CN117579174A

CN117579174A - Combined equalization method and device for PMD and RSOP damage

Info

Publication number: CN117579174A
Application number: CN202311558874.4A
Authority: CN
Inventors: 许恒迎; 孙祖楷; 王鸣娇; 姚东虎; 董婷婷; 乔京帅; 白成林; 杨立山; 罗青龙
Original assignee: Liaocheng University
Current assignee: Liaocheng University
Priority date: 2023-11-21
Filing date: 2023-11-21
Publication date: 2024-02-20

Abstract

The invention provides a combined equalization method and device for PMD and RSOP damage, wherein the method comprises the following steps: according to the characteristics of polarization damage in an optical fiber link in a thunderstorm scene, constructing a joint equalization model of the polarization damage, and initializing SCKF parameters; performing time update on the SCKF to predict damage values of the damage signals acquired by the current sliding window; performing measurement updating of the SCKF according to a measurement equation of the sliding window to obtain a measurement predicted value; performing ring judgment operation based on maximum posterior probability on the measurement predicted value by combining the radius distribution of the received symbols to obtain the optimized radius of the constellation ring to which the measurement predicted value belongs, calculating an innovation matrix, and fusing the predicted estimated value and the measurement estimated value to obtain the posterior estimated value; the sliding window moves forward to perform damage equalization on the signal of the next window. The invention has excellent performance in a low OSNR scene, and has the advantages of high tracking precision, high tolerance to initial errors and high convergence speed.

Description

Combined equalization method and device for PMD and RSOP damage

Technical Field

The invention belongs to the technical field of optical fiber communication, and particularly relates to a PMD and RSOP damage joint equalization method and device.

Background

First, when a thunderstorm occurs, lightning strikes instantaneously cause a sharp rise in polarization Rotation (RSOP), up to 5.1Mrad/s, for fiber optic composite overhead ground wire (OPGW) links used in large scale in power communication backbone networks. Second, due to the strong correlation between RSOP evolution and Polarization Mode Dispersion (PMD) impairments, the faster the RSOP is, the faster the time domain correlation between PMD at different times fades, making it difficult for classical polarization demultiplexing algorithms based on multiple-input multiple-output (MIMO) structures, such as constant mode/multimode algorithms (CMA/MMA), to equalize such joint polarization impairments. Again, as a breakthrough technique, probability Constellation Shaping (PCS) approaches the shannon limit of the achievable information rate of an optical communication system by changing the probability distribution of constellation points, and is currently being applied to long-range coherent optical communication systems in a large scale. However, since the PCS technique causes different amplitude constellation points not to follow an equal profile, many Digital Signal Processing (DSP) algorithms developed for standard Quadrature Amplitude Modulation (QAM) signals will suffer from serious degradation or even failure in the PCS system. Meanwhile, as the position of the polarization demultiplexing (PolDemux) algorithm is relatively forward in the DSP flow of the whole Probability Constellation Shaping (PCS) system, the algorithm performance directly influences the accuracy of the rear Frequency Offset Estimation (FOE) and the Carrier Phase Recovery (CPR), so that the joint equalization of the RSOP and the PMD damage of the Probability Constellation Shaping (PCS) system in a thunderstorm scene has important theoretical research and practical application values.

The existing polarization demultiplexing algorithm has a plurality of problems, is not suitable for a probability shaping system, cannot cope with balanced pressure in thunderstorm environment, or has weak adaptability to high-order modulation formats. For example, in the method for blind polarization demultiplexing in the probability shaping constellation modulation coherent optical communication system proposed in the prior art, circular radius symbols occupying a larger proportion in the PCS signal are selected, and least square plane fitting is performed on the symbols in a Stoke space to realize polarization demultiplexing, but the method has poor dynamic RSOP equalization capability and can only be suitable for a short-range transmission system. A polarization demultiplexing algorithm based on maximum likelihood independent component analysis (ML-ICA) is proposed in the prior art, which uses ML-ICA to estimate an inverse Jones matrix W, so that mutual information between input and output of X polarization and Y polarization is maximized, thereby realizing polarization demultiplexing. However, the method has low performance upper limit, and can not solve the problem of polarization equalization of the probability shaping system in the thunderstorm environment.

Disclosure of Invention

Aiming at the defects in the prior art, the method and the device for jointly balancing the PMD and the RSOP damage solve the problem of jointly balancing the PMD and the RSOP damage of a PCS-64QAM system in a thunderstorm scene.

In order to achieve the above purpose, the invention adopts the following technical scheme: a joint equalization method of PMD and RSOP impairments, comprising the steps of:

s1, constructing a joint equalization model of polarization damage according to the characteristics of the polarization damage in an optical fiber link in a thunderstorm scene, and initializing parameters of an SCKF (square root volume Kalman filter);

s2, according to a prediction equation, taking a posterior estimation value of a state parameter at the previous moment as an priori estimation value of a state parameter at the next moment, and carrying out time update on a square root volume Kalman filter SCKF so as to predict a damage value of a damage signal acquired by a current sliding window;

s3, according to a measurement equation of the sliding window, performing measurement updating on the square root volume Kalman filter SCKF to obtain a measurement predicted value;

s4, carrying out ring judgment operation based on the maximum posterior probability on the measurement predicted value by combining the radius distribution of the received symbols to obtain the optimized radius of the constellation ring to which the measurement predicted value belongs, calculating an innovation matrix, and calculating a posterior estimated value of the state parameter by combining the damage predicted value and the measurement predicted value;

s5, judging whether iteration is completed, if yes, ending the flow, and completing joint equalization of PMD and RSOP damage, otherwise, sending a posterior estimation value of a state parameter and an error covariance matrix square root coefficient to a step S2, updating iteration times k, and carrying out the next iteration.

The beneficial effects of the invention are as follows: based on a combined damage equalization model of RSOP and PMD and a square root volume Kalman filter, the invention combines a rice distribution model, carries out ring judgment by a maximum posterior probability method, and calculates an optimization radius. Compared with the traditional EKF scheme, the SCKF effectively reduces linearization errors, and in addition, the invention can avoid ring decision errors caused by uneven distribution of constellation points and ASE noise, and especially can solve the problem of polarization damage combined equalization in a thunderstorm scene. The probability perception information is introduced in the invention, so that the problem of noise amplification caused by continuous multiplication information is effectively solved, and the calculation accuracy of the PDM PCS-64QAM system in a low optical signal to noise ratio (OSNR) scene is greatly improved. The invention has excellent performance in a low OSNR scene, and has the advantages of high tracking precision, high tolerance to initial errors and high convergence speed.

Further, the step S1 includes the steps of:

s101, constructing a joint equalization model of polarization damage according to the characteristics of the polarization damage in an optical fiber link in a thunderstorm scene, and selecting and normalizing state parameters of an SCKF (square root volume Kalman filter) according to the joint equalization model;

S102, initializing the square root volume Kalman filter according to the setting of the square root volume Kalman filter, wherein the square root volume Kalman filter has the following expression of the measurement noise covariance R:

R＝diag([1；1])

wherein diag (·) represents a diagonal matrix operation;

the expression of the predicted noise covariance Q of the square root volume kalman filter SCKF is as follows:

Q＝diag([1E-4；1E-4；1E-4；1E-6；1E-6；1E-6])

wherein E is represented by scientific counting method, 1E-4 is 0.0001,1E-6 and 0.000001;

error covariance matrix S of square root volume Kalman filter SCKF _0|0 The expression of (2) is as follows:

S _0|0 ＝diag[(1E-2；1E-2；1E-2；1E-2；1E-2；1E-2)]。

the beneficial effects of the above-mentioned further scheme are: the invention is based on the correct establishment of the joint equalization model of polarization damage, can exert the performance of the SCKF to the greatest extent, and the normalized operation can ensure that the state parameters are in the same order of magnitude, thereby reducing the error. Meanwhile, the parameters of the filter are initialized, so that the equalization accuracy and the upper limit of the equalization performance of the scheme can be improved to the greatest extent.

Still further, the step S101 includes the steps of:

s1011, tracking RSOP in a time domain and compensating PMD in a frequency domain according to the characteristics of polarization damage in an optical fiber link in a thunderstorm scene to construct a joint equalization model of the polarization damage, wherein the RSOP tracking matrix is R _eq The PMD compensation matrix is U _comp ；

The expression for tracking the RSOP in the time domain is as follows:

wherein R is _eq Equalizing operator, e, representing a three-parameter RSOP ^(·) The method comprises the steps of representing exponential operation, j representing imaginary units, ζ and η representing phase rotation angles of RSOP damage to be tracked, and κ representing azimuth rotation angles of RSOP damage to be tracked;

the expression for compensating PMD in the frequency domain is as follows:

wherein U is _comp (ω) represents a compensation matrix for first-order PMD, ω represents the optical angular frequency, Δτ represents the value of the differential group delay DGD, I represents the identity matrix,vectors representing PMD>Representing the Brix matrix, τ ₁ ,τ ₂ ,τ ₃ Representing three components of the PMD vector in stokes space, (·) ^T Representing a transpose operation;

s1012, selecting state parameters of a square root volume Kalman filter SCKF according to a joint equalization model, and normalizing:

wherein X is _norm State parameter, T, representing square root volume Kalman filter SCKF _s Representing the symbol period of the current PCS-64QAM system.

The beneficial effects of the above-mentioned further scheme are: according to the invention, by carrying out equalization processing on the RSOP in the time domain and compensating the PMD in the frequency domain, six parameters tracked by the square root volume Kalman filter for realizing polarization equalization can be obtained, and meanwhile, the state parameters are normalized, so that errors can be effectively reduced.

Still further, the step S2 includes the steps of:

s201, calculating 2n columns of volume points X of a square root volume Kalman filter SCKF time update state _i,k-1|k-1 ；

S202, updating the 2n column capacity of the state with timeIntegration point X _i,k-1|k-1 Propagating through a predictive equation;

s203, predicting the volume point after propagation by using the prediction equationPerforming averaging operation to obtain damage prediction value +.>

S204, according to the damage predicted value of the damage signal acquired by the current sliding windowSquare root factor S for prediction error covariance matrix _k|k-1 To predict the impairment value of the impairment signal acquired by the current kth sliding window.

Still further, the square root factor S _k|k-1 The expression of (2) is as follows:

wherein Tria (·) represents an orthogonal triangular QR decomposition operation,represents a center weighting matrix, S _Q,k-1 Representing a prediction noise covariance matrix Q _k-1 Square root factor of>And->All represent the predicted value of the volume point propagated through the prediction equation, n represents the number of state parameters, i represents the sequence number of the volume point, i=1, 2,..2 n, s _k-1|k-1 A posterior estimate, ζ, representing the square root factor of the error covariance matrix at the previous time _i The point of the volume is indicated,a posterior estimate representing the last moment in time of the tracked state parameter, [1 ]] _i The ith column of point set 1 is shown.

The beneficial effects of the above-mentioned further scheme are: at the time of transmission, the polarization damage in the system is random, but the auto-correlation function characteristic shows that the polarization damage has higher correlation in a short time. Therefore, the establishment of the process equation can be better adapted to the continuously changing channel environment.

Still further, the step S3 includes the steps of:

s301, according to square root factor S _k|k-1 Volume point xi _i And predicted valueThe volume point of the measurement update state of the square root volume kalman filter SCKF is obtained by the following calculation:

s302, according to the volume point X after updating the state _i,k|k-1 Calculating to obtain the offsetOutputting a sliding window signal sequence by the kth after vibration damage combined equalization;

s303, calculating to obtain a measurement predicted value of the square root volume Kalman filter SCKF according to the equalized kth output sliding window signal sequence and a measurement equation integrating the sliding window

Wherein n represents the number of state variables, i represents the sequence number of volume points, i=1, 2,..2 n, z _i,k|k-1 Representing the measured and predicted volume point values, abs (·) representing a complex modulo operation, And->Intermediate elements of the series of X and Y polarized volume points of the ith group in the kth sliding window, respectively,/->Representing a rounding up operation.

The beneficial effect of above-mentioned scheme is: the noise value can be truly reflected to the greatest extent by carrying out modular value operation on the symbols of the sliding window intermediate sequence.

Still further, the step S302 includes the steps of:

s3021, intercepting a signal by a sliding windowWherein S is _x,k And S is equal to _y,k Respectively representing damaged X and Y polarization signal sequences intercepted in a kth sliding window;

s3022, performing Fourier transform on the intercepted signal, and converting the signal into a frequency domain;

s3023, according to the signals converted into the frequency domain, using the PMD compensation matrix to propagate the volume points after the updating state, and obtaining measurement prediction volume points after the PMD compensation;

the expression of the PMD compensation matrix is as follows:

wherein U is _comp,i (ω) represents the PMD compensation matrix, Δτ _i PMD compensation matrix U representing volume points using the i-th set of state updates as parameters _comp,i (ω) the calculated DGD,vector τ representing PMD obtained from the i-th group of volume points as parameters _i,1,k|k-1 Representing Stokes component τ ₁ Corresponding value τ in the ith row of volume points of the measured update state _i,2,k|k-1 Representing Stokes component τ ₂ Corresponding value τ in the ith row of volume points of the measured update state _i,3,k|k-1 Stokes component τ ₃ Corresponding values in the ith row of volume points of the measurement update state;

s3024, converting the PMD compensated measurement prediction volume point to a time domain through inverse fast Fourier transform;

s3025, propagating the PMD compensated measurement prediction volume point converted to the time domain by using an RSOP tracking matrix to obtain a PSOP tracked measurement prediction volume point;

the expression of the RSOP tracking matrix is as follows:

wherein R is _eq,i Represents zeta as a tracking matrix of RSOP a state parameter corresponding to the ith column of volume points _i,k|k-1 Representing the value of the phase rotation angle ζ corresponding to the i-th row volume point in the measurement update state, η _i,k|k-1 Representing the value corresponding to the phase rotation angle eta in the ith row volume point of the measurement update state, kappa _i,k|k-1 Representing a value of the azimuth rotation angle kappa corresponding to an ith row volume point in a measurement update state;

s3026, carrying out average value calculation on the measured and predicted volume points tracked by the PSOP to obtain a kth output sliding window signal sequence after polarization damage joint equalization;

the expression of the averaging operation is as follows:

wherein, And->Respectively representing output sequences of X and Y polarization sliding windows after final joint equalization, n represents the number of state parameters, i represents the serial numbers of volume points, i=1, 2,..2, 2n, and #>And->Respectively indicate passing U _comp,i And RSOP tracking matrix R _eq,i Combining the balanced X-polarization and Y-polarization volume point sequences, U _comp,i Volume point X representing updated state using column i measurement _i,k|k-1 The first three parameters act as matrices for PMD compensation matrix parameters.

The beneficial effect of above-mentioned scheme is: the measurement equation is propagated through the volume points, the state mean value and covariance of the nonlinear system with the additive Gaussian white noise are approximated through a group of volume points, and the method is an approximation algorithm closest to Bayesian filtering in theory, and even in a high-dimensional state space, the filtering weight is always positive, so that the method has higher robustness and filtering precision than Unscented Kalman (UKF); RSOP occurs in the time domain, PMD occurs in the frequency domain, RSOP is tracked in the time domain by means of time-frequency conversion, PMD is compensated in the frequency domain, physical model constraint is met, and the performance upper limit of polarization damage combined equalization can be improved to the greatest extent.

Still further, the step S4 includes the steps of:

s401, estimating square root coefficient S of innovation covariance matrix _zz,k|k-1 ：

Wherein Tria (·) represents an orthogonal triangular QR decomposition operation,represents a weighted center matrix, S _R,k-1 Representing a noise covariance matrix R _k-1 N represents the number of state variables, i represents the number of volume points, i=1, 2,..2 n,/-2>Indicating the measurement predicted value, Z _2n,k|k-1 Representing measured and predicted volume point values S _R,k-1 Representing a noise covariance matrix R _k-1 Square root factor of>

S402, estimating a cross covariance matrix P _xz,k|k-1 ：

Wherein χ is _k|k-1 Andall represent a central weighting matrix, X _2n,k|k-1 Volume point representing update status +.>A damage prediction value representing a state parameter;

s403, according to square root coefficient S _zz,k|k-1 And a cross covariance matrix P _xz,k|k-1 Calculating to obtain Kalman gain W _k ：

S404, combining the radius distribution of the received symbols, namely, the Lees distribution model, to measure the predicted valuePerforming a ring judgment operation based on the maximum posterior probability to obtain an optimized radius of a constellation ring to which the ring belongs, and calculating an innovation matrix;

s405, combining the damage predicted value based on the innovation matrixMeasurement of the predicted value->Kalman gain W _k Calculating to obtain posterior estimation value of state parameter +.>

Wherein Z is _k Representing the target observations of the kth sliding window,representing an innovation matrix calculation process;

s406, updating the average root coefficient S of the error covariance matrix according to the following method _k|k ：

Wherein χ is _k|k-1 Representing the central weighting matrix of the system,represents a center weighting matrix, S _R,k-1 Representing a noise covariance matrix R _k-1 Square root factor of>

The beneficial effect of above-mentioned scheme is: estimating cross covariance matrix P by calculation _xz,k|k-1 And the square root coefficient S of the innovation covariance matrix _zz,k|k-1 The Kalman gain can be calculated, and the Kalman gain is an important parameter for measuring the trust degree of the observed value and directly influences the state parameter posterior estimation value. Error covariance matrix average root coefficient S _k|k Is prepared for the next kalman filter iteration.

Still further, the innovation matrix calculating process in step S404 includes the following steps:

s4041, combining with the rice distribution model, calculating based on the maximum posterior probability to obtain a measurement predicted valueStar with highest probabilityOptimal radius of seat ring +.>Wherein, for the measurement prediction value->The judgment process of the ring is as follows:

wherein,represents the value of m when the search function takes the maximum value, m represents each of 9 rings in the ideal PCS-64QAM constellation diagram, +.>Representing the amplitude of the received signal as +.>Under the condition that the amplitude of the transmitting signal is +.>P (·) represents the probability calculation,/-)>Constellation circle radius representing PCS-64QAM signal at transmitting end +. >Measurement prediction value, sigma, representing X or Y polarization in kth sliding window of square root volume Kalman filter SCKF ² Representing the variance of noise, I ₀ (. Cndot.) represents the modified Bessel function of order 0,>representing transmission via probability shaping codingDifferent radii->Probability of occurrence;

s4042, calculating to obtain an optimized radius by using the average value of the rice distributionWherein the radius is optimized->The expression of (2) is as follows:

wherein I is ₁ (x) Representing a first order modified Bessel function, exp (·) representing an e-exponent operation, ln (·) representing a log operation;

s4043 optimizing the radius Z of the circular ring with the maximum posterior probability _k And measuring the predicted valuePerforming difference to obtain an innovation matrix e:

wherein,represents the optimal radius of the ring to which the measurement predicted value of the X polarization of the PCS-64QAM system belongs, < >>Represents the optimal radius of the ring to which the measured predicted value of the Y polarization of the PCS-64QAM system belongs, < >>Representing X polarizationThe measurement prediction value of (2) is +.> The measurement prediction value of Y polarization is +.>L represents the length of the sliding window, S _x,k And S is equal to _y,k Representing the sequence of the corrupted X-or Y-polarized signal intercepted by the kth sliding window, respectively.

The beneficial effect of above-mentioned scheme is: in PCS systems, the traditional approach based on euclidean distance decisions is suboptimal, subject to uneven distribution of constellation points and amplifier spontaneous emission noise (ASE). By introducing the maximum posterior probability estimation, the decision error caused by the traditional Euclidean distance decision threshold can be effectively solved, the probability of the occurrence of the ring decision error in the low OSNR scene is effectively reduced, and the filtering precision in the low OSNR scene is improved.

The invention provides a joint equalization device of a joint equalization method of PMD and RSOP damage, which comprises the following components:

the first processing module is used for constructing a joint equalization model of polarization damage according to the characteristics of the polarization damage in the optical fiber link in a thunderstorm scene and initializing the SCKF parameters of the square root volume Kalman filter; the second processing module is used for carrying out time update on the square root volume Kalman filter SCKF according to a prediction equation by taking the posterior estimation value of the state parameter at the previous moment as the prior estimation value of the state parameter at the next moment so as to predict the damage value of the damage signal acquired by the current sliding window; the third processing module is used for carrying out measurement updating on the square root volume Kalman filter SCKF according to a measurement equation fused with the sliding window to obtain a measurement predicted value; the fourth processing module is used for carrying out ring judgment operation based on the maximum posterior probability on the measurement predicted value by combining the radius distribution of the received symbols to obtain the optimized radius of the constellation ring to which the measurement predicted value belongs, calculating an innovation matrix, and combining the damage predicted value and the measurement predicted value to obtain the posterior estimated value of the state parameter; and the fifth processing module is used for judging whether iteration is finished, if yes, ending the flow, finishing the joint equalization of PMD and RSOP damage, otherwise, sending the posterior estimation value of the state parameter and the square root coefficient of the error covariance matrix to the second processing module, updating the iteration number k, and carrying out the next iteration.

The invention has the beneficial effects that: the invention is based on the joint damage equalization model of RSOP and PMD and SCKF, and integrates the probability perception model of maximum posterior probability, thereby effectively reducing linearization error compared with the traditional EKF scheme. In addition, the invention can avoid the error of ring judgment caused by uneven distribution of constellation points and ASE noise, and especially can solve the problem of polarization damage joint equalization in thunderstorm scenes. The probability perception innovation is introduced, so that the problem of noise amplification caused by continuous multiplication innovation is effectively solved, and the calculation accuracy of the PDM PCS-64QAM system in a low OSNR scene is greatly improved. The invention has excellent performance in a low OSNR scene, and has the advantages of high tracking precision, high tolerance to initial errors and high convergence speed.

Drawings

FIG. 1 is a flow chart of the method of the present invention.

FIG. 2 is a schematic diagram of a simulation system of the present invention.

Fig. 3 is a schematic diagram showing the upper limit of RSOP performance at different DGD schemes with osnr=25db in this embodiment.

FIG. 4 is a graph showing the relationship between OSNR and NGMI under different polarization impairments in this example.

Fig. 5 is a schematic diagram of a relationship between the source entropy H and normalized generalized mutual information NGMI under different polarization impairments in this embodiment.

Fig. 6 is a schematic view of the structure of the device of the present invention.

Detailed Description

The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.

Example 1

The parameters k and i are described before the description of the invention:

the kth iteration is the kth sliding window;

and taking the ith row of state parameter volume points as RSOP and PMD compensation matrix parameters, wherein the compensated sequence is the ith group of signal sequence volume points.

Aiming at the defects in the prior art, the combined equalization method for RSOP and PMD damage in a PDM-PCS-64QAM system in a thunderstorm scene, provided by the invention, can jointly equalize RSOP of a plurality of Mrad/s and PMD of a plurality of symbol periods in the thunderstorm environment, and is shown in figure 1, and the implementation method is as follows:

s1, constructing a joint equalization model of polarization damage according to the characteristics of the polarization damage in an optical fiber link in a thunderstorm scene, and initializing parameters of a square root volume Kalman filter (SCKF), wherein the implementation method is as follows:

S101, constructing a joint equalization model of polarization damage according to the characteristics of the polarization damage in an optical fiber link in a thunderstorm scene, selecting state parameters of a square root volume Kalman filter (SCKF) according to the joint equalization model, and normalizing, wherein the implementation method is as follows:

s1011, tracking RSOP in a time domain and compensating PMD in a frequency domain according to the characteristics of polarization damage in an optical fiber link in a thunderstorm scene so as to construct a joint equalization model of the polarization damage; s1012, selecting and normalizing state parameters of a square root volume Kalman filter SCKF according to a joint equalization model;

s102, initializing the square root volume Kalman filter according to the SCKF setting;

s2, according to a prediction equation, taking a posterior estimation value of a state parameter at the previous moment as an priori estimation value of a state parameter at the next moment, and carrying out time update on a square root volume Kalman filter SCKF so as to predict a damage value of a damage signal acquired by a current sliding window, wherein the implementation method is as follows:

s201, calculating 2n columns of volume points X of a square root volume Kalman filter SCKF time update state _i,k-1|k-1 The method comprises the steps of carrying out a first treatment on the surface of the S202, time update state 2n rows of volume points X _i,k-1|k-1 Propagating through a predictive equation; s203, predicting the volume point after propagation by using the prediction equationPerforming averaging operation to obtain damage prediction value +.>S204, according to a damage prediction value of the damage signal acquired by the current sliding window +.>Square root factor S for prediction error covariance matrix _k|k-1 To predict the damage value of the damage signal collected by the current kth sliding window;

s3, according to a measurement equation fused with a sliding window, performing measurement updating on the square root volume Kalman filter SCKF to obtain a measurement predicted value, wherein the implementation method is as follows:

s302, according to the volume point X after updating the state _i,k|k-1 The k output sliding window signal sequence after polarization damage combined equalization is obtained through calculation, and the implementation method is as follows:

s3021, intercepting a signal by a sliding windowWherein S is _x,k And S is equal to _y,k Respectively representing the damaged X or Y polarized signal sequence intercepted by the kth sliding window; s3022, performing Fourier transform on the intercepted signal, and converting the signal into a frequency domain; s3023, according to the signals converted into the frequency domain, using the PMD compensation matrix to propagate the volume points after the updating state, and obtaining measurement prediction volume points after the PMD compensation; s3024, converting the PMD compensated measurement prediction volume point to a time domain through inverse fast Fourier transform; s3025, propagating the PMD compensated measurement prediction volume point converted to the time domain by using an RSOP tracking matrix to obtain a PSOP tracked measurement prediction volume point; s3026, carrying out average value calculation on the measured and predicted volume points tracked by the PSOP to obtain a kth output sliding window signal sequence after polarization damage joint equalization;

S4, carrying out ring judgment operation based on the maximum posterior probability on the measurement predicted value by combining the radius distribution of the received symbol to obtain the optimized radius of the constellation ring to which the measurement predicted value belongs, calculating an innovation matrix, and calculating the posterior estimated value of the state parameter by combining the damage predicted value and the measurement predicted value, wherein the implementation method is as follows:

s401, estimating square root coefficient S of innovation covariance matrix _zz,k|k-1 ；

S402, estimating a cross covariance matrix P _xz,k|k-1 ；

S403, according to square root coefficient S _zz,k|k-1 And a cross covariance matrix P _xz,k|k-1 Calculating to obtain Kalman gain W _k ；

S404, for the measurement predicted valueThe ring judgment operation of fusing the maximum posterior probability is carried out, the standard radius of the ring is obtained, and the innovation matrix is calculated, and the implementation method is as follows:

s4041, combining with the rice distribution model, calculating based on the maximum posterior probability to obtain a measurement predicted valueOptimal radius of constellation circle with maximum probability +.>S4042 calculating an optimized radius +.>S4043 optimizing the radius Z of the circular ring with the maximum posterior probability _k And measure the predicted value->Performing difference to obtain an innovation matrix e;

s405, combining the damage predicted value based on the innovation matrixMeasurement of the predicted value->Kalman gain W _k Calculating to obtain a state parameter posterior estimation value +.>

S406, updating the average root coefficient S of the error covariance matrix _k|k ；

S5, judging whether iteration is completed, if yes, ending the flow, and completing joint equalization of PMD and RSOP damage, otherwise, sending a state parameter posterior estimation value and an error covariance matrix square root coefficient to a step S2, updating k, and carrying out the next iteration, wherein k represents the kth iteration;

in this embodiment, a joint equalization model is constructed, and state parameters are selected: according to the damage characteristics, using the formula (1) to balance the RSOP in the time domain, and using the formula (2) to carry out PMD compensation in the frequency domain:

wherein R is _eq Equalizing quanta representing three-parameter PSOP, e representing an exponential operation, j representing an imaginary number, ζ and η each representing a phase rotation angle, κ representing an azimuth rotation angle, U _comp (ω) represents the compensation matrix for first-order PMD, ω represents the optical angular frequency, and the PMD vector is described asThe upper corner mark T indicates the transpose operation, τ ₁ ,τ ₂ ,τ ₃ Representing three components in Stokes space, DGD value +.>I represents an identity matrix, ">Representing the brix matrix.

Thus τ ₁ ,τ ₂ ,τ ₃ Kappa, eta, zeta become six parameters tracked by the square root volume Kalman filter to achieve polarization equalization. In order to reduce errors and normalize the state parameters, the state parameters of the SCKF are finally expressed as:

In the embodiment, the joint equalization model of polarization damage is correctly established, so that the performance of the SCKF can be exerted to the greatest extent, the normalization operation can ensure that state parameters are in the same order of magnitude, and errors are reduced.

In this embodiment, the square root volume kalman filter is initialized according to the square root volume kalman filter setting.

Measuring a noise covariance R:

R＝diag([1；1])；

wherein diag (·) represents the diagonal matrix operation.

Prediction noise covariance Q:

Q＝diag([1E-4；1E-4；1E-4；1E-6；1E-6；1E-6])；

error covariance matrix S _0|0 ：

S _0|0 ＝diag[(1E-2；1E-2；1E-2；1E-2；1E-2；1E-2)]。

In this embodiment, the parameters of the filter are initialized, so that the equalization accuracy and the upper limit of the equalization performance of the scheme can be improved to the greatest extent.

In the present embodiment, 2n columns of volume points X of the time update state are calculated according to the formula (4) _i,k-1|k-1 。

Wherein,[1] _i the ith column (i=1, 2,3, …, n) representing the point set 1, n being the number of state parameters, and the index k representing the index number of the iteration number of the filter, i.e. the number of sliding windows, S _k-1|k-1 A.A. estimate of the square root factor representing the covariance matrix of the error at the previous moment,/and a.c. estimate of the square root factor representing the covariance matrix of the error at the previous moment>It should be noted that the number of columns of volume points is 2n, which is determined according to the third order spherical radial volume rule, representing the posterior estimate of the last moment in the tracked state parameter.

In this embodiment, 2n columns of volume points of the time update state are propagated through the prediction equation. For the construction process of the prediction equation in the invention, because of the high randomness of the polarization damage, accurate prediction cannot be performed on the damage, so that the predicted value of the current kth iteration is assumed to be the posterior estimated value of the kth-1 iteration, and the propagation process of the instant update state volume point is calculated according to the following formula:

wherein,representing the predicted value of the volume point, X, after propagation through the prediction equation _k-1|k-1 The posterior estimation value of the state parameter at the last moment is represented, n is the number of the state parameters, and i is the serial number of the volume point.

In this embodiment, the predicted value of the state parameter is calculatedVolume point prediction value propagated through prediction equation +. >Averaging to obtain predictive value +.>The calculation formula is as follows:

in this embodiment, the square root factor S of the prediction error covariance matrix is estimated according to the following formula _k|k-1 ：

Wherein, tria (& gt)) Representing an orthogonal triangular QR decomposition operation,represents a center weighting matrix, S _Q,k-1 Representing a prediction noise covariance matrix Q _k-1 Square root factor of>T represents a transpose operation, ">And->All represent the predicted value of the volume point propagated through the prediction equation, n represents the number of state parameters, i represents the sequence number of the volume point, i=1, 2,..2 n, s _k-1|k-1 A posterior estimate, ζ, representing the square root factor of the error covariance matrix at the previous time _i Representing the volume point +.>A posterior estimate representing the last moment in time of the tracked state parameter, [1 ]] _i The ith column of point set 1 is shown.

In this embodiment, during transmission, the polarization impairments in the system are random, but the auto-correlation function characteristics indicate that the polarization impairments have a higher correlation in a short time, so that the establishment of the process equation can better adapt to the continuously changing channel environment.

In the present embodiment, the square root factor S obtained in step S2 is used _k|k-1 Volume point xi _i And predicted valueThe volume point (i=1, 2, …,2 n) of the measurement update state is calculated according to the following formula:

In this embodiment, the signal sequence after polarization impairment joint equalization is calculated according to the measurement equation:

intercept a signal through a sliding window:

wherein S is _x,k And S is equal to _y,k The damaged X and Y polarized signal sequences intercepted by the kth sliding window are respectively represented, the intercepted signals are subjected to Fourier transformation, and the signals are converted into frequency domains to obtain:

wherein FFT {.cndot. } represents the fast fourier transform.

The signal formula (10) converted into the frequency domain is subjected to volume point propagation by using a PMD compensation matrix formula (11):

wherein U is _comp,i (ω) represents the PMD compensation matrix, Δτ _i PMD compensation matrix U representing volume points using the i-th set of state updates as parameters _comp,i (ω) the calculated DGD,vector τ representing PMD obtained from the i-th group of volume points as parameters _i,1,k|k-1 Representing Stokes component τ ₁ Corresponding value τ in the volume point of the i-th row measurement update state _i,2,k|k-1 Representing Stokes component τ ₂ Corresponding value τ in the volume point of the i-th row measurement update state _i,3,k|k-1 Stokes component τ ₃ Measuring a corresponding value in the volume point of the updated state in the ith row;

it should be noted that the propagation of the volume point in actual operation requires attention to the state parameter position, which in equation (3) has been specified to be tracked i=1, i.e. column 1, of the state update, the corresponding state parameter order isWherein τ _1,1,k|k-1 Representing Stokes component τ ₁ Corresponding value in column 1 measurement update state volume point, τ _2,1,k|k-1 Representing Stokes component τ ₂ The corresponding values in the volume points of the updated state are measured in column 1, and so on. Therefore U _comp,i Is to measure the volume point X of the updated state by using the ith row _i,k|k-1 The first three parameters are used as the matrix of PMD compensation matrix parameters, namely:

since there are 12 groups of volume points, 12 PMD compensation matrices U can be obtained _comp,i After compensating the damaged signals, obtaining 12 groups of measurement prediction volume points after PMD compensation:

then, the measured predicted volume points after the 12 sets of PMD compensation are converted to the time domain by inverse fast fourier transform IFFT:

the measured and predicted volume point (i.e., equation (13)) after PMD compensation converted to the time domain is propagated according to the RSOP tracking matrix (14):

wherein R is _eq,i Representing the corresponding state in the ith row of volume pointsParametric as a tracking matrix for RSOP, ζ _i,kk-1 Representing the value, η, of the phase rotation angle ζ corresponding to the volume point in the i-th row measurement update state _i,kk-1 Representing the value corresponding to the phase rotation angle eta at the volume point of the ith row measurement update state, kappa _i,k|k-1 Representing a value of the azimuth rotation angle kappa corresponding to a volume point in an ith row measurement update state;

the parameters of the RSOP tracking matrix are determined according to the volume points in the measurement update state, and since the volume points have 12 groups, there are 12 RSOP tracking matrices R _eq,i And (3) respectively carrying out RSOP tracking on the 12 groups of PMD compensated time domain measurement predicted volume points obtained by the formula (13) to obtain 12 groups of RSOP tracked measurement predicted volume points:

for convenience of description, the sequence after joint equalization of formula (15) is written as And->Respectively indicate passing U _comp,i And R is _eq,i The sequence of X-polarized and Y-polarized volume points after equalization is combined.

A sequence of volume points according to equation (15)There are 12 groups, and in order to obtain the final symbol sequence after polarization impairment joint equalization, the volume point sequence needs to be averaged according to the following formula:

wherein,and->Respectively representing output sequences of X and Y polarization sliding windows after final joint equalization, n represents the number of state parameters, i represents the serial number of the volume point, i=1, 2, & gt, 2n, & gt>And->Respectively indicate passing U _comp,i And RSOP tracking matrix R _eq,i Combining the balanced X-polarization and Y-polarization volume point sequences, U _comp,i Volume point X representing updated state using column i measurement _i,k|k-1 The first three parameters act as matrices for PMD compensation matrix parameters.

Finally, according to the measurement equation, calculating to obtain a measurement predicted value

In this embodiment, the volume point sequence is obtained according to equation (15)There are 12 groups, and the measured and predicted volume point value Z is calculated according to the formula (17) _i,k|k-1 And taking the middle element of each group of volume point sequences to perform modular value operation. Since the sequence length may be odd or even, we have performed a rounding up operation on it in order to prevent a decimal situation.

12 sets of measured and predicted volume point values Z obtained according to formula (17) _i,k|k-1 Calculating the average value to obtain the measurement predicted value

Wherein Z is _i,k|k-1 Representing the measured and predicted volume point values, abs (·) representing a complex modulo operation,andintermediate elements of the series of X and Y polarized volume points of the ith group in the kth sliding window, respectively,/->Representing a rounding up operation.

In this embodiment, the innovation covariance matrix square root coefficient S _zz,k|k-1 Calculation is performed according to formula (19):

Performing a cross covariance matrix P according to equation (20) _xz,k|k-1 Is estimated by (a):

wherein,χ _k|k-1 and->All represent a central weighting matrix, X _2n,k|k-1 Volume point representing update status +.>The damage prediction value of the state parameter is represented, and the upper corner mark T represents the transposition operation.

Calculating Kalman gain W _k . The calculation of the Kalman gain depends on the cross covariance matrix P _xz,k|k-1 And the innovation covariance matrix square root coefficient S _zz,k|k-1 The calculation formula is shown as formula (21):

calculating posterior estimateThe process is to fuse the predicted result and the measured result to obtain a more accurate state parameter posterior estimated value, and the calculation formula is as follows:

wherein Z is _k Representing the target observations of the kth sliding window,i.e. the innovation calculation process, is an important component of the SCKF design, which can measure the reliability of the measurement results.

In this embodiment, the innovation calculation method integrating maximum posterior probability perception is as follows: in the invention, because the measurement predicted value is influenced by probability constellation shaping and amplifier spontaneous emission noise ASE noise, the traditional Euclidean distance judgment scheme is suboptimal for a probability constellation shaping system, and in order to adapt to a PDM PCS-64QAM system, the invention provides a judgment scheme based on maximum posterior probability perception, and a more accurate target observed value Z can be obtained _k To assist in the calculation of the innovation. Because the system has frequency offset phase noise, the constellation point of the PDM PCS-64QAM system after polarization equalization presents a plurality of circular rings, the invention firstly combines the radius distribution of the received symbols, namely the Lais distribution model, and measures the predicted valuePerforming a circular ring judgment operation based on the maximum posterior probability, and then optimizing the radius Z with the maximum probability _k And measure the predicted value->And (5) making a difference, and calculating the innovation e.

In this embodiment, the specific decision process for the constellation ring to which the measurement prediction value belongs can be expressed as:

wherein,represents the value of m when the search function takes the maximum value, m represents each of 9 rings in the ideal PCS-64QAM constellation diagram, +.>Representing the amplitude of the received signal as +.>Under the condition that the amplitude of the transmitting signal is +.>P (·) represents the probability calculation,/-)>Constellation circle radius representing PCS-64QAM signal at transmitting end +.>Measurement prediction value, sigma, representing X or Y polarization in kth sliding window of square root volume Kalman filter SCKF ² Representing the variance of noise, I ₀ (. Cndot.) is a modified Bessel function of order 0,>is encoded by probability shaping and transmitting end with different radiuses>Probability of occurrence;

optimizing radiusIs obtained from the mean value of the rice distribution. Adopts optimized radius- >As target observation Z in SCKF _k To calculate more accurate innovation. Optimized radius->The calculation formula of (2) is as follows:

wherein I is ₁ (x) Representing a first order modified Bessel function, exp (·) represents an e-exponent operation, ln(. Cndot.) represents a logarithmic operation

At this time, the obtained innovation matrix e can be written as:

wherein,represents the optimal radius of the ring to which the measurement predicted value of the X polarization of the PCS-64QAM system belongs, < >>Represents the optimal radius of the ring to which the measured predicted value of the Y polarization of the PCS-64QAM system belongs, < >>The measurement prediction value of X polarization is +.> The measurement prediction value of Y polarization is +.>L represents the length of the sliding window, S _x,k And S is equal to _y,k Representing the sequence of the corrupted X-or Y-polarized signal intercepted by the kth sliding window, respectively. In this embodiment, the error covariance matrix square root coefficient S is updated according to equation (27) _k|k 。

S _k|k ＝Tria([χ _k|k-1 -W _k z _k|k-1 W _k S _R,k ]) (27)

In this embodiment, the sliding window slides forward with a step Δl=1 symbol, and the signal of the next window is subjected to impairment equalization, and steps S2, S3, and S4 are repeated repeatedly until the polarization impairment joint equalization of all the signals is completed.

In this embodiment, the sliding window is continuously moved in a recursive iteration manner, so that the time delay of the filter can be effectively reduced, and the iterative operation is repeated until the polarization damage equalization of all signals is completed.

