Balanced enhanced phase noise compensation method

Abstract

The invention relates to the technical field of coherent optical fiber communication and digital signal processing, in particular to an equalization enhancement phase noise compensation method. According to the invention, a Gardner timing recovery loop and dispersion-related phase recovery are jointly designed, timing synchronization and carrier phase recovery are not separated any more, and equivalent sampling jitter and additional phase rotation caused by EEPN are suppressed at the same time through a unified digital signal processing flow. A relatively low bit error rate and relatively high receiving sensitivity can still be kept under a strong EEPN condition; according to the method provided by the invention, timing information output by Gardner timing recovery is closely combined with a dispersion-related phase compensation process, so that combined suppression of time offset and phase rotation caused by EEPN is realized, the robustness of a coherent receiver is improved, the compensation effect is effectively improved, and the system performance is improved.

Description

Technical Field

[0001] This application relates to the fields of coherent optical fiber communication and digital signal processing technology, and more specifically, to a method for equalization enhancement phase noise compensation. Background Technology

[0002] As the data transmission rate of optical communication systems continues to rise, the operating rate of the corresponding analog-to-digital converters (ADCs) also needs to be increased to meet the sampling requirements of high-speed signals. In long-distance optical signal transmission scenarios, the signal processing flow at the existing receiver typically involves first performing dispersion compensation and then phase noise compensation. However, on the one hand, the dispersion compensation stage has a significant coupling effect with the local oscillator phase noise, directly introducing equalization-enhanced phase noise (EEPN); on the other hand, the increase in ADC rate will further change the sampling characteristics and signal processing bandwidth of the system, thereby exacerbating the intensity of EEPN or expanding its influence range. The superposition of these problems directly deteriorates the receiver's sensitivity, significantly reduces the transmission stability and reliability of the entire optical communication system, and becomes a key technical bottleneck restricting the achievement of high-performance transmission in high-speed, long-distance optical communication links.

[0003] Currently, typical existing technologies for Wiener phase noise and EEPN in coherent optical communication systems include: 1. Traditional Carrier Phase Recovery (CPE) algorithms: such as decision-guided phase-locked loops, Viterbi & Viterbi, and Mth-power algorithms. These methods typically assume that the phase noise changes slowly and is approximately linear, and are effective for phase noise with "memoryless" or short correlation lengths. However, in the presence of EEPN, due to its longer memory related to dispersion and more complex statistical characteristics, traditional CPEs struggle to track it accurately, resulting in larger residual phase errors. 2. Blind Phase Search (BPS) algorithms: BPS tests each block on several candidate phases and selects the candidate phase that minimizes the distance between the constellation point and the ideal constellation, thus achieving phase recovery. It is widely used in high-order quadrature amplitude modulation (QAM) systems and has strong robustness to general laser phase noise. However, the computational complexity of BPS is directly proportional to the number of test phases and the block size, resulting in a huge computational load in high-speed systems. Furthermore, its performance significantly degrades when faced with phase noise with strong dispersion correlation, such as EEPN. 3. Gardner Timing Recovery Algorithm: The Gardner algorithm is primarily used for sampling timing recovery / symbol synchronization. It gradually corrects the sampling timing through interpolation and error signal construction; however, it is not itself an algorithm for compensating for laser phase noise.

[0004] Existing solutions achieve good performance under low to medium symbol rates and low dispersion conditions. However, under conditions of high speed, long distance, and narrow band laser linewidth of 100 GBaud and above, EEPN dominates system performance, and traditional solutions have high bit error rates and are sensitive to linewidth and dispersion. Although BPS has good performance, it is complex and has certain power consumption and real-time bottlenecks in large-scale high-speed implementations. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies that neglect the influence of EEPN in compensation schemes, which leads to limited system performance. This invention provides a balanced enhancement phase noise compensation method that effectively improves the compensation effect and enhances system performance.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for equalizing and enhancing phase noise compensation is provided, comprising: S1. Received signal: Receives dispersion-compensated complex baseband signal. ; S2. Pilot processing and maximum likelihood estimation in the first window: Insert known pilot symbols in the first regression window, construct the received symbols using the product of the pilot symbols and the received symbols, construct the covariance matrix using the EEPN variance model, and use the maximum likelihood criterion to obtain the initial estimate of the phase noise of the transmitter and receiver in the first window. S3. Windowed Least Squares Linear Fitting: In subsequent windows, the sign after the decision is used as a reference to calculate the phase observation value of each sampling point, and the least squares method is used to calculate the linear fitting parameters of the phase noise of the transmitter and receiver respectively. S4. Calculate dispersion-related phase compensation: Based on the translation mismatch relationship between the dispersion transfer function and the electronic dispersion compensation filter in the frequency domain, substitute the linear fitting result into the dispersion-compensated signal to obtain the EEPN phase compensation sequence. S5. Phase Rotation and Signal Update: Based on the EEPN phase compensation sequence obtained in step S4, the phase rotation and signal update within the window are performed. Perform phase rotation update to obtain the compensated signal. ; S6. Gardner Timed Recovery: For the compensated signal... Perform a timed Gardner recovery and output the results. S7. Window sliding and loop processing: Slide the regression window one symbol at a time, and repeat steps S3 to S6 until the complete frame signal is processed.

