A method and apparatus for fast polarization rotation and inter-symbol interference compensation

Abstract

The application relates to the technical field of communication, and provides a method and device for compensating for fast polarization rotation and inter-symbol interference. k The method comprises the following steps: constructing an initial simplified Kalman filter; the Kalman gain of the initial simplified Kalman filter is used to iteratively update a covariance matrix P And a state vector are used to compensate for polarization damage of a signal; an FIR filter is used to compensate for inter-symbol interference of the signal. The application simplifies the calculation process of the Kalman filter, thereby simplifying the complex matrix operation into linear operation, improving the precision, solving the fast polarization damage of the high-speed dual polarization system and the inter-symbol interference caused by the bandwidth limitation, and having the advantages of low complexity and better precision, thereby being suitable for the fast polarization rotation and inter-symbol interference damage of the high-speed polarization system.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and in particular to a method and apparatus for compensating for rapid polarization rotation and inter-symbol interference. Background Technology

[0002] With the continuous development of the network world, global data traffic is exploding, leading to increasingly higher demands for data transmission rates. Partial multiplexing (DP) systems are an excellent solution for addressing high-speed requirements. By polarization multiplexing two orthogonal polarization states of light in a single-mode fiber, the data transmission rate can be significantly increased, making it an ideal solution for future high-volume demands. However, DP systems are highly sensitive to polarization impairments, especially when environmental changes are drastic. For example, strong magnetic fields generated by lightning strikes can cause rapid polarization rotation (RSOP) of the two polarized beams, sometimes reaching 20 Mrad / s. Traditional equalization algorithms may fail, leading to reception interruptions. Simultaneously, the increased communication rates place higher demands on the bandwidth of optical communication system devices such as photodetectors (PDs). Intersymbol interference caused by device bandwidth or other factors can also degrade the performance of the communication system.

[0003] Kalman filtering is a time-varying prediction algorithm that predicts the current state based on the state at the past moment. It is widely used in the navigation field and can handle tracking and prediction in various scenarios. Due to its excellent tracking performance, Kalman filtering has been applied to demultiplexing in recent years. Although Kalman filtering can track fast RSOP and handle fast RSOP impairment encountered by polarization systems, it cannot handle intersymbol interference (ISI) introduced by device bandwidth. Therefore, the communication degradation caused by ISI introduced by device bandwidth cannot be resolved. Furthermore, Kalman filtering involves nonlinear matrix operations during calculation, resulting in high resource consumption and low computational efficiency, making it unsuitable for commercial implementation.

[0004] Therefore, overcoming the shortcomings of the existing technology is an urgent problem to be solved in this technical field. Summary of the Invention

[0005] The technical problem to be solved by this invention is that although a Kalman filter can track fast RSOP and handle fast RSOP damage encountered by polarization systems, it cannot handle intersymbol interference introduced by device bandwidth. As a result, the communication degradation caused by intersymbol interference introduced by device bandwidth cannot be resolved. Furthermore, the Kalman filter involves nonlinear matrix operations during the calculation process, resulting in large resource consumption and low computational efficiency, making it unsuitable for commercial implementation.

[0006] The present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a method for compensating for rapid polarization rotation and inter-symbol interference, comprising:

[0008] Construct an initial simplified Kalman filter; wherein the Kalman gain of the initial simplified Kalman filter is...

[0009] The covariance matrix P is updated iteratively using a simplified Kalman filter. k and state vector To compensate for polarization impairments of the signal; in the first iteration update, the initial state vector and the initial covariance matrix are updated using an initial simplified Kalman filter. In subsequent iteration updates, a simplified Kalman filter for the next iteration update is obtained based on the covariance matrix and state vector obtained after the previous iteration update, so as to facilitate the next iteration update.

[0010] Use an FIR filter to compensate for intersymbol interference in the signal.

[0011] Preferably, the construction of the initial simplified Kalman filter specifically includes:

[0012] Based on the Kalman gain of the basic Kalman filter Will The nonlinear operations in the matrix are converted into operations between the diagonal elements of the matrix, resulting in...

[0013] Construct the gain factor N = (c1*c4 - c2*c3) -1 The Kalman gain of the initial simplified Kalman filter is obtained. This yields the initial simplified Kalman filter.

