CN115622633A - Polarization state rotation tracking and compensation method based on adaptive volume Kalman filtering - Google Patents
Polarization state rotation tracking and compensation method based on adaptive volume Kalman filtering Download PDFInfo
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Abstract
The embodiment of the invention discloses a polarization state rotation tracking and compensating method based on adaptive volume Kalman filtering. The method adopts the adaptive volume Kalman filtering algorithm based on the mean decision error covariance to realize the tracking and compensation of polarization state rotation, dynamically updates the tuning parameters, solves the problem that the tuning parameters of the volume Kalman filtering algorithm can not be adaptively updated, can adapt to different values in different scenes, furthest improves the tolerance of the algorithm to polarization rotation noise, can realize quick convergence, further improves the filtering precision and stability of the algorithm, and has important application prospect in the field of polarization demultiplexing related to coherent optical communication.
Description
Technical Field
The invention relates to the technical field of optical fiber communication, in particular to a polarization state rotation tracking and compensation method based on adaptive volume Kalman filtering.
Background
In the field of optical communications, a larger bandwidth, a longer transmission distance, and a higher reception sensitivity are currently pursued. The development of coherent optical communication technology and polarization division multiplexing technology has greatly improved the capacity of optical fiber communication systems. A coherent optical communication system can be used in the communication of signals of multiple modulation formats while satisfying the above-described objects.
In order to meet the increasing bandwidth demand, a partial division multiplexing system is often used to improve the utilization rate of the frequency spectrum. The polarization division multiplexing technology utilizes two paths of mutually orthogonal polarization states to transmit optical signals, and improves the frequency spectrum efficiency by two times. However, polarization rotation effects generated during transmission of the signal can introduce additional channel crosstalk at the receiving end.
The Kalman filter is an algorithm for carrying out optimal estimation on the system state through inputting and outputting observation data of the system. In recent years, the Kalman filtering algorithm has strong dynamic tracking capability and high convergence speed, and has an obvious effect on tracking the polarization state rotation damage. The extended Kalman filtering algorithm is already applied to the compensation of polarization state rotation damage, and the first-order Taylor series expansion precision can be realized. The volume Kalman filtering algorithm can realize the third-order Taylor series expansion precision by adopting a third-order sphere-phase path volume principle. Compared with an extended Kalman filter, the tracking performance of the cubature Kalman filter is better, and the calculation complexity is lower because the Jacobian is not required to be calculated.
However, in the process of polarization state rotation equalization by using the volumetric kalman filter algorithm, the performance of the method is easily influenced by tuning parameter selection, so that the kalman filter diverges. The current problem is how to realize the self-adaptive updating of the noise covariance in the initial process and the measurement noise covariance, so that the self-adaptive performance of the algorithm is improved, and the quick tracking capability of the algorithm is further improved.
Disclosure of Invention
The invention aims to overcome the defect that the existing cubature Kalman filter algorithm is easily influenced by optimization parameter selection, and provides a polarization state rotation tracking and compensating method based on adaptive cubature Kalman filtering.
In order to achieve the above purpose, the invention provides the following technical scheme:
the invention provides a polarization state rotation tracking and compensating method based on adaptive volume Kalman filtering, which comprises the following steps:
s1, calculating volume points and volume points after state equation propagation according to a state vector and an error covariance matrix at a previous moment, and constructing a volume point set to obtain a predicted value of the state vector and a predicted value of the error covariance matrix at the current moment;
s2, calculating the volume point and the volume point after the propagation of the measurement equation again through the predicted state vector to obtain a predicted value of the observation vector, and recovering the signal based on the currently solved state vector and measurement vector to obtain an auto-covariance matrix and a cross-covariance matrix;
s3, taking the constellation points as reference bases for the recovery signals, calculating by using the recovery signals to obtain innovation vectors, and further updating the state vectors and the error covariance matrix;
and S4, calculating to obtain the mean decision error covariance to guide the self-adaptive updating of the tuning parameters for the estimation of the next discrete moment.
Further, in step S1, the received dual-polarization signal is represented as:
r(t)＝Js(t)+η(t) (1)
wherein s (t) is a transmitting signal, J is a Jones matrix with a rotating polarization state, and eta (t) is additive white Gaussian noise in an optical fiber link;
constructing a volume point chi and a volume point chi after propagation of a state equation * ：
Wherein, P k-1|k-1 Is an error covariance matrix, S k-1|k-1 Is P k-1|k-1 The lower triangular real matrix of (a) is,
is P k-1|k-1 The transpose of the lower triangular real matrix of (1),
is the predicted value of the state vector at the last moment, xi i Is a volume point set, L is twice the dimension of the state variable, and D is an identity matrix.
