CN107707310B - Polarization demultiplexing and carrier phase recovery method based on adaptive Kalman - Google Patents

Polarization demultiplexing and carrier phase recovery method based on adaptive Kalman Download PDF

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CN107707310B
CN107707310B CN201710851125.9A CN201710851125A CN107707310B CN 107707310 B CN107707310 B CN 107707310B CN 201710851125 A CN201710851125 A CN 201710851125A CN 107707310 B CN107707310 B CN 107707310B
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杨彦甫
向前
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Shenzhen Graduate School Harbin Institute of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/60—Receivers
    • H04B10/61—Coherent receivers
    • H04B10/616—Details of the electronic signal processing in coherent optical receivers
    • H04B10/6162—Compensation of polarization related effects, e.g., PMD, PDL
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/60—Receivers
    • H04B10/61—Coherent receivers
    • H04B10/616—Details of the electronic signal processing in coherent optical receivers
    • H04B10/6161—Compensation of chromatic dispersion
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/60—Receivers
    • H04B10/61—Coherent receivers
    • H04B10/616—Details of the electronic signal processing in coherent optical receivers
    • H04B10/6164—Estimation or correction of the frequency offset between the received optical signal and the optical local oscillator
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/60—Receivers
    • H04B10/61—Coherent receivers
    • H04B10/616—Details of the electronic signal processing in coherent optical receivers
    • H04B10/6165—Estimation of the phase of the received optical signal, phase error estimation or phase error correction

Abstract

The invention provides a polarization demultiplexing and carrier phase recovery method based on adaptive Kalman, which comprises the following steps: firstly, polarization demultiplexing and carrier phase recovery are carried out by utilizing an extended Kalman filter; and secondly, updating the Q value of the tuning parameter by a covariance matching method, and judging the convergence condition of the algorithm according to the mean value dz of the measurement margin so as to guide the updating of the Q value of the tuning parameter. The invention has the beneficial effects that: the polarization aliasing and the carrier phase noise of a coherent optical communication system can be processed simultaneously, the tuning parameters can be self-adapted to different values under different scenes, and the tolerance of the algorithm to the polarization rotation and the phase noise can be improved to the maximum extent; meanwhile, the performance of the algorithm is irrelevant to the initial tuning parameter Q, and the excellent performance of quick convergence and high-precision estimation can be realized.

Description

Polarization demultiplexing and carrier phase recovery method based on adaptive Kalman
Technical Field
The invention relates to the field of optical communication, in particular to a polarization demultiplexing and carrier phase recovery method based on adaptive Kalman.
Background
With the rapid development of technologies such as Pre 5G, data centers, big data and the like, people have increasingly sharply increased requirements for network communication traffic, and a coherent optical communication technology with the advantages of high speed, large capacity and the like is undoubtedly one of the key technologies for meeting the requirements. During transmission, the signal is susceptible to random birefringence effects in the fiber. And as the modulation format increases, carrier phase noise caused by the laser linewidth will cause a sharp rotation of the signal, further degrading the quality of the signal.
In a single-carrier coherent optical communication system, signal polarization crosstalk caused by random birefringence in an optical fiber and carrier phase noise caused by laser phase inconsistency of a transceiver are one of main influence factors for degrading an optical signal. For the above-mentioned impairments, the conventional offline digital signal processing scheme mainly includes: CMA (Constant module algorithm), VV (Viterbi-Viterbi) algorithm, FFT (Fast Fourier transform) algorithm, BPS (Blind phase search) algorithm, and EKF (Extended Kalman filter) algorithm. However, these algorithms also have some essential disadvantages, such as: CMA convergence speed is slow, VV line width tolerance is small, and BPS calculation complexity is high. Compared with other algorithms, the EKF algorithm has the characteristics of high-speed convergence, high estimation precision and the like, but the convergence speed and precision are seriously influenced by the Q value of the tuning parameter, and the traditional EKF algorithm is difficult to provide an optimal solution on the tracking precision and speed.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a polarization demultiplexing and carrier phase recovery method based on adaptive Kalman.
The invention provides a polarization demultiplexing and carrier phase recovery method based on adaptive Kalman, which comprises the following steps:
firstly, polarization demultiplexing and carrier phase recovery are carried out by utilizing an extended Kalman filter;
and secondly, updating the Q value of the tuning parameter by a covariance matching method, and judging the convergence condition of the algorithm according to the mean value dz of the measurement margin so as to guide the updating of the Q value of the tuning parameter.
As a further improvement of the invention, the size of the measurement margin is detected in real time by a decision detector, and when the mean value dz of the measurement margin is smaller than the critical value β, the decision algorithm is converged at the moment, so that the updating of the tuning parameter Q value is stopped.
As a further improvement of the present invention, a clock recovery algorithm, a dispersion/nonlinearity compensation algorithm, and a frequency offset compensation algorithm are used to compensate for timing errors, dispersion/nonlinearity, and system frequency offsets of the received signal, and then the signal is simplified as:
Figure BDA0001413597910000021
wherein Z isn,mn,hn,Ts,θn,ξnRespectively representing an nth received signal, an nth transmitted signal, a signal transmission matrix, a symbol period, carrier phase noise and Gaussian white noise;
the state space model based on adaptive kalman-based polarization demultiplexing and carrier phase recovery is represented as follows:
Sn＝Sn-1+wn(2)
Un＝HnZn+vn(3)
wherein equations (2) - (3) describe the states separatelyEquations and measurement equations, the state quantity S can be expressed as Sn＝[ab c d θ]TA, b, c, d are respectively 4 parameters of the inverse channel Jones matrix, theta is the estimated carrier phase noise, UnAnd HnRespectively, the output of the measurement equation and the measurement matrix, and HnIs shown as
Figure BDA0001413597910000034
w and v are process noise and measurement noise, respectively;
the main formulas of polarization demultiplexing and carrier phase recovery based on adaptive kalman are summarized as follows:
Sn＝ASn-1(4)
Figure BDA0001413597910000031
Figure BDA0001413597910000032
Figure BDA0001413597910000033
Sn+1＝Sn+Kdz (8)
equations (4) - (8) are mainly used to calculate state parameters, prior covariance, kalman gain, posterior covariance, and updated state parameters, where a is a state transition matrix expressed as a 5 × 5 unit matrix, Mn is a jacobian matrix linearized with a measurement matrix, and R and Q represent a measurement error and a process error, respectively, and meanwhile, tuning parameter Q determines the estimation accuracy and tracking speed of the extended kalman filter. dz is the average value of the measurement margin and is used to guide the extended Kalman filter to perform the next state parameter update.
As a further refinement of the invention, the process noise is expressed as:
wn＝Sn+1-Sn＝Kdz (9)
thereby, the parameter Q is adjusted and optimizednExpressed as:
Figure BDA0001413597910000041
wherein E (×) represents the expectation of a pair, and in order to simplify the calculation of the desired complexity, the forgetting factor α is used to give the Q of the previous calculationn-1And calculated QnDifferent weighting factors instead of the sliding window required to calculate the expectation, QnThe expression of (c) is written as:
Qn＝αQn-1+(1-α)Qn(11)
in order to ensure the convergence speed and estimation accuracy of the algorithm, a decision detector is used for detecting the size of the measurement margin in real time, when the mean value dz of the measurement margin is smaller than a critical value beta, the algorithm is judged to be converged at the moment, so that the updating of Q is stopped, and therefore QnThe expression of (c) is rewritten as:
Figure BDA0001413597910000042
the invention has the beneficial effects that: by the scheme, the polarization aliasing and the carrier phase noise of the coherent optical communication system can be processed simultaneously, the tuning parameters can be self-adapted to different values under different scenes, and the tolerance of the algorithm to the polarization rotation and the phase noise can be improved to the maximum extent; meanwhile, the performance of the algorithm is irrelevant to the initial tuning parameter Q, and the excellent performance of quick convergence and high-precision estimation can be realized.
Drawings
Fig. 1 is a flow chart of a polarization demultiplexing and carrier phase recovery method based on adaptive kalman according to the present invention.
FIG. 2 is a schematic diagram of a 14GS/s 16QAM coherent optical communication system.
FIG. 3 is a graph of the Q-value of AKF convergence for different polarization rotation rates.
FIG. 4 is a polarization tracking curve for AKF and EKF at different Q values.
