CN117155743A - Compensation method and device for fast polarization rotation and inter-code crosstalk - Google Patents
Compensation method and device for fast polarization rotation and inter-code crosstalk Download PDFInfo
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Abstract
The application relates to the technical field of communication, and provides a compensation method and device for fast polarization rotation and intersymbol interference. Wherein the method comprises constructing an initial reduced kalman filter; wherein the Kalman gain of the initial reduced Kalman filterThe method comprises the steps of carrying out a first treatment on the surface of the Iterative updating of covariance matrix P using reduced Kalman filter k And state vectorTo compensate for polarization impairments of the signal; the inter-symbol interference of the signal is compensated using an FIR filter. The application simplifies the calculation process of the Kalman filter, thereby simplifying complex matrix operation into linear operation, improving the precision and solving the problem of high-speed double-bias systemThe fast polarization impairment and the inter-code crosstalk introduced by bandwidth limitation have the advantages of low complexity and better precision, thereby being applicable to the fast polarization rotation and the inter-code crosstalk impairment of a high-speed polarization system.
Description
Technical Field
The present application relates to the field of communications technologies, and in particular, to a method and apparatus for compensating for fast polarization rotation and inter-code crosstalk.
Background
With the continuous development of the network world, global data traffic is explosively developed, so that the requirement on the data transmission rate is higher and higher. A polarization division multiplexing (DP) system is an excellent solution for solving the high-rate requirement, and the data transmission rate can be directly and greatly improved by polarization multiplexing of two orthogonal polarization states of light in a single-mode fiber, so that the DP system is an excellent solution for solving the high-traffic requirement in the future. However, DP systems are very sensitive to polarization impairments, especially when the environment changes drastically, such as a strong magnetic field generated by lightning can cause a fast polarization Rotation (RSOP) of two polarized light beams, sometimes up to 20Mrad/s, and conventional equalization algorithms can fail to cause reception interruption, while the increase in communication rate places higher demands on the bandwidth of optical communication system devices such as Photodetectors (PD), which can also degrade the performance of the communication system due to inter-code crosstalk caused by device bandwidth or other factors.
The Kalman filtering is a time-varying prediction algorithm for predicting the current moment state based on the past moment state, is widely applied to the navigation field, and can cope with tracking prediction of various scenes. Due to the excellent tracking performance of the kalman filter, the kalman filter is applied to the de-biased division multiplexing in recent years, although the kalman filter can track a fast RSOP to realize the fast RSOP damage processing encountered by a polarization system, but cannot process the inter-code crosstalk caused by the device bandwidth, so that the communication degradation caused by the inter-code crosstalk caused by the device bandwidth cannot be solved, and the kalman filter has large resource occupation amount and low calculation efficiency due to the nonlinear matrix operation involved in the calculation process, and is not suitable for commercial implementation.
In view of this, overcoming the drawbacks of the prior art is a problem to be solved in the art.
Disclosure of Invention
The technical problem to be solved by the application is to provide a Kalman filter which can track a fast RSOP, realize fast RSOP damage processing encountered by a polarization system, but cannot process inter-code crosstalk caused by device bandwidth, so that communication degradation caused by inter-code crosstalk caused by device bandwidth cannot be solved, and the Kalman filter has large resource occupation amount and low calculation efficiency due to nonlinear matrix operation in the calculation process, and is not suitable for commercial implementation.
The application adopts the following technical scheme:
in a first aspect, the present application provides a method for compensating for fast polarization rotation and inter-symbol crosstalk, including:
constructing an initial simplified Kalman filter; wherein the Kalman gain of the initial reduced Kalman filter
Iterative updating of covariance matrix P using reduced Kalman filter k And state vectorTo compensate for polarization impairments of the signal; in the first iteration updating process, an initial state vector and an initial covariance matrix are updated by using an initial simplified Kalman filter, and in the subsequent iteration updating process, the simplified Kalman filter for the next iteration updating is obtained according to the covariance matrix and the state vector obtained after the previous iteration updating so as to facilitate the next iteration updating;
the inter-symbol interference of the signal is compensated using an FIR filter.
Preferably, the constructing an initial simplified kalman filter specifically includes:
kalman gain from a basic Kalman filterWill->The nonlinear operation in (a) is converted into the operation between diagonal elements in the matrix, and the obtained result is
Construction gain factor n= (c 1 x c4-c2 x c 3) -1 Obtaining the Kalman gain of the initial simplified Kalman filterThus obtaining an initial reduced kalman filter.
