Method and device for eliminating nonlinear damage in KK receiver

Abstract

The invention provides a method and a device for eliminating nonlinear damage in a KK receiver, which can perform accurate modeling and reconstruction on a beat frequency process between a pilot frequency and a transmission field signal as well as between the pilot frequency and a carrier field signal in a digital domain of the KK receiver, and combine least square normalization and an iterative feedback mechanism to eliminate nonlinear damage in the KK receiver. Non-linear damage introduced by pilot frequency beat frequency is effectively eliminated from a sampling receiving power signal, and residual non-linear distortion in a recovery field signal is remarkably reduced. Therefore, the requirements of the system on the bias stability of the transmitting end and the linearity of the device are reduced, the bit error rate performance is improved, the tolerance of the optical fiber transmission system on optical signal-to-noise ratio degradation and the achievable transmission distance are improved, and high-performance KK direct detection receiving in a complex nonlinear environment is realized.

Description

Technical Field

[0001] This disclosure relates to the field of optical fiber communication technology, and more specifically, to a method and apparatus for eliminating nonlinear impairments in a KK receiver. Background Technology

[0002] With the rapid development of emerging technologies such as cloud computing, the Internet of Things, connected vehicles, and virtual reality, global communication data network traffic is growing exponentially. Statistics show that 99% of global communication data network traffic is related to data centers, presenting both significant challenges and opportunities for optical interconnects in data centers. While coherent optical communication technology offers advantages such as high spectral efficiency, better receiver noise sensitivity, and better dispersion tolerance, its complex structure and high cost fail to meet the low-cost requirements of data center optical interconnects. On the other hand, direct detection technology has attracted widespread research interest due to its simple structure and cost-effectiveness. Among these, single-sideband modulation (SSB) technology, with its simple structure, low cost, high fiber dispersion tolerance, and high spectral efficiency, is considered one of the best solutions currently available to meet the needs of data center optical interconnects.

[0003] Currently, the commonly used single-sideband (SSB) signal implementation scheme is optical SSB transmission based on IQ modulators, which has advantages such as simple structure, high signal quality, and a wide range of carrier-to-signal power ratio (CSPR) adjustment. IQ modulators typically require three bias controllers to stabilize the bias voltage and employ pilot-based automatic bias control (ABC) technology to eliminate bias voltage drift caused by temperature, mechanical vibration, and other external environmental changes. However, the double-sideband pilots introduced by the ABC device violate the minimum phase condition, leading to a degraded KK receiver performance. Furthermore, due to the square-law detection of the single-ended photodetector, beat frequency interference between the pilot and the signal cannot be completely eliminated by the KK receiver, thus significantly impacting system performance. Summary of the Invention

[0004] This disclosure provides at least one method and apparatus for eliminating nonlinear impairments in a KK receiver. It enables accurate modeling and reconstruction of the beat frequency process between the pilot and transmitted field signals, and between the pilot and carrier field signals, within the digital domain of the KK receiver. By combining least-squares normalization and iterative feedback mechanisms, it effectively eliminates the nonlinear impairments introduced by the beat frequency of the pilot and other signal components from the sampled received power signal, significantly reducing residual nonlinear distortion in the recovered field signal. This not only reduces the system's requirements for transmitter bias stability and device linearity, improving transