , first and second optical data modulators 24 , 26 , respectively, electrical drivers 28 , 30 for the optical data modulators 24 , 26 , and a digital signal processor (DSP) 32 .

[0039] The light source 22 is typically a narrowband telecommunications laser. As shown, the optical wavelength carrier from the light source 22 is directed as an input to an optical polarization splitter PS. The two outputs of the splitter PS, which have orthogonal polarizations, are input to respective optical data modulators 24, 26 via optical paths OP. Each optical data modulator 24, 26 optically modulates a digital data stream onto its respective polarization component of the optical wavelength carrier. The optical outputs of the optical data modulators 24, 26 are connected via optical paths OP to the optical inputs of a polarization combiner PC. The polarization combiner PC has an optical output that connects to the proximal end of the optical fiber line 16. The modulated optical signals from the modulators 24, 26 are injected into the proximal end of the optical fiber line 16 and carried through the optical fiber line 16 in the respective orthogonal polarization states of the optical wavelength carrier.

[0040] Each electrical driver 28, 30 receives a digital control signal from the DSP 32 and, in response, outputs a respective analog voltage drive signal to operate the optical data modulators 24, 26. More specifically, each electrical driver 28, 30 receives a digital control signal

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[0041] The x-series and y-series digital control signals control the modulation of the x- and y-polarization components of the optical carrier, respectively. In some embodiments, the drive control signals can also provide pre-compensation for nonlinear optical effects, and possibly dispersion, of the optical fiber line 16.

[0042] As shown in the figure, the DSP32 receives as input a digital symbol stream {X k}=X k ,X k+1 , etc., and the digital symbol stream {Y k}=Y k ,Y k+1 , etc., and the DSP32 processes these received digital symbol streams to generate corresponding digital signals

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[0043] A digital modulator produces a digital symbol stream by mapping input data, in the form of a binary bit stream, to symbols selected from a desired modulation constellation.

[0044] 3 illustrates an exemplary embodiment 14′ of the optical data receiver 14 of FIG. 1 configured for use in a coherent optical fiber communication system. As described below, the optical data receiver 14′ digitally at least partially post-compensates for nonlinear optical effects occurring in the entire optical fiber line 16.

[0045] The optical data receiver 14' can receive an independent signal on each of multiple optical carriers having different wavelengths. In other words, the optical data receiver 14' can receive on multiple wavelength channels. However, for simplicity of explanation, the optical data receiver 14' is described herein without explicit reference to more than a single wavelength channel.

[0046] As shown in the figure, the optical data receiver 14' includes a local optical oscillator 40, first and second polarization splitters 41.1, 41.2, first and second optical mixers 42, 44, photodetector arrays 46, 48, two electrical hardware series 50, 52, and a DSP 54.

[0047] Local optical oscillator 40 is typically a narrowband telecommunications laser with a wavelength close to that of optical data transmitter 12 of FIG. 1, for example, suitable for intradyne coherent optical detection.

[0048] In the illustrated example, an optical signal received from the end of optical fiber line 16 is directed to optical polarization splitter 41.1, which separates the two orthogonally polarized components of the received light and sends them via optical paths OP to the respective optical inputs of first and second optical mixers 42, 44. The optical output from local oscillator 40 is directed via optical path OP to optical polarization splitter 41.2, which separates the two orthogonally polarized components of the light from local oscillator 40 and sends them via optical paths OP to the respective optical inputs of first and second optical mixers 42, 44. Thus, each of optical mixers 42, 44 receives a respective one of the orthogonally polarized components of the optical signal, i.e., the x component or the y component, from each of polarization splitters 41.1 and 41.2.

[0049] Each of the optical mixers 42, 44 combines light received from an optical input signal with light received from a local optical oscillator to produce a respective one of the two modulated components of the received optical input signal. By way of example, the optical mixer 42 may combine the x component of the light received from, for example, an optical polarization splitter to provide as an output an optical signal representing the in-phase (I) component of the received optical signal. Correspondingly, the optical mixer 44 may combine the y component of the light received from, for example, an optical polarization splitter to provide as an output an optical signal representing the quadrature (Q) component of the received optical signal.