Preferably, the iterative updating of the covariance matrix P using a reduced Kalman filter k And state vectorThe method specifically comprises the following steps:
let p=diag (μa, μb, μc, μd), a simplified kalman filter is obtained; wherein the Kalman gain of the reduced Kalman filter
Wherein xa, xb, xc, xd, ya, yb, yc, yd represent the derivatives of the observation matrix, i.e. the error function, to the state vector in the unbiasing, respectively, expressed as:
updating covariance matrix P using reduced Kalman filter k And state vector
Preferably, the updating of covariance matrix P using a reduced Kalman filter k And state vectorThe method specifically comprises the following steps:
using a first formulaUpdating the state vector to obtain an updated state vector
Updating diagonal elements of the covariance matrix by using a simplified Kalman filter to obtain an updated covariance matrix
Will beDiagonalization to obtain updated covariance matrix
Preferably, the compensating the inter-code crosstalk of the signal by using the FIR filter specifically includes:
inputting the signal after polarization damage compensation into two first-order FIR filters, and calculating the error of an output signal;
and updating the tap coefficient of the FIR filter by using a gradient descent method according to the error magnitude of the output signal so as to use the updated tap coefficient to carry out the next inter-code crosstalk compensation.
Preferably, before the iteratively updating the covariance matrix P and the state vector using the reduced kalman filter, the method further comprises: determining an initial Kalman state vector, an initial covariance matrix P, a covariance matrix Q of state transition process noise and a covariance matrix R of matrix noise according to the polarization damage matrix, wherein the method specifically comprises the following steps:
according to polarization damage matrixConstructing an inverse matrix to obtain a polarization impairment matrix
Constructing and obtaining an initial state vector x according to the inverse matrix of the polarization damage matrix k ＝(a,b,c,d) T And construct and get the compensation signal
Constructing and selecting an error function asWherein R is 1, E xout (k)，E yout (k) Is the output of the Kalman filter;
based on Kalman observation matrixThe form of the jacobian matrix is derived as:
wherein xa, xb, xc and xd represent the derivatives of ex with respect to the state vector in the observation matrix, respectively, and ya, yb, yc and yd represent the derivatives of ey with respect to the state vector in the observation matrix, respectively;
let p=diag (2 e-5 ), q=diag (2 e-5 ), construct to get the initial covariance matrixQ is the covariance matrix of the observation process noise.
Preferably, the signal is obtained by IQ orthogonalization of the input electrical signal, dispersion compensation and clock recovery.
Preferably, the signal is one or more of a QPSK signal, a DPSK signal, and a BPSK signal.
In a second aspect, the application also provides a compensation device for fast polarization rotation and inter-code crosstalk, which comprises a polarization damage compensation module and an inter-code crosstalk compensation module;
the polarization damage compensation module is used for constructing an initial simplified Kalman filter; wherein the Kalman gain of the initial reduced Kalman filterIteratively updating the covariance matrix P and the state vector using a reduced kalman filter to compensate for polarization impairments of the signal; wherein, in the first iteration updating, an initial state vector and an initial covariance matrix are updated by using an initial simplified Kalman filter, and in the subsequent iteration updating process, the covariance matrix P obtained after the last iteration updating is used k And state vector->Obtaining a simplified Kalman filter for next iteration update so as to facilitate the next iteration update;
the inter-code crosstalk compensation module is used for compensating inter-code crosstalk of signals by using an FIR filter.
In a third aspect, the present application further provides a device for compensating for fast polarization rotation and inter-code crosstalk, for implementing the method for compensating for fast polarization rotation and inter-code crosstalk according to the first aspect, where the device includes:
at least one processor; and a memory communicatively coupled 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 inter-symbol interference compensation method of the first aspect.
In a fourth aspect, the present application also provides a non-volatile computer storage medium storing computer executable instructions for execution by one or more processors to perform the method of fast polarization rotation and inter-symbol interference compensation of the first aspect.