Further, the calculation formulas of the predicted value of the state vector at the current time and the predicted value of the error covariance matrix in step S1 are respectively:
wherein,
is a process noise covariance matrix estimate.
Further, the step S2 of predicting the measurement vector includes:
z i,k|k+1 ＝h(χ i,k|k-1 ) (9)
wherein,
is an a priori state estimate, P k|k-1 Is the covariance between the true and predicted values,
is a predicted value of the measurement vector.
Further, the autocovariance matrix P in step S2 zz,k|k-1 And cross covariance matrix P xz,k|k-1 The calculation formulas of (a) and (b) are respectively as follows:
wherein, R is a measurement noise covariance matrix.
Further, step S3 updates the state vector and the error covariance matrix by calculating a kalman gain matrix and using the following formula:
K k ＝P xz,k|k-1 (P zz,k|k-1 ) -1 (13)
wherein K k Is a Kalman gain matrix, P zz,k|k-1 Is an autocovariance matrix, P xz,k|k-1 Is a cross covariance matrix.
Further, the tuning parameters of step S4 include a process noise covariance matrix and a measurement noise covariance matrix, which are respectively expressed as:
wherein E (#) represents the expectation value, α, over Q And alpha R Respectively representing forgetting factors of Q and R, beta is a set threshold value, and the decision error is the minimum difference d between the current predicted value and the ideal constellation point coordinate k ：
The mean decision error covariance is expressed as:
wherein N is the length of the sliding window.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a polarization state rotation tracking and compensating method based on adaptive volume Kalman filtering. The method adopts the adaptive volume Kalman filtering algorithm based on the mean decision error covariance to realize the tracking and compensation of polarization state rotation, dynamically updates the tuning parameters, solves the problem that the tuning parameters of the volume Kalman filtering algorithm can not be adaptively updated, can adapt to different values in different scenes, furthest improves the tolerance of the algorithm to polarization rotation noise, can realize quick convergence, further improves the filtering precision and stability of the algorithm, and has important application prospect in the field of polarization demultiplexing related to coherent optical communication.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for the embodiments will be briefly described below. It should be apparent that the drawings in the following description are merely some of the embodiments described in the present invention, and that other drawings may be obtained by those skilled in the art.
Fig. 1 is a flowchart of an adaptive cubature kalman filter algorithm according to an embodiment of the present invention.
Fig. 2 is a frame diagram of an adaptive cubature kalman filter algorithm according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a polarization demultiplexing scheme of a coherent optical communication system according to an embodiment of the present invention.
Fig. 4 is a system simulation diagram based on the OptiSystem platform according to an embodiment of the present invention.
Detailed Description
For a better understanding of the present solution, the method of the present invention is described in detail below with reference to the accompanying drawings.
The main design parameters in the design method of the invention comprise: volume point χ, propagation volume point χ * Prior state estimate
Covariance P between true and predicted values k|k-1 Auto-covariance matrix P zz,k|k-1 The cross covariance matrix P xz,k|k-1 Process noise covariance matrix Q, kalman gain matrix K k Posterior state estimation
Measuring the noise covariance matrix R, the target matrix z k The predicted value of the measured value
Two times of state variable dimension L, unit matrix I and bit error rate BER.
The invention provides a polarization state rotation tracking and compensating method based on adaptive volume Kalman filtering, which comprises the following steps:
s1, calculating volume points and volume points after state equation propagation according to a state vector and an error covariance matrix at a previous moment, and constructing a volume point set to obtain a predicted value of the state vector and a predicted value of the error covariance matrix at the current moment;
s2, calculating the volume point and the volume point after the propagation of the measurement equation again through the predicted state vector to obtain a predicted value of the observation vector, and recovering the signal based on the currently solved state vector and measurement vector to obtain an auto-covariance matrix and a cross-covariance matrix;
s3, taking the constellation points as reference bases for the recovery signals, calculating by using the recovery signals to obtain innovation vectors, and further updating the state vectors and the error covariance matrix;
and S4, calculating to obtain the mean decision error covariance to guide the self-adaptive updating of the tuning parameters Q and R values for the estimation of the next discrete moment. This means that the tuning parameters can adapt to different values in different scenes, and the adaptive performance of the cubature Kalman filtering algorithm is improved.
Specifically, the signals are simplified in the present invention as follows:
r(t)＝Js(t)+η(t) (1)
wherein s (t) is a transmission signal, J is a Jones matrix with a rotation of polarization state, η (t) is additive white Gaussian noise in an optical fiber link, and r (t) is a dual-polarization signal received after transmission.
The main formula based on the adaptive cubature kalman filter algorithm is as follows.
First, construct volume points and propagate volume points through the system function:
wherein,
d is an identity matrix.