[0050] Each of the optical mixers 42 and 44 has a pair of optical outputs that are phase shifted relative to one another, as shown in Figure 3. These phase shifts condition the output signals for coherent optical detection according to principles well known in the art.

[0051] Each pair of outputs from the optical mixers 42 and 44 is directed to a respective photodetector array 46, 48. Each of the photodetector arrays 46, 48 is configured to generate an analog electrical signal indicative of the I or Q component, respectively, of the received optical signal, responsive to the input received from the respective optical mixer. According to typical convention in the art, the signal in the x-polarization channel corresponds to the I component, and the signal in the y-polarization channel corresponds to the Q component of the received optical signal.

[0052] In the illustrative example, each of the optical mixers 42, 44 includes a 90-degree optical hybrid, and each of the light intensity photodetector arrays 46, 48 includes a balanced pair of photodiodes connected for differential detection of light intensity.

[0053] In the example shown in Figure 3, the electrical output from each photodetector array 46, 48 is directed to a respective series 50, 52 of electronic hardware components. As known in the art, each series 50, 52 can include, for example, electronic amplifiers, electronic low-pass filters, and analog-to-digital converters. Series 50 and series 52 process the photodetector outputs of the respective x-polarization and y-polarization channels using known methods, such as low-pass filtering. The processing in series 50 and series 52 includes analog-to-digital conversion (not explicitly shown in the figure), whereby digital electrical signals are output for each polarization channel.

[0054] The digital signal streams output from series 50 and series 52 are directed to a digital signal processor (DSP) 54 .

[0055] DSP 54 digitally processes the x-channel digital signal stream and the y-channel digital signal stream received from series 50 and series 52, thereby recovering the data symbol stream transmitted by optical data transmitter 12 of Figure 1. In a typical example, DSP 54 includes a linear processing circuit (LC), as shown in Figure 3, for example. The linear processing circuit can be used to at least partially compensate for signal degradation due to causes such as chromatic dispersion, polarization dispersion, polarization rotation, and attenuation in optical fiber line 16.

[0056] DSP 54 also typically includes circuitry for correcting for frequency offsets between local optical oscillator 40 and the optical input signal received from optical fiber line 16. Frequency offset compensation is typically considered part of linear processing. As such, frequency offset compensation is not separately called out in FIG. 3 but should instead be understood as being included among the operations performed by the linear processing circuitry. (In contrast, linear processing is represented by separate "Linear Equalizer" and "Demodulator" blocks in FIG. 10, discussed below. The Demodulator block in FIG. 10 performs carrier frequency recovery and carrier phase recovery.)

[0057] The output of the linear processing circuit LC is, in the example shown, a digital signal stream {x k}=x k ,x k+1 and a y-channel digital signal stream {y k}=y k ,y k+1 .... The index "k" is the consecutive label of the sampling time slot.

[0058] Downstream of the linear processing circuit LC, the DSP 54 converts the digital signal stream {x k} and {y k} to generate a digital signal stream

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[0059] Signal Stream

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[0060] More specifically, the DSP 54 converts the digital signal stream {x k} and {y k}. k} and {y k}, the nonlinear processing circuit NPC generates a respective stream of correction coefficients {Δx k}=Δx k ,Δx k+1 and {Δy k}=Δy k ,Δy k+1 The DSP 54 outputs the correction coefficient Δx as shown in FIG. k , Δy k and their corresponding digital signal elements x k and y k to produce an at least partially compensated digital data output signal.

[0061]

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[0062] As explained above, the optical data transmitter 12 of Figure 1 includes a digital modulator that creates a digital symbol stream for transmission by mapping input data in the form of a binary bit stream to symbols selected from a desired modulation constellation. Returning to Figure 3, the DSP 54 can include processing stages that operate to recover the binary bit stream transmitted by the optical data transmitter 12.

[0063] More specifically, the DSP 54 may include, for example, a conventional digital decoder DD that operates to recover the transmitted data symbols as a binary bit stream.

