A method and apparatus for carrier phase recovery in an optical fiber communication system
By combining Kalman filtering and power iteration, the carrier phase recovery method solves the problems of accuracy and complexity of traditional algorithms at low signal-to-noise ratios, and achieves efficient estimation of carrier phase noise in optical fiber communication systems.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIJING UNIV OF POSTS & TELECOMM
- Filing Date
- 2022-11-28
- Publication Date
- 2026-05-29
AI Technical Summary
Traditional carrier phase recovery algorithms are easily affected by low signal-to-noise ratios, cannot accurately estimate and track phase noise, and have high computational complexity.
A carrier phase recovery method combining Kalman filtering and power iteration is adopted. Through prediction, pre-rotation, residual estimation and update stages, the carrier phase noise is accurately estimated and the computational complexity is reduced.
The accuracy and robustness of carrier phase recovery are improved under low signal-to-noise ratio conditions, while reducing computational complexity.
Smart Images
Figure CN116527466B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of optical communication, and in particular to optical fiber communication systems with significant carrier phase noise, such as non-homogeneous light sources at the transmitting and receiving ends and large linewidths. Background Technology
[0002] Driven by the explosive growth of internet services, high-speed, high-capacity, high-spectral-efficiency, and long-distance signal transmission have become crucial goals for optical fiber communication. In optical fiber communication systems, the phase of the transmitted signal contains noise due to the influence of laser linewidth, leading to bit errors in the final signal and severely impacting communication quality. Therefore, research on carrier phase recovery algorithms is necessary. Furthermore, the introduction of advanced coding, modulation, and signal processing algorithms has enabled optical fiber communication systems to achieve transmission at lower signal-to-noise ratios (SNRs). Consequently, carrier phase recovery algorithms with high SNR tolerance are a research hotspot in this field.
[0003] Blind Phase Search (BPS) algorithms are favored for their superior carrier phase tracking capabilities, but their high complexity and increased false alarm rates at low signal-to-noise ratios (SNRs) reduce their carrier phase tracking performance. Kalman filtering-based algorithms, on the other hand, offer fast parameter estimation and tracking speed with high accuracy. They have been proposed and proven to achieve carrier phase estimation, addressing the high complexity issue of BPS. However, because these algorithms employ maximum likelihood estimation and obtain measurement states through decision-driven operations, their performance is also affected at low SNRs. Therefore, carrier phase recovery algorithms with low complexity and good performance even at low SNRs require further research.
[0004] To address the aforementioned problems, this invention proposes a carrier phase recovery method for optical fiber communication systems. This method employs Kalman filtering and power iteration, retaining the fast and accurate parameter estimation capabilities of Kalman filtering while utilizing power iteration for residual estimation, thereby further enhancing the carrier phase recovery performance under low signal-to-noise ratio conditions. Summary of the Invention
[0005] To address the shortcomings of existing technologies, the present invention aims to provide a carrier phase recovery method for optical fiber communication systems, which solves the problems that traditional carrier phase recovery is easily affected by low signal-to-noise ratio, cannot accurately estimate and track phase noise, and has high computational complexity.
[0006] To achieve the above objectives, this invention provides a carrier phase recovery method based on Kalman filtering and power iteration, comprising the following steps:
[0007] In the prediction phase, Kalman filtering is used at the receiver end of the optical fiber communication system to predict the carrier phase noise of the received signal.
[0008] In the pre-rotation stage, the received signal is pre-rotated according to the predicted carrier phase noise, and the carrier phase noise is pre-compensated.
[0009] In the residual estimation stage of the power iteration method, the residual error of the received signal after pre-rotation is estimated by the power iteration method, which is used to extract the error between the carrier phase noise predicted by the Kalman filter and the actual carrier phase noise received by the received signal.
[0010] In the update phase, the state variables of the Kalman filter in the prediction are updated based on the error between the extracted predicted phase noise and the actual phase noise, thereby achieving carrier phase recovery.