After a volume point set is constructed, a state vector predicted value and an error covariance predicted value are calculated:
next, the measurement vector is predicted:
based on the presently solved state vector and measurement vector, the autocovariance matrix and the cross-covariance matrix can be solved:
calculating a Kalman gain matrix, and updating a state vector and an error covariance matrix:
K k ＝P xz,k|k-1 (P zz,k|k-1 ) -1 (13)
equations (2) to (6) represent the state prediction stage, equations (7) to (12) represent the measurement prediction stage, and equations (13) to (15) represent the state update stage. The volume Kalman filter is based on a third-order spherical surface radial volume criterion, a group of volume points are used for approximating the state mean value and the covariance of a nonlinear system with additional Gaussian noise, and then two parameters of polarization state rotation are tracked.
The present invention employs an adaptive update method based on mean decision error covariance to determine Q and R. In order to be able to better estimate the process noise and the measurement noise by simultaneously using the estimated value at the previous time and the predicted value at this time, the parameter Q is adjusted k And R k Expressed as:
Q k ＝α Q Q k-1 +(1-α Q )(K k E[d k d k T ]K k T ) (16)
R k ＝α R R k-1 +(1-α R )(E[d k d k T ]+H k P k H k T ) (17)
wherein E (#) represents the expectation value, α, over Q And alpha R Respectively representing forgetting factors of Q and R, and the decision error is the minimum difference d between the current predicted value and the ideal constellation point coordinate k ：
Mean decision error covariance E d k d k T ]Can be expressed as:
wherein, N is the length of the sliding window, and the selection of the length of the sliding window has certain influence on the performance and the speed of the Kalman filter.
The self-adaptive updating method based on the mean decision error covariance can overcome the filtering divergence phenomenon, but can cause larger error at the same time, needs to be slightly improved on the basis of the formulas (16) and (17) to adjust the optimal parameter Q k And R k Further expressed as:
wherein, beta is a set threshold value.
The scheme of the invention can compensate the polarization state rotation effect caused by extreme weather and the like in the optical fiber channel and track the high-speed polarization state rotation. Under different scenes, the tuning parameters can be self-adaptive to different values, and the self-adaptive performance of the cubature Kalman filtering algorithm is improved.
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following description is taken with reference to the accompanying drawings by taking a QPSK system as an example for transmission. The present embodiment is implemented on the premise of the design method, and designs a polarization rotation tracking and compensation method based on adaptive volumetric kalman filter, but is not limited to the transmission system.
Tracking each parameter in the QPSK signal polarization state rotation process by using an adaptive-volume Kalman filtering algorithm, wherein the detailed flow of the algorithm is shown in figure 1. In the method, the tracking and compensation of the polarization state rotation are performed through a cubature Kalman filter at the current moment. And then, the noise statistical characteristics are estimated on line through the measurement information, and the mean decision error covariance is obtained by utilizing the calculation of the recovery signal to guide the self-adaptive updating of the tuning parameters.
The invention mainly relates to a signal processing process of a receiving end of a polarization multiplexing system, and focuses on the balance of polarization state rotation. The principles of the present invention are explained in detail below.
(1) The polarization state rotation is balanced in the Jones space, and the balanced matrix selects a polarization state rotation matrix model with two parameters:
where a is the amplitude ratio angle and p is the phase difference angle.
(2) Setting the state vector to x by the relation given in the previous section k ＝[a p] T Wherein a and p are respectively 2 parameters of the polarization rotation matrix.
(3) And selecting the Jones space as a measurement space, wherein the decision error is the minimum difference value between the current predicted value and the ideal constellation point coordinate.
(4) And compensating the polarization state rotation by using a cubature Kalman filtering algorithm. For the nonlinear effects introduced by the polarization state rotation, a unitary matrix representation of the Cayley-Klein form in Jones space is used. And guiding the volume Kalman filter to update the next state parameter by iterative computation by adopting a third-order sphere-phase diameter volume rule.
(5) The tuning parameter initialization part adopts an adaptive updating method based on mean decision error covariance, and an algorithm framework is shown in figure 2. In the iterative process, the tuning parameters Q and R are adaptively updated in a mode of calculating the covariance of the average decision error. Estimating the noise statistical characteristics and simultaneously carrying out covariance matrix Q k And R k And performing real-time judgment. When the mean decision error covariance is larger than the threshold, it indicates that the current symbol kalman filter may be in an unstable state, and needs to be adjusted by updating Q and R. Conversely, when the mean decision error covariance is less than the threshold, indicating that the kalman filter is operating well, the current symbols Q and R stop updating.