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[0064] FIG. 4 is a block diagram of a PNC equalizer circuit, which is configured to equalize an input signal stream {x k} and {y k} by performing nonlinear processing to generate a stream of perturbation terms {Δxk} and {Δy k} and each symbol component x k or y k Each perturbation term Δx k or Δy k Each symbol component x is combined with k or y k and the corrected signal stream

[0065]

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[0066] Therefore, Figure 4 shows that the stream {Δx k}, and a block 60 for x-channel perturbation calculations that produces stream {Δy k}, and a block 62 for the y-channel perturbation calculation for each perturbation term Δx k the corresponding symbol component x k and subtract it from the corresponding corrected symbol component

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[0067] Although omitted from the drawing for simplicity of illustration, those skilled in the art will appreciate that the equalizer circuit of FIG. 4 divides each symbol component x k and y k is time-aligned with the corresponding perturbation term in each summation element. k} and {yk} It will be appreciated that the .send() method further includes a delay element for the stream.

[0068] FIG. 4 further shows a look-up table (LUT) 68, which receives perturbation coefficients C as inputs to the x-channel and y-channel perturbation calculations. m,n The perturbation coefficients and their role in the perturbation calculation are defined in more detail below. The perturbation coefficients depend on the link configuration. In an example, the perturbation coefficients can be calculated offline or, alternatively, estimated by a least mean squares (LMS) algorithm, for example, as reported in W. Peng et al, "Training-based Determination of Perturbation Coefficients for Fiber Nonlinearity Mitigation," 2015 Optical Fiber Communications Conference and Exhibition (OFC) (2015) 1-3.

[0069] The calculation of the perturbation coefficients can be based on a priori known transmitter information about, for example, channel chromatic dispersion, fiber nonlinear coefficients, inhomogeneous span length, and random fiber launch power.

[0070] The resulting values ​​for the perturbation coefficients may be stored quasi-statically in the LUT 68 .

[0071] As an example, a useful calculation of the perturbation coefficients can be based on the channel model reported in R. Dar et al., "Inter-Channel Nonlinear Interference Noise in WDM Systems: Modeling and Mitigation," J. Lightwave Technol. 33 (2015) 1044-1053. As reported there, the model of fiber nonlinearity assumes a temporal pulse matching condition, as reported, for example, in A. Ghazisaeidi and R. Essiambre, "Calculation of coefficients of perturbative nonlinear pre-compensation for Nyquist pulses," The European Conference on Optical Communication (ECOC), Cannes (2014) 1-3. Under those models, the perturbation coefficients are given by C m,n =-S m,n,m+n (1)

[0072]

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[0073] In the above expression, S m,n,l are complex coefficients, m, n, and l are discrete time indices, t is a (continuous) time variable, L is the total link length, the function f(z) describes the loss / gain profile of the fiber link, and h(z,t) is the pulse-shaped waveform that has propagated in the fiber up to distance z.

[0074] For example, the perturbation calculation that may be performed by the PNC circuit of FIG.

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[0075] The total limits M and N in the above equations depend primarily on the signal accumulation dispersion in the fiber link. As such, they are system parameters. For a given system scenario, there will generally be a most favorable pair of M and N values ​​that optimizes equalizer performance. In practical applications, these values ​​have a wide range, up to values ​​of approximately 1000 or more, depending on the system architecture. Reducing the M and N values ​​can simplify circuit complexity, but such simplification may come at the cost of degraded equalizer performance.

[0076] The optimum value depends on the signal accumulation variance, but this relationship is not well modeled as a closed-form expression due to the complexity of modeling nonlinear behavior, so the optimum value is generally obtained by numerical simulation.

[0077] A computational technique that can reduce the complexity of the perturbation calculations is reported in the above-cited publication EP 3,157,180. As explained there, equations (3) and (4) are written as follows: the k-th perturbation term is a perturbation term with 2M+1 symbols x k-m or y k-m where each of the weights is a perturbation coefficient C m,n and the product term

[0078]

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[0079] That is, the amount

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[0080]

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[0081] Therefore, the convolutions are evaluated in the discrete time domain. However, each of the convolutions in equations (6) and (7) can be equivalently formulated as a linear filter evaluated in the frequency domain. The filter taps in the time domain are the coefficients C m,n is.

