Method for compensating polarization mode dispersion in optical fiber channel
By performing block processing and matrix operation on the signals in the fiber channel, the calculation complexity of the Kalman filtering algorithm is reduced, the high calculation amount problem in polarization mode dispersion compensation is solved, and the transmission performance of the optical communication system is improved.
Patent Information
- Application Number
- CN202510684079.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-26
- Publication Date
- 2025-08-15
AI Technical Summary
The Kalman filtering algorithm is too complex to compensate for polarization mode dispersion in fiber channels, especially in the face of super-large polarization state rotation and differential group delay.
By blocking the input signal and multiplying it with the polarization mode dispersion compensation matrix in the frequency domain, the Kalman observation matrix and the Jacobian matrix are constructed, and the Kalman gain and state vector covariance matrix is updated to reduce the computational complexity.
On the premise of ensuring the equalization performance of polarization damage, the calculation complexity of the Kalman filtering algorithm is reduced and the transmission performance of the system under complex channel conditions is improved.
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Figure CN120498544A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of optical communications, and in particular to a method for compensating polarization mode dispersion in an optical fiber channel. Background Art
[0002] Against the backdrop of the rapid evolution of information and communication technologies, the scale of global data traffic is experiencing exponential growth, placing ever-stricter demands on the spectral efficiency of optical fiber transmission systems. Polarization multiplexing, due to its efficient spectrum utilization, has become a key means of increasing single-mode optical fiber transmission rates. This technology doubles channel capacity by independently modulating the two orthogonal polarization states of an optical carrier and is considered a key solution for breaking through future bottlenecks in high-capacity transmission.
[0003] Due to birefringence, light pulses in optical fibers experience different propagation velocities and phase differences along their fast and slow axes. This difference causes the different polarization components of the pulse to arrive at the output at different times, resulting in pulse broadening. This phenomenon is called polarization mode dispersion (PMD). PMD is the time delay difference between the different polarization components of a light pulse during transmission between the fast and slow axes, also known as the differential group delay (DGD), and is measured in picoseconds. PMD is caused by fiber birefringence and mode coupling. The different core shapes of each fiber segment in an optical fiber link, combined with the uneven stress applied to it, disrupt the cylindrical symmetry of the fiber, causing birefringence. Due to birefringence, light pulses in optical fibers experience different propagation velocities and phase differences along their fast and slow axes. This difference causes the different polarization components of the pulse to arrive at the output at different times, resulting in pulse broadening.
[0004] However, in actual engineering applications, due to its high sensitivity to polarization impairments, especially when the environment changes drastically, extremely large polarization state rotation (RSOP) and differential group delay (DGD) can cause reception interruption.
[0005] In optical coherent communication architectures, the Kalman filter method, as an effective solution for the digital signal processing link at the receiver, undertakes multiple critical signal processing functions. It is typically deployed in the digital signal processing unit following the coherent detection unit, specifically involving key technical links such as polarization state separation and recovery, symbol timing error correction, carrier frequency offset compensation, and phase noise compensation. Through its dynamic parameter estimation and error correction capabilities, the Kalman filter algorithm significantly improves the system's transmission performance under complex channel conditions. The Kalman filter method requires real-time iterative solutions to nonlinear state equations and updates to the covariance matrix. These operations involve multidimensional tensor operations and matrix inversion, resulting in a significant increase in computational complexity of the order of O(N³), making it unsuitable for commercial implementation. Summary of the Invention
[0006] The present invention proposes a method for compensating polarization mode dispersion in an optical fiber channel to solve the problem of high computational complexity in the process of compensating for ultra-large polarization state rotation and differential group delay using a Kalman filter algorithm.
[0007] In order to achieve the above object, the present invention adopts the following technical solutions: The present invention provides a method for compensating polarization mode dispersion in an optical fiber channel, the method comprising the following steps: Set and initialize the Kalman state vector and construct the state vector covariance matrix; Divide the input damaged signal into blocks to obtain a blocked damaged signal; After transferring each block of damaged signals to the frequency domain, the damaged signals are multiplied by the constructed polarization mode dispersion compensation matrix to obtain the damaged signals after polarization mode dispersion frequency domain compensation. Transfer each damaged signal after PMD frequency domain compensation to the time domain to obtain the time domain matrix after PMD compensation; Constructing a polarization state rotation compensation matrix and multiplying it with the time domain matrix after polarization mode dispersion compensation to obtain the filter output signal; An error function is constructed based on the ideal signal amplitude and the filter output signal, and the error function is used to construct a Kalman measurement matrix in the form of a Jacobian matrix, and the Kalman gain is updated based on the matrix; Update the Kalman state vector and the state vector covariance matrix.
