A method for nonlinear compensation of long distance fiber optic communications

Abstract

The application discloses a nonlinear compensation method for long-distance optical fiber communication, and comprises the following steps: acquiring an optical fiber transmission signal, grouping the signal to obtain a group signal, wherein K is a group number; setting a nonlinear parameter r , solving a nonlinear operator according to the nonlinear parameter r ; performing nonlinear preprocessing on the group signal by using the nonlinear operator to obtain a preprocessed signal T ; adopting a step-by-step Fourier method to process the preprocessed signal T to obtain a compensation signal; wherein the step-by-step Fourier method comprises linear recovery, nonlinear recovery, overcompensation recovery and serial data recovery. The application has the beneficial effect of solving the nonlinear influence on the signal in the long-distance transmission process and reducing the error code rate after transmission through compensation.

Description

Technical Field

[0001] This invention relates to the field of optical fiber communication, and more particularly to a nonlinear compensation method for long-distance optical fiber communication. Background Technology

[0002] High-speed optical communication networks have become an indispensable part of modern communication networks. To increase the transmission distance of modern communication networks, low-loss optical fibers were invented, making long-distance communication using optical signals possible. The emergence of signal amplification devices such as EDFAs (Erbium-Doped Fiber Amplifiers) can compensate for signal attenuation during transmission in optical fibers, making long-distance communication a reality. However, as communication distances increase, signals are highly susceptible to nonlinear impairments. Compensating for these nonlinear impairments has become a major challenge hindering the expansion of optical communication network capacity.

[0003] Optical signals in optical fibers are primarily affected by three types of damage: attenuation, dispersion, and nonlinearity. Limited by current material processing capabilities, the medium in optical fibers cannot achieve zero absorption of the optical signal; the medium will absorb some of the signal, leading to attenuation. Simultaneously, due to limitations in laser development, ideal single-mode optical signals cannot be generated. Modern single-mode signals also encompass a frequency range, and differences in group velocities result in dispersion. Furthermore, optical signals are affected by the Kerr effect and other factors during propagation, causing nonlinear phase shifts, with the magnitude of the phase shift exhibiting a positive nonlinear relationship with the signal intensity. These three types of damage interact, forming a challenging triangular problem. Balancing these relationships and transforming the signal into a mode suitable for backend processing has become a pressing issue in expanding the transmission capacity and distance of optical communication networks. Summary of the Invention

[0004] To address the technical challenge of simultaneously balancing transmission capacity and transmission distance in optical communication networks, this invention proposes a nonlinear compensation method for long-distance optical fiber communication, comprising the following steps:

[0005] S1. Acquire the fiber optic transmission signal and group it into groups to obtain group signals. , where k is the group number; M The maximum number of signals in a group;

[0006] S2. Set nonlinear parameters r According to nonlinear parameters r Solving nonlinear operators ;

[0007] S3. Utilizing nonlinear operators Group signals Nonlinear preprocessing is performed to obtain the preprocessed signal. T ;

[0008] S4. Process the pre-processed signal T The compensation signal is obtained by using the step-by-step Fourier method; wherein the step-by-step Fourier method includes: linear recovery, nonlinear recovery, overcompensation recovery and serial data recovery.

[0009] Furthermore, nonlinear operators The calculation formula is as follows:

[0010] .

[0011] Furthermore, the preprocessed signal T The calculation formula is as follows:

[0012]

[0013] in, h This refers to the transmission distance of the fiber optic signal.

[0014] Furthermore, the specific process of the linear recovery is as follows:

[0015] S411, preprocess the signal T Converted into a frequency domain signal by Fast Fourier Transform F temp :

[0016]

[0017] in, Represented as Fast Fourier Transform;

[0018] S412, Combine the frequency domain signal with a linear operator Perform exponential operations to obtain the linearly recovered signal. F : .

[0019] Furthermore, the linear operator The calculation formula is as follows:

[0020]

[0021] in, w The equivalent angular frequency in the frequency domain, the number of which is related to the number of signals in the group of signals. is the dispersion coefficient.

[0022] Furthermore, the specific process of the nonlinear recovery is as follows:

[0023] S421, The linearly recovered signal FConverted into a time-domain temporary signal T temp :

[0024]

[0025] in, This is the inverse Fourier transform;

[0026] S422, For nonlinear operators The following updates have been made:

[0027]

[0028] S423, Based on the updated nonlinear operator The nonlinear recovery is completed, and the nonlinearly recovered time-domain signal is obtained. T : .