Fig. 3 is an experimental model of coherent optical communication provided by the embodiment of the present invention, and a system simulation diagram of the experimental model on the OptiSystem platform is shown in fig. 4, and the specific flow is as follows:
firstly, a binary sequence with the sequence length of 65536bit is subjected to series-parallel conversion to obtain four paths of parallels, and two paths of signals are respectively input into an I/Q modulator with x and y polarized light as a carrier to obtain x and y polarized QPSK signals. The two signals are coupled through a polarization beam combiner.
The polarization multiplexed signal was then transmitted over an optical fiber link with a transmission distance of 160km and a center wavelength of 1550nm, and the fiber loss (0.2 dB/km) was compensated by an amplifier. At the receiving end, the optical signal is filtered by an optical band-pass filter with a bandwidth set to 60 GHz.
Subsequently, the coherent receiver receives the optical signal. The photoelectrically converted electrical signal is then subjected to a series of digital signal processing algorithms including resampling and normalization, orthogonalization, CD compensation, PMD compensation. Dynamic polarization rotation effects are added to the transmitted signal by digital signal off-line processing techniques. The rotation of the signal polarization state is tracked and compensated by adopting the adaptive cubature Kalman filtering algorithm.
And finally, judging and outputting the signal.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.
Claims (7)
1. A polarization state rotation tracking and compensation method based on adaptive volume Kalman filtering is characterized by comprising the following steps:
s1, calculating volume points and volume points after state equation propagation according to a state vector and an error covariance matrix at a previous moment, and constructing a volume point set to obtain a predicted value of the state vector and a predicted value of the error covariance matrix at the current moment;
s2, calculating the volume point and the volume point after the propagation of the measurement equation again through the predicted state vector to obtain a predicted value of the observation vector, and recovering the signal based on the currently solved state vector and measurement vector to obtain an auto-covariance matrix and a cross-covariance matrix;
s3, taking the constellation points as reference bases for the recovery signals, calculating by using the recovery signals to obtain innovation vectors, and further updating the state vectors and the error covariance matrix;
and S4, calculating to obtain the mean decision error covariance to guide the self-adaptive updating of the tuning parameters for the estimation of the next discrete moment.
2. The adaptive volumetric kalman filter-based polarization rotation tracking and compensation method according to claim 1, wherein in step S1, the received dual-polarization signal is represented as:
r(t)＝Js(t)+η(t) (1)
wherein s (t) is a transmitting signal, J is a Jones matrix with a rotating polarization state, and eta (t) is additive white Gaussian noise in an optical fiber link;
constructing a volume point chi and a volume point chi after propagation of a state equation * ：
Wherein, P k-1|k-1 Is an error covariance matrix, S k-1|k-1 Is P k-1|k-1 The lower triangular real matrix of (a) is,
is P k-1|k-1 The transpose of the lower triangular real matrix of (1),
is a predicted value of the state vector at the previous moment, xi i Is a volume point set, L is twice the dimension of the state variable, and D is an identity matrix.
3. The polarization state rotation tracking and compensation method based on adaptive cubature Kalman filter according to claim 1, characterized in that the calculation formulas of the predicted value of the state vector at the current moment and the predicted value of the error covariance matrix in step S1 are respectively:
wherein,
is the process noise covariance matrix estimate.
4. The polarization rotation tracking and compensation method based on adaptive cubature kalman filter according to claim 1, wherein the prediction process of the measurement vector in step S2 is:
z i,k|k+1 ＝h(χ i,k|k-1 ) (9)
wherein,
is a priori state estimate, P k|k-1 Is the covariance between the true and predicted values,
is a predicted value of the measurement vector.
5. According to the claimsThe method for calculating 1 based on polarization state rotation tracking and compensation of adaptive cubature Kalman filter is characterized in that in step S2, an autocovariance matrix P zz,k|k-1 And cross covariance matrix P xz,k|k-1 The calculation formulas of (A) and (B) are respectively as follows:
wherein, R is a measurement noise covariance matrix.
6. The adaptive volumetric kalman filter-based polarization state rotation tracking and compensation method according to claim 1, wherein step S3 updates the state vector and the error covariance matrix by calculating a kalman gain matrix and using the following equations:
K k ＝P xz,k|k-1 (P zz,k|k-1 ) -1 (13)
wherein K k Is a Kalman gain matrix, P zz,k|k-1 Is an autocovariance matrix, P xz,k|k-1 Is a cross covariance matrix.
7. The adaptive cubature kalman filter-based polarization state rotation tracking and compensating method according to claim 1, wherein the tuning parameters of step S4 include a process noise covariance matrix and a measurement noise covariance matrix, respectively expressed as:
wherein E (#) represents the expectation value, α, over Q And alpha R Respectively representing forgetting factors of Q and R, beta is a set threshold value, and the decision error is the minimum difference d between the current predicted value and the ideal constellation point coordinate k ：
The mean decision error covariance is expressed as:
wherein N is the length of the sliding window.
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