[0082] The transformation between the time domain and the frequency domain is achieved, for example, by using a fast Fourier transform (FFT) and an inverse fast Fourier transform (IFFT). Calculating the filtering in the frequency domain with a fast Fourier transform (FFT) and then inverse transforming with an inverse fast Fourier transform (IFFT) is beneficial because the computational complexity is reduced to O(M log N).

[0083] Therefore, the cumulative double sum terms in equations (6) and (7) can each be calculated in the following three steps: (i) Product

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[0084] Figure 5 is a simplified block diagram of a PNC implementation using FFT processing. In the diagram, blocks 70 and 71 are multipliers.

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[0085] In Figure 5, symbol C M and C -M indicates, together with the legend 2*M+1, that there are 2M+1 banks of branches, only two of which are explicitly depicted in the diagram. For each index m=-M, ,0, ,M, the full set of perturbation coefficients, or equivalently the full set of taps of the corresponding linear filter, is given by C m ={C m,-N ,···,C m,N}. Similarly, the symbol

[0086]

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[0087] The above-referenced U.S. Patent Application No. 10,756,822 reports a technique that can further reduce the computational complexity. Figure 6 is a simplified block diagram of an architecture that can implement such a technique. As shown in the figure, the architecture includes, as in Figure 5,

[0088]

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[0089]

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[0090] The bandwidth of the low-pass anti-aliasing filter P(z) is determined by the decimation rate. Different impulse responses can be adopted for the low-pass anti-aliasing filter. After low-pass filtering,

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[0091] Next,

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[0092] The perturbation terms are expressed by the following equations (8) and (9):

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[0093] Equations (8) and (9) are similar to equations (3) and (4), except that the computed perturbation terms are marked with the superscript "soft" to emphasize that these terms are computed from received input symbols, which are soft symbols.

[0094] 7 is a simplified block diagram of a soft-decision PNC scheme. Corrected symbols are calculated in PNC block 100. To simplify the diagram, the summation over n in equations (8) and (9) is implicitly implied to be contained in 2M+1 calculation branches, each with index m, and the legend "m∈[-M,M]" indicates that it takes on values ​​-M, , , M. As shown in the diagram, the soft symbols x k and y k takes two paths. In the upper path, the soft symbols are delayed 102. In the lower path, the soft symbols pass through a PNC block 100, which outputs a perturbation term. The perturbation term is the sum of the delayed soft symbols x k and y k 104, 106 are added to.

[0095] As noted above, the evaluation of perturbation terms by the method of Figure 7 requires at least the form x in equations (8) and (9). k-mx k-n x * k-m-n ,x k-m y k-n y * k-m-n ,y k-m y k-n y * k-m-n , and y k-m x k-n x * k-m-n is computationally expensive since the multiplicative product of involves multiple multiplications between complex-valued soft symbols.

[0096] Under our new hard-decision PNC scheme, the perturbation term is

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[0097] Equations (10) and (11) are of similar form to equations (8) and (9). However, the perturbation term is marked with the superscript "hard" to emphasize that it is calculated from hard symbols rather than soft symbols. Similarly, x in equations (10) and (11) k and y k Terms are marked with a circumflex to emphasize that they are calculated from hard symbols rather than soft symbols.

[0098] Figure 8 is a simplified block diagram of our new hard-decision PNC scheme. Elements that Figure 8 has in common with Figure 7 are referred to by similar reference numerals. The architecture of Figure 8 is similar to that of Figure 7, except that the input to the PNC block 100 is now hard symbols. More specifically, the input soft symbols x k and y k takes two paths. In the upper path, the soft symbols are delayed 102. In the lower path, the soft symbols are delayed 103 for each decision direction (D Dir ) Pass through blocks 108 and 110. D DirThe output from the block is a hard symbol.

[0099]

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[0100] After the perturbation is calculated using the hard symbols, it is calculated using the delayed soft symbols x k and y k 104, 106 are added to.

[0101] The hard-decision PNC scheme of Figure 8 has a single PNC stage. While such a single-stage scheme offers a beneficial reduction in computational complexity, it also has the disadvantage that, at least under some scenarios, it is susceptible to performance degradation because hard decisions on received symbols can introduce decision errors.