[0014] Preferably, the method of iteratively updating the covariance matrix P using a simplified Kalman filter is described. k and state vector Specifically, it includes:

[0015] Let P = diag(μa,μb,μc,μd), then we obtain the simplified Kalman filter; where the Kalman gain of the simplified Kalman filter is...

[0016] Where xa,xb,xc,xd,ya,yb,yc,yd in the partial solution represent the derivatives of the observation matrix, i.e., the error function, with respect to the state vector, respectively, as follows:

[0017] Update the covariance matrix P using a simplified Kalman filter. k and state vector

[0018] Preferably, the method of updating the covariance matrix P using a simplified Kalman filter is described. k and state vector Specifically, it includes:

[0019] Use the first formula Update the state vector to obtain the updated state vector.

[0020] The diagonal elements of the covariance matrix are updated using a simplified Kalman filter to obtain the updated covariance matrix.

[0021] Will Diagonalization yields the updated covariance matrix

[0022] Preferably, the method of using an FIR filter to compensate for intersymbol interference of the signal specifically includes:

[0023] The polarization-damped signal is input into two first-order FIR filters, and the error of the output signal is calculated.

[0024] Based on the magnitude of the output signal error, the tap coefficients of the FIR filter are updated using the gradient descent method, so that the updated tap coefficients can be used for the next intersymbol interference compensation.

[0025] Preferably, before iteratively updating the covariance matrix P and the state vector using a simplified Kalman filter, the method further includes: determining the initial Kalman state vector, the initial covariance matrix P, the covariance matrix Q of the state transition process noise, and the covariance matrix R of the matrix noise based on the polarization impairment matrix, specifically including:

[0026] According to the polarization damage matrix Construct the inverse matrix of the polarization damage matrix.

[0027] Based on the inverse of the polarization damage matrix, the initial state vector x is constructed. k =(a,b,c,d) T And construct the compensation signal

[0028] Construct the selection error function as follows Where R is 1, E xout (k), E yout (k) is the output of the Kalman filter;

[0029] According to the Kalman observation matrix The Jacobian matrix takes the following form: Where xa, xb, xc and xd represent the derivatives of ex in the observation matrix with respect to the state vector, and ya, yb, yc and yd represent the derivatives of ey in the observation matrix with respect to the state vector.

[0030] Let P = diag(2e-5, 2e-5, 2e-5, 2e-5), Q = diag(2e-5, 2e-5, 2e-5, 2e-5), and we can construct the initial covariance matrix. Q is the covariance matrix of the observation process noise.

[0031] Preferably, the signal is obtained by performing IQ orthogonalization on the input electrical signal, followed by dispersion compensation and clock recovery.

[0032] Preferably, the signal is one or more of QPSK, DPSK, and BPSK signals.

[0033] Secondly, the present invention also provides a compensation device for rapid polarization rotation and inter-symbol interference, including a polarization damage compensation module and an inter-symbol interference compensation module.

[0034] The polarization impairment compensation module is used to construct an initial simplified Kalman filter; wherein, the Kalman gain of the initial simplified Kalman filter is... A simplified Kalman filter is used to iteratively update the covariance matrix P and the state vector to compensate for polarization impairments in the signal. In the first iteration, the initial simplified Kalman filter is used to update the initial state vector and the initial covariance matrix. In subsequent iterations, the covariance matrix P obtained from the previous iteration is used... k and state vector A simplified Kalman filter is obtained for the next iteration update, so that the next iteration update can be performed;

[0035] The inter-symbol interference compensation module is used to compensate for inter-symbol interference in the signal using an FIR filter.

[0036] Thirdly, the present invention also provides a compensation device for fast polarization rotation and inter-symbol interference (ISI), used to implement the compensation method for fast polarization rotation and ISI described in the first aspect, the device comprising:

[0037] At least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor for performing the fast polarization rotation and intersymbol interference compensation method described in the first aspect.

[0038] Fourthly, the present invention also provides a non-volatile computer storage medium storing computer-executable instructions that are executed by one or more processors to perform the fast polarization rotation and intersymbol interference compensation method described in the first aspect.