The application simplifies the calculation process of the Kalman filter, converts nonlinear matrix calculation into gain factor N, thereby simplifying complex matrix operation into linear operation similar to CMA, simultaneously aiming at the fact that the Kalman filter can not process inter-code crosstalk, after simplifying the Kalman filter, cascading two first-order FIR filters for processing inter-code crosstalk between signals, compared with Kalman filter and traditional CMA, reduces complexity, improves precision, solves the fast polarization damage of a high-speed double-polarization system and inter-code crosstalk caused by bandwidth limitation, has the advantages of low complexity and better precision compared with the CMA and traditional Kalman, thereby being suitable for fast polarization rotation and inter-code crosstalk damage of the high-speed polarization system, and providing a basis for commercial implementation.
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In order to more clearly illustrate the technical solution of the embodiments of the present application, the drawings that are required to be used in the embodiments of the present application will be briefly described below. It is evident that the drawings described below are only some embodiments of the present application and that other drawings may be obtained from these drawings without inventive effort for a person of ordinary skill in the art.
Fig. 1 is a flow chart of a first method for compensating for fast polarization rotation and inter-code crosstalk according to an embodiment of the present application;
FIG. 2 is a flow chart of a second method for compensating for fast polarization rotation and inter-symbol interference according to an embodiment of the present application;
FIG. 3 is a flowchart of a third method for compensating for fast polarization rotation and inter-symbol interference according to an embodiment of the present application;
FIG. 4 is a flowchart of a fourth method for compensating for fast polarization rotation and inter-symbol interference according to an embodiment of the present application;
fig. 5 is a schematic diagram of an application scenario of a fast polarization rotation and inter-code crosstalk compensation method according to an embodiment of the present application;
FIG. 6 is a flowchart of a fifth method for compensating for fast polarization rotation and inter-symbol interference according to an embodiment of the present application;
FIG. 7 is a schematic diagram of a fast polarization rotation and inter-symbol crosstalk compensation method according to an embodiment of the present application;
FIG. 8 is a schematic flow chart of a fast polarization rotation and inter-symbol interference compensation method according to an embodiment of the present application;
FIG. 9 is a schematic diagram of a compensation device for fast polarization rotation and inter-symbol interference according to an embodiment of the present application;
fig. 10 is a schematic diagram of another architecture of a compensation device for fast polarization rotation and inter-code crosstalk according to an embodiment of the present application.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
The terms "first," "second," and the like herein are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first", "a second", etc. may explicitly or implicitly include one or more such feature. In the description of the present application, unless otherwise indicated, the meaning of "a plurality" is two or more.
In addition, the technical features of the embodiments of the present application described below may be combined with each other as long as they do not collide with each other.
Example 1:
the embodiment 1 of the present application provides a fast polarization rotation and inter-code crosstalk compensation method, as shown in fig. 1 and fig. 7, including:
in step 201, an initial reduced Kalman filter is constructed; wherein the Kalman gain of the initial reduced Kalman filterWherein K is k Represents the Kalman gain, N represents the proposed reduced Kalman filterGain coefficient, P k Represents the covariance matrix of the error, and H represents the jacobian matrix of the error function.
In step 202, the covariance matrix P is iteratively updated using a reduced kalman filter k And state vectorTo compensate for polarization impairments of the signal; in the first iteration updating process, an initial state vector and an initial covariance matrix are updated by using an initial simplified Kalman filter, and in the subsequent iteration updating process, the simplified Kalman filter for the next iteration updating is obtained according to the covariance matrix and the state vector obtained after the previous iteration updating so as to facilitate the next iteration updating; wherein the signal is obtained by IQ orthogonalization of an input electrical signal, dispersion compensation and clock recovery. The signals are one or more of QPSK signals, DPSK signals and BPSK signals.
In step 203, the inter-symbol interference of the signal is compensated using a finite impulse response filter (FIR, finite impulse filter, abbreviated as FIR).
It should be noted that, in the comparison process of the previous iteration update and the next iteration update described in this embodiment, for example, three iteration updates have been performed by a certain time, and for convenience of description, these three iteration updates are referred to as: the first iteration update is the 'last 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 'last iteration update' of the third iteration update, and the third iteration update is the 'next iteration update' of the second iteration update.