[0007] This invention provides an equalization enhancement phase noise compensation method that jointly designs the Gardner timing recovery loop and dispersion-correlated phase recovery. It no longer separates timing synchronization and carrier phase recovery, but instead uses a unified digital signal processing flow to simultaneously suppress equivalent sampling jitter and additional phase rotation caused by EEPN. Even under strong EEPN conditions, it can maintain a low bit error rate and high receiver sensitivity. This method tightly integrates the timing information output from Gardner timing recovery with the dispersion-correlated phase compensation process, achieving joint suppression of time offset and phase rotation caused by EEPN. This improves the robustness of the coherent receiver, effectively enhances the compensation effect, and improves system performance.

[0008] Furthermore, it also includes signal modeling, based on the phase noise and dispersion of the transmitting laser and the phase noise of the receiving local oscillator laser: (1) In the formula, for The received signal at any given moment; Indicates the time of the transmitter The output is a shaped complex baseband signal; and The phase noise processes of the transmitting laser and the receiving local oscillator laser are respectively represented, both modeled as discrete Wiener processes at the simulation sampling frequency, and their statistical characteristics are determined by the laser linewidth; Indicates having group velocity dispersion parameters and transmission distance Dispersive optical fiber at frequency The dispersion transfer function at that point; This represents the additive white Gaussian noise superimposed on the received signal; and These represent the discrete Fourier transform and its inverse transform performed on the corresponding time variables, respectively. For continuous time variables, For frequency variables; the transmitter phase noise and receiver phase noise are simulated as a Wiener process, with the following for the transmitter and receiver respectively: (2) (3) In the formula, Indicates the phase noise at the transmitter at discrete times / index k The value of ; Indicates the phase noise at the receiver at discrete times / index k The value of ; Indicates the initial phase of the transmitter; Indicates the initial phase of the receiver; This represents the phase increment at the transmitting end, with a mean of 0 and a variance of . Independent and identically distributed Gaussian random variables; This represents the phase increment at the receiving end, with a mean of 0 and a variance of . Independent and identically distributed Gaussian random variables; 、 For the laser linewidth of the transmitter and receiver, This is the simulated sampling frequency.

[0009] Further, in step S2, the received symbol is constructed using the product of the pilot signal and the received symbol, as follows: (4) In the formula, This indicates the first phase after eliminating the modulation phase using pilot symbols. k One received symbol; Indicates known pilot symbols, for The complex conjugate; This represents the window signal after taking the value corresponding to the current symbol time; The covariance matrix constructed using the EEPN variance model is expressed as follows: (5) in, Represents the variance of phase noise; (6) In the formula, Represents the additive noise / equivalent noise covariance matrix; This represents the noise power spectral density / equivalent noise variance term; Indicates the variance of EEPN; Indicates received symbol The square of the amplitude; N Indicates half the length of the window; The initial estimate of the phase noise at the transmitter and receiver within the first window is obtained using the maximum likelihood criterion, expressed as: (7) in, (8); In the formula, This represents the maximum likelihood phase estimate within the first window; Indicates the received symbol Take the phase angle; Represents a vector consisting entirely of 1s; This represents the covariance matrix of the received symbol r; This represents the phase noise covariance matrix introduced by the laser at the transmitting and receiving ends.

[0010] Further, in step S3, the linear fitting parameters of the phase noise at the transmitting end and the receiving end are calculated using the least squares method, and are expressed as follows: (9) (10) (11) (12) (13) In the formula, N Indicates the half-length of the window, 2 N +1 indicates the total length of the window; Indicates a relative index within the window. ∈[- N , N ]; This represents the slope of the linear fit to the transmitter phase noise within window k; The linear fitting intercept of the transmitter phase noise within window k represents the input phase noise. This represents the slope of the linear fit of the receiver phase noise within window k; This represents the linear fitting intercept of the receiver phase noise within window k; This represents the regression time variable / continuous time offset variable within the window. ∈[- N , N ]; Indicates within the window, relative The phase noise value at that location; Display window k The linear rate of change of internal phase noise; Represents the complex exponential phase factor. For phase.

[0011] Further, step S4 includes: Substituting the linear fitting parameters into the dispersion-compensated signal, it can be expressed as: (14) Since linear fitting of phase noise is equivalent to a shift of the signal spectrum in the frequency domain, it will cause a mismatch between the dispersive channel and its compensation filter. The product of the dispersive transfer function and the compensation filter can be expressed as: (15) Corresponding to the regression time variable The inverse Fourier transform of the upper part is expressed as: (16) The receiving end is in the window The signal inside is represented as: (17) When only considering the current symbol time The relevant value, let Then, the above equation (17) simplifies to: (18) In the formula, Display window k Inside, with The received signal is represented by a variable; This represents the window signal after taking the value corresponding to the current symbol time; Display window k internal signal The frequency domain; the EEPN phase compensation sequence is obtained from formula (18): .