[0102] However, the inventors have developed a multi-stage scheme that can make the decisions more reliable. Figure 9 is a simplified block diagram of our multi-stage hard-decision PNC scheme. As shown in the figure, the PNC computation is now split into multiple serial stages 121, 122, 123, each of which involves a hard-decision operation 125 on the soft symbols in each of the two polarization channels.

[0103] At each stage, a different nonlinear contribution is evaluated and applied to the input signal. What is meant by "nonlinear contribution" is best understood by referring back to Figure 5, which shows an example in which the perturbation terms are calculated in 2M+1 computation branches, each indexed by a respective value of index m. Each of the 2M+1 computation branches provides a respective "nonlinear contribution."

[0104] Returning to FIG. 9, note that each PNC stage in FIG. 9 computes perturbation terms by implementing only a selected few computation branches rather than all of the 2M+1 computation branches.

[0105] In each stage of a multi-stage scheme, the index m identifying the selected branch can only take on a subset of all possible values ​​between -M and M. Each stage implements a subset that is independent of the subsets implemented by other stages, i.e., no two of these subsets have any elements in common. As an example, Figure 9 provides a non-limiting example in which in the first stage, m takes on values ​​of -2, -1, 1, 2; in the second stage, m takes on values ​​of -4, -3, 3, 4; and in the third stage, m takes on values ​​of -6, -5, 5, 6. This type of serial scheme is feasible because each nonlinear contribution is independent of the others.

[0106] 9 provides an example with three stages, this number should not be understood as limiting: in certain embodiments there may be as few as two stages, or even a single stage, while in other embodiments the number of stages may be greater than three.

[0107] After each PNC stage, the soft symbols are updated by summing them with the new values ​​of the perturbation coefficients. After each update, the updated symbols for each polarization channel proceed to the next update in the upper branch and to the hard decision before the next PNC stage in the lower branch. In this way, the effective signal-to-noise ratio (SNR) of the signal can be improved with each stage. As a result, the hard decisions made before each stage can become increasingly reliable, which can reduce the overall decision error compared to a hard-decision PNC with a single stage.

[0108] An exemplary embodiment of an optical data receiver was discussed above with reference to Figure 3. Returning to Figure 3, it will be seen that the illustrated optical data receiver 14' includes a local optical oscillator 40, first and second polarization splitters 41.1, 41.2, first and second optical mixers 42, 44, photodetector arrays 46, 48, two electrical hardware series 50, 52, and a DSP 54. One of the two photodetector arrays produces an electrical output for the x-polarized channel, and the other photodetector array produces an electrical output for the y-polarized channel.

[0109] It will also be appreciated that the electrical output from each photodetector array 46, 48 is directed to a respective series 50, 52 of electronic hardware components, each series including, for example, electronic amplifiers, electronic low-pass filters, and analog-to-digital converters (ADCs). There is an ADC output for each of the two polarization channels.

[0110] As shown in FIG. 3, the ADC outputs of each polarization channel (shown in the figure as respective outputs of series 50 and series 52) are directed to a digital signal processor (DSP) 54.

[0111] With further reference to FIG. 3, it can be seen that DSP 54 includes a linear processing circuit (LC), a non-linear processing circuit NPC that calculates perturbation terms, elements that combine the perturbation terms with corresponding symbols from the received signal, and processing stages such as the digital decoder DD shown in the figure.

[0112] The various processing stages shown in Figure 3 that may be performed by a digital signal processor (DSP) may, in an alternative diagrammatic representation, be shown as elements of a DSP chain. Figure 10 is a block diagram in which the architecture of Figure 3 is partially represented as a DSP chain 130.

[0113] In Figure 10, the optical front end 132 includes the local optical oscillator, polarization splitter, optical mixer, and photodetector array of Figure 3. The optical front end 132 also includes some of the electrical hardware components of Figure 3. However, in Figure 10, the ADC function has been removed from the optical front end and is instead shown as the front portion of the DSP chain 132. Thus, the ADC function is represented in Figure 10 by ADC 134 for one of the two polarization channels and ADC 136 for the other of the two polarization channels.