According to the embodiment, the calculation process of the Kalman filter is simplified aiming at a depolarization scene, nonlinear matrix calculation is converted into a gain factor N, so that complex matrix operation is simplified into linear operation similar to CMA, meanwhile, the Kalman filter cannot process inter-code crosstalk, two first-order FIR filters are cascaded after the Kalman filter is simplified to process inter-code crosstalk between signals, complexity is reduced compared with Kalman filtering and traditional CMA, accuracy is improved, fast polarization damage of a high-speed double-polarization system and inter-code crosstalk introduced due to bandwidth limitation are solved, and the method has the advantages of being low in complexity and high in accuracy compared with the CMA and traditional Kalman, is suitable for fast polarization rotation and inter-code crosstalk damage of the high-speed polarization system, and provides a foundation for commercial implementation.
The construction of the initial simplified kalman filter, as shown in fig. 2, specifically includes:
in step 301, kalman gain according to a basic Kalman filterWherein R represents the covariance matrix of the observation matrix, will +.>The nonlinear operation in (a) is converted into the operation between diagonal elements in the matrix, and the +.>Wherein c1, c2, c3 and c4 are all values obtained by matrix operation.
In the embodiment of the present application, the signs between two parameters in the corresponding formulas represent multiplication operations.
In step 302, a gain factor n= (c 1×c4-c2×c3) is constructed -1 Obtaining the Kalman gain of the initial simplified Kalman filterThus obtaining an initial reduced kalman filter.
In an alternative embodiment, the covariance matrix P is iteratively updated using a reduced kalman filter k And state vectorThe method specifically comprises the following steps:
let p=diag [ μa, μb, μc, μd]Wherein the values of P represent the variances of the corresponding four state vectors, respectively, μa, μb, μc and μd represent the covariance of the respective parameters of the covariance matrix, diag []Representing the Kalman gain resulting in a simplified Kalman filter if the diagonal matrix is formed
Wherein xa, xb, xc, xd, ya, yb, yc and yd represent the derivatives of the observation matrix, i.e. the error function, to the state vector in the unbiasing, respectively, expressed as:
wherein, the multiplication is represented by the parameter located between the two parameters, the conjugation of the parameter is represented by the parameter located at the upper right corner of the corresponding parameter, re () represents the real part of the parameter in the bracket, im () represents the imaginary part of the parameter in the bracket, and j is the imaginary unit. Such as E yin *E yout * Representative calculation E yout After conjugation of E yin And the conjugate.
Updating covariance matrix P using reduced Kalman filter k And state vector
The covariance matrix P is updated by using a simplified Kalman filter k And state vectorAs shown in fig. 3, the method specifically includes:
in step 401, a first formula is usedUpdating the state vector to obtain an updated state vector +.>Wherein ex and ey represent values in the Kalman observation matrix, respectively, which in the subsequent embodiments are also written as ex, and ey is also written as e y 。
In step 402, diagonal elements of the covariance matrix are updated using a reduced Kalman filter to obtain an updated covariance matrix
In step 403, the process willDiagonalization to obtain updated covariance matrix
In this embodiment, the covariance matrix P k And state vectorThe updating of (a) is an iterative process, and the steps 401-403 are described with respect to one updating process in the iterative process, in this embodiment, for the sake of simplicity of expression, the covariance matrices before and after updating in each iterative process are denoted by P k Expressed in terms of (1) the state vector before and after update in each iteration is expressed in +.>Is expressed in terms of (a).
The compensation for the inter-code crosstalk of the signal by using the FIR filter, as shown in fig. 4, specifically includes:
in step 501, the polarization-impaired signal is input to two first-order FIR filters, and the error magnitude of the output signal is calculated.
In step 502, the tap coefficients of the FIR filter are updated by using a gradient descent method according to the error magnitude of the output signal, so that the next inter-symbol crosstalk compensation is performed by using the updated tap coefficients.
In practical use, the polarization impairment compensation and the inter-code crosstalk compensation are both implemented through iteration, as shown in fig. 7, specifically:
according to covariance matrix P obtained after last iteration k State vectorCalculating to obtain a gain factor N, generating a simplified Kalman filter according to the gain factor N, and compensating an output signal obtained in the last iteration by using the simplified Kalman filter to obtain an updated covariance matrix P k Updated state vector->And the signal after polarization damage compensation is input to two first-order FIR filters to obtain an output signal, the error size of the output signal is calculated, the tap coefficient of the FIR filter is updated according to the error size, and the covariance matrix P after updating k Updated state vector->And obtaining a gain factor N of the next iteration, so as to perform polarization damage compensation of the next round, and performing inter-code crosstalk compensation of the next round by using the FIR filter with updated tap coefficients.