[0012] Further, step S6 includes: Let the oversampled signal at the receiving end after coherent demodulation and dispersion compensation be... , record and the The current sampling point corresponding to each symbol is The sampling points at the interval between the first and second half of the symbol are respectively denoted as and The Gardner timing error is then expressed as: (19) The obtained timing error The signal is fed into a loop filter for smoothing to obtain the timing adjustment amount. : (20) In the formula, Indicates the loop gain coefficient; This represents the accumulated value of the timing error; Using a numerically controlled oscillator according to Update the sampling phase of the next symbol And the signal is adjusted at the new timing position using an interpolation filter. Resampling is performed to obtain a timing-corrected symbol-level sequence. .

[0013] The present invention also provides an equalization enhancement phase noise compensation system, comprising: Signal receiving unit: used to receive dispersion-compensated complex baseband signals. ; First Window Pilot Processing and Maximum Likelihood Estimation Unit: This unit inserts known pilot symbols into the first regression window, constructs the received symbol using the product of the pilot and the received symbol, constructs the covariance matrix using the EEPN variance model, and obtains the initial estimate of the phase noise of the transmitter and receiver within the first window using the maximum likelihood criterion. Windowed least squares linear fitting unit: used in subsequent windows, taking the decided sign as a reference, to calculate the phase observation value of each sampling point, and to calculate the linear fitting parameters of the phase noise of the transmitter and receiver respectively using the least squares method; Dispersion-related phase compensation calculation unit: It is used to substitute the linear fitting result into the dispersion-compensated signal based on the translation mismatch relationship between the dispersion transfer function and the electronic dispersion compensation filter in the frequency domain, so as to obtain the EEPN phase compensation sequence. Phase rotation and signal update unit: used to update the EEPN phase compensation sequence obtained from the dispersion-correlation phase compensation calculation unit within the window. Perform phase rotation update to obtain the compensated signal. ; Gardner Timed Recovery Unit: Used for processing compensated signals Perform a timed Gardner recovery and output the results. Window sliding and loop processing unit: used to slide the regression window by one symbol interval, repeating the processing of the windowed least squares linear fitting unit, dispersion correlation phase compensation calculation unit, phase rotation and signal update unit, and Gardner timing recovery unit until the complete frame signal is processed.

[0014] Furthermore, it also includes a signal modeling unit for modeling based on the phase noise and dispersion of the transmitting laser and the phase noise of the receiving local oscillator laser.

[0015] In the formula, for The received signal at any given moment; Indicates the time of the transmitter The output is a shaped complex baseband signal; and The phase noise processes of the transmitting laser and the receiving local oscillator laser are respectively represented, both modeled as discrete Wiener processes at the simulation sampling frequency, and their statistical characteristics are determined by the laser linewidth; Indicates having group velocity dispersion parameters and transmission distance Dispersive optical fiber at frequency The dispersion transfer function at that point; This represents the additive white Gaussian noise superimposed on the received signal; and These represent the discrete Fourier transform and its inverse transform performed on the corresponding time variables, respectively. For continuous time variables, For frequency variables; the transmitter phase noise and receiver phase noise are simulated as a Wiener process, with the following for the transmitter and receiver respectively:

[0016]

[0017] In the formula, Indicates the phase noise at the transmitter at discrete times / index k The value of ; Indicates the phase noise at the receiver at discrete times / index k The value of ; Indicates the initial phase of the transmitter; Indicates the initial phase of the receiver; This represents the phase increment at the transmitting end, with a mean of 0 and a variance of . Independent and identically distributed Gaussian random variables; This represents the phase increment at the receiving end, with a mean of 0 and a variance of . Independent and identically distributed Gaussian random variables; 、 For the laser linewidth of the transmitter and receiver, This is the simulated sampling frequency.

[0018] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described above.

[0019] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method described above.

[0020] Compared with the prior art, the beneficial effects of the present invention are: The present invention provides an equalization enhancement phase noise compensation method and system that closely integrates the timing information of Gardner timing recovery output with the dispersion-related phase compensation process, thereby achieving joint suppression of time offset and phase rotation caused by EEPN, improving the robustness of the coherent receiver, effectively improving the compensation effect, and enhancing system performance. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating a method for equalization enhancement phase noise compensation according to the present invention. Detailed Implementation

[0022] The present invention will be further described below with reference to specific embodiments. The accompanying drawings are for illustrative purposes only, representing schematic diagrams rather than actual physical objects, and should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some components in the drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions of the product. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0023] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0024] Example 1 This embodiment is a first embodiment of an equalization enhancement phase noise compensation method. This embodiment proposes an EEPN compensation method based on jitter estimation. Utilizing known dispersion parameters, transmission distance, symbol rate, and other information, a time window and equivalent jitter model related to the EEPN are constructed to accurately estimate and compensate for the EEPN. Jitter-based EEPN compensation is organically combined with timing recovery algorithms (such as Gardner), proposing a joint scheme based on Gardner timing recovery and dispersion-related phase recovery. This improves both phase and timing performance with minimal increase in complexity. The principle and detailed steps of the method proposed in this embodiment will be explained below.