[0011] At the receiver of an optical fiber communication system, a Kalman filter is used to predict the mean and covariance of the carrier phase noise. After digital signal processing algorithms such as channel equalization, clock recovery, dispersion nonlinearity compensation, and frequency offset compensation, the received signal can be simplified to:
[0012] r(n)=s(n)e jθ(n) +ξ(n) (1)
[0013] Where r, s, θ and ξ represent the received signal, the transmitted signal, the carrier phase noise and the Gaussian white noise, respectively, and n represents the nth time series.
[0014] In the prediction phase, Kalman filtering is used to predict the carrier phase noise of the received signal. The state equation and prediction equation based on the carrier phase recovery using the Kalman filter are expressed as follows:
[0015] S n =S n-1 +w n (2)
[0016] S n =AS n-1 (3)
[0017] Where S n Let S be the state parameter. n =θ, here used as a state parameter in the carrier phase recovery problem, the carrier phase noise estimated by the Kalman filter, w n Let A represent process noise, and let A represent the state transition matrix, which is the identity matrix.
[0018] In the pre-rotation stage, the received signal is pre-rotated based on the predicted carrier phase noise, and the corresponding equation is expressed as:
[0019] U n =H n r(n)+v n (4)
[0020] Among them Un To measure the output of the equation, H n The measurement matrix of the measurement equation is then represented as:
[0021] H n =e -jθ(n) (5)
[0022] That is, the received signal r(n) is pre-rotated by an angle equal to the estimated carrier phase noise, and the output U of the measurement equation is... n As input to the mean-reduction stage in the power-law iterative residual estimation stage.
[0023] In the residual estimation stage, the residual error of the received signal after pre-rotation is estimated using the power iteration method. The error between the predicted carrier phase noise and the actual received carrier phase noise is extracted from the residual error, specifically including:
[0024] Mean removal stage: Calculate the mean of the pre-rotated received signal and subtract the mean from the pre-rotated received signal. The purpose is to make the mean 0 and eliminate the influence of possible bias on the accuracy of residual error extraction. The formula is as follows:
[0025]
[0026] Among them U n The output signal of the measurement equation is N, where N is the number of symbols in the output signal, and ∑(.) represents the summation operation.
[0027] Squared phase: For the mean-removed signal U n Square the values, then take the real and imaginary parts respectively, and use them as inputs for the covariance calculation stage;
[0028] Covariance calculation stage: The input signal after squaring is multiplied by its transpose matrix to calculate the covariance matrix of the input signal;
[0029] Power iteration stage: The calculated covariance is iteratively multiplied with the initial value of the residual error. After multiple iterations, an accurate estimate of the residual error of the pre-rotated received signal is obtained. Phase extraction stage: From the accurate estimate of the residual error obtained in the power iteration stage, the phase is extracted from the residual error by taking the phase angle. The purpose is to extract the error Ne between the carrier phase noise predicted by the Kalman filter and the carrier phase noise actually received by the received signal.
[0030] Carrier phase recovery mainly relies on the following formula:
[0031]
[0032]
[0033]
[0034] Formulas (7) to (9) are used to calculate the prior covariance of the carrier phase noise. The gain K of the Kalman filter and the posterior covariance P of the carrier phase noise. n Among them, M n Let R be the Jacobian matrix of the measurement matrix, where R represents the measurement error and Q represents the process error.
[0035] The formula for updating the state based on residual phase noise is:
[0036] S n+1 =S n +KNe (10)
[0037] Where K represents the Kalman gain, and Ne represents the residual phase noise extracted by the power iteration method in the residual estimation stage. After updating, the state variables are used as an accurate estimate of the actual carrier phase noise received by the received signal, and carrier phase recovery is performed on the received signal. The updated state parameters are then used as the initial values for the next state variable update.
[0038] Furthermore, embodiments of the present invention also disclose a carrier phase recovery device for an optical fiber communication system, comprising:
[0039] The state parameter prediction module, connected to the state parameter update module and the complex signal rotation module, is used to receive the state parameters output by the state parameter update module and predict the next state parameters.