Before iteratively updating the covariance matrix P and the state vector using the reduced kalman filter, the method further comprises: determining an initial Kalman state vector, an initial covariance matrix P, a covariance matrix Q of state transition process noise and a covariance matrix R of matrix noise according to the polarization damage matrix, wherein the method specifically comprises the following steps:
according to polarization damage matrixWherein a, b, c and d represent the coefficient sizes of the injury matrix, respectively. Constructing an inverse matrix of the polarization impairment matrix>Constructing and obtaining an initial state vector x according to the inverse matrix of the polarization damage matrix k ＝(a,b,c,d) T And construct and get the compensation signal
Constructing and selecting an error function asWherein R is 1, E xout (k)，E yout (k) Is the output of the Kalman filter; according to the Kalman observation matrix->The form of the jacobian matrix is derived as:wherein xa, xb, xc, xd respectively represent e in the observation matrix x The derivatives of the state vector, ya, yb, yc, yd, respectively represent e in the observation matrix y Derivative of the state vector; let p=diag (2 e-5 ), q=diag (2 e-5 ), construct to get the initial covariance matrixQ is covariance matrix of observation process noise, pk and P k - All can be understood as covariance matrices of the errors from the last iteration, as understood herein: adding Q to the covariance matrix Pk obtained in the previous iteration to obtain a covariance matrix P used next time k 。
Example 2:
the application is based on the method described in embodiment 1, and combines specific application scenes, and the implementation process in the characteristic scene of the application is described by means of technical expression in the relevant scene. The application takes an application scene as shown in fig. 5 as an example to provide a fast polarization rotation and intersymbol interference compensation algorithm, as shown in fig. 6, comprising the following steps:
in step 601, the number of kalman state vectors is determined according to the polarization impairment matrix, and a covariance matrix P and a covariance matrix Q of the state transition process noise, a covariance matrix R of the matrix noise, and a gain factor N based on simplified kalman are determined.
In step 602, based on determining the initial parameters of the kalman filter (i.e. the kalman gain of the initial simplified kalman filter in embodiment 1), the calculation process of the kalman filter is simplified based on the unbiased scene, and the complex matrix operation is converted into a simple linear operation through reasonable approximation.
In step 603, based on the simplified kalman filter, the error between the signal and the standard constellation point is calculated according to the signal at the previous time, and the simplified kalman filter is used to update the diagonal element of the covariance matrix P, further update the magnitude of the state vector, and compensate the polarization impairment of the signal.
In step 604, based on the polarization damage compensated signal, inputting the signal into two subsequent first-order FIR filters and calculating the error size; and updating the tap coefficient of the FIR filter by using a gradient descent method according to the calculated error size to complete the inter-code crosstalk compensation of the signal.
When the input signal is QPSK as shown in fig. 7, two paths of electric signals received by the receiving end of the dual-bias system undergo RSOP damage and PMD, and frequency offset caused by the local oscillator laser and phase noise caused by the transmitting end laser and the local oscillator laser, and meanwhile, the bandwidth of the IQ modulator also introduces inter-code crosstalk between signals, and loss in a link, spontaneous amplification noise and the like affect the quality of the signals.
It can be expressed as a hermitian conjugate matrix form for both RSOP and PMD lesions:
under extreme conditions, the strong magnetic field is induced by lightning, so that the optical fiber can generate a strong Faraday rotation effect, and the RSOP can even reach tens of Mrad/s, for example, when the RSOP is 5Mrad/s, the DP-QPSK signal is damaged, and serious crosstalk occurs between the two paths of signals.
To equalize the impairments, we need to construct an inverse j-matrix to compensate the signal, the inverse being:
the original Kalman unbiasing procedure can be described as follows:
first, a state vector initial value and a compensation signal are given:
x k ＝(a,b,c,d) T
the error function can be selected according to the characteristics of QPSK signals:
wherein R is 1, E xout (k)，E yout (k) As output of the Kalman filter, it is possible to base on the Kalman observation matrix:
the form of the jacobian matrix is derived as:
wherein xa, xb, xc, xd respectively represent the derivatives of ex to the state vector in the observation matrix, ya, yb, yc, yd respectively represent the derivatives of ey to the state vector in the observation matrix, then the covariance matrix is updated, the Kalman gain, the state vector and the covariance matrix are updated, and the iteration is continued:
P k ＝P k +Q
we linearize the Kalman operation based on the following assumption:
(1) The influence of diagonal elements on the unbiasing in matrix operation is approximately considered to be dominant, and only the diagonal elements of the matrix are considered.