[0025] I. Signal Model and the Impact of Equalization on Phase Noise 1. Signal Model: This embodiment considers a single-carrier fiber optic communication system. The transmitted signal is affected by the phase noise and dispersion of the laser at the transmitting end and the phase noise of the local oscillator laser at the receiving end, which can be expressed as: (1) In the formula, for The received signal at any given moment; Indicates the time of the transmitter The output is a shaped complex baseband signal; and The phase noise processes of the transmitting laser and the receiving local oscillator laser are respectively represented, both of which are modeled as discrete Wiener processes at the simulation sampling frequency, and their statistical characteristics are determined by the laser linewidth. Indicates having group velocity dispersion parameters and transmission distance Dispersive optical fiber at frequency The dispersion transfer function at that point; This represents the additive white Gaussian noise superimposed on the received signal; and These represent the discrete Fourier transform and its inverse transform performed on the corresponding time variables, respectively. For continuous time variables, For frequency variables. Furthermore, the transmitter phase noise and receiver phase noise can be simulated as a Wiener process, where, for the transmitter and receiver respectively: (2) (3) Phase increment , With a mean of 0 and variances of , and Independent and identically distributed Gaussian random variables, where , For the laser linewidth of the transmitter and receiver, The sampling frequency is for simulation. In fiber optic communication systems, because dispersion has the greatest impact, digital signal processing at the receiver often compensates for dispersion before performing phase recovery. However, dispersion compensation in the digital domain can couple with the phase noise of the receiver laser, thus introducing EEPN.

[0026] II. EEPN Suppression Method Based on Timing Recovery and Phase Compensation 1. EEPN for signal impairment modeling This embodiment focuses on designing an EEPN suppression method, therefore assuming that dispersion has been perfectly compensated. It is also assumed that the transmitter phase noise and receiver phase noise are known. Within a window, a least-squares algorithm can be used to linearly fit the transmitter and receiver phase noise within the window, as shown in the following expression: (4) (5) (6) (7) (8) In the formula, N Indicates the half-length of the window, 2N +1 indicates the total length of the window; Indicates a relative index within the window. ∈[- N , N ]; This represents the slope of the linear fit to the transmitter phase noise within window k; The linear fitting intercept of the transmitter phase noise within window k represents the input phase noise. This represents the slope of the linear fit of the receiver phase noise within window k; This represents the linear fitting intercept of the receiver phase noise within window k; This represents the regression time variable / continuous time offset variable within the window. ∈[- N , N ]; Indicates within the window, relative The phase noise value at that location; Display window k The linear rate of change of internal phase noise; j Represents the imaginary unit. Represents the complex exponential phase factor. For phase.

[0027] Substituting the fitted phase noise parameters into the above-mentioned dispersion-compensated received signal, i.e., formula (1), we can obtain: (9) Furthermore, since linear fitting of phase noise is equivalent to a shift of the signal spectrum in the frequency domain, it will cause a mismatch between the dispersive channel and its compensation filter. The product of the dispersive transfer function and the compensation filter can be written as: (10) Corresponding to the regression time variable Taking the inverse Fourier transform above, we have: (11) Based on this, the receiving end is in the window The signal inside can be represented as: (12) When only considering the current symbol time The relevant value, that is, let Then, the above equation (12) can be simplified to: (13) In the formula, Display window k Inside, with The received signal is represented by a variable; Indicates the window signal after taking the value corresponding to the current symbol moment; Indicates the window k The signal within Frequency domain.

[0028] As can be seen from the above formula (13), EEPN not only causes the influence of phase, but also causes the influence of time offset. Therefore, the present invention adopts a clock recovery + phase compensation mechanism to suppress the influence of EEPN.

[0029] 2. EEPN suppression method based on timing recovery and phase compensation The above analysis of the influence of EEPN is based on the assumption that the phase noise at the transmitting and receiving ends is known. However, in actual optical communication, the phase noise at the transmitting and receiving ends is unknown. Therefore, in this embodiment, the Gardner algorithm is adopted for clock synchronization, and the dispersion-related phase noise is compensated based on the estimated phase. Specifically, it includes: (1) Gardner algorithm: In order to eliminate the symbol timing deviation, in this embodiment, the Gardner timing recovery algorithm is first used to perform timing estimation and compensation on the received signal. Let the oversampled signal after coherent demodulation and dispersion compensation at the receiving end be , the oversampling rate is , and each symbol contains 4 sampling points. Denote the current sampling point corresponding to the th symbol as , and the sampling points at the front and back half-symbol intervals are respectively denoted as and . Then the Gardner timing error can be expressed as: (14) That is, by multiplying the difference between the sample values at the front and back half-symbols of the same symbol by the conjugate of the sample value at the center of the current symbol, an error signal that is sensitive to the symbol timing deviation and insensitive to the symbol data itself is obtained. The obtained timing error is sent to the loop filter for smoothing processing to obtain the timing adjustment amount: (15) where is the loop gain coefficient. Then, according to , the numerically controlled oscillator is used to update the sampling phase of the next symbol, and the signal is resampled at the new timing position through the interpolation filter, so as to obtain the symbol-level sequence with corrected timing. Through the above timing recovery loop based on the Gardner algorithm, at the oversampling rate Under the given conditions, it effectively suppresses timing jitter and sampling offset, providing a stable input for subsequent phase noise estimation and dispersion-related phase noise compensation.