Fig. 5 is a comparison graph of AKF performance results at 1Mrad/s polarization rotation rate, (a) pre-processing constellation, (b) post-processing constellation, (c) estimated carrier phase noise, and (d) estimated jones matrix parameters.
Detailed Description
The invention is further described with reference to the following description and embodiments in conjunction with the accompanying drawings.
A polarization demultiplexing and carrier phase recovery method based on adaptive Kalman comprises the following steps:
first, a timing error, dispersion/nonlinearity, and system frequency offset of a received signal are compensated using a clock recovery algorithm, a dispersion/nonlinearity compensation algorithm, and a frequency offset compensation algorithm. We can then simply express the signal as:
Figure BDA0001413597910000051
wherein Z isn,mn,hn,Ts,θn,ξnRespectively, the nth received signal, the nth transmitted signal, the signal transmission matrix, the symbol period, the carrier phase noise and the white gaussian noise.
The state space model based on EKF polarization demultiplexing and carrier phase recovery can be represented as follows:
Sn＝Sn-1+wn(2)
Un＝HnZn+vn(3)
equations (2) - (3) describe the state equation and the measurement equation, respectively. The state quantity S can be denoted Sn＝[ab c d θ]TA, b, c and d are respectively 4 parameters of the inverse channel Jones matrix, and theta is estimated carrier phase noise. U shapenAnd HnThe output of the measurement equation and the measurement matrix, respectively. And HnCan be expressed as
Figure BDA0001413597910000052
w and v are process noise and measurement noise, respectively.
The main formulas for EKF-based polarization demultiplexing and carrier recovery can be summarized as follows:
Sn＝ASn-1(4)
Figure BDA0001413597910000061
Figure BDA0001413597910000062
Figure BDA0001413597910000063
Sn+1＝Sn+Kdz (8)
equations (4) to (8) are mainly used to calculate the state parameters, the prior covariance, the kalman gain, the a posteriori covariance, and the updated state parameters. Where a is the state transition matrix, which can be represented as a 5 × 5 unit matrix. Mn is the Jacobian matrix after linearization of the measurement matrix. R and Q represent measurement error and process error, respectively. At the same time, Q also determines the estimation accuracy and tracking speed of the EKF. dz is the mean value of the measurement margin and is used to guide the kalman filter to perform the next state parameter update.
In order to track the higher-speed polarization rotation rate and improve the tolerance to the laser line width, an adaptive kalman algorithm which can change the tuning parameter Q in real time must be found.
A polarization demultiplexing and carrier phase recovery method based on adaptive Kalman mainly comprises two parts: EKF and tuning parameter updating module. First, polarization demultiplexing and carrier phase recovery are performed using EKF. And secondly, updating the Q value by a covariance matching method, and judging the convergence condition of the algorithm according to the mean value dz of the measurement margin so as to guide the updating of the Q value of the tuning parameter.
From equation (2), the process noise can be expressed as:
wn＝Sn+1-Sn＝Kdz (9)
thereby, the parameter Q is adjusted and optimizednCan be expressed as:
Figure BDA0001413597910000064
wherein E (, p) represents the expected value for Q, and in order to simplify the calculation of the expected complexity, the previously calculated Q is given a forgetting factor αn-1And calculated QnDifferent weighting factors are substituted for the sliding window required to calculate the expectation. Thereby QnThe expression of (c) can be written as:
Qn＝αQn-1+(1-α)Qn(11)
in order to ensure the convergence speed and estimation accuracy of the algorithm, a decision detector is used for detecting the size of the measurement margin in real time, and when the mean value dz of the measurement margin is smaller than a critical value β, the algorithm is judged to have converged at the moment, so that the updating of Q is stoppednThe expression of (c) can be rewritten as:
Figure BDA0001413597910000071
so far, the adaptive kalman based polarization demultiplexing and carrier phase recovery algorithm has been described, and it can be mainly characterized by equations (4), (6) to (8) and (11) to (12). The basic frame diagram is shown in fig. 1.
The polarization demultiplexing and carrier phase recovery method based on the adaptive Kalman can simultaneously process the polarization aliasing and carrier phase noise of a coherent optical communication system, the tuning parameters of the method can be adaptive to different values under different scenes, and the tolerance of an algorithm to polarization rotation and phase noise can be improved to the maximum extent. Meanwhile, the performance of the algorithm is irrelevant to the initial tuning parameter Q, and the excellent performance of quick convergence and high-precision estimation can be realized.
Fig. 2 is an experimental model of coherent optical communication according to an embodiment of the present invention, and the specific flow is as follows:
an electrical drive signal of 14GS/s is generated in the AWG for driving the optical I/Q modulator. To implement the polarization multiplexing technique, the PBS is used to split the modulated light into two orthogonal signal lights, and one of them is delayed by 4 ns. The local oscillator light and the signal light are beat-frequency in the optical receiver clock to receive signals. At the receiving end, the signal is subjected to orthogonalization, resampling, timing and dynamic channel equalization for resampling and compensating for timing errors and PMD effects. And part of the signals are subjected to polarization demultiplexing through CMA and FFT and system frequency offset is calculated. The obtained signal frequency offset is used for compensating the signal frequency offset. The dynamic polarization rotation effect is added by digital signal off-line processing techniques in the presence of only phase noise signals. The AKF algorithm is used to compensate the polarization and carrier phase of the signal. Fig. 3 shows the convergence Q of two parameters, polarization and phase, for AKF at different polarization rotation rates. To fully compare the polarization tracking capabilities of AKF and EKF, Qabcd is set to [5E-4,1E-4,1E-5], and Qphase is set to 5E-5. The polarization tracking performance curves of AKF and EKF are shown in fig. 4, the tracking performance of EKF is greatly affected by Q value, and the tracking rate is relatively low. The tracking performance of the AKF is relatively stable, and meanwhile, the AKF has relatively high polarization tracking capability. The estimated polarization parameters and phase noise of the constellation before and after AKF processing are shown in fig. 5. The experimental results show that: AKF has good polarization tracking capability, and the performance of the AKF is irrelevant to the Q value of the tuning parameter. Meanwhile, the experimental result is consistent with the theoretical analysis, so that the AKF has a good application prospect in the future dynamic optical network.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (3)