[0114] 10, it can be seen that DSP chain 130 includes linear equalizer blocks 138 and 140 for each polarization channel. These blocks correspond to the linear processing circuit (LC) of FIG. 3. Demodulator blocks 142 and 144 follow the linear equalizer blocks. These demodulators, which were implicit in the linear circuit LC in FIG. 3, extract the soft symbols x from the ADC output after linear equalization. k , y k Carrier frequency recovery and carrier phase recovery are performed to calculate

[0115] The nonlinear equalization block 146 in Figure 10 corresponds to the nonlinear processing circuit NPC in Figure 3, and the decoder blocks 148 and 150 in Figure 10 correspond to the digital decoder DD shown in Figure 3. As an example, the decoder blocks 148 and 150 may perform FEC decoding.

[0116] 10, the equalizer for hard-decision NPC is preferably placed after linear equalization and signal demodulation, as shown. This provides a way to ensure that calculations can be performed at a rate of one sample per symbol. After being calculated, each perturbation term output by the nonlinear equalizer can be directly subtracted from the corresponding symbol before FEC decoding. This sequence is called "hard-decision compensation."

[0117] Alternatively, the perturbation term can be included in the calculation of the symbol log-likelihood ratios (LLRs) required for soft-decision FEC decoding. This alternative sequence is called "soft-decision compensation."

[0118] 11 is a simplified block diagram of an exemplary scheme for soft decision compensation. Drawing elements common to FIGS. 8 and 11 are designated with like reference numerals. As shown in FIG. 11, the soft symbols x k and y k is passed to the soft FEC decoder 160 after a timing delay 102. The output from the PNC stage 100 is the perturbation term Δx k and Δy k , which are also passed to the soft FEC decoder.

[0119] As shown in Figure 11, there is only a single PNC stage before the perturbation terms are passed to the soft FEC decoder for soft decision compensation. If the PNC is performed in multiple stages, the perturbation terms calculated in the last stage may be passed to the soft FEC decoder.

[0120] Whether hard-decision or soft-decision compensation is used, nonlinear compensation at the receiver side is performed by the LMS algorithm. m,n A potential benefit is that it can be implemented in an adaptive equalizer that estimates the coefficients.

[0121] As described above, an optical data receiver can receive independent signals on multiple optical carriers each having a different wavelength. In other words, the optical data receiver can receive multiple wavelength channels. However, for simplicity, the description of the optical data receiver and the accompanying drawings do not explicitly refer to more than a single wavelength channel. FIG. 12 is a simplified block diagram of an optical receiver architecture illustrating the processing of multiple wavelength channels. As shown in the drawing, an optical input signal 170 is wavelength-demultiplexed into individual wavelength channels in a demultiplexer 175. The signals of each wavelength channel are directed to respective optical front ends 180.1, 180.2, ..., 180.n and respective DSP chains 185.1, 185.2, ..., 185.n. Although omitted from the drawing for simplicity, signals of multiple wavelength channels can be routed to each DSP chain to facilitate compensation for inter-channel interactions.

[0122] It is worth noting that the hard-decision NPC techniques described herein can be applied to any standard modulation format for optical fiber transmission systems without introducing additional computational complexity.

[0123] FIG. 13 summarizes in a flow diagram a method according to some of the principles described herein. The method is performed in one or more stages. The diagram shows a first stage 190 and a last stage 195. Referring initially to the first stage 190, soft data symbols are obtained from an input signal stream 205 in block 200. In block 210, the soft data symbols are converted to hard symbols. In block 220, weighting coefficients are formed using data from a channel model 225. In block 230, perturbation terms are generated as a weighted sum using the weighting coefficients. Blocks 210, 220, and 230 jointly constitute an operation 235 that provides perturbation terms. In block 240, the soft data symbols are compensated using the perturbation terms, thereby providing compensated soft data symbols that may be output to a decoder in a single-stage approach or passed to the next stage in a multi-stage approach, as shown in FIG. 13.

[0124] In the final stage 195 of the multi-stage approach, the most recently compensated soft data symbols are obtained from the previous stage in block 250 and perturbation terms are provided in block 260, similar to block 235 discussed above. A stream of compensated soft data symbols is generated in block 270 and passed to decoder block 280 for decoding into an output stream of decoded bits.