[0040] The complex signal rotation module, connected to the state parameter update module and the power iteration residual estimation module, is used to pre-rotate the received signal based on the carrier phase noise predicted by the prediction module, and serve as the input to the power iteration residual estimation module.
[0041] The power iteration residual estimation module, connected to the complex signal rotation module and the state parameter update module, is used to estimate the residual error of the received signal after pre-rotation and extract the error between the predicted phase noise and the actual phase noise from the residual error.
[0042] The state parameter update module, connected to the phase recovery module and the state parameter prediction module, is used to update the state parameters based on the error output by the residual estimation module and output an accurate estimate of the carrier phase noise.
[0043] The phase recovery module, connected to the state parameter update module, is used to recover the carrier phase of the signal based on the accurate phase noise output by the update module.
[0044] The beneficial effects of this invention are that, through the above scheme, accurate estimation of carrier phase noise in optical fiber communication systems can be achieved, and the robustness of the algorithm is guaranteed under low signal-to-noise ratio conditions. Compared with the traditional blind phase search method, it has higher accuracy in phase noise estimation under low signal-to-noise ratio conditions and lower computational complexity. Attached Figure Description
[0045] Figure 1 This is a flowchart of a carrier phase recovery method for an optical fiber communication system.
[0046] Figure 2 This is a flowchart of the algorithm for the power-law iterative residual estimation stage in a carrier phase recovery method for an optical fiber communication system in Example 1.
[0047] Figure 3 This is the carrier phase recovery device for optical fiber communication systems in Example 1. Detailed Implementation
[0048] Referring to the accompanying drawings, the foregoing and other features of the embodiments of the present invention will become apparent from the following description. These embodiments are merely exemplary and not intended to limit the invention. To enable those skilled in the art to readily understand the principles and implementation methods of the present invention, the embodiments of the present invention are described below. Figure 1 The working principle of this invention will be explained using the clock recovery loop shown as an example.
[0049] The specific embodiments of the present invention will now be described with reference to the accompanying drawings.
[0050] Example 1:
[0051] In an optical fiber communication system, the receiver receives a probabilistically shaped 16QAM signal transmitted via a link, which then passes through the signal processing module of the coherent optical communication system. After undergoing digital signal processing algorithms such as channel equalization, clock recovery, dispersion nonlinearity compensation, and frequency offset compensation, the signal is processed as follows: Figure 1 The carrier phase recovery method for the optical fiber communication system shown has the following device composition: Figure 3 As shown.
[0052] After digital signal processing algorithms such as channel equalization, clock recovery, dispersion nonlinearity compensation, and frequency offset compensation, the received probability-shaped 16QAM signal can be simplified as follows:
[0053] r(n)=s(n)e jθ(n) +ξ(n) (1)
[0054] Where r, s, θ and ξ represent the received signal, the transmitted signal, the carrier phase noise and the Gaussian white noise, respectively, and n represents the nth time series.
[0055] Subsequently, a carrier phase recovery algorithm based on Kalman filtering and power iteration is used to perform carrier phase recovery on probabilistic shaped 16QAM, including:
[0056] In the prediction phase, Kalman filtering is used to predict the carrier phase noise of the received signal;
[0057] In the pre-rotation stage, the received signal is pre-rotated based on the predicted carrier phase noise, and the pre-rotated 16QAM signal U is output. n As input to the mean-reduction stage in the power-law iterative residual estimation stage.
[0058] like Figure 2 As shown, in the residual estimation stage, the residual error of the received signal after pre-rotation is estimated using the power iteration method. The error between the predicted carrier phase noise and the actual received carrier phase noise is extracted from the residual error, specifically including:
[0059] Mean removal stage: Calculate the mean of the pre-rotated received 16QAM signal, and subtract the mean from the pre-rotated received signal to set the mean to 0, thereby eliminating the influence of possible bias on the accuracy of residual error extraction.