[0030] (2) Dispersion-correlated phase noise compensation As can be seen from the above formula, in addition to the traditional Wiener phase noise, dispersion will also introduce an additional phase noise coupled with it. To address this issue, this project proposes to adopt a processing approach of "first estimating the phase noise, then performing windowed linear fitting based on the least squares method, and finally compensating the phase according to formula (13)" to achieve overall phase recovery.

[0031] 1) To estimate the phase noise, EEPN is initially treated as additive white Gaussian noise. Existing literature gives the variance of EEPN as... Due to the high transmission rate and the fact that the laser used is typically an external cavity laser (ECL), it can be assumed that the laser phase noise is constant within a short window, and that the data in the first window is assumed to be known pilot symbols. Therefore, for the first window, the pilot symbol information can be used to first eliminate the phase modulation of the received signal after dispersion compensation, denoted as: (16) Based on this data, we can obtain the maximum likelihood phase estimate under the influence of additive EEPN: (17) in, (18) (19) (20) In the formula, The variance of the phase noise; This indicates the first phase after eliminating the modulation phase using pilot symbols. One received symbol; Indicates known pilot symbols, for The complex conjugate; This represents the window signal after taking the value corresponding to the current symbol time; Represents the additive noise / equivalent noise covariance matrix; This represents the noise power spectral density / equivalent noise variance term; Indicates the variance of EEPN; Indicates received symbol The square of the amplitude; N Indicates half the length of the window; This represents the maximum likelihood phase estimate within the first window; Indicates the received symbol Take the phase angle; Represents a vector consisting entirely of 1s; This represents the covariance matrix of the received symbol r; This represents the phase noise covariance matrix introduced by the laser at the transmitting and receiving ends.

[0032] 2) After obtaining Then, using the derivation from the previous section... , , , This compensates for phase noise on the next received symbol.

[0033] 3) Apply the obtained phase estimate to the received signal in the next window (the window slides one bit by symbol interval) for compensation, and make a symbol decision on the compensated signal; then use the decision result as the ideal transmitted symbol in the window, and repeat steps 1) and 2) until the phase of all received signals is recovered.

[0034] Based on the above analysis, this embodiment proposes an equalization enhancement phase noise compensation method, which specifically includes the following steps: Step S1. Receive signal: Receive the dispersion-compensated complex baseband signal. ; Step S2. Pilot processing and maximum likelihood estimation in the first window: Insert known pilot symbols in the first regression window, construct the received symbols using the product of the pilot symbols and the received symbols, construct the covariance matrix using the EEPN variance model, and use the maximum likelihood criterion to obtain the initial estimate of the phase noise of the transmitter and receiver in the first window. Step S3. Windowed Least Squares Linear Fitting: In subsequent windows, the sign after the decision is used as a reference to calculate the phase observation value of each sampling point, and the least squares method is used to calculate the linear fitting parameters of the phase noise at the transmitting end and the receiving end respectively. Step S4. Calculate dispersion-related phase compensation: Based on the translation mismatch relationship between the dispersion transfer function and the electronic dispersion compensation filter in the frequency domain, substitute the linear fitting result into the dispersion-compensated signal to obtain the EEPN phase compensation sequence. Step S5. Phase Rotation and Signal Update: Based on the EEPN phase compensation sequence obtained in step S4, perform phase rotation and signal update within the window. Perform phase rotation update to obtain the compensated signal. ; Step S6. Gardner Timed Recovery: This step involves periodically restoring the compensated signal. Perform a timed Gardner recovery and output the results. Step S7. Window sliding and loop processing: Slide the regression window one symbol at a time, and repeat steps S3 to S6 until the complete frame signal is processed.

[0035] The equalization enhancement phase noise compensation method proposed in this embodiment has the following beneficial effects: 1. Based on the signal model and EEPN impairment mechanism described in Formula (1), this embodiment combines the Gardner timing recovery loop with the dispersion-related phase recovery module. The timing synchronization and carrier phase recovery are no longer separated. Instead, the equivalent sampling jitter and additional phase rotation caused by EEPN are suppressed simultaneously through a unified digital signal processing flow, so that the system can still maintain a low bit error rate and high receiving sensitivity under strong EEPN conditions.

[0036] 2. In this embodiment, a known pilot symbol is introduced in the first regression window. By eliminating the modulation phase, an observation including the EEPN is obtained. Combined with the EEPN variance model, a maximum likelihood phase estimate is constructed to achieve an accurate initial estimate of the phase noise at the transmitter and receiver. Compared with the completely blind phase estimation method, this scheme has a faster convergence speed and a smaller steady-state residual phase error, providing a reliable initial value for the subsequent sliding window decision feedback phase tracking.

[0037] 3. This embodiment employs a sliding linear regression window in the time domain, approximating the phase noise at both the transmitting and receiving ends as a linear function within a short window. The slope and intercept parameters are then calculated using the least squares method. Finally, by combining the mismatch relationship between the dispersion transfer function and its compensation filter, the linear fitting result is mapped to the dispersion-related phase compensation amount. This mechanism explicitly utilizes the deterministic relationship between the EEPN and system parameters such as the dispersion coefficient, transmission distance, and symbol rate. Compared to the traditional method that simply treats the EEPN as "larger phase noise," this provides more comprehensive compensation and has a wider range of applications.