In the unbiasing process, parameters are generally set as follows: p=diag [2e-5,2e-5 ], q=diag [2e-5,2e-5 ], for the initial procedure of Kalman, can be written as:
where μa ', μb', μc ', μd' respectively represent the initial set point of P, Q is the covariance matrix of the given observation process noise, which is typically a fixed value, here taken as 2e-5.
Then calculate the error value compensated by the initial state vector:
the general calculation formula of the Kalman gain is as follows:
wherein the method comprises the steps ofIs a big difficulty in calculation of (a) and analysis can be known about +.>Is an N x N order matrix, where a given R is typically writable as r=diag [ C, C ]]Where C is a constant, and diagonalizing the calculation result according to the assumption 1:
in the process, we can useSeen as a pair->For simplicity of operation, the values of c4, c1 are approximately considered as N, let n= (c 1 x c4-c2 x c 3) -1 The gain calculation of Kalman can be reduced to: />
We call N the gain factor of the Kalman gain, in fact N is not a constant value, although N varies continuously with iteration in the original Kalman, N is set to a fixed value here for simplicity of calculation. By converting a complex matrix operation into a simple linear operation by reasonable approximation, whereby we convert the non-linear calculation into a simple linear calculation, p=diag [ μa, μb, μc, μd ], the H matrix according to the foregoing is available and thus the Kalman gain can be written as:
wherein xa, xb, xc, xd, ya, yb, yc, yd represent the derivatives of the observation matrix, i.e. the error function, with respect to the state vector in the unbiasing, respectively, and can be expressed as:
the update of the state vector is then performed:
the update process of substituting kalman gain into the state vector can be obtained as follows:
the system then updates the covariance matrix:
it can be seen that this is a scaling of P, our reasoning is based on P being a diagonal matrix, calculating the error between the signal at the previous time and the standard constellation point according to the simplified kalman filter, updating the diagonal element of the covariance matrix P by using the simplified kalman filter, and further updating the magnitude of the state vector, for the signalTo compensate for polarization impairments of (a). Therefore we will P k The update process of p becomes diagonal, and in fact the simulation also finds that elements outside the diagonal have little effect on it, at which point the update process of p becomes:
will beDiagonalization can be achieved:
it can be seen that P k Each iteration is updated, with different update rates for the state vectors, and the subsequent update process is the same as described above, except that the diagonal elements of P are updated values here.
Inputting the error into two subsequent first-order FIR filters and calculating the error size; and updating the tap coefficient of the FIR filter by using a gradient descent method according to the calculated error size to complete the inter-code crosstalk compensation of the signal.
Fig. 8 is a schematic diagram of a comparison between the fast polarization rotation and inter-code crosstalk compensation method and other existing algorithms according to the present embodiment, that is, the method and other existing algorithms according to the present embodiment are respectively simulated by using a 28GBaud polarization division multiplexing OPSK system, so as to obtain the change of the system error rate along with the RSOP size under different algorithms. Wherein CMA is a conventional algorithm and can see that the error rate exceeds the FEC threshold when RSOP is 2Mrad/S, EKF is a kalman filter in the prior art, S-EKF is a simplified kalman filter described in this embodiment and can see that the two performances are almost the same, which illustrates that the simplified kalman filter described in this embodiment keeps high performance while reducing complexity, and S-EKF-N represents that the subsequent cascade FIR filter of the simplified kalman filter processes inter-code crosstalk, i.e., the method described in this embodiment can see that the error rate performance is better than that of the kalman filter without FIR, because the addition of the subsequent FIR filter processes inter-code crosstalk that the kalman filter cannot solve, and thus the effect is better.