[0029] Furthermore, the overcompensation recovery specifically involves performing a positive nonlinear operator operation on the excess compensation portion in the nonlinear compensation, as shown in the following formula: ,in .

[0030] Furthermore, if the fiber length is L The transmission distance is h , L / h = n Then linear recovery was performed. n Next, nonlinear recovery was performed. Next, for overcompensation in nonlinear recovery, overcompensation recovery is performed.

[0031] Furthermore, the serial data recovery specifically refers to the process of restoring the grouped signals into a complete data stream through linear recovery, nonlinear recovery, and overcompensation recovery, followed by serial-to-parallel conversion, before transmission.

[0032] The beneficial effects provided by this invention are: it solves the nonlinear effects on signals during long-distance transmission and reduces the bit error rate after transmission through compensation. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0034] Figure 2 This is a schematic diagram of the processing result of the algorithm of this invention. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0036] Please refer to Figure 1 , Figure 1 This is a schematic diagram of the method flow of the present invention;

[0037] This invention provides a nonlinear compensation method for long-distance optical fiber communication, comprising:

[0038] S1. Acquire the fiber optic transmission signal and group it into groups to obtain group signals. , where k is the group number; M The maximum number of signals in a group;

[0039] It should be noted that during fiber optic transmission, signals are continuously sent and received over time, and it is impossible to process all of them at once. Therefore, the signals need to be grouped and processed.

[0040] In this example, the signal sampled by the ADC can be... The data are processed in groups of 1 to facilitate subsequent Fourier transform. It should be an integer power of 2.

[0041] Each group of signals can be named a , The composition is as follows.

[0042]

[0043]

[0044] S2. Set nonlinear parameters r According to nonlinear parameters r Solving nonlinear operators Nonlinear operators The calculation formula is as follows:

[0045] .

[0046] It should be noted that, in the propagation over extremely short distances in optical fibers, nonlinear effects are mainly distributed at both ends of this short distance, while linear effects are mainly distributed in the middle of this short distance, as shown in the attached diagram. Figure 2 As shown. Therefore, for ease of calculation, a pre-forward propagation is required to facilitate subsequent loop propagation.

[0047] When performing pre-forward propagation, nonlinear parameters need to be set. The value of is related to the intrinsic characteristics of the optical fiber. Using the nonlinear parameters, the nonlinear operator can be solved. The value of is related to the power of the optical signal. The specific solution formula is as follows:

[0048] .

[0049] S3. Utilizing nonlinear operators Group signals Nonlinear preprocessing is performed to obtain the preprocessed signal. T ;

[0050] Preprocessed signal T The calculation formula is as follows:

[0051]

[0052] in, h This refers to the transmission distance of the fiber optic signal.

[0053] It should be noted that, using the solution Performing exponential operations and time-domain multiplication allows for nonlinear preprocessing. The signal obtained after preprocessing is... As shown in the following formula: .

[0054] It should be noted that after the signal undergoes nonlinear preprocessing, it will enter a loop processing stage. Because the loop processing requires frequent use of Fourier transform and inverse Fourier transform, it is called the step-by-step Fourier algorithm.

[0055] S4. Process the pre-processed signal T The compensation signal is obtained by using the step-by-step Fourier method; wherein the step-by-step Fourier method includes: linear recovery, nonlinear recovery, overcompensation recovery and serial data recovery.

[0056] It should be noted that the signal obtained after nonlinear preprocessing The signal is still a time-domain signal. When performing linear compensation, less computation is required in the frequency domain, so it needs to be converted into a frequency-domain signal.

[0057] The specific process of linear recovery is as follows:

[0058] S411, preprocess the signal T Converted into a frequency domain signal by Fast Fourier Transform F temp :

[0059]

[0060] in, Represented as Fast Fourier Transform;

[0061] In digital signal processing, the Fast Fourier Transform (FFT) is often used to replace the Fourier Transform in its theoretical derivation. After processing, Once it becomes a frequency domain signal, the linear part can be recovered simply by performing an exponential operation with a linear operator.

[0062] S412, Combine the frequency domain signal with a linear operator Perform exponential operations to obtain the linearly recovered signal. F : .

[0063] The linear operator The calculation formula is as follows:

[0064]

[0065] in, w The equivalent angular frequency in the frequency domain, the number of which is related to the number of signals in the group of signals. is the dispersion coefficient.

[0066] It should be noted that, in the theoretical derivation, the signal is at a very small distance. The linear and nonlinear effects experienced by the signal can be independent of each other; therefore, the linear and nonlinear recovery of the signal can be calculated independently. After frequency domain linear recovery, the signal is within this minimal distance. Only the nonlinear effect remains unrecovered. Since nonlinear effects are processed faster in the time domain, it is necessary to... The signal is inverse Fourier transformed to the time domain.