[0038] 4. This embodiment has lower complexity and is easier to implement in engineering. Unlike the BPS algorithm, which requires multi-phase traversal of each data block, this embodiment mainly relies on pilot correlation, addition, subtraction and multiplication operations within the sliding window and a small number of matrix operations. The overall complexity is approximately linearly related to the window length. It does not require exhaustive search on multiple candidate phases, has lower requirements for hardware resources and power consumption, and is more suitable for real-time implementation in high-speed ADC and DSP chips.

[0039] 5. The method in this embodiment only depends on system parameters such as symbol rate, dispersion coefficient, transmission distance, and laser linewidth, as well as the configuration of pilot structure and regression window length. It does not depend on a specific modulation order or a single link structure. It can be directly extended to 16-QAM and higher-order coherent modulation formats and is applicable to long-distance fiber optic links of different lengths and dispersion levels. It has good engineering versatility and scalability.

[0040] Example 2 This embodiment is an example of an equalization enhancement phase noise compensation system. The working principle of this embodiment is similar to that of Embodiment 1. Specifically, it includes: Signal receiving unit: used to receive dispersion-compensated complex baseband signals. ; First Window Pilot Processing and Maximum Likelihood Estimation Unit: This unit inserts known pilot symbols into the first regression window, constructs the received symbol using the product of the pilot and the received symbol, constructs the covariance matrix using the EEPN variance model, and obtains the initial estimate of the phase noise of the transmitter and receiver within the first window using the maximum likelihood criterion. Windowed least squares linear fitting unit: used in subsequent windows, taking the decided sign as a reference, to calculate the phase observation value of each sampling point, and to calculate the linear fitting parameters of the phase noise of the transmitter and receiver respectively using the least squares method; Dispersion-related phase compensation calculation unit: It is used to substitute the linear fitting result into the dispersion-compensated signal based on the translation mismatch relationship between the dispersion transfer function and the electronic dispersion compensation filter in the frequency domain, so as to obtain the EEPN phase compensation sequence. Phase rotation and signal update unit: used to update the EEPN phase compensation sequence obtained from the dispersion-correlation phase compensation calculation unit within the window. Perform phase rotation update to obtain the compensated signal. ; Gardner Timed Recovery Unit: Used for processing compensated signals Perform a timed Gardner recovery and output the results. Window sliding and loop processing unit: used to slide the regression window by one symbol interval, repeating the processing of the windowed least squares linear fitting unit, dispersion correlation phase compensation calculation unit, phase rotation and signal update unit, and Gardner timing recovery unit until the complete frame signal is processed.

[0041] In the simulation experiment, the signal processing flow can be represented as follows: random symbol / pilot sequence generator → QAM modulation → RRC shaping filter → fiber dispersion channel (including transmitter phase noise) → receiver local oscillator phase noise superposition + AWGN → analog-to-digital conversion and digital sampling → frequency domain dispersion compensation → dispersion-related phase recovery module → Gardner timing recovery unit → RRC matched filtering → QAM demodulation and symbol decision → bit error rate statistics.

[0042] The dispersion-correlated phase recovery module receives the time-aligned signal and completes EEPN explicit compensation and carrier phase recovery. It includes the aforementioned first-window pilot processing and maximum likelihood estimation unit, windowed least-squares linear fitting unit, dispersion-correlated phase compensation calculation unit, and phase rotation and signal update unit. The Gardner timing recovery unit includes a timing error calculation unit (based on the Gardner decision formula), a loop filter, a numerically controlled oscillator (NCO), and an interpolation filter, which are used to resample the oversampled signal to the optimal symbol time.

[0043] The equalization enhancement phase noise compensation system proposed in this embodiment has the following beneficial effects: 1. This embodiment differs from the traditional serial cascaded structure of "digital dispersion compensation + CPE + Gardner timing recovery". This embodiment models and processes timing jitter and EEPN simultaneously under a unified algorithm framework. It closely integrates the timing information output by Gardner timing recovery with the dispersion-related phase compensation process to achieve joint suppression of time offset and phase rotation caused by EEPN, thereby improving the robustness of the coherent receiver at the system level.

[0044] 2. This embodiment proposes to construct a maximum likelihood estimator using pilot symbols and the EEPN variance model within the first window to distinguish and estimate the phase noise at the transmitting and receiving ends. Then, in subsequent windows, a decision feedback method is used to iteratively update the phase estimate. This approach balances the high accuracy of the pilot-assisted algorithm with the high efficiency of the decision feedback algorithm, achieving phase recovery with good convergence and tracking capabilities even under strong EEPN conditions.

[0045] 3. The windowed linear regression approach proposed in this embodiment approximates the phase noise over a short period of time as a linear change. By combining the frequency domain translation mismatch relationship between the dispersion transfer function and the electronic dispersion compensation filter, the phase compensation factor for EEPN suppression and its calculation formula are derived, realizing the structured modeling and explicit compensation of EEPN. This approach is different from the existing empirical methods that treat EEPN as "equivalent additive noise".