[0039] This invention simplifies the calculation process of the Kalman filter by converting nonlinear matrix calculations into a gain factor N, thereby simplifying complex matrix operations into linear operations similar to CMA. Furthermore, addressing the Kalman filter's inability to handle inter-symbol interference (ISI), two first-order FIR filters are cascaded after the simplified Kalman filter to handle ISI between signals. Compared to Kalman filtering and traditional CMA, this reduces complexity and improves accuracy, solving the problems of rapid polarization impairment and ISI introduced by bandwidth limitations in high-speed dual-polarization systems. It offers advantages of lower complexity and better accuracy compared to CMA and traditional Kalman filtering, making it suitable for rapid polarization rotation and ISI impairment in high-speed polarization systems, thus providing a foundation for commercial implementation. Attached Figure Description

[0040] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments of the present invention will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0041] Figure 1 This is a flowchart illustrating the first method for compensating for rapid polarization rotation and inter-symbol interference provided in this embodiment of the invention.

[0042] Figure 2 This is a flowchart illustrating the second method for compensating for rapid polarization rotation and inter-symbol interference provided in this embodiment of the invention.

[0043] Figure 3 This is a flowchart illustrating the third method for compensating for rapid polarization rotation and inter-symbol interference provided in this embodiment of the invention.

[0044] Figure 4 This is a flowchart illustrating the fourth method for compensating for rapid polarization rotation and inter-symbol interference provided in this embodiment of the invention.

[0045] Figure 5 This is a schematic diagram illustrating an application scenario of a fast polarization rotation and inter-symbol interference compensation method provided in an embodiment of the present invention.

[0046] Figure 6 This is a flowchart illustrating the fifth method for compensating for rapid polarization rotation and inter-symbol interference provided in this embodiment of the invention.

[0047] Figure 7 This is a schematic diagram of a method for compensating for rapid polarization rotation and inter-symbol interference provided in an embodiment of the present invention;

[0048] Figure 8This is a flowchart illustrating a method for compensating for rapid polarization rotation and inter-symbol interference provided in an embodiment of the present invention.

[0049] Figure 9 This is a schematic diagram of the architecture of a fast polarization rotation and inter-symbol interference compensation device provided in an embodiment of the present invention;

[0050] Figure 10 This is a schematic diagram of the architecture of another fast polarization rotation and inter-symbol interference compensation device provided in an embodiment of the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0052] In this invention, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this application, unless otherwise stated, "a plurality of" means two or more.

[0053] Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0054] Example 1:

[0055] Embodiment 1 of the present invention provides a method for compensating for fast polarization rotation and intersymbol interference, such as... Figure 1 and Figure 7 As shown, it includes:

[0056] In step 201, an initial simplified Kalman filter is constructed; wherein, the Kalman gain of the initial simplified Kalman filter is... Among them, K k P represents the Kalman gain, N represents the gain coefficient of the proposed simplified Kalman filter, and P represents the gain coefficient of the Kalman filter. k H represents the covariance matrix of the error, and H represents the Jacobian matrix of the error function.

[0057] In step 202, the covariance matrix P is updated iteratively using a simplified Kalman filter. k and state vector To compensate for polarization impairments in the signal; wherein, in the first iteration update, an initial simplified Kalman filter is used to update the initial state vector and initial covariance matrix; in subsequent iteration updates, based on the covariance matrix and state vector obtained after the previous iteration update, a simplified Kalman filter is obtained for the next iteration update, facilitating the next iteration update; wherein, the signal is obtained by performing IQ orthogonalization on the input electrical signal, followed by dispersion compensation and clock recovery. The signal is one or more of QPSK, DPSK, and BPSK signals.

[0058] In step 203, a finite impulse filter (FIR) is used to compensate for intersymbol interference of the signal.

[0059] It should be noted that the "previous iteration update" and "next iteration update" mentioned in this embodiment are relative to two adjacent comparison processes. For example, if three iteration updates have been performed up to a certain time, for ease of description, these three iteration updates are referred to in chronological order as: the first iteration update, the second iteration update, and the third iteration update. Then, the first iteration update is the "previous iteration update" of the second iteration update, the second iteration update is the "next iteration update" of the first iteration update, the second iteration update is the "previous iteration update" of the third iteration update, and the third iteration update is the "next iteration update" of the second iteration update.