[0008] As a possible implementation, the Kalman state vector is denoted as , the expression is:
[0009] in, represents the component of polarization mode dispersion in the S1 direction of Stokes space, represents the component of polarization mode dispersion in the S1 direction of Stokes space, represents the component of polarization mode dispersion in the S1 direction of Stokes space, is the diagonal real part of the polarization rotation compensation matrix; is the diagonal imaginary part of the polarization rotation compensation matrix; is the negative diagonal real part of the polarization rotation compensation matrix; is the negative diagonal imaginary part of the polarization rotation compensation matrix.
[0010] As a possible implementation method, the input damaged signal is divided into blocks, specifically, each cycle is intercepted with a cycle window signal, each cycle window moves A signal.
[0011] As a possible implementation method, the number of blocks of the damaged signal after segmentation is , is the total length of the signal, is the length of each moving cycle window, that is, the number of signals.
[0012] As a possible implementation, The value range is 20 to 200. The value range is 2 to .
[0013] As a possible implementation method, the constructed polarization mode dispersion compensation matrix is obtained by inverting the unitary matrix.
[0014] As a possible implementation method, the error function expression is:
[0015] in, represents the amplitude of the ideal signal; express x Error function in polarization direction; express y Error function in polarization direction; and For the The output of the moment filter.
[0016] As a possible implementation, the Kalman measurement matrix in Jacobian form is denoted as H , the expression is:
[0017] in, Represents the error function right The partial derivative of Represents the error function right The partial derivative of Represents the error function right The partial derivative of Represents the error function right The partial derivative of is the diagonal real part of the polarization rotation compensation matrix; is the diagonal imaginary part of the polarization rotation compensation matrix; is the negative diagonal real part of the polarization rotation compensation matrix; is the negative diagonal imaginary part of the polarization rotation compensation matrix.
[0018] As a possible implementation method, the Kalman gain is updated according to the Kalman measurement matrix, specifically: S1. Construct the state vector covariance matrix, and the error covariance matrix of the prior estimate is recorded as , the expression is:
[0019] S2, original Kalman gain, expressed as:
[0020] in, for The state vector covariance matrix at time t; for The moment Jacobian matrix, is the noise covariance matrix at time k; S3, yes Make updates; According to the actual situation analysis, ; but, ;
[0021]
[0022] in, for The coefficients of the equation equivalent to the matrix inversion, , for The eigenvalues of a matrix.
[0023] As a possible implementation method, the Kalman state vector and the state vector covariance matrix are updated as follows: and To update, the update expression is:
[0024] in, is the process noise covariance matrix; Indicates the state quantity estimated value of; is the Kalman measurement matrix, and its expression is: ; is the actual measured value.
[0025] Compared with the prior art, the present invention has the following beneficial effects: This paper proposes a method for compensating polarization mode dispersion in optical fiber channels. While ensuring polarization damage equalization, it proposes a low-complexity Kalman filter algorithm. This solves the problem of excessive computational complexity in the Kalman filter algorithm when compensating for very large polarization state rotations and differential group delay. The proposed method also improves the Kalman gain coefficient and state covariance matrix. BRIEF DESCRIPTION OF THE DRAWINGS The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 The flowchart of the method for compensating polarization mode dispersion in optical fiber channels is shown in FIG. DETAILED DESCRIPTION
[0026] To facilitate a clear description of the technical solutions of the embodiments of the present invention, the words "first" and "second" are used in the embodiments of the present invention to distinguish between identical or similar items with substantially the same functions and effects. For example, the first threshold and the second threshold are merely used to distinguish between different thresholds and do not limit their order. Those skilled in the art will understand that the words "first" and "second" do not limit the quantity or execution order, and the words "first" and "second" do not necessarily mean different.
[0027] It should be noted that, in the present invention, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the present invention should not be construed as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.
[0028] In the present invention, "at least one" means one or more, and "more" means two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can mean: the existence of A alone, the existence of A and B at the same time, and the existence of B alone, where A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. The following at least one item (item) or similar expressions refers to any combination of these items, including any combination of single items (items) or plural items (items). For example, at least one item (item) of a, b or c can mean: a, b, c, the combination of a and b, the combination of a and c, the combination of b and c, or the combination of a, b and c, where a, b, c can be single or plural.
[0029] The present invention aims to provide a method for compensating polarization mode dispersion in optical fiber channels to address the high computational complexity of the Kalman filter algorithm in compensating for very large polarization state rotation and differential group delay. Specifically, the method reduces computational complexity while ensuring polarization impairment equalization performance. Specific implementation methods are as follows: The embodiment of the present invention provides a method for compensating polarization mode dispersion in an optical fiber channel, see Figure 1 , the method comprises the following steps: Set and initialize the Kalman state vector and construct the state vector covariance matrix; As a possible implementation, the Kalman state vector is denoted as , the expression is:
[0030] in, represents the component of polarization mode dispersion in the S1 direction of Stokes space, represents the component of polarization mode dispersion in the S1 direction of Stokes space, represents the component of polarization mode dispersion in the S1 direction of Stokes space, is the diagonal real part of the polarization rotation compensation matrix; is the diagonal imaginary part of the polarization rotation compensation matrix; is the negative diagonal real part of the polarization rotation compensation matrix; is the negative diagonal imaginary part of the polarization rotation compensation matrix.