[0046] 4. In typical high-speed scenarios such as 100 GBaud and 16-QAM, this embodiment effectively improves constellation cluster compactness and bit error rate performance by combining timing synchronization and dispersion-related phase recovery, providing a scalable EEPN suppression technology route for future coherent fiber optic systems with higher symbol rates, longer transmission distances, and higher-order modulation formats.

[0047] Example 3 This embodiment is an embodiment of a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the method described in Embodiment 1.

[0048] Example 4 This embodiment provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0049] In the specific implementation of the above embodiments, the technical features can be combined in any non-contradictory way. For the sake of brevity, not all possible combinations of the above technical features are described. However, as long as the combination of these technical features is not contradictory, it should be considered to be within the scope of this specification.

[0050] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for equalizing and enhancing phase noise compensation, characterized in that, include: S1. Received signal: Receives dispersion-compensated complex baseband signal. ; S2. Pilot processing and maximum likelihood estimation in the first window: Insert known pilot symbols in the first regression window, construct the received symbols using the product of the pilot symbols and the received symbols, construct the covariance matrix using the EEPN variance model, and use the maximum likelihood criterion to obtain the initial estimate of the phase noise of the transmitter and receiver in the first window. S3. Windowed Least Squares Linear Fitting: In subsequent windows, the sign after the decision is used as a reference to calculate the phase observation value of each sampling point, and the least squares method is used to calculate the linear fitting parameters of the phase noise of the transmitter and receiver respectively. S4. Calculate dispersion-related phase compensation: Based on the translation mismatch relationship between the dispersion transfer function and the electronic dispersion compensation filter in the frequency domain, substitute the linear fitting result into the dispersion-compensated signal to obtain the EEPN phase compensation sequence. S5. Phase Rotation and Signal Update: Based on the EEPN phase compensation sequence obtained in step S4, the phase rotation and signal update within the window are performed. Perform phase rotation update to obtain the compensated signal. ; S6. Gardner Timed Recovery: For the compensated signal... Perform a timed Gardner recovery and output the results. S7. Window sliding and loop processing: Slide the regression window one symbol at a time, and repeat steps S3 to S6 until the complete frame signal is processed.

2. The equalization enhancement phase noise compensation method according to claim 1, characterized in that, It also includes signal modeling, based on the phase noise and dispersion of the transmitting laser and the phase noise of the receiving local oscillator laser: （1） In the formula, for The received signal at any given moment; Indicates the time of the transmitter The output is a shaped complex baseband signal; and The phase noise processes of the transmitting laser and the receiving local oscillator laser are respectively represented, both modeled as discrete Wiener processes at the simulation sampling frequency, and their statistical characteristics are determined by the laser linewidth; Indicates having group velocity dispersion parameters and transmission distance Dispersive optical fiber at frequency The dispersion transfer function at that point; This represents the additive white Gaussian noise superimposed on the received signal; and These represent the discrete Fourier transform and its inverse transform performed on the corresponding time variables, respectively. For continuous time variables, For frequency variables; the transmitter phase noise and receiver phase noise are simulated as a Wiener process, with the following for the transmitter and receiver respectively: （2） （3） In the formula, Indicates the phase noise at the transmitter at discrete times / index k The value of ; Indicates the phase noise at the receiver at discrete times / index k The value of ; Indicates the initial phase of the transmitter; Indicates the initial phase of the receiver; This represents the phase increment at the transmitting end, with a mean of 0 and a variance of . Independent and identically distributed Gaussian random variables; This represents the phase increment at the receiving end, with a mean of 0 and a variance of . Independent and identically distributed Gaussian random variables; 、 For the laser linewidth of the transmitter and receiver, This is the simulated sampling frequency.

3. The equalization enhancement phase noise compensation method according to claim 2, characterized in that, In step S2, the received symbol is constructed using the product of the pilot signal and the received symbol, as follows: （4） In the formula, This indicates the first phase after eliminating the modulation phase using pilot symbols. k One received symbol; Indicates known pilot symbols, for The complex conjugate; This represents the window signal after taking the value corresponding to the current symbol time; The covariance matrix constructed using the EEPN variance model is expressed as follows: （5） in, Represents the variance of phase noise; （6） In the formula, Represents the additive noise / equivalent noise covariance matrix; This represents the noise power spectral density / equivalent noise variance term; Indicates the variance of EEPN; Indicates received symbol The square of the amplitude; N Indicates half the length of the window; The initial estimate of the phase noise at the transmitter and receiver within the first window is obtained using the maximum likelihood criterion, expressed as: （7） in, (8); In the formula, This represents the maximum likelihood phase estimate within the first window; Indicates the received symbol Take the phase angle; Represents a vector consisting entirely of 1s; This represents the covariance matrix of the received symbol r; This represents the phase noise covariance matrix introduced by the laser at the transmitting and receiving ends.