[0060] This embodiment simplifies the calculation process of the Kalman filter for depolarization scenarios, converting nonlinear matrix calculations into gain factor N, thereby simplifying complex matrix operations into linear operations similar to CMA. Furthermore, addressing the Kalman filter's inability to handle inter-symbol interference (ISI), two first-order FIR filters are cascaded after the simplified Kalman filter to handle ISI between signals. Compared to Kalman filtering and traditional CMA, this reduces complexity and improves accuracy, resolving the rapid polarization impairments and ISI introduced by bandwidth limitations in high-speed dual-polarization systems. It offers advantages over CMA and traditional Kalman filtering in terms of lower complexity and better accuracy, making it suitable for rapid polarization rotation and ISI impairments in high-speed polarization systems, thus providing a foundation for commercial implementation.

[0061] Wherein, the construction of the initial simplified Kalman filter, such as Figure 2 As shown, it specifically includes:

[0062] In step 301, based on the Kalman gain of the basic Kalman filter... Where R represents the covariance matrix of the observation matrix, The nonlinear operations in the matrix are converted into operations between the diagonal elements of the matrix, resulting in... c1, c2, c3, and c4 are all values ​​obtained from matrix operations.

[0063] In this embodiment of the invention, the asterisk (*) between two parameters in the corresponding formula represents a multiplication operation.

[0064] In step 302, the gain factor N = (c1*c4 - c2*c3) is constructed. -1 The Kalman gain of the initial simplified Kalman filter is obtained. This yields the initial simplified Kalman filter.

[0065] In an optional implementation, the covariance matrix P is iteratively updated using a simplified Kalman filter. k and state vector Specifically, it includes:

[0066] Let P = diag[μa,μb,μc,μd], where the values ​​of P represent the variances of the four corresponding state vectors, μa, μb, μc, and μd represent the covariances of the parameters of the covariance matrix, and diag[] represents forming a diagonal matrix. Then we obtain the Kalman gain of the simplified Kalman filter.

[0067] Where xa, xb, xc, xd, ya, yb, yc, and yd represent the derivatives of the observation matrix (i.e., the error function) with respect to the state vector in the partial solution, expressed as: ,

[0068] In this context, the asterisk (*) between two parameters represents multiplication, the asterisk at the top right of the corresponding parameter represents its conjugate, Re() represents taking the real part of the parameter within the parentheses, Im() represents taking the imaginary part of the parameter within the parentheses, and j is the imaginary unit. For example, E yin *E yout * Represents the calculation of E yout After conjugation, E yin The product of the conjugate.

[0069] Update the covariance matrix P using a simplified Kalman filter. k and state vector

[0070] The covariance matrix P is updated using a simplified Kalman filter. k and state vector like Figure 3 As shown, it specifically includes:

[0071] In step 401, the first formula is used. Update the state vector to obtain the updated state vector. Where ex and ey represent the values ​​in the Kalman observation matrix, respectively. In subsequent embodiments, ex is also written as ex and ey is also written as e. y .

[0072] In step 402, a simplified Kalman filter is used to update the diagonal elements of the covariance matrix, resulting in the updated covariance matrix.

[0073] In step 403, Diagonalization yields the updated covariance matrix

[0074] It should be noted that in this embodiment, the covariance matrix P... k and state vector The update is an iterative process. Steps 401-403 above describe one update process within the iterative process. In this embodiment, for the sake of brevity, the covariance matrix before and after the update in each iteration is represented by P. k Represented in the form of , the state vector before and after the update in each iteration is expressed as . It is represented in the form of .

[0075] The use of an FIR filter to compensate for intersymbol interference in the signal, such as... Figure 4 As shown, it specifically includes:

[0076] In step 501, the polarization-damped signal is input into two first-order FIR filters, and the error of the output signal is calculated.

[0077] In step 502, the tap coefficients of the FIR filter are updated using the gradient descent method according to the magnitude of the error in the output signal, so as to use the updated tap coefficients for the next inter-symbol interference compensation.

[0078] In practical applications, both polarization impairment compensation and inter-symbol interference compensation are achieved iteratively, such as... Figure 7 As shown, specifically:

[0079] Based on the covariance matrix P obtained after the previous iteration k and state vector The gain factor N is calculated, a simplified Kalman filter is generated based on the gain factor N, and the output signal obtained from the previous iteration is compensated using the simplified Kalman filter to obtain the updated covariance matrix P. k Updated state vector The signal after polarization damage compensation is input into two first-order FIR filters to obtain the output signal. The error magnitude of the output signal is calculated, and the tap coefficients of the FIR filters are updated based on this error magnitude. The updated covariance matrix P is then used to determine the output signal. k Updated state vector The gain factor N for the next iteration is obtained, and the next round of polarization impairment compensation is performed. The FIR filter with updated tap coefficients is used for the next round of intersymbol interference compensation.