[0031] For example, the Kalman state vector is initialized .
[0032] Divide the input damaged signal into blocks to obtain a blocked damaged signal; As a possible implementation method, the input damaged signal is divided into blocks, specifically, each cycle is intercepted with a cycle window signal, each cycle window moves A signal.
[0033] For example, the input signal is r, the output signal is u, and Length window interception signals, and the window moves △s each time.
[0034] As a possible implementation method, the number of blocks of the damaged signal after segmentation is , is the total length of the signal, is the length of each moving cycle window, that is, the number of signals.
[0035] As a possible implementation, The value range is 20 to 200. The value range is 2 to .
[0036] After transferring each block of damaged signals to the frequency domain, the damaged signals are multiplied by the constructed polarization mode dispersion compensation matrix to obtain the damaged signals after polarization mode dispersion frequency domain compensation. For example, the damaged signal after each block is transferred to the frequency domain, specifically, the input Perform Fourier transform on the signal to convert it into frequency domain.
[0037] As a possible implementation method, the constructed polarization mode dispersion compensation matrix is recorded as , the expression is:
[0038] in, is the center frequency of optical fiber transmission, is the Pauli matrix, is the magnitude of the polarization mode dispersion vector, represents the polarization mode dispersion vector.
[0039] Transfer each damaged signal after PMD frequency domain compensation to the time domain to obtain the time domain matrix after PMD compensation; Exemplarily, each block of the damaged signal after polarization mode dispersion frequency domain compensation is subjected to inverse Fourier transform to convert the signal into the time domain.
[0040] Constructing a polarization state rotation compensation matrix and multiplying it with the time domain matrix after polarization mode dispersion compensation to obtain the filter output signal; Exemplarily, constructing a polarization state rotation compensation matrix is specifically as follows: obtaining the inverse of a unitary matrix; The unitary matrix is denoted as , the expression is:
[0041] Then, the polarization rotation compensation matrix .
[0042] Exemplarily, the filter output signal , expressed as and .
[0043] Construct an error function based on the ideal signal amplitude and the filter output signal; As a possible implementation method, the error function expression is:
[0044] in, represents the amplitude of the ideal signal; express x Error function in polarization direction; express y Error function in polarization direction; and For the The output of the moment filter.
[0045] Apply the error function to construct the Kalman observation matrix in the form of Jacobian matrix; For example, the Kalman observation matrix .
[0046] As a possible implementation, the Kalman measurement matrix in Jacobian form is denoted as H , the expression is:
[0047] in, Represents the error function right The partial derivative of Represents the error function right The partial derivative of Represents the error function right The partial derivative of Represents the error function right The partial derivative of is the diagonal real part of the polarization rotation compensation matrix; is the diagonal imaginary part of the polarization rotation compensation matrix; is the negative diagonal real part of the polarization rotation compensation matrix; is the negative diagonal imaginary part of the polarization rotation compensation matrix.
[0048] Update the Kalman gain according to the Kalman observation matrix; As a possible implementation method, the Kalman gain is updated according to the Kalman measurement matrix, specifically: S1. Construct the state vector covariance matrix, and the error covariance matrix of the prior estimate is recorded as , the expression is:
[0049] S2, the original Kalman gain is recorded as , the expression is:
[0050] in, for The state vector covariance matrix at time t; for The moment Jacobian matrix, is the noise covariance matrix at time k; S3, yes Make updates; According to the actual situation analysis, ; but, ;
[0051]
[0052] in, for The coefficients of the equation equivalent to the matrix inversion, , is a matrix The eigenvalue of .
[0053] Update the Kalman state vector and the state vector covariance matrix; As a possible implementation method, the Kalman state vector and the state vector covariance matrix are updated as follows: and To update, the update expression is:
[0054] in, is the process noise covariance matrix; Indicates the state quantity estimated value of; is the Kalman measurement matrix, and its expression is: ; is the actual measured value.
[0055] The present invention proposes a method for compensating polarization mode dispersion in an optical fiber channel, which proposes a low-complexity Kalman filtering algorithm while ensuring the polarization damage equalization performance, and solves the problem of high computational complexity in the process of compensating for ultra-large polarization state rotation and differential group delay by the Kalman filtering algorithm.
[0056] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art may understand and implement other variations of the disclosed embodiments by reviewing the drawings, the disclosure, and the accompanying drawings. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude multiple situations. A single processor or other unit can implement several functions listed in the specification. Certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.