In this embodiment, in order to verify the effectiveness of the present invention, the feasibility of the proposed solution is verified by using the optical communication simulation software VPI transmission Makers 11.2.2 and MATLAB in this embodiment. A schematic diagram of the simulation system is shown in fig. 2. To obtain a PCS-64QAM signal, the transmitter first generates the required bit sequence to be transmitted, then generates the required probability distribution through CCDM, and then generates the 28Gbaud PDM-PCS-64QAM constellation symbols using a symbol mapping step. The transmitter adopts a square root raised cosine filter with a roll-off coefficient of 0.1 to perform pulse forming, the central wavelength of the laser is 1550nm, and signals output by the transmitter are firstly overlapped with ASE noise and then sequentially pass through a three-section polarization damage simulator of RSOP1, PMD and RSOP 2. The PSPs in the emulator changes at the same rate as the RSOP rotates, and both the azimuth and phase angle of the RSOP increase linearly with time. Before entering the receiver, the noise is suppressed by a 10-order Bessel filter with the bandwidth of 33.6GHz, and the line width and the frequency offset of the local oscillator laser are respectively set to be 100kHz and 100MHz at the receiver. After entering a coherent receiver, the DSP process firstly performs clock recovery, then the signal is resampled to 2 sample/symbol, normalized and standardized, then polarization equalization is performed, after the polarization equalization, the signal is downsampled to 1 symbol/sample, then frequency offset estimation is performed to perform frequency offset recovery, and a Blind Phase Search (BPS) scheme is adopted to perform carrier phase recovery. The Normalized Generalized Mutual Information (NGMI) of the signal is finally calculated. SCKF-PA is used as an abbreviation for the present invention. In contrast, the EKF scheme of the successive approximation innovation was used to abbreviation it as EKF-CM and the traditional multimode algorithm as MMA.

In this embodiment, in order to test the performance upper limit of the proposed scheme, the test of the system performance upper limit is performed in the states of OSNR of 25dB and source entropy h=4.5 bit/symbol, respectively, as shown in fig. 3. It can be found that: the MMA and EKF-CM schemes, as compared, hardly outperform the combined polarization impairments at any RSOP as DGD increases gradually from 30ps to 90 ps. While the SCKF-PA scheme of the present invention shows excellent performance, in the case of strong shaping with h=4.5 bits/symbol, the present invention can combine balance RSOP up to 8.34Mrad/s with DGD impairments of 90ps at an NGMI threshold of 0.9.

In this embodiment, the present invention verifies the OSNR penalty for a source entropy of 4.5bit/symbol, as shown in fig. 4. When the OSNR test range is increased from 17dB to 27dB and the interval is 1dB, joint damage recovery in the scene of dgd=35 ps, rsop=3 Mrad/s and joint damage recovery in the scene of dgd=70 ps, rsop=6 Mrad/s are performed, respectively. Simulation results indicate that for a damage-free curve, the NGMI threshold needs to be reached at approximately 18dB OSNR. Neither the EKF-CM scheme nor the MMA scheme by comparison balances such high polarization impairments. Compared with a polarization-free damage curve under the conditions of dgd=35 ps and rsop=3 Mrad/s, the invention has an OSNR cost of only 0.79dB when reaching the NGMI threshold of 0.9, and the OSNR cost of the invention is only 0.9dB even under more extreme dgd=70 ps and rsop=6 Mrad/s scenes. Therefore, the OSNR of the present invention is lower in cost and excellent in performance.

In this embodiment, to illustrate the applicability and flexibility of the SCKF-PA scheme to PCS-64QAM systems, fig. 5 shows NGMI curves for 3 schemes with different shaping strength and different polarization impairments at osnr=23 dB. The abscissa of fig. 5 is the source entropy H, which ranges from 4.1bit/symbol to 5.9bit/symbol, with an interval of 0.1bit/symbol, and the ordinate is NGMI. It can be seen that: under the condition of no polarization damage, when the OSNR is 23dB, due to the influence of ASE noise and probability constellation shaping, when the information source entropy is increased from 4.1bit/symbol to 5.69bit/symbol, the NGMI value of the PCS-64QAM system is above a threshold value of 0.9. As a comparative scheme, MMA and EKF-CM schemes were all not balanced in the case listed in FIG. 5. When DGD=35 ps and RSOP=3 Mrad/s in the channel, the invention can realize that NGMI can reach more than 0.9 threshold value within the range of source entropy from 4.1bit/symbol to 5.56 bit/symbol; when the damage is further increased to dgd=70 ps, rsop=6 Mrad/s, the maximum source entropy that the invention can cope with is in the range of 4.1bit/symbol to 5.3bit/symbol.

Example 2

As shown in fig. 6, the present invention provides a joint equalization apparatus for a joint equalization method of PMD and RSOP impairments, including:

The joint equalization registering device provided in the embodiment shown in fig. 6 may implement the technical solution shown in the joint equalization registering method in the embodiment of the method, and its implementation principle is similar to that of the beneficial effects, and will not be repeated here.

In this embodiment, the functional units may be divided according to a joint equalization registration method, for example, each function may be divided into each functional unit, or two or more functions may be integrated into one processing unit. The integrated units may be implemented in hardware or in software functional units. It should be noted that the division of the units in the present invention is schematic, only one logic division, and other division manners may be implemented in practice.

In the embodiment of the invention, in order to realize the principle and the beneficial effect of the joint equilibrium registration method, the joint equilibrium registration device comprises a hardware structure and/or a software module which execute the corresponding functions. Those of skill in the art will readily appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein are capable of being implemented as a combination of hardware and/or hardware and computer software, where a function is performed in either a hardware or a computer software driven manner, where different methods may be employed to implement the described functions for each particular application depending upon the specific application and design constraints, but such implementation is not to be considered beyond the scope of the present application.

In the embodiment, the invention is based on the joint damage equalization model of RSOP and PMD and SCKF, and integrates the probability perception model of the maximum posterior probability, so that linearization error is effectively reduced compared with the traditional EKF scheme. In addition, the invention can avoid the error of ring judgment caused by uneven distribution of constellation points and ASE noise, and especially can solve the problem of polarization damage joint equalization in thunderstorm scenes. The probability perception innovation is introduced, so that the problem of noise amplification caused by continuous multiplication innovation is effectively solved, and the calculation accuracy of the PDM PCS-64QAM system in a low OSNR scene is greatly improved. The invention has excellent performance in a low OSNR scene, and has the advantages of high tracking precision, high tolerance to initial errors and high convergence speed.