[0080] Before iteratively updating the covariance matrix P and the state vector using a simplified Kalman filter, the method further includes: determining the initial Kalman state vector, the initial covariance matrix P, the covariance matrix Q of the state transition process noise, and the covariance matrix R of the matrix noise based on the polarization impairment matrix, specifically including:

[0081] According to the polarization damage matrix Where a, b, c, and d represent the magnitudes of the coefficients in the damage matrix. The inverse matrix of the polarization damage matrix is ​​then constructed. Based on the inverse of the polarization damage matrix, the initial state vector x is constructed. k =(a,b,c,d) T And construct the compensation signal

[0082] Construct the selection error function as follows Where R is 1, E xout (k), E yout (k) is the output of the Kalman filter; according to the Kalman observation matrix The Jacobian matrix takes the following form: Where xa, xb, xc, and xd represent the values ​​of e in the observation matrix. x The derivatives of the state vector with respect to the state vector, ya, yb, yc, and yd, respectively represent the values ​​of e in the observation matrix. y The derivative with respect to the state vector; let P = diag(2e-5,2e-5,2e-5,2e-5), Q = diag(2e-5,2e-5,2e-5,2e-5), to construct the initial covariance matrix. Q is the covariance matrix of the observation process noise, Pk and P k - Both can be understood as the covariance matrix of the error obtained in the previous iteration. For example, in this case, it can be understood as: the covariance matrix Pk obtained in the previous iteration plus Q to obtain the covariance matrix P used in the next iteration. k .

[0083] Example 2:

[0084] This invention is based on the method described in Embodiment 1, and combines it with specific application scenarios, using technical descriptions within those scenarios to illustrate the implementation process of the invention's features in those scenarios. This invention uses, as shown in... Figure 5 The application scenario shown is used as an example to provide a fast polarization rotation and inter-symbol interference compensation algorithm, such as... Figure 6 As shown, it includes the following steps:

[0085] In step 601, the number of Kalman state vectors is determined based on the polarization damage matrix, and the covariance matrix P, the covariance matrix Q of the state transition process noise, the covariance matrix R of the matrix noise, and the gain factor N based on the simplified Kalman are determined.

[0086] In step 602, based on the determination of the initial parameters of the Kalman filter (i.e., the Kalman gain of the initial simplified Kalman filter in Example 1), the calculation process of the simplified Kalman filter is based on the debiased scenario, and the complex matrix operation is converted into a simple linear operation through reasonable approximation.

[0087] In step 603, based on the simplified Kalman filter, the error between the signal and the standard constellation points is calculated according to the signal at the previous moment. The diagonal elements of the covariance matrix P are updated using the simplified Kalman filter, and then the magnitude of the state vector is updated to compensate for the polarization damage of the signal.

[0088] In step 604, based on the polarization impairment compensation, the signal after polarization impairment compensation is input into two subsequent first-order FIR filters and the error magnitude is calculated; the tap coefficients of the FIR filters are updated using the gradient descent method according to the calculated error magnitude to complete the inter-symbol interference compensation of the signal.

[0089] like Figure 7 As shown, when the input signal is QPSK, the two electrical signals received by the receiver of the dual-biased system will experience RSOP impairment and PMD, as well as frequency offset caused by the local oscillator laser and phase noise caused by the transmitting laser and the local oscillator laser. At the same time, the bandwidth of the IQ modulator will also introduce inter-symbol interference between the signals. The loss in the link and self-amplified noise will all affect the signal quality.

[0090] Both RSOP damage and PMD damage can be represented as a Hermitian conjugate matrix form:

[0091]

[0092] Under extreme conditions, such as lightning strikes, strong magnetic fields can be generated, which in turn can cause strong Faraday rotation in optical fibers. In such cases, RSOP can even reach tens of Mrad / s. If RSOP is 5 Mrad / s, after the aforementioned damage, the DP-QPSK signal will experience severe crosstalk between the two signals.