[0067] The specific process of nonlinear recovery is as follows:

[0068] S421, The linearly recovered signal F Converted into a time-domain temporary signal T temp :

[0069]

[0070] in, This is the inverse Fourier transform;

[0071] It should be noted that, unlike linear operators, the values ​​of nonlinear operators depend not only on the intrinsic parameters of the optical fiber but also on the current energy intensity of the signal. The values ​​of the nonlinear operators need to be updated in each iteration.

[0072] S422, For nonlinear operators The following updates have been made:

[0073]

[0074] S423, Based on the updated nonlinear operator The nonlinear recovery is completed, and the nonlinearly recovered time-domain signal is obtained. T : .

[0075] It should be noted that steps S411~S412 and steps S421~S423 are cyclic steps, and the number of cycles is determined according to the fiber length and transmission distance.

[0076] Assuming the fiber length is Therefore, STEP3 above needs to be executed together. However, since the optical signal was pre-compensated in STEP1, the linear compensation in the entire algorithm is [number missing]. This is the second time, and nonlinear compensation has been achieved. Therefore, it is necessary to restore the overcompensation, which is done by performing positive nonlinear operator operations.

[0077] The overcompensation recovery specifically involves performing a positive nonlinear operator operation on the excess compensation portion in the nonlinear compensation, as shown in the following formula: ,in .

[0078] The serial data recovery specifically refers to the process of restoring the grouped signals into a complete data stream through linear recovery, nonlinear recovery, and overcompensation recovery, followed by serial-to-parallel conversion, before sending it.

[0079] To verify the feasibility of this invention, the corresponding theoretical derivation is also performed as follows.

[0080] The propagation of optical signals in optical fibers follows the nonlinear Schrödinger equation, as shown below.

[0081]

[0082] Where parameters The optical signal transmitted in the optical fiber. for Dispersion of order, This represents the distance in the direction of optical signal propagation within the optical fiber. Measured for the current time. The imaginary unit, It is a nonlinear factor. This refers to signal loss in optical fiber.

[0083] According to the nonlinear Schrödinger equation, the damage to optical signals transmitted in optical fibers mainly includes dispersion and higher-order dispersion, nonlinear phase shift, and loss. Among these, dispersion and loss are linear damages, while nonlinear phase shift is a nonlinear damage. Separating and treating these two types of damages can more effectively compensate for the damage to the optical signal.

[0084] By separating the linear and nonlinear parts of the nonlinear Schrödinger equation and summarizing them separately, the nonlinear Schrödinger equation can be rewritten in the following form:

[0085]

[0086] The above formula represents the dispersion and loss in optical fiber. It is named a linear operator.

[0087]

[0088] The above equation represents the nonlinear phase shift in optical fiber. It is named a nonlinear operator.

[0089] Simplifying the nonlinear Schrödinger equation, we obtain the following equation:

[0090]

[0091] The simplified nonlinear Schrödinger equation can be described by the above equation: the differential of the optical signal along the direction of propagation is equal to the combined action of linear and nonlinear operators on the optical signal. Since the differential operator only indicates the transmission of the optical signal over extremely short distances, it is reasonable to assume that the transmission of the optical signal over extremely short distances can separate the linear and nonlinear operators.

[0092]

[0093] Since linear operators and nonlinear operators can be separated, the following derivation can be made only for linear operators:

[0094]

[0095] in This represents a minimal distance along the direction of optical signal propagation. Interchanging the left and right sides of the above equation yields:

[0096]

[0097] Using the limit theorem, the above equation can be replaced with:

[0098]

[0099] In summary, the optical signal propagates along the direction of optical signal propagation. The effect of distance can be equivalent to the optical signal at a distance. It is multiplied by an exponential operator that contains linear (or nonlinear) operators.

[0100] Since the linear and nonlinear effects on optical signals can be separated, the overall propagation formula for optical signals can be derived as follows:

[0101]

[0102] For the propagation of an optical signal, through the above transformation, the damage it suffers during propagation in an optical fiber can be equivalent to the form of the above equation.

[0103] In the spread After a certain distance, the optical signal suffers linear damage, and then nonlinear damage.

[0104] In the first part, it is only affected by linear impairments due to dispersion and loss, while in the second part, it is only affected by nonlinear impairments due to nonlinearity. This applies to transmission processing. When the size is sufficiently small, the error introduced by this equivalent method can be ignored.