[0125] 14 summarizes in a flow diagram an alternative method according to some of the principles described herein. As shown, the method is performed in a single stage 285, although multi-stage implementations are not excluded.

[0126] Some of the blocks shown in FIG. 14 represent operations similar to those represented in corresponding blocks in FIG. 13 and are therefore designated using similar reference numerals.

[0127] Soft data symbols are obtained from an input signal stream 205 in block 200. The soft data symbols are converted to hard symbols in block 210. Weighting coefficients are formed using data from a channel model 225 in block 220. Perturbation terms are generated as weighted sums in block 230 using the weighting coefficients. Blocks 210, 220, and 230 collectively comprise an operation 235 that provides the perturbation terms.

[0128] Departing from the method of FIG. 13, the perturbation terms and soft data symbols are passed 290 to a decoder block for soft decision compensation and FEC decoding. [Explanation of symbols]

[0129] 10 Optical Fiber Communication Systems 12 Optical Data Transmitter 12' transmitter 14 Optical Data Receiver 16 Fiber Optic Lines 22 Light source 24, 26 Optical Data Modulator 28, 30 Electric screwdriver 32 Digital Signal Processor (DSP) 40 Local Optical Oscillator 41.1, 41.2 Polarization Splitter 42, 44 Optical mixer 46, 48 Photodetector array 50, 52 Electrical Hardware Series 54 DSP 60 x Blocks for channel perturbation calculations 62 Block for y-channel perturbation calculation 64, 66 Addition elements 68 Look-Up Tables (LUTs) 70, 71 Blocks that calculate the product 72, 73 Blocks that transform the problem into the frequency domain 74, 75 Blocks that calculate IFFT 76, 77 Multiplier 80, 81 calculation 82, 83 FFT stages 84 multiplier stages 86, 87 IFFT Stage 88, 89 Filtering 90, 91 decimated 92, 93 Interpolation 94, 95 Blocks representing the low-pass anti-imaging filter G(z) 100 PNC Stage 102 Timing Delay 104, 106 circuits 108, 110 Judgment instruction (D Dir )block 121, 122, 123 series stages 125 Hard decision operations 130 DSP Chain 132 Optical Front End 134, 135 ADC 138, 140 linear equalizer 142, 144 Demodulator 146 Nonlinear Equalization 148, 150 decoder blocks 160 Soft FEC Decoder 170 Optical Input Signal 175 Demultiplexer 180.1, 180.2, 180.n Optical Front End 185.1, 185.2, 185.n DSP Chain 190 First Stage 195 Final Stage 200 Block to get soft data symbols 205 Input Signal Stream 210 Blocks to convert to hard data symbols 220 Blocks forming weighting factors 225 channel model 230 Block that generates perturbation terms as a weighted sum 235 Operations that provide perturbation terms 240 Soft Data Symbol Compensation Block 250 Blocks to get soft data symbols 260 Blocks to convert to hard data symbols 270 Soft Data Symbol Compensation Block 280 Decoder Block 285 Single Stage 290 Passed to the decoder block for soft decision compensation and FEC decoding LC linear processing circuit NPC Nonlinear Processing Circuit D Delay Elements DD Digital Decoder

Claims

1. In each of one or more stages in a digital signal processor for a coherent optical receiver, Obtaining an input stream of soft data symbols (200); generating (235) a stream of perturbation terms representing optical nonlinearities in the optical transmission channel; using the perturbation term to compensate each one of the soft data symbols in the input stream of soft data symbols for the optical nonlinearity (240, 290); A method comprising: generating the stream of perturbation terms includes converting (210) the input stream of soft data symbols into an input stream of hard data symbols and operating on the input stream of hard data symbols to produce the perturbation terms; said operating on the input stream of hard data symbols includes forming weighting factors (220) and, for each of said perturbation terms, forming a weighted sum of said hard data symbols using said weighting factors (230); the digital signal processor is configured to produce the input stream of soft data symbols for a first stage of the one or more stages from a stream of measurements of an optical signal received by the coherent optical receiver; said compensating each one of said soft data symbols using said perturbation term comprises subtracting said perturbation term from each one of said soft data symbols to produce said compensated one of said soft data symbols (240); The method is performed in a series of stages, each stage estimating a different nonlinear contribution and applying the estimated different nonlinear contribution to an input stream of soft data symbols, and in each stage after the first stage of the series, obtaining (200) includes obtaining (250) the compensated soft data symbols generated by a previous one of the stages in the series.