According to the embodiment, the complex matrix operation is converted into the simple linear operation by reasonable approximation aiming at the depolarization scene, the calculation process of the Kalman filter is simplified, two first-order FIR filters are cascaded after the Kalman filter is simplified to process inter-code crosstalk between signals, the complexity is reduced compared with Kalman filtering and traditional CMA, the precision is improved, the fast polarization damage of a high-speed double-polarization system and the inter-code crosstalk introduced by bandwidth limitation are solved, and the method has the advantages of being low in complexity and better in precision compared with the CMA and traditional Kalman, so that the method is suitable for fast polarization rotation and inter-code crosstalk damage of the high-speed polarization system, and provides a basis for commercial implementation.
Example 3:
on the basis of embodiment 1 and embodiment 2, this embodiment further provides a compensation device for fast polarization rotation and inter-code crosstalk, as shown in fig. 9, where the device includes a polarization impairment compensation module and an inter-code crosstalk compensation module; the polarization damage compensation module is used for constructing an initial simplified Kalman filter; wherein the Kalman gain of the initial reduced Kalman filterIteratively updating the covariance matrix P and the state vector using a reduced kalman filter to compensate for polarization impairments of the signal; wherein, in the first iteration updating, an initial state vector and an initial covariance matrix are updated by using an initial simplified Kalman filter, and in the subsequent iteration updating process, the covariance matrix P obtained after the last iteration updating is used k And state vector->Obtaining a simplified Kalman filter for next iteration update so as to facilitate the next iteration update; the inter-code crosstalk compensation module is used for using the FIR filter pairThe inter-symbol interference of the signal is compensated.
It should be noted that the methods described in embodiment 1 and embodiment 2 are applicable in this embodiment, and are not described in detail herein.
Fig. 10 is a schematic diagram of an architecture of a fast polarization rotation and inter-code crosstalk compensation apparatus according to an embodiment of the present application. The fast polarization rotation and inter-symbol interference compensation device of this embodiment includes one or more processors 21 and a memory 22. In fig. 10, a processor 21 is taken as an example.
The processor 21 and the memory 22 may be connected by a bus or otherwise, which is illustrated in fig. 10 as a bus connection.
The memory 22 is used as a non-volatile computer readable storage medium for storing non-volatile software programs and non-volatile computer executable programs, such as the fast polarization rotation and inter-code crosstalk compensation methods of example 1. The processor 21 performs a fast polarization rotation and inter-symbol crosstalk compensation method by running non-volatile software programs and instructions stored in the memory 22.
The memory 22 may include high-speed random access memory, and may also include non-volatile memory, such as at least one magnetic disk storage device, flash memory device, or other non-volatile solid-state storage device. In some embodiments, memory 22 may optionally include memory located remotely from processor 21, which may 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.
The program instructions/modules are stored in the memory 22 and when executed by the one or more processors 21 perform the fast polarization rotation and inter-symbol interference compensation method of embodiment 1 described above.
It should be noted that, because the content of information interaction and execution process between modules and units in the above-mentioned device and system is based on the same concept as the processing method embodiment of the present application, specific content may be referred to the description in the method embodiment of the present application, and will not be repeated here.
Those of ordinary skill in the art will appreciate that all or a portion of the steps in the various methods of the embodiments may be implemented by a program that instructs associated hardware, the program may be stored on a computer readable storage medium, the storage medium may include: read Only Memory (ROM), random access Memory (RAM, random Access Memory), magnetic or optical disk, and the like.
The foregoing description of the preferred embodiments of the application is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the application.
Claims (10)
1. A method for compensating for fast polarization rotation and inter-symbol crosstalk, comprising:
constructing an initial simplified Kalman filter; wherein the Kalman gain of the initial reduced Kalman filter
Iterative updating of covariance matrix P using reduced Kalman filter k And state vectorTo compensate for polarization impairments of the signal; in the first iteration updating process, an initial state vector and an initial covariance matrix are updated by using an initial simplified Kalman filter, and in the subsequent iteration updating process, the simplified Kalman filter for the next iteration updating is obtained according to the covariance matrix and the state vector obtained after the previous iteration updating so as to facilitate the next iteration updating;
the inter-symbol interference of the signal is compensated using an FIR filter.
2. The method for compensating for fast polarization rotation and inter-symbol interference according to claim 1, wherein said constructing an initial reduced kalman filter comprises:
kalman gain from a basic Kalman filterWill->The nonlinear operation in (a) is converted into the operation between diagonal elements in the matrix, and the obtained result is
Construction gain factor n= (c 1 x c4-c2 x c 3) -1 Obtaining the Kalman gain of the initial simplified Kalman filterThus obtaining an initial reduced kalman filter.