[0105] Linear operators contain higher-order partial derivatives, which are very complex to solve in the time domain, increasing the complexity of the algorithm and reducing its speed.

[0106] To improve the algorithm, the linear operator can be subjected to Fourier transform, and after frequency domain processing, an inverse transform can be performed, which can significantly reduce the algorithm complexity.

[0107] The frequency domain solution for a linear operator is as follows:

[0108]

[0109] in, For Fourier transform, It is the angular frequency in the frequency domain. This is the inverse Fourier transform.

[0110] By converting the linear operations to the frequency domain, the computational burden of solving higher-order partial derivatives can be reduced. After processing the linear part in the frequency domain, the signal still needs to be converted to the time domain to process the nonlinear part. A complete processing step is shown in the following equation:

[0111]

[0112] The signal is first compensated for linearity in the frequency domain, and then for nonlinearity in the time domain, to achieve this over a relatively short transmission distance. Under these conditions, the algorithm's error can be ignored.

[0113] To ensure that the compensation effect of the algorithm matches the actual transmission impairment, the algorithm's A smaller value is needed, usually 10km.

[0114] For long-distance compensation, simply perform a cyclic superposition of the above formula. The complete theoretical derivation of the algorithm is shown in the following formula.

[0115]

[0116] Finally, as an embodiment, this invention employs a single-channel 16QAM modulation communication system, with single-mode optical fiber as the transmission medium. Each span is 80 km long, and EDFA power compensation is used for each span. The receiving end performs coherent reception after OBPF filtering. The signal at the receiving end is sampled by an ADC to obtain a time-domain signal, which is then processed by the algorithm described above in this application. Finally, refer to... Figure 2 When the re-entry fiber power is less than 4dBm, the signal can be transmitted without error.

[0117] The beneficial effects of this invention are: it solves the nonlinear effects on signals during long-distance transmission and reduces the bit error rate after transmission through compensation.

[0118] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A nonlinear compensation method for long-distance optical fiber communication, characterized in that: Includes the following steps: S1. Acquire the fiber optic transmission signal and group it into groups to obtain group signals. , where k is the group number; M The maximum number of signals in a group; S2. Set nonlinear parameters r Solving the nonlinear operator based on the nonlinear parameter r ; S3. Utilizing nonlinear operators Group signals Nonlinear preprocessing is performed to obtain the preprocessed signal. T ; S4. Process the pre-processed signal T The compensation signal is obtained by using the split-step Fourier method; The step-by-step Fourier method includes: linear recovery, nonlinear recovery, overcompensated recovery, and serial data recovery; Nonlinear operators The calculation formula is as follows: ; i The imaginary unit; to The power of the optical signal; The formula for calculating the preprocessed signal T is as follows: in, h This refers to the transmission distance of the fiber optic signal. The specific process of linear recovery is as follows: S411, preprocess the signal T Converted into a frequency domain signal by Fast Fourier Transform F temp : in, Represented as Fast Fourier Transform; S412, Combine the frequency domain signal with a linear operator Perform exponential operations to obtain the linearly recovered signal. F : ; The specific process of nonlinear recovery is as follows: S421, The linearly recovered signal F Converted into a time-domain temporary signal T temp : in, This is the inverse Fourier transform; S422, For nonlinear operators The following updates have been made: S423, Based on the updated nonlinear operator The nonlinear recovery is completed, and the nonlinearly recovered time-domain signal is obtained. T : ; The overcompensation recovery specifically involves performing a positive nonlinear operator operation on the excess compensation portion in the nonlinear compensation, as shown in the following formula: ,in .

2. The nonlinear compensation method for long-distance optical fiber communication as described in claim 1, characterized in that: The linear operator The calculation formula is as follows: in, w The equivalent angular frequency in the frequency domain, the number of which is related to the number of signals in the group of signals. is the dispersion coefficient.

3. The nonlinear compensation method for long-distance optical fiber communication as described in claim 1, characterized in that: The excess compensation portion specifically refers to: if the fiber length is... L The transmission distance is h , L / h = n Then linear recovery was performed. n Next, nonlinear recovery was performed. Next, for overcompensation in nonlinear recovery, overcompensation recovery is performed.

4. The nonlinear compensation method for long-distance optical fiber communication as described in claim 1, characterized in that: The serial data recovery specifically refers to the process of restoring the grouped signals into a complete data stream through linear recovery, nonlinear recovery, and overcompensation recovery, followed by serial-to-parallel conversion, before sending it.

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