[0093] To balance the damage, we need to construct an inverse matrix j- to compensate for the signal. The inverse matrix is:

[0094]

[0095] The original Kalman partial resolution process can be described as follows:

[0096] First, the initial value of the state vector and the compensation signal are given:

[0097] x k =(a,b,c,d) T

[0098]

[0099] Based on the characteristics of QPSK signals, the following error function can be selected:

[0100]

[0101] Where R is 1, and E xout (k), E yout (k) is the output of the Kalman filter, from which the Kalman observation matrix can be derived:

[0102]

[0103] The Jacobian matrix takes the following form:

[0104]

[0105] Where xa, xb, xc, and xd represent the derivatives of the observation matrix ex with respect to the state vector, and ya, yb, yc, and yd represent the derivatives of the observation matrix ey with respect to the state vector. Then, the covariance matrix, Kalman gain, state vector, and covariance matrix are updated iteratively.

[0106] P k =P k +Q

[0107]

[0108]

[0109]

[0110] We linearize the Kalman computation process based on the following assumptions:

[0111] (1): It is assumed that the influence of diagonal elements on the solution bias is dominant in matrix operations, and only the diagonal elements of the matrix are considered.

[0112] During the debiasing process, the parameters are generally set as follows: P = diag[2e-5, 2e-5, 2e-5, 2e-5], Q = diag[2e-5, 2e-5, 2e-5, 2e-5]. For the Kalman initialization process, it can be written as:

[0113]

[0114] Where μa′, μb′, μc′, and μd′ represent the initial values ​​of P, and Q is the covariance matrix of the given observation process noise, which is generally a fixed value; in this paper, it is taken as 2e-5.

[0115] Then, the error value after compensation by the initial state vector is calculated:

[0116]

[0117] The general formula for calculating Kalman gain is:

[0118]

[0119] in The calculation is a major challenge, as analysis shows. Let R be an N×N matrix, where the given R can generally be written as R = diag[C,C], where C is a constant. Based on Assumption 1, the calculated result is diagonalized.

[0120]

[0121] In this process we can View as a pair The weighting factor is n, and to simplify the calculation, the values ​​of c4 and c1 are approximated as the same. Let N = (c1*c4 - c2*c3) -1 Then the Kalman gain calculation can be simplified to:

[0122] We call N the gain factor of the Kalman gain. In fact, N is not a constant value. Although N changes continuously with iterations in the original Kalman, we set N to a fixed value here to simplify the calculation. By reasonably approximating complex matrix operations into simple linear operations, we transform nonlinear calculations into simple linear calculations. P = diag[μa,μb,μc,μd]. According to the H matrix mentioned earlier, the Kalman gain can therefore be written as:

[0123]

[0124] Where xa, xb, xc, xd, ya, yb, yc, and yd represent the derivatives of the observation matrix (i.e., the error function) with respect to the state vector in the partial solution, and can be expressed as:

[0125]

[0126]

[0127] Then the state vector is updated:

[0128]

[0129] Substituting the Kalman gain, the state vector update process can be obtained as follows:

[0130]

[0131] The system then updates the covariance matrix:

[0132]

[0133] This can be seen as a scaling of P. Our above reasoning is based on P being a diagonal matrix. We calculate the error between the signal at the previous time step and the standard constellation points using a simplified Kalman filter, update the diagonal elements of the covariance matrix P using the simplified Kalman filter, and then update the magnitude of the state vector to compensate for polarization artifacts in the signal. Therefore, we scale P... k The update process is diagonalized. In fact, simulations have shown that elements outside the diagonal have little effect on it. At this time, the update process of p becomes:

[0134]

[0135] Will Diagonalization yields:

[0136]

[0137] It can be seen that P k Each iteration updates the state vector. Different state vectors have different update speeds. The subsequent update process is the same as described above, except that the diagonal elements of P are the updated values.

[0138] The error is then fed into two subsequent first-order FIR filters, and the magnitude of the error is calculated. Based on the calculated error magnitude, the tap coefficients of the FIR filters are updated using the gradient descent method to complete the intersymbol interference compensation for the signal.