1. A polarization demultiplexing and carrier phase recovery method based on adaptive Kalman is characterized by comprising the following steps:
firstly, polarization demultiplexing and carrier phase recovery are carried out by utilizing an extended Kalman filter;
secondly, updating the Q value of the tuning parameter is realized by a covariance matching method, and the convergence condition of the algorithm is judged according to the mean value dz of the measurement margin, so that the updating of the Q value of the tuning parameter is guided;
wherein the content of the first and second substances,
compensating for timing error, dispersion/nonlinearity and system frequency offset of the received signal using a clock recovery algorithm, a dispersion/nonlinearity compensation algorithm and a frequency offset compensation algorithm, and then simplifying the signal as:
Figure FDA0002247516030000011
wherein Z isn,mn,hn,Ts,θn,ξnRespectively representing an nth received signal, an nth transmitted signal, a signal transmission matrix, a symbol period, carrier phase noise and Gaussian white noise;
the state space model of polarization demultiplexing and carrier phase recovery based on adaptive kalman is represented as follows:
Sn＝Sn-1+wn(2)
Un＝HnZn+vn(3)
equations (2) - (3) describe the equation of state and the measurement equation, respectively, and the state parameter S can be expressed as Sn＝[a b cd θ]TA, b, c, d are respectively 4 parameters of the inverse channel Jones matrix, theta is the estimated carrier phase noise, UnAnd HnRespectively, the output of the measurement equation and the measurement matrix, and HnIs shown as
Figure FDA0002247516030000012
w and v are process noise and measurement noise, respectively; the main formulas of polarization demultiplexing and carrier phase recovery based on adaptive kalman are summarized as follows:
Sn＝ASn-1(4)
Figure FDA0002247516030000023
Figure FDA0002247516030000022
Figure FDA0002247516030000021
Sn+1＝Sn+Kdz (8)
equations (4) - (8) are mainly used to calculate state parameters, prior covariance, kalman gain, posterior covariance, and updated state parameters, where a is a state transition matrix expressed as a 5 × 5 unit matrix, Mn is a jacobian matrix linearized with a measurement matrix, R and Q represent a measurement error and a process error, respectively, and meanwhile, an optimization parameter Q determines an estimation accuracy and a tracking speed of an extended kalman filter, and dz is a mean value of a measurement margin, and is used to guide the extended kalman filter to update the state parameters next time.
2. the adaptive Kalman-based polarization demultiplexing and carrier phase recovery method according to claim 1, wherein the magnitude of the measurement margin is detected in real time by a decision detector, and when the mean value dz of the measurement margin is smaller than a critical value β, the decision algorithm is converged at this moment, so that the updating of the tuning parameter Q value is stopped.
3. The adaptive kalman based polarization demultiplexing and carrier phase recovery method according to claim 1, wherein:
according to equation (2), the process noise is expressed as:
wn＝Sn+1-Sn＝Kdz (9)
thereby, the parameter Q is adjusted and optimizednExpressed as:
Figure FDA0002247516030000031
wherein E (×) represents the expectation of a pair, and in order to simplify the calculation of the desired complexity, the forgetting factor α is used to give the Q of the previous calculationn-1And calculated QnDifferent weighting factors instead of the sliding window required to calculate the expectation, QnThe expression of (c) is written as:
Qn＝αQn-1+(1-α)Qn(11)
in order to ensure the convergence speed and estimation accuracy of the algorithm, a decision detector is used for detecting the size of the measurement margin in real time, when the mean value dz of the measurement margin is smaller than a critical value beta, the algorithm is judged to be converged at the moment, so that the updating of Q is stopped, and therefore QnThe expression of (c) is rewritten as:
Figure FDA0002247516030000032
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CN109217934B (en) * 2018-09-20 2020-04-21 哈尔滨工业大学（深圳） Polarization demultiplexing algorithm based on maximum likelihood independent component analysis method
CN109000782A (en) * 2018-09-27 2018-12-14 哈尔滨工程大学 A kind of ellipse fitting non-linear error calibration method based on Kalman filtering
CN110011733B (en) * 2019-03-25 2020-10-16 华中科技大学 Method and system for depolarization multiplexing based on momentum factor
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CN110266388B (en) * 2019-06-18 2020-09-04 北京邮电大学 PMD (polarization mode dispersion) equalization method and device, electronic equipment and storage medium
CN110445610B (en) * 2019-08-26 2021-11-30 上海循态量子科技有限公司 Polarization tracking method, system and medium for continuous variable quantum key distribution system
CN112737547A (en) * 2020-12-18 2021-04-30 北京邮电大学 Kalman filtering based signal compensation method and device
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