2. each of said weighting coefficients is formed at least in part by performing a convolution between a set of channel coefficients and a set of multiplicative products of hard data symbols; The method of claim 1 , wherein the channel coefficients are complex numbers that characterize nonlinear effects of the optical transmission channel.

3. The method of claim 2 , wherein each respective convolution is performed numerically in the time domain.

4. The method of claim 2 , wherein each convolution corresponds to a respective linear filter, and each respective convolution is performed numerically by evaluating the corresponding linear filter in the frequency domain.

5. the series having one or more of the stages (190, 195); at each stage, said generating each of the perturbation terms in a stream of perturbation terms includes forming a weighted sum of a set of N terms from the input stream of hard data symbols for that stage, where N is a predetermined positive integer; The method of claim 2 , wherein each set of N terms used in two or more of the stages are independent of each other.

6. a final stage (195) of the one or more stages directs the stream of compensated soft data symbols to a decoder; 2. The method of claim 1, further comprising: decoding (280) the derived stream at the decoder.

7. said compensating for each of said soft data symbols using said perturbation terms; passing at least some of the perturbation terms to a soft-decision FEC decoder; performing soft-decision compensation of at least some of the soft data symbols using the advanced at least some of the perturbation terms in the soft-decision FEC decoder (290); The method of claim 1 , comprising:

8. 1. An apparatus comprising a digital signal processor including one or more PNC stages (121, 122, 123) for performing perturbation-based optical nonlinearity compensation of measurements of an optical data signal in an optical receiver, the apparatus comprising: Each PNC stage: a circuit (108) configured to convert the stream of soft data symbols into a stream of hard data symbols; a PNC circuit (100) configured to generate a stream of perturbation terms from the hard data symbols, the PNC circuit (100) configured to generate each of the perturbation terms as a weighted sum of the hard data symbols; Including, the digital signal processor further includes at least one circuit (104, 106) configured to compensate for individual ones of the soft data symbols using corresponding ones of the perturbation terms; the digital signal processor includes a series of the PNC stages (121, 122, 123), each PNC stage configured to estimate a different nonlinear contribution and to apply the estimated different nonlinear contribution to an input stream of soft data symbols; the PNC circuit in each PNC stage is configured to subtract a respective one of the perturbation terms from each of the soft data symbols to generate corrected soft data symbols; the PNC circuit in each PNC stage except the last PNC stage of the series is configured to output the corrected soft data symbols therefrom to a next PNC stage in the series; The apparatus, wherein the PNC circuit of the last PNC stage (123) of the series is configured to output the corrected soft data symbols therefrom to a decoder (148, 150).

9. the PNC circuitry in each PNC stage is configured to perform a convolution between a set of channel coefficients and a set of multiplicative products of hard data symbols to generate weighting coefficients; The apparatus of claim 8 , wherein the channel coefficients represent nonlinear effects of an optical transmission channel.

10. 10. The apparatus of claim 9, wherein the PNC circuitry in each PNC stage is adapted to perform the convolution numerically by evaluating a corresponding linear filter in the frequency domain.

11. the series includes two or more of the PNC stages; the PNC circuitry in each PNC stage is configured to form each of its respective weighted sums from a set of N terms selected from a stream of hard data symbols, where N is a predetermined positive integer; The apparatus of claim 9 , wherein the sets of N terms used by each PNC stage are independent of each other.

12. the digital signal processor further comprises a soft-decision FEC decoder (160); the PNC circuit of a last stage of the one or more PNC stages is configured to output a stream of soft data symbols and a stream of perturbation terms to the soft-decision FEC decoder (160); The apparatus of claim 8 , wherein the soft-decision FEC decoder is configured to perform soft-decision compensation of the output soft data symbols using the output perturbation terms.

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