CN109687912B - Time domain cubature Kalman phase noise compensation method in coherent light OFDM system - Google Patents

Time domain cubature Kalman phase noise compensation method in coherent light OFDM system Download PDF

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CN109687912B
CN109687912B CN201910059644.0A CN201910059644A CN109687912B CN 109687912 B CN109687912 B CN 109687912B CN 201910059644 A CN201910059644 A CN 201910059644A CN 109687912 B CN109687912 B CN 109687912B
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CN109687912A (en
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袁建国
南蜀崇
刘书涵
辛雪琪
庞宇
林金朝
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Chongqing University of Post and Telecommunications
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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
    • 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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H04L25/0202—Channel estimation
    • H04L25/021—Estimation of channel covariance
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0224—Channel estimation using sounding signals
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    • H04L25/0264—Arrangements for coupling to transmission lines
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

The invention relates to a phase noise compensation scheme of a CO-OFDM system, in particular to a novel time domain volume Kalman phase noise compensation algorithm scheme. In the scheme, pilot frequency information is used for compensating CPE phase noise through an extended Kalman and linear interpolation algorithm, signals after the phase noise first-order compensation are subjected to pre-judgment, and then the signals after the pre-judgment are subjected to secondary symbol processing in a time domain. And combining the time domain signal after the secondary symbol processing, and performing a cubature Kalman phase noise compensation algorithm on the judged data in the time domain to realize the fine compensation of the ICI phase noise. And carrying out iterative operation on the data after fine compensation, thereby improving the compensation effect. Simulation analysis shows that when the phase noise line width is large, the novel time domain volume Kalman algorithm can effectively enhance the compensation effect on ICI phase noise, improve the tolerance of a CO-OFDM system to the laser line width and improve the performance of the system.

Description

Time domain cubature Kalman phase noise compensation method in coherent light OFDM system
Technical Field
The invention belongs to the technical field of coherent optical orthogonal frequency division multiplexing (CO-OFDM) system phase noise compensation, and relates to a novel time domain Kalman Filter (CKF) phase noise compensation method.
Background
A Coherent Optical Orthogonal Frequency Division Multiplexing (CO-OFDM) technique is a technique that combines an Orthogonal Frequency Division Multiplexing technique, an Optical communication system, and Coherent detection. The method has the advantages of high transmission rate, high Chromatic Dispersion (CD) and Polarization Mode Dispersion (PMD) resistance, high spectral efficiency, flexible bandwidth resource allocation and the like, and can effectively compensate various damages of a system through digital signal processing.
Phase noise can destroy the orthogonality among subcarriers and reduce the system performance, and is one of the key problems to be solved urgently in a coherent optical communication system. The factors causing phase noise are many, and the laser linewidth is the main factor causing phase noise. It is therefore necessary to find an effective phase noise compensation algorithm. The effect of phase noise in CO-OFDM systems has two main aspects: common Phase Error (CPE) caused by the zeroth order spectral component of the Phase noise and Inter-Carrier Interference (ICI) caused by the non-zeroth order spectral component. In order to effectively compensate the influence of phase noise on a CO-OFDM system, experts and scholars at home and abroad provide a plurality of solution algorithms aiming at the phase noise, such as an EKF phase noise compensation algorithm, a self-adaptive subspace phase noise compensation algorithm, an ICI self-elimination algorithm and the like. In the current solution algorithm, the EKF phase noise compensation algorithm is a promising technology, and the estimated value of the next sampling point is obtained through the phase noise value of the previous sampling point and the kalman gain, so that the compensation effect of the phase noise can be obviously improved, and the complexity is low. However, because the EKF algorithm approximates the true value by using a first-order taylor series expansion, a large linearization error is caused, and sometimes the result is unstable and even deviates far from the true value.
Disclosure of Invention
In view of the above, the present invention provides a novel time domain volumetric kalman phase noise compensation method.
In order to achieve the above purpose, the present invention provides the following technical algorithms:
(1) firstly, at a receiving end, after channel equalization, a signal is input to a phase noise modulation module. Time domain EKF filtering and linear interpolation are performed by using the pilot frequency to compensate CPE phase noise. Next, the secondary symbol is used to preprocess the ICI phase noise, and prepare for the CKF phase noise compensation algorithm. In the ICI phase noise preprocessing process, firstly, tentative judgment is carried out on a signal after first-order processing, the processed signal and a result of the tentative judgment are respectively divided into a plurality of sub-symbols with the same number in a time domain, the CPE in each sub-symbol is estimated according to an LS criterion to compensate the phase noise by comparing the corresponding sub-symbols in the two signals, and therefore the effect of improving the time domain resolution of the phase noise by dividing the sub-symbols in the time domain and further preprocessing the ICI phase noise is achieved.