[0139] Figure 8This diagram illustrates a comparison between the fast polarization rotation and inter-symbol interference (ISI) compensation method described in this embodiment and other existing algorithms. Simulations were performed on a 28 GBaud partial multiplexing OPSK system to compare the method with other existing algorithms, revealing the variation of the system bit error rate (BER) with the RSOP size under different algorithms. CMA represents the conventional algorithm, where the BER exceeds the FEC threshold at an RSOP of 2 Mrad / s. EKF represents a Kalman filter in existing technology, and S-EKF represents the simplified Kalman filter described in this embodiment. Their performance is comparable, indicating that the simplified Kalman filter in this embodiment maintains high performance while reducing complexity. S-EKF-N represents the method described in this embodiment, where an FIR filter is cascaded after the simplified Kalman filter to handle ISI. Compared to a Kalman filter without FIR, this method demonstrates better BER performance because the subsequent FIR filter addresses ISI that the Kalman filter cannot handle, resulting in better performance.

[0140] This embodiment simplifies the calculation process of the Kalman filter by converting complex matrix operations into simple linear operations through reasonable approximation for the depolarization scenario. After simplifying the Kalman filter, two first-order FIR filters are cascaded to handle inter-symbol interference between signals. Compared with Kalman filtering and traditional CMA, this reduces complexity and improves accuracy, solving the problems of rapid polarization damage and inter-symbol interference introduced by bandwidth limitations in high-speed dual-polarization systems. It has the advantages of lower complexity and better accuracy compared with CMA and traditional Kalman, thus being suitable for rapid polarization rotation and inter-symbol interference damage in high-speed polarization systems, providing a foundation for commercial implementation.

[0141] Example 3:

[0142] Based on Embodiments 1 and 2, this embodiment also provides a compensation device for rapid polarization rotation and intersymbol interference, such as... Figure 9 As shown, the device includes a polarization impairment compensation module and an inter-symbol interference (ISI) compensation module; the polarization impairment compensation module is used to construct an initial simplified Kalman filter; wherein, the Kalman gain of the initial simplified Kalman filter is... A simplified Kalman filter is used to iteratively update the covariance matrix P and the state vector to compensate for polarization impairments in the signal. In the first iteration, the initial simplified Kalman filter is used to update the initial state vector and the initial covariance matrix. In subsequent iterations, the covariance matrix P obtained from the previous iteration is used... k and state vector A simplified Kalman filter is obtained for the next iteration update, so as to facilitate the next iteration update; the inter-symbol interference compensation module is used to compensate for the inter-symbol interference of the signal using an FIR filter.

[0143] It should be noted that the methods described in Examples 1 and 2 are applicable to this example, and will not be repeated here.

[0144] like Figure 10 The diagram shown is a schematic representation of the architecture of a fast polarization rotation and inter-symbol interference (ISI) compensation device according to an embodiment of the present invention. The fast polarization rotation and ISI compensation device of this embodiment includes one or more processors 21 and a memory 22. Figure 10 Take a processor 21 as an example.

[0145] Processor 21 and memory 22 can be connected via a bus or other means. Figure 10 Taking the example of a connection between China and Israel via a bus.

[0146] The memory 22, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs and non-volatile computer-executable programs, such as the fast polarization rotation and inter-symbol interference compensation method in Embodiment 1. The processor 21 executes the fast polarization rotation and inter-symbol interference compensation method by running the non-volatile software program and instructions stored in the memory 22.

[0147] Memory 22 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some embodiments, memory 22 may optionally include memory remotely located relative to processor 21, which can be connected to processor 21 via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0148] The program instructions / modules are stored in the memory 22. When executed by one or more processors 21, they perform the fast polarization rotation and intersymbol interference compensation method described in Embodiment 1.

[0149] It is worth noting that the information interaction and execution process between the modules and units in the above-mentioned device and system are based on the same concept as the processing method embodiment of the present invention. For details, please refer to the description in the method embodiment of the present invention, and will not be repeated here.

[0150] Those skilled in the art will understand that all or part of the steps in the various methods of the embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, which may include: read-only memory (ROM), random access memory (RAM), magnetic disk or optical disk, etc.