Claims

1. A method for joint equalization of PMD and RSOP impairments, comprising the steps of:

2. The joint equalization method of PMD and RSOP impairments according to claim 1, wherein the step S1 comprises the steps of:

R＝diag([1；1])

Wherein diag (·) represents a diagonal matrix operation;

Q＝diag([1E-4；1E-4；1E-4；1E-6；1E-6；1E-6])

square root volume kalman filterError covariance matrix S of SCKF _0|0 The expression of (2) is as follows:

S _0|0 ＝diag[(1E-2；1E-2；1E-2；1E-2；1E-2；1E-2)]。

3. the joint equalization method of PMD and RSOP impairments according to claim 2, wherein the step S101 comprises the steps of:

The expression for tracking the RSOP in the time domain is as follows:

the expression for compensating PMD in the frequency domain is as follows:

wherein U is _comp (ω) represents the compensation matrix of first-order PMD, ω represents the light angleThe frequency, Δτ, represents the value of the differential group delay DGD, I represents the identity matrix, Vectors representing PMD>Representing the Brix matrix, τ ₁ ,τ ₂ ,τ ₃ Representing three components of the PMD vector in stokes space, (·) ^T Representing a transpose operation;

4. The joint equalization method of PMD and RSOP impairments according to claim 1, wherein the step S2 comprises the steps of:

S202, time update state 2n rows of volume points X _i,k-1|k-1 Propagating through a predictive equation;

5. The joint equalization method of PMD and RSOP impairments of claim 4, wherein the square root factor S _k|k-1 The expression of (2) is as follows:

wherein Tria (·) represents an orthogonal triangular QR decomposition operation,represents a center weighting matrix, S _Q,k-1 Representing a prediction noise covariance matrix Q _k-1 Square root factor of> And->All represent the predicted value of the volume point propagated through the prediction equation, n represents the number of state parameters, i represents the sequence number of the volume point, i=1, 2,..2 n, s _k-1|k-1 A posterior estimate, ζ, representing the square root factor of the error covariance matrix at the previous time _i Representing the volume point +.>A posterior estimate representing the last moment in time of the tracked state parameter, [1 ]] _i The ith column of point set 1 is shown.

6. The joint equalization method of PMD and RSOP impairments as defined in claim 5, wherein said step S3 comprises the steps of:

s302, according to the volume point X after updating the state _i,k|k-1 After the polarization damage combined equalization is calculatedA kth output sliding window signal sequence of (2);

Wherein n represents the number of state variables, i represents the sequence number of volume points, i=1, 2,..2 n, z _i,k|k-1 Representing the measured and predicted volume point values, abs (·) representing a complex modulo operation,and->Intermediate elements of the series of X and Y polarized volume points of the ith group in the kth sliding window, respectively,/->Representing a rounding up operation.

7. The joint equalization method of PMD and RSOP impairments as defined in claim 6, wherein said step S302 comprises the steps of:

the expression of the PMD compensation matrix is as follows:

the expression of the RSOP tracking matrix is as follows:

wherein R is _eq,i Represents zeta as a tracking matrix of RSOP a state parameter corresponding to the ith column of volume points _i,k|k-1 Representing the value of the phase rotation angle ζ corresponding to the i-th row volume point in the measurement update state, η _i,k v _x-1 Representing the value corresponding to the phase rotation angle eta in the ith row volume point of the measurement update state, kappa _i,k|k-1 Representing a value of the azimuth rotation angle kappa corresponding to an ith row volume point in a measurement update state;

The expression of the averaging operation is as follows:

wherein,and->Respectively representing output sequences of X and Y polarization sliding windows after final joint equalization, n represents the number of state parameters, i represents the serial numbers of volume points, i=1, 2,..2, 2n, and #>And->Respectively indicate passing U _comp,i And RSOP tracking matrix R _eq,i Combining the balanced X-polarization and Y-polarization volume point sequences, U _comp,i Volume point X representing updated state using column i measurement _i,k|k-1 The first three parameters act as matrices for PMD compensation matrix parameters.

8. The joint equalization method of PMD and RSOP impairments according to claim 1, wherein the step S4 comprises the steps of:

Wherein Tria (·) represents an orthogonal triangular QR decomposition operation,represents a weighted center matrix, S _R,k-1 Representing a noise covariance matrix R _k-1 N represents the number of state parameters, i represents the number of volume points, i=1, 2, 2n,indicating the measurement predicted value, Z _2n,k|k-1 Representing measured and predicted volume point values S _R,k-1 Representing a noise covariance matrix R _k-1 Square root factor of>

S402, estimating a cross covariance matrix P _xz,k|k-1 ：

Wherein χ is _k|k-1 Andall represent a central weighting matrix, X _2n,k|k-1 Volume point representing update status +. >A damage prediction value representing a state parameter;

9. The joint equalization method of PMD and RSOP impairments according to claim 8, wherein the innovation matrix calculation process in step S404 comprises the steps of:

S4041. combining with a rice distribution model, calculating based on maximum posterior probability to obtain a measurement predicted valueOptimal radius of constellation circle with maximum probability +. >Wherein, for the measurement prediction value->The judgment process of the ring is as follows:

wherein,represents the value of m when the search function takes the maximum value, m represents each of 9 rings in the ideal PCS-64QAM constellation diagram, +.>Representing the amplitude of the received signal as +.>Under the condition that the amplitude of the transmitting signal is +.>P (·) represents the probability calculation,/-)>Constellation circle radius representing PCS-64QAM signal at transmitting end +.>Measurement prediction value, sigma, representing X or Y polarization in kth sliding window of square root volume Kalman filter SCKF ² Representing the variance of noise, I ₀ (. Cndot.) represents the modified Bessel function of order 0,>representing different radiuses of transmitting end after probability shaping coding>Probability of occurrence;

wherein,represents the optimal radius of the ring to which the measurement predicted value of the X polarization of the PCS-64QAM system belongs, < >>Represents the optimal radius of the ring to which the measured predicted value of the Y polarization of the PCS-64QAM system belongs, < > >The measurement prediction value of X polarization is +.> The measurement prediction value of Y polarization is +.>L represents the length of the sliding window, S _x,k And S is equal to _y,k Representing the sequence of the corrupted X-or Y-polarized signal intercepted by the kth sliding window, respectively.

10. A joint equalization apparatus for performing the joint equalization method of PMD and RSOP impairments as defined in any of claims 1-9, comprising:

the first processing module is used for constructing a joint equalization model of polarization damage according to the characteristics of the polarization damage in the optical fiber link in a thunderstorm scene and initializing the SCKF parameters of the square root volume Kalman filter;

the second processing module is used for carrying out time update on the square root volume Kalman filter SCKF according to a prediction equation by taking the posterior estimation value of the state parameter at the previous moment as the prior estimation value of the state parameter at the next moment so as to predict the damage value of the damage signal acquired by the current sliding window;

the third processing module is used for carrying out measurement updating on the square root volume Kalman filter SCKF according to a measurement equation fused with the sliding window to obtain a measurement predicted value;

the fourth processing module is used for carrying out ring judgment operation based on the maximum posterior probability on the measurement predicted value by combining the radius distribution of the received symbols to obtain the optimized radius of the constellation ring to which the measurement predicted value belongs, calculating an innovation matrix, and combining the damage predicted value and the measurement predicted value to obtain the posterior estimated value of the state parameter;

And the fifth processing module is used for judging whether iteration is finished, if yes, ending the flow, finishing the joint equalization of PMD and RSOP damage, otherwise, sending the posterior estimation value of the state parameter and the square root coefficient of the error covariance matrix to the second processing module, updating the iteration number k, and carrying out the next iteration.