[0060] Squaring stage: The mean-removed 16QAM signal is squared, and then the real and imaginary parts are taken separately as inputs for the covariance calculation stage;
[0061] Covariance calculation stage: Multiply the output after squaring by its transpose matrix to obtain the covariance matrix of the input signal;
[0062] Power iteration stage: The calculated covariance is iteratively multiplied with the initial value of the residual error. After multiple iterations, an accurate estimate of the residual error of the pre-rotated received signal is obtained. Phase extraction stage: From the accurate estimate of the residual error obtained in the power iteration stage, the phase is extracted from the residual error by taking the phase angle. The error between the carrier phase noise predicted by the Kalman filter and the carrier phase noise actually received by the received signal is extracted.
[0063] The residual phase noise extracted using the power iteration method in the residual estimation stage is updated, and the state variables are used as an accurate estimate of the actual carrier phase noise received by the received signal to perform carrier phase recovery. The updated state parameters are then used as the initial values for the next state variable update.
Claims
1. A carrier phase recovery method for an optical fiber communication system, characterized in that, Based on Kalman filtering and power iteration, the implementation includes the following steps: In the prediction phase, Kalman filtering is used at the receiver of the optical fiber communication system to predict the carrier phase noise of the received signal. In the pre-rotation stage, the received signal is pre-rotated based on the carrier phase noise predicted by the Kalman filter, and the carrier phase noise is pre-compensated. The residual estimation stage of the power iteration method specifically includes: Mean removal stage: Calculate the mean of the pre-rotated received signal and subtract the mean from the pre-rotated received signal. The purpose is to make the mean 0 and eliminate the influence of the existing bias on the accuracy of residual error extraction. Squaring stage: Squaring the mean-removed signal and then taking the real and imaginary parts respectively, which are used as inputs for the covariance calculation stage; Covariance calculation stage: The input signal after squaring is multiplied by its transpose matrix to calculate the covariance matrix of the input signal; Power iteration stage: The calculated covariance is iteratively multiplied with the set initial value of residual error. After multiple iterations, an accurate estimate of the residual error of the received signal after pre-rotation is obtained. Phase extraction stage: From the accurate estimate of the residual error obtained in the power iteration stage, the phase is extracted from the residual error by taking the phase angle. The purpose is to extract the error between the carrier phase noise predicted by the Kalman filter and the actual carrier phase noise of the received signal. In the update phase, the Kalman filter state parameters in the prediction phase are updated based on the error between the carrier phase noise predicted by the extracted Kalman filter and the actual carrier phase noise of the received signal, thereby achieving carrier phase recovery.
2. The carrier phase recovery method for an optical fiber communication system according to claim 1, characterized in that... The update phase includes: taking the error between the carrier phase noise predicted by the Kalman filter obtained in the power iteration residual estimation phase and the actual carrier phase noise of the received signal as the measurement error required for the recursive state parameters of the Kalman filter, and using it together with the Kalman filter gain to guide the update of the filter's state parameters.
3. A carrier phase recovery device for an optical fiber communication system, the device being applied to the carrier phase recovery method for an optical fiber communication system as described in claim 1, comprising: The state parameter prediction module, connected to the state parameter update module and the complex signal rotation module, is used to receive the state parameters output by the state parameter update module and predict the next state parameters. The complex signal rotation module, connected to the state parameter update module and the power iteration residual estimation module, is used to pre-rotate the received signal based on the carrier phase noise predicted by the prediction module, and serve as the input to the power iteration residual estimation module. The power iteration residual estimation module, connected to the complex signal rotation module and the state parameter update module, is used to estimate the residual error of the received signal after pre-rotation, and extract the error between the phase noise predicted by Kalman filter and the actual carrier phase noise of the received signal from the residual error. The state parameter update module, connected to the phase recovery module and the state parameter prediction module, is used to update the state parameters based on the error output by the power iteration residual estimation module and output an accurate estimate of the carrier phase noise. The phase recovery module, connected to the state parameter update module, is used to recover the carrier phase of the signal based on the accurate phase noise output by the state parameter update module.