[0151] 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, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for compensating for fast polarization rotation and intersymbol interference, characterized in that, include: Construct an initial simplified Kalman filter; wherein the Kalman gain of the initial simplified Kalman filter is... The construction of the initial simplified Kalman filter includes: Based on the Kalman gain of the basic Kalman filter ,Will The nonlinear operations in the matrix are converted into operations between the diagonal elements of the matrix, resulting in... ;in, , , and All values ​​are obtained from matrix operations; Construct the gain factor N= The Kalman gain of the initial simplified Kalman filter is obtained. Thus, the initial simplified Kalman filter is obtained; Iteratively update the covariance matrix using a simplified Kalman filter. and state vector To compensate for polarization impairments of the signal; in the first iteration update, the initial state vector and initial covariance matrix are updated using an initial simplified Kalman filter. In subsequent iteration updates, a simplified Kalman filter for the next iteration update is obtained based on the covariance matrix and state vector obtained after the previous iteration update, so as to facilitate the next iteration update. Use an FIR filter to compensate for intersymbol interference in the signal; Before iteratively updating the covariance matrix P and the state vector using a simplified Kalman filter, the method further includes: determining the initial Kalman state vector, the initial covariance matrix P, the covariance matrix Q of the state transition process noise, and the covariance matrix R of the matrix noise based on the polarization impairment matrix, specifically including: According to the polarization damage matrix The inverse matrix of the polarization damage matrix is ​​constructed. ; The initial state vector is constructed based on the inverse of the polarization damage matrix. And construct the compensation signal ; Construct the selection error function as follows Where R is 1, , This is the output of the Kalman filter; According to the Kalman observation matrix The Jacobian matrix is ​​then derived as follows: ;in , , and Representing the observation matrix respectively The derivative with respect to the state vector, , , and Representing the observation matrix respectively The derivative with respect to the state vector; make , The initial covariance matrix is ​​constructed. ; Let be the covariance matrix of the noise during the observation process.

2. The method for compensating for fast polarization rotation and intersymbol interference according to claim 1, characterized in that, The simplified Kalman filter is used to iteratively update the covariance matrix. and state vector Specifically, it includes: make This yields a simplified Kalman filter; where the Kalman gain of the simplified Kalman filter is... ; in, , , , , , , and In the partial solution, the derivatives of the observation matrix (i.e., the error function) with respect to the state vector are expressed as: , ; Update the covariance matrix using a simplified Kalman filter. and state vector .

3. The method for compensating for fast polarization rotation and inter-symbol interference according to claim 2, characterized in that, The method of updating the covariance matrix using a simplified Kalman filter and state vector Specifically, it includes: Use the first formula Update the state vector to obtain the updated state vector. ; The diagonal elements of the covariance matrix are updated using a simplified Kalman filter to obtain the updated covariance matrix. ; Will Diagonalization yields the updated covariance matrix .

4. The method for compensating for fast polarization rotation and intersymbol interference according to claim 1, characterized in that, The method of using an FIR filter to compensate for intersymbol interference of the signal specifically includes: The polarization-damped signal is input into two first-order FIR filters, and the error of the output signal is calculated. Based on the magnitude of the output signal error, the tap coefficients of the FIR filter are updated using the gradient descent method, so that the updated tap coefficients can be used for the next intersymbol interference compensation.

5. The method for compensating for fast polarization rotation and intersymbol interference according to any one of claims 1-4, characterized in that, The signal is obtained by orthogonalizing the input electrical signal using the IQ method, and then performing dispersion compensation and clock recovery.

6. The method for compensating for fast polarization rotation and intersymbol interference according to any one of claims 1-4, characterized in that, The signal is one or more of QPSK, DPSK, and BPSK signals.

7. A compensation device for rapid polarization rotation and intersymbol interference, used to implement the compensation method as described in any one of claims 1 to 6, characterized in that, Includes a polarization damage compensation module and an inter-symbol interference compensation module; The polarization impairment compensation module is used to construct an initial simplified Kalman filter; wherein, the Kalman gain of the initial simplified Kalman filter is... The covariance matrix P and state vector are iteratively updated using a simplified Kalman filter to compensate for polarization impairments in the signal. In the first iteration, the initial state vector and initial covariance matrix are updated using the initial simplified Kalman filter. In subsequent iterations, the covariance matrix obtained from the previous iteration is used... and state vector This yields a simplified Kalman filter for the next iteration update, facilitating the next iteration update. The inter-symbol interference compensation module is used to compensate for inter-symbol interference in the signal using an FIR filter.

8. A compensation device for rapid polarization rotation and intersymbol interference, characterized in that, The device includes: At least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor for performing the fast polarization rotation and intersymbol interference compensation method according to any one of claims 1-6.

Images