4. The equalization enhancement phase noise compensation method according to claim 3, characterized in that, In step S3, the linear fitting parameters of the phase noise at the transmitting and receiving ends are calculated using the least squares method and are expressed as follows: （9） （10） （11） （12） （13） In the formula, N Indicates the half-length of the window, 2 N +1 indicates the total length of the window; Indicates a relative index within the window. ∈[- N , N ]; Display window k The slope of the linear fit for the phase noise at the internal emitter; The linear fitting intercept of the transmitter phase noise within window k represents the input phase noise. This represents the slope of the linear fit of the receiver phase noise within window k; This represents the linear fitting intercept of the receiver phase noise within window k; This represents the regression time variable / continuous time offset variable within the window. ∈[- N , N ]; Indicates within the window, relative The phase noise value at that location; Display window k The linear rate of change of internal phase noise; j Represents the imaginary unit. Represents the complex exponential phase factor. For phase.

5. The equalization enhancement phase noise compensation method according to claim 4, characterized in that, Step S4 includes: Substituting the linear fitting parameters into the dispersion-compensated signal, it can be expressed as: （14） Since linear fitting of phase noise is equivalent to a shift of the signal spectrum in the frequency domain, it will cause a mismatch between the dispersive channel and its compensation filter. The product of the dispersive transfer function and the compensation filter can be expressed as: （15） Corresponding to the regression time variable The inverse Fourier transform of the upper part is expressed as: （16） The receiving end is in the window The signal inside is represented as: （17） When only considering the current symbol time The relevant value, let Then, the above equation (17) simplifies to: （18） In the formula, Display window k Inside, with The received signal is represented by a variable; This represents the window signal after taking the value corresponding to the current symbol time; Display window k internal signal The frequency domain; the EEPN phase compensation sequence is obtained from formula (18): .

6. The equalization enhancement phase noise compensation method according to claim 5, characterized in that, Step S6 includes: Let the oversampled signal at the receiving end after coherent demodulation and dispersion compensation be... , record and the The current sampling point corresponding to each symbol is The sampling points at the interval between the first and second half of the symbol are respectively denoted as and The Gardner timing error is then expressed as: （19） The obtained timing error The signal is fed into a loop filter for smoothing to obtain the timing adjustment amount. : （20） In the formula, Indicates the loop gain coefficient; This represents the accumulated value of the timing error; Using a numerically controlled oscillator according to Update the sampling phase of the next symbol And the signal is adjusted at the new timing position using an interpolation filter. Resampling is performed to obtain a timing-corrected symbol-level sequence. .

7. A balanced enhancement phase noise compensation system, characterized in that, include: Signal receiving unit: used to receive dispersion-compensated complex baseband signals. ; First Window Pilot Processing and Maximum Likelihood Estimation Unit: This unit inserts known pilot symbols into the first regression window, constructs the received symbol using the product of the pilot and the received symbol, constructs the covariance matrix using the EEPN variance model, and obtains the initial estimate of the phase noise of the transmitter and receiver within the first window using the maximum likelihood criterion. Windowed least squares linear fitting unit: used in subsequent windows, taking the decided sign as a reference, to calculate the phase observation value of each sampling point, and to calculate the linear fitting parameters of the phase noise of the transmitter and receiver respectively using the least squares method; Dispersion-related phase compensation calculation unit: It is used to substitute the linear fitting result into the dispersion-compensated signal based on the translation mismatch relationship between the dispersion transfer function and the electronic dispersion compensation filter in the frequency domain, so as to obtain the EEPN phase compensation sequence. Phase rotation and signal update unit: used to update the EEPN phase compensation sequence obtained from the dispersion-correlation phase compensation calculation unit within the window. Perform phase rotation update to obtain the compensated signal. ; Gardner Timed Recovery Unit: Used for processing compensated signals Perform a timed Gardner recovery and output the results. Window sliding and loop processing unit: used to slide the regression window by one symbol interval, repeating the processing of the windowed least squares linear fitting unit, dispersion correlation phase compensation calculation unit, phase rotation and signal update unit, and Gardner timing recovery unit until the complete frame signal is processed.

8. The equalization enhancement phase noise compensation system according to claim 7, characterized in that, It also includes a signal modeling unit for modeling based on the phase noise and dispersion of the transmitting laser and the phase noise of the receiving local oscillator laser. In the formula, for The received signal at any given moment; Indicates the time of the transmitter The output is a shaped complex baseband signal; and The phase noise processes of the transmitting laser and the receiving local oscillator laser are respectively represented, both modeled as discrete Wiener processes at the simulation sampling frequency, and their statistical characteristics are determined by the laser linewidth; Indicates having group velocity dispersion parameters and transmission distance Dispersive optical fiber at frequency The dispersion transfer function at that point; This represents the additive white Gaussian noise superimposed on the received signal; and These represent the discrete Fourier transform and its inverse transform performed on the corresponding time variables, respectively. For continuous time variables, For frequency variables; the transmitter phase noise and receiver phase noise are simulated as a Wiener process, with the following for the transmitter and receiver respectively: In the formula, Indicates the phase noise at the transmitter at discrete times / index k The value of ; Indicates the phase noise at the receiver at discrete times / index k The value of ; Indicates the initial phase of the transmitter; Indicates the initial phase of the receiver; This represents the phase increment at the transmitting end, with a mean of 0 and a variance of . Independent and identically distributed Gaussian random variables; This represents the phase increment at the receiving end, with a mean of 0 and a variance of . Independent and identically distributed Gaussian random variables; 、 For the laser linewidth of the transmitter and receiver, This is the simulated sampling frequency.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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