Converting the OFDM symbol after first-order coarse compensation into the frequency domain
Figure GDA0003112567760000021
Making tentative judgment, and predicting the data sent by sending end, and its tentative judgment result is
Figure GDA0003112567760000022
Converting the first-order tentative decision result into a time-domain signal:
Figure GDA0003112567760000023
wherein Q (-) denotes the operation of a tentative decision, FHRepresenting the inverse fast fourier transform and deltaξ the decision error of the tentative decision. Dividing tentative decision results of the mth OFDM symbol into N in the time domainbAnd then performing secondary symbol processing, and estimating the average phase noise in the nth secondary symbol according to an LS criterion as follows:
Figure GDA0003112567760000024
in the formula, N is more than or equal to 1 and less than or equal to Nb,b＝N/NbIs the length of each secondary symbol. Obtained by calculation
Figure GDA0003112567760000025
For OFDM symbol after first-order compensation
Figure GDA0003112567760000026
To carry outTime domain secondary symbol processing:
Figure GDA0003112567760000027
(2) after the first-order phase noise compensation and preprocessing, the bit error rate of the system can be reduced to a lower level, but the phase noise has insufficient compensation degree for the ICI phase noise. The literature proposes to use the EKF to compensate the residual phase noise finely, but the EKF algorithm sometimes causes the result to be unstable or even deviate from the true value because of the large linearization error.
Therefore, the method adopts a high-density CKF phase noise compensation algorithm to filter the sub-carriers in the OFDM symbol one by one, obtains a phase noise estimation value of fine compensation, and improves the compensation degree of ICI phase noise. And performing CKF phase noise compensation algorithm on all sampling points in the OFDM symbol. And taking the residual ICI phase noise as a state equation and taking the time domain signal as an observation equation. The method includes the steps that signals processed by secondary symbols and signals pre-decided are brought into a CKF phase noise compensation algorithm, and equations (4) and (5) are a state equation and an observation equation of the CKF phase noise compensation algorithm.
Figure GDA0003112567760000028
Figure GDA0003112567760000029
In the formula, wm,k-1Is the state noise of the (k-1) th time domain sampling point of the mth OFDM symbol, and meets the requirement of wm,k-1N (0, Q), wherein
Figure GDA00031125677600000210
vm,kIs the observation noise of the kth sampling point of the mth OFDM symbol and satisfies vm,kN (0, R), wherein
Figure GDA0003112567760000031
Calculating basic volume sampling point according to third-order spherical radial volume criterion
Figure GDA0003112567760000032
And corresponding weight value
Figure GDA0003112567760000033
i 1,2, M represents the number of basic volume points, and the number of volume points is 2 times of the state dimension number by the third-order spherical radial volume criterion. [1]Is a complete set of fully symmetric points.
The CKF (Sub-symbol CKF, SCKF) phase noise compensation algorithm adopting the secondary symbol processing comprises the following specific steps:
step1 initializes the phase noise value and the CKF variance.
Step2 brings in the secondary symbol processed value and the predetermined value.
Step3 time update. And carrying out SVD on the variance of the last sampling point, and sequentially calculating a state equation volume point, a prediction state and a prediction variance.
Step4 measures the update. And carrying out SVD on the prediction variance, and sequentially calculating a measurement equation volume point, a measurement prediction value, an innovation variance and a covariance estimation value.
Step5 calculates the CKF gain.
Step6 carries in the phase noise value and the CKF variance, the value after the pre-judgment and the CKF gain at the last moment, and calculates the updating of the state value and the updating of the covariance value. Go to Step3 until all sample point signals are traversed. And carrying out iterative operation on the data after fine compensation, thereby improving the compensation effect.