3. The method for compensating for fast polarization rotation and inter-symbol interference according to claim 1, wherein said iteratively updating covariance matrix P using a reduced kalman filter k And state vectorThe method specifically comprises the following steps:
let p=diag [ μa, μb, μc, μd]Obtaining a simplified Kalman filter; wherein the Kalman gain of the reduced Kalman filter
Wherein xa, xb, xc, xd, ya, yb, yc and yd represent the derivatives of the observation matrix, i.e. the error function, to the state vector in the unbiasing, respectively, expressed as:
updating covariance matrix P using reduced Kalman filter k And state vector
4. The method of claim 3, wherein the covariance matrix P is updated using a reduced kalman filter k And state vectorThe method specifically comprises the following steps:
using a first formulaUpdating the state vector to obtain an updated state vector
Updating diagonal elements of the covariance matrix by using a simplified Kalman filter to obtain an updated covariance matrix
Will beDiagonalization to obtain updated covariance matrix
5. The method for compensating for fast polarization rotation and inter-symbol interference according to claim 1, wherein said compensating for inter-symbol interference of signals using FIR filters comprises:
inputting the signal after polarization damage compensation into two first-order FIR filters, and calculating the error of an output signal;
and updating the tap coefficient of the FIR filter by using a gradient descent method according to the error magnitude of the output signal so as to use the updated tap coefficient to carry out the next inter-code crosstalk compensation.
6. The method of claim 1, wherein prior to iteratively updating the covariance matrix P and the state vectors using a reduced kalman filter, the method further comprises: determining an initial Kalman state vector, an initial covariance matrix P, a covariance matrix Q of state transition process noise and a covariance matrix R of matrix noise according to the polarization damage matrix, wherein the method specifically comprises the following steps:
according to polarization damage matrixConstructing an inverse matrix to obtain a polarization impairment matrix
Constructing and obtaining an initial state vector x according to the inverse matrix of the polarization damage matrix k ＝(a,b,c,d) T And construct and get the compensation signal
Constructing and selecting an error function asWherein R is 1, E xout (k)，E yout (k) Is the output of the Kalman filter;
based on Kalman observation matrixThe form of the jacobian matrix is derived as:
wherein xa, xb, xc and xd represent the derivatives of ex with respect to the state vector in the observation matrix, respectively, and ya, yb, yc and yd represent the derivatives of ey with respect to the state vector in the observation matrix, respectively;
let p=diag (2 e-5 ), q=diag (2 e-5 ), construct to get the initial covariance matrixQ is the covariance matrix of the observation process noise.
7. The method of compensating for fast polarization rotation and inter-symbol interference according to any of claims 1 to 6, wherein said signal is obtained by IQ orthogonalizing an input electrical signal, performing dispersion compensation and clock recovery.
8. The method of compensating for fast polarization rotation and inter-symbol interference according to any of claims 1 to 6, wherein the signal is one or more of a QPSK signal, a DPSK signal, and a BPSK signal.
9. The device for compensating the fast polarization rotation and the inter-code crosstalk is characterized by comprising a polarization damage compensation module and an inter-code crosstalk compensation module;
the polarization damage compensation module is used for constructing an initial simplified Kalman filter; wherein the Kalman gain of the initial reduced Kalman filterIteratively updating the covariance matrix P and the state vector using a reduced kalman filter to compensate for polarization impairments of the signal; wherein, in the first iteration updating, an initial state vector and an initial covariance matrix are updated by using an initial simplified Kalman filter, and in the subsequent iteration updating process, the covariance matrix P obtained after the last iteration updating is used k And state vector->Obtaining a simplified Kalman filter for next iteration update so as to facilitate the next iteration update;
the inter-code crosstalk compensation module is used for compensating inter-code crosstalk of signals by using an FIR filter.
10. A compensation device for fast polarization rotation and inter-symbol interference, the device comprising:
at least one processor; and a memory communicatively coupled 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 inter-symbol crosstalk compensation method of any of claims 1-8.
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| CN117614789B (en) * | 2024-01-18 | 2024-04-09 | 浙江赛思电子科技有限公司 | Carrier phase tracking method and device based on Kalman-like unbiased FIR filter |
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