[0057] Although the present invention has been described with reference to specific features and embodiments thereof, it will be apparent that various modifications and combinations thereof may be made without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely illustrative of the present invention and are deemed to cover any and all modifications, variations, combinations or equivalents within the scope of the invention. It will be apparent that various modifications and variations of the present invention may be made by those skilled in the art without departing from the spirit and scope of the invention. Thus, the present invention is intended to include such modifications and variations as fall within the scope of the invention and its equivalents.
Claims
1. A method for compensating polarization mode dispersion in an optical fiber channel, characterized in that: The steps include: Set and initialize the Kalman state vector and construct the state vector covariance matrix; Divide the input damaged signal into blocks to obtain a blocked damaged signal; After transferring each block of damaged signals to the frequency domain, the damaged signals are multiplied by the constructed polarization mode dispersion compensation matrix to obtain the damaged signals after polarization mode dispersion frequency domain compensation. Transfer each damaged signal after PMD frequency domain compensation to the time domain to obtain the time domain matrix after PMD compensation; Constructing a polarization state rotation compensation matrix and multiplying it with the time domain matrix after polarization mode dispersion compensation to obtain the filter output signal; An error function is constructed based on the ideal signal amplitude and the filter output signal, and the error function is used to construct a Kalman measurement matrix in the form of a Jacobian matrix, and the Kalman gain is updated based on the matrix; Update the Kalman state vector and the state vector covariance matrix.
2. The method for compensating polarization mode dispersion in an optical fiber channel according to claim 1, wherein: The Kalman state vector is denoted as , the expression is: in, represents the component of polarization mode dispersion in the S1 direction of Stokes space, represents the component of polarization mode dispersion in the S1 direction of Stokes space, represents the component of polarization mode dispersion in the S1 direction of Stokes space, is the diagonal real part of the polarization state rotation compensation matrix; is the diagonal imaginary part of the polarization rotation compensation matrix; is the negative diagonal real part of the polarization rotation compensation matrix; is the negative diagonal imaginary part of the polarization rotation compensation matrix.
3. The method for compensating polarization mode dispersion in an optical fiber channel according to claim 1, wherein: The input damaged signal is divided into blocks, specifically, each cycle is intercepted with a cycle window signal, each cycle window moves A signal.
4. The method for compensating polarization mode dispersion in an optical fiber channel according to claim 1, wherein: The number of blocks of the damaged signal after segmentation is , is the total length of the signal, is the length of each moving cycle window, that is, the number of signals.
5. The method for compensating polarization mode dispersion in an optical fiber channel according to claim 3 or 4, The value range is 20 to 200. The value range is 2 to .
6. The method for compensating polarization mode dispersion in an optical fiber channel according to claim 1, wherein: The constructed polarization mode dispersion compensation matrix is recorded as , the expression is: in, is the center frequency of optical fiber transmission, is the Pauli matrix, is the magnitude of the polarization mode dispersion vector, represents the polarization mode dispersion vector.
7. The method for compensating polarization mode dispersion in an optical fiber channel according to claim 1, wherein: The error function expression is: in, represents the amplitude of the ideal signal; express x Error function in polarization direction; express y Error function in polarization direction; and For the The output of the moment filter.
8. The method for compensating polarization mode dispersion in an optical fiber channel according to claim 1, wherein: The Kalman measurement matrix in Jacobian matrix form is recorded as H , the expression is: in, Represents the error function right The partial derivative of Represents the error function right The partial derivative of Represents the error function right The partial derivative of Represents the error function right The partial derivative of is the diagonal real part of the polarization state rotation compensation matrix; is the diagonal imaginary part of the polarization rotation compensation matrix; is the negative diagonal real part of the polarization rotation compensation matrix; is the negative diagonal imaginary part of the polarization rotation compensation matrix.
9. The method for compensating polarization mode dispersion in an optical fiber channel according to claim 1, wherein: Update the Kalman gain according to the Kalman measurement matrix, specifically: S1. Construct the state vector covariance matrix, and the error covariance matrix of the prior estimate is recorded as , the expression is: S2, original Kalman gain, expressed as: in, for The state vector covariance matrix at time t; for The moment Jacobian matrix, is the noise covariance matrix at time k; S3, yes Make updates; According to the actual situation analysis, ; but, ; in, for The coefficients of the equation equivalent to the matrix inversion, , for The eigenvalues of a matrix.
10. The method for compensating polarization mode dispersion in an optical fiber channel according to claim 1, wherein: The updating of the Kalman state vector and the state vector covariance matrix is specifically as follows: and To update, the update expression is: in, is the process noise covariance matrix; Indicates the state quantity estimated value of; is the Kalman observation matrix, and its expression is: ; is the actual measured value.