(3) After the operations of the step (1) and the step (2), fusing a Linear Interpolation EKF (LI-EKF) algorithm for CPE phase noise compensation with an SCKF algorithm for ICI phase noise compensation to obtain a final LI-EKF-SCKF phase noise compensation algorithm, wherein the final compensated signal output is:
Figure GDA0003112567760000034
the invention has the beneficial effects that:
from theory and computer simulation, the algorithm improves the problem of low ICI phase noise tolerance in a CO-OFDM system to a certain extent, compared with the method only adopting an LI-SCPEC algorithm, the algorithm is remarkably improved in phase noise compensation performance, can have better error rate performance under the condition of large line width, and achieves good balance between calculation complexity and error rate. Therefore, in practical application, when the performance between the phase noise compensation effect and the system calculation complexity is considered, the algorithm has high utilization value and practical significance in the practical application of compensating the phase noise of the CO-OFDM system.
Drawings
In order to make the objects, technical algorithms and advantages of the present invention more apparent, the present invention is illustrated in the accompanying drawings in which:
FIG. 1 is a technical roadmap for the algorithm of the present invention;
FIG. 2 is a functional block diagram of an EKF algorithm;
FIG. 3 is a functional block diagram of the SCKF algorithm;
FIG. 4 is a schematic block diagram of the LI-EKF-SCKF algorithm of the present invention;
FIG. 5 is a constellation diagram of the LI-EKF-SCKF algorithm of the present invention;
FIG. 6 is a comparison of the error rate performance of the algorithm of the present invention with two other algorithms when the linewidth is 500 kHz;
fig. 7 is a comparison of the error rate performance of the algorithm of the present invention with that of the other two algorithms when the line width is 2 MHz.
Detailed Description
The following detailed description of the preferred embodiments and preferred simulation examples of the present invention will be described with reference to the accompanying drawings.
1. As explained in connection with fig. 2, the EKF algorithm is mostly used when compensating for fine phase noise. Although the EKF algorithm can compensate for phase noise, it has a large linearization error because it uses a first-order taylor series expansion to approximate the true value. Thus, there is some error in fine phase noise compensation, but it can be better applied when compensating CPE phase noise. Thus, the EKF using the time domain pilot at the previous stage is combined with the linear interpolation value to compensate the CPE phase noise. The method mainly includes inputting signals before and after pre-decision, and obtaining an estimated value of a next sampling point through a signal of a previous sampling point and Kalman gain.
The formula (1) and the formula (2) are used as an EKF state equation and an observation equation.
Figure GDA0003112567760000041
Figure GDA0003112567760000042
Wherein, m is 1,2OFDM。wm,k-1Is the k-1 sampling point state noise of the mth OFDM symbol and meets wm,k-1N (0, Q), wherein
Figure GDA0003112567760000043
vm,kIs the observation noise of the kth sampling point of the mth OFDM symbol and satisfies vm,kN (0, R), wherein
Figure GDA0003112567760000044
The first order result is obtained by using Taylor expansion to omit higher order terms for equations (1) and (2):
Figure GDA0003112567760000045
Φm,kis a state transition matrix in the EKF algorithm, Hm,kAre measurement matrices in the EKF algorithm, both of which are Jacobian matrices.
Let the number of subcarriers be N and the length of Cyclic Prefix (CP) in the system be NcpInserting N per time domain OFDM symbolpA pilot frequency with interval of Nspace＝(N+Ncp)/Np. Recording the phase of the p pilot signal of the mth OFDM symbolNoise is
Figure GDA0003112567760000046
The first pilot information is the front end of the OFDM symbol.
The EKF phase noise compensation algorithm comprises the following 5 steps:
1) setting initial conditions
Figure GDA0003112567760000051
Figure GDA0003112567760000052
Wherein the content of the first and second substances,
Figure GDA0003112567760000053
is an estimate of the phase noise of the first pilot signal of the first OFDM symbol, P1，1Is the covariance value of the pilot signal of the first OFDM symbol. Since the phase noise follows the wiener process with the mean value of 0, the initial condition is set to 0.
2) State prediction and covariance prediction
Figure GDA0003112567760000054
Pm,p|p-1＝Pm,p-1+Qm,p-1 (7)
Wherein the content of the first and second substances,
Figure GDA0003112567760000055
is the phase noise one-step predicted value of the P pilot subcarrier of the m-th OFDM symbol, Pm,p|p-1Is the covariance predictor for the p-th pilot subcarrier of the mth OFDM symbol,
Figure GDA0003112567760000056
is the phase difference between adjacent pilot frequencies, satisfies
Figure GDA0003112567760000057
4) EKF gain
Figure GDA0003112567760000058
4) Calculating measurement estimation value and residual sequence
Figure GDA0003112567760000059
Figure GDA00031125677600000510
Equation (9) is a measured estimation value of the p pilot subcarrier of the m-th OFDM symbol with the state-predicted phase noise being introduced, and equation (10) is a difference value between the estimation value and the true value, i.e., a residual.
5) State update and covariance update
Figure GDA00031125677600000511
Pm,p＝[I-Km,pHm,p]Pm,p|p-1 (12)
Equation (11) is the phase noise state value after updating the p-th pilot of the mth OFDM symbol, and equation (12) is the covariance value after updating the p-th pilot of the mth OFDM symbol. And then returning to the step2 until the phase noise estimation value at the pilot frequency is completely calculated.
After time domain EKF filtering, the phase noise estimation value of the pilot frequency is utilized to obtain global time domain estimation phase noise by linear interpolation
Figure GDA00031125677600000512
After obtaining the phase noise estimation value of the whole OFDM symbol, directly compensating the received signal in the time domain, then:
Figure GDA00031125677600000513
FIG. 2 is a schematic block diagram of an EKF algorithm.
2. Referring to fig. 3, for ICI phase noise compensation, the algorithm of the present invention uses the CKF phase noise compensation of secondary symbol processing to perform fine compensation on the residual phase noise. The CKF phase noise compensation is realized by using a third-order spherical radial rule, transmitting through a volume point and respectively updating in time and a measured value to obtain a final phase noise compensation value. By using
Figure GDA0003112567760000061
Represents the estimated value of the kth sampling point of the mth OFDM symbol after CPE phase noise compensation, M is the number of volume points,
Figure GDA0003112567760000062
is the weight corresponding to the volume point.
Converting the OFDM symbol after first-order coarse compensation into the frequency domain
Figure GDA0003112567760000063
Making tentative judgment, and predicting the data sent by sending end, and its tentative judgment result is
Figure GDA0003112567760000064
Converting the result of the first-order tentative decision into a time-domain signal:
Figure GDA0003112567760000065
wherein Q (-) denotes the operation of a tentative decision, FHRepresenting the inverse fast fourier transform and deltaξ the decision error of the tentative decision. The state equation and the measurement equation of the CKF phase noise compensation algorithm:
Figure GDA0003112567760000066
Figure GDA0003112567760000067
wherein, wm,k-1Is the state noise of the (k-1) th time domain sampling point of the mth OFDM symbol, and meets the requirement of wm,k-1N (0, Q), wherein
Figure GDA0003112567760000068
vm,kIs the observation noise of the kth sampling point of the mth OFDM symbol and satisfies vm,kN (0, R), wherein
Figure GDA0003112567760000069
The CKF phase noise compensation algorithm adopting the secondary symbol processing comprises the following specific steps:
1) secondary symbol processing
Dividing tentative decision results of the mth OFDM symbol into N in the time domainbAnd then performing secondary symbol processing, and estimating the average phase noise in the nth secondary symbol according to an LS criterion as follows:
Figure GDA00031125677600000610
in the formula, N is more than or equal to 1 and less than or equal to Nb,b＝N/NbIs the length of each secondary symbol. Obtained by calculation
Figure GDA00031125677600000611
For OFDM symbol after first-order compensation
Figure GDA00031125677600000612
And (3) performing time domain secondary symbol processing:
Figure GDA00031125677600000613
2) initializing phase noise values and CKF variances
Figure GDA00031125677600000614
Figure GDA00031125677600000615
Wherein the content of the first and second substances,
Figure GDA00031125677600000616
is an estimate of the phase noise, P, of the first sampled signal of the first OFDM symbol1，1Is the covariance value of the first OFDM symbol sample signal. Since the phase noise follows the wiener process with the mean value of 0, the initial condition is set to 0.
3) Phase noise update
And (3) carrying in the phase noise and covariance estimated value of the previous sampling point, carrying out SVD (singular value decomposition) and obtaining a corresponding volume point and a volume point of a state equation:
[Um,k-1,Sm,k-1,Vm,k-1]＝svd(Pm,k-1) (21)
Figure GDA0003112567760000071
Φm,k|k-1(i)＝Φm,k-1(i) (23)
and calculating a prediction state and a prediction variance according to the obtained state equation volume points:
Figure GDA0003112567760000072
Figure GDA0003112567760000073
4) measurement update
According to the prediction variance obtained in the phase noise updating and the time domain signal value after the pre-judgment, SVD decomposition is carried out and corresponding volume points and volume points of a measurement equation are obtained:
[Um,k|k-1,Sm,k-1,Vm,k-1]＝svd(Pm,k|k-1) (26)
Figure GDA0003112567760000074
Figure GDA0003112567760000075
calculating a measurement predicted value, an innovation variance and a covariance estimated value according to the obtained measurement equation volume points:
Figure GDA0003112567760000076
Figure GDA0003112567760000077
Figure GDA0003112567760000078
5) calculating a gain matrix, and updating a phase noise value and a covariance value according to the time domain signal after the secondary symbol processing:
Figure GDA0003112567760000079
Figure GDA00031125677600000710
Figure GDA00031125677600000711
equation (33) is the phase noise state value updated at the kth sampling point of the mth OFDM symbol, and equation (34) is the covariance value updated at the kth sampling point of the mth OFDM symbol. And then returning to the step2 until the phase noise estimation values of all the sampling points are completely calculated. The functional block diagram of the SCKF algorithm is shown in FIG. 3.
3. The invention provides a novel time domain cubature Kalman phase noise compensation algorithm, and a basic principle block diagram of the algorithm is shown in FIG. 4. As can be seen from FIG. 4, the specific implementation process of the LI-EKF-SCKF algorithm is as follows:
(1) firstly, at a receiving end, after channel equalization, a signal is input to a phase noise modulation module. Time domain EKF filtering and linear interpolation are performed by using the pilot frequency to compensate CPE phase noise. Next, the secondary symbol is used to preprocess the ICI phase noise, and prepare for the CKF phase noise compensation algorithm. In the ICI phase noise preprocessing process, firstly, tentative judgment is carried out on a signal after first-order processing, the processed signal and a result of the tentative judgment are respectively divided into a plurality of sub-symbols with the same number in a time domain, the CPE in each sub-symbol is estimated according to an LS criterion to compensate the phase noise by comparing the corresponding sub-symbols in the two signals, and therefore the effect of improving the time domain resolution of the phase noise by dividing the sub-symbols in the time domain and further preprocessing the ICI phase noise is achieved.
Converting the OFDM symbol after first-order coarse compensation into the frequency domain
Figure GDA0003112567760000081
Making tentative judgment, and predicting the data sent by sending end, and its tentative judgment result is
Figure GDA0003112567760000082
Converting the result of the first-order tentative decision into a time-domain signal:
Figure GDA0003112567760000083
wherein Q (-) denotes the operation of a tentative decision, FHRepresenting the inverse fast Fourier transformThe transformation, Δ ξ, represents the decision error of a tentative decision. Dividing tentative decision results of the mth OFDM symbol into N in the time domainbAnd then performing secondary symbol processing, and estimating the average phase noise in the nth secondary symbol according to an LS criterion as follows:
Figure GDA0003112567760000084
in the formula, N is more than or equal to 1 and less than or equal to Nb,b＝N/NbIs the length of each secondary symbol. Obtained by calculation
Figure GDA0003112567760000085
For OFDM symbol after first-order compensation
Figure GDA0003112567760000086
And (3) performing time domain secondary symbol processing:
Figure GDA0003112567760000087
(2) after the first-order phase noise compensation and preprocessing, the bit error rate of the system can be reduced to a lower level, but the ICI phase noise is not compensated enough in the phase noise. The literature proposes to use the EKF to compensate the residual phase noise finely, but the EKF algorithm sometimes causes the result to be unstable or even deviate from the true value because of the large linearization error.
Therefore, the method adopts a high-density CKF phase noise compensation algorithm to filter the sub-carriers in the OFDM symbol one by one to obtain a phase noise estimation value with fine compensation, so that the compensation degree of ICI phase noise is improved. And performing CKF phase noise compensation algorithm on all sampling points in the OFDM symbol. And taking the residual ICI phase noise as a state equation and taking the time domain signal as an observation equation. The signal after secondary symbol processing and the signal after pre-judgment are brought into a CKF phase noise compensation algorithm, and a formula (4) and a formula (5) are used as a state equation and an observation equation of the CKF phase noise compensation algorithm.
Figure GDA0003112567760000088
Figure GDA0003112567760000089
In the formula, wm,k-1Is the state noise of the (k-1) th time domain sampling point of the mth OFDM symbol, and meets the requirement of wm,k-1N (0, Q), wherein
Figure GDA0003112567760000091
vm,kIs the observation noise of the kth sampling point of the mth OFDM symbol and satisfies vm,kN (0, R), wherein
Figure GDA0003112567760000092
Calculating basic volume sampling point according to third-order spherical radial volume criterion
Figure GDA0003112567760000093
And corresponding weight value
Figure GDA0003112567760000094
Figure GDA0003112567760000094
Figure GDA0003112567760000094
1,2, M represents the number of basic volume points, which is 2 times the state dimension by the third order sphere radial volume criterion, [1 ═ M]Is a complete set of fully symmetric points.
The CKF phase noise compensation algorithm adopting the secondary symbol processing comprises the following specific steps:
step1 initializes the phase noise value and the CKF variance.
Step2 brings in the secondary symbol processed value and the predetermined value.
Step3 time update. And carrying out SVD on the variance of the last sampling point, and sequentially calculating a state equation volume point, a prediction state and a prediction variance.
Step4 measures the update. And carrying out SVD on the prediction variance, and sequentially calculating a measurement equation volume point, a measurement prediction value, an innovation variance and a covariance estimation value.
Step5 calculates the CKF gain.
Step6 carries in the phase noise value and the CKF variance, the value after the pre-judgment and the CKF gain at the last moment, and calculates the updating of the state value and the updating of the covariance value. Go to Step3 until all sample point signals are traversed. And carrying out iterative operation on the data after fine compensation, thereby improving the compensation effect. FIG. 4 is a schematic block diagram of the LI-EKF-SCKF algorithm.
(3) After the operation of the step (2) and the LI-EKF-SCKF algorithm, the final compensated signal output is as follows:
Figure GDA0003112567760000095
the implementation steps can be obtained, in the step (1), firstly, pilot frequency information is utilized, an extended Kalman and linear interpolation algorithm is adopted to compensate CPE phase noise, signals after the phase noise first-order compensation are subjected to pre-decision, and then, sub-symbol processing is carried out on the signals after the pre-decision in a time domain. In the step (2), the time domain signal after the secondary symbol processing is combined, and the volume Kalman is performed on the judged data in the time domain to realize the fine compensation of the ICI phase noise. And carrying out iterative operation on the data after fine compensation, thereby improving the compensation effect. And (4) finally compensating the phase noise in the time domain through the step (3) to obtain a time domain compensated signal.
4. In order to further illustrate that the algorithm of the present invention has a significant improvement in the compensation performance for the phase noise to some extent, an experiment is performed below with reference to fig. 5, fig. 6, and fig. 7.
Experiment:
TABLE 1 parameter settings used in simulation
Figure GDA0003112567760000096
Figure GDA0003112567760000101
The phase noise compensation performance realized by the algorithm of the invention after passing through the CO-OFDM system is simulated in the experiment, as shown in fig. 5, and the simulation parameters used are shown in table 1.
Fig. 5 is a constellation diagram after the CKF phase noise compensation algorithm proposed in the present patent when the signal-to-noise ratio is 20dB and the laser linewidth is 2 MHz. The first-order algorithm for compensating CPE phase noise is marked as 'LI-EKF', the algorithm for finely compensating ICI phase noise in the patent is marked as 'LI-EKF-SCKF', and the algorithm after one iteration is marked as 'LI-EKF-SCKF-ite'. As can be seen from fig. 5, although the constellation diagram of the first-order phase noise compensation algorithm LI-EKF is basically compensated for the common phase noise, points on the constellation diagram are more divergent and insufficient in compensating for the ICI phase noise. Points on a constellation diagram passing through the final LI-EKF-SCKF phase noise compensation algorithm are more concentrated, and ICI phase noise is compensated to a certain extent. The compensation effect of the LI-EKF-SCKF-ite algorithm after one iteration is slightly enhanced.
FIG. 6 is a plot of the bit error rate for a laser line width of 500kHz and a signal-to-noise ratio of 0 to 20 dB. The comparison algorithm comprises a combination of Linear interpolation and a secondary symbol processing algorithm (the patent is marked as 'LI-SCPEC') and a combination algorithm adopting Linear interpolation and Kalman filtering (the patent is marked as 'Linear-LI-EKF'). At a bit error rate of 10-5In time, the gain of the LI-EKF-SCKF is improved by 1.6dB compared with the gain of an LI-EKF algorithm only using a first-order compensation CPE phase noise, and the performance of the algorithm can be improved only by a small amount by the LI-EKF-SCKF-ite algorithm of one iteration. The LI-SCPEC algorithm exhibits an error floor around 16 dB. The LI-EKF-SCKF-ite algorithm is improved by 0.1dB compared with the Linear-LI-EKF algorithm.
FIG. 7 is a plot of the bit error rate for a laser line width of 2MHz with a signal-to-noise ratio of 0 to 20 dB. Wherein the comparison algorithm is a combination of linear interpolation and sub-symbol processing algorithm. At a bit error rate of 10-5In the process, the gain of the LI-EKF-SCKF is improved by 4.5dB compared with the gain of an LI-EKF algorithm only using the first-order compensation CPE phase noise, the final compensation gain is improved by 0.5dB compared with the algorithm gain after the secondary symbol processing, and the performance of the algorithm can be improved by a small amount only by the algorithm of one iteration. The LI-SCPEC algorithm exhibits an error floor around 14 dB. In the wrong placeCode rate of 10 BER-4In time, the LI-EKF-SCKF algorithm of the patent is improved by 1.5dB compared with the Linear-LI-EKF algorithm. And the Linear-LI-EKF algorithm also has error floor around 16 dB.
In conclusion, the invention can effectively compensate the influence of phase noise on signals in a CO-OFDM system, can effectively enhance the compensation effect on ICI phase noise when the line width of the phase noise is larger, improves the tolerance of the CO-OFDM system on the line width of a laser and effectively improves the performance of the system.
Finally, it should be noted that the above preferred simulation examples are only intended to illustrate the technical algorithms of the present invention and are not limiting, and although the present invention has been described in detail by the above preferred simulation examples, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the present invention as defined by the appended claims.

Claims (1)

1. A time domain cubature Kalman phase noise compensation method in a coherent light OFDM system is characterized in that: in the method, firstly, by using pilot frequency information, Common Phase noise (CPE) is compensated through Extended Kalman Filter (EKF) and linear interpolation algorithm, including the following 5 steps;
1) setting initial conditions
Figure FDA0003112567750000011
Figure FDA0003112567750000012
Wherein the content of the first and second substances,
Figure FDA0003112567750000013
is an estimate of the phase noise of the first pilot signal of the first OFDM symbol, P1，1Is the covariance value of the pilot signal of the first OFDM symbol, all with the initial condition of0；
2) State prediction and covariance prediction
Figure FDA0003112567750000014
Pm，p|p-1＝Pm，p-1+Qm，p-1 (7)
Wherein the content of the first and second substances,
Figure FDA0003112567750000015
is the phase noise one-step predicted value of the P pilot subcarrier of the m-th OFDM symbol, Pm，p|p-1Is the covariance predictor for the p-th pilot subcarrier of the mth OFDM symbol,
Figure FDA0003112567750000016
is the phase difference between adjacent pilot frequencies, satisfies
Figure FDA0003112567750000017
3) EKF gain
Figure FDA0003112567750000018
4) Calculating measurement estimation value and residual sequence
Figure FDA0003112567750000019
Figure FDA00031125677500000110
Equation (9) is the measured estimated value of the p pilot subcarrier of the m-th OFDM symbol with the state-predicted phase noise, and equation (10) is the difference between the estimated value and the true value, i.e. the residual error;
5) state update and covariance update
Figure FDA00031125677500000111
Pm，p＝[I-Km，pHm，p]Pm，p|p-1 (12)
Equation (11) is the updated phase noise state value of the p pilot of the mth OFDM symbol, and equation (12) is the updated covariance value of the p pilot of the mth OFDM symbol; then returning to the step2 until all phase noise estimation values at the pilot frequency are calculated; after time domain EKF filtering, the phase noise estimation value of the pilot frequency is utilized to obtain global time domain estimation phase noise by linear interpolation
Figure FDA0003112567750000021
After obtaining the phase noise estimation value of the whole OFDM symbol, directly compensating the received signal in the time domain, then:
Figure FDA0003112567750000022
secondly, pre-judging the signal after the first-order compensation of the phase noise, and then carrying out secondary symbol processing on the pre-judged signal in a time domain; thirdly, combining the time domain signal after the secondary symbol processing, performing a CKF phase noise compensation algorithm on the judged data in the time domain to realize the fine compensation of Inter-Carrier Interference (ICI) phase noise; the method specifically comprises the following steps:
(1) firstly, at a receiving end, after channel equalization, inputting a signal to a phase noise modulation module, and utilizing a pilot frequency to perform time domain EKF filtering and an LI algorithm to compensate CPE phase noise, wherein a first-order algorithm for compensating the CPE phase noise is recorded as an LI-EKF algorithm; preprocessing ICI phase noise by using a secondary symbol to prepare for a CKF phase noise compensation algorithm; in the ICI phase noise preprocessing process, firstly, tentatively judging the signal after the first-order processing, respectively dividing the processed signal and the result of the tentative judgment into a plurality of sub-symbols with the same number in a time domain, comparing the corresponding sub-symbols in the two signals, and estimating CPE in each sub-symbol according to an LS criterion to compensate the phase noise, thereby achieving the effect of dividing the sub-symbols in the time domain to improve the time domain resolution of the phase noise and further preprocessing the ICI phase noise;
converting the OFDM symbol after first-order coarse compensation into the frequency domain
Figure FDA0003112567750000023
Making tentative judgment, and predicting the data sent by sending end, and its tentative judgment result is
Figure FDA0003112567750000024
Converting the result of the first-order tentative decision into a time-domain signal:
Figure FDA0003112567750000025
wherein Q (-) denotes the operation of a tentative decision, FHRepresents the inverse fast fourier transform, Δ ξ represents the decision error of the tentative decision; dividing tentative decision results of the mth OFDM symbol into N in the time domainbAnd then performing secondary symbol processing, and estimating the average phase noise in the nth secondary symbol according to an LS criterion as follows:
Figure FDA0003112567750000026
in the formula, N is more than or equal to 1 and less than or equal to Nb，b＝N/NbIs the length of each secondary symbol; obtained by calculation
Figure FDA0003112567750000027
For OFDM symbol after first-order compensation
Figure FDA0003112567750000028
And (3) performing time domain secondary symbol processing:
Figure FDA0003112567750000029
(2) after first-order phase noise compensation and preprocessing, the bit error rate of the system can be reduced to a lower level, but the compensation degree of the phase noise to the ICI phase noise is not enough; the method adopts a high-density CKF phase noise compensation algorithm to filter subcarriers in an OFDM symbol one by one, obtains a phase noise estimation value of fine compensation, and improves the compensation degree of ICI phase noise; performing a CKF phase noise compensation algorithm on all sampling points in the OFDM symbol; taking the residual ICI phase noise as a state equation and taking a time domain signal as an observation equation; the signals after the secondary symbol processing and the signals after the pre-judgment are brought into a CKF phase noise compensation algorithm, and the formula (4) and the formula (5) are used as a state equation and an observation equation of the CKF phase noise compensation algorithm;
Figure FDA0003112567750000031
Figure FDA0003112567750000032
in the formula, wm，k-1Is the state noise of the (k-1) th time domain sampling point of the mth OFDM symbol, and meets the requirement of wm，k-1N (0, Q), wherein
Figure FDA0003112567750000033
vm，kIs the observation noise of the kth sampling point of the mth OFDM symbol and satisfies vm，kN (0, R), wherein
Figure FDA0003112567750000034
Calculating the basic volume sampling according to the third-order spherical radial volume criterionSampling point
Figure FDA0003112567750000035
And corresponding weight value
Figure FDA0003112567750000036
1,2, M represents the number of basic volume points, which is 2 times the state dimension by the third order sphere radial volume criterion, [1 ═ M]Is a complete set of fully symmetric points;
the CKF (Sub-symbol CKF, SCKF) phase noise compensation algorithm adopting the secondary symbol processing comprises the following specific steps:
step1 initializes the phase noise value and the CKF variance;
step2, substituting the value after secondary symbol processing and the value after pre-judgment;
step3 time updating; carrying out SVD on the variance of the last sampling point, and sequentially calculating a state equation volume point, a prediction state and a prediction variance;
step4 measurement update; carrying out SVD decomposition on the prediction variance, and sequentially calculating a measurement equation volume point, a measurement prediction value, an innovation variance and a covariance estimation value;
step5 calculating the CKF gain;
step6, substituting the phase noise value and the CKF variance, the value after the pre-judgment and the CKF gain at the last moment, and calculating the updating of the state value and the updating of the covariance value; turning to Step3 until all sampling point signals are traversed; performing iterative operation on the data after fine compensation, thereby improving the compensation effect;
(3) through the operations of the steps (1) and (2), fusing a linear interpolation EKF (Linear interpolation EKF, LI-EKF) algorithm of CPE phase noise compensation with an SCKF algorithm of ICI phase noise compensation to obtain a final LI-EKF-SCKF phase noise compensation algorithm, wherein the final compensated signal output is as follows:
Figure FDA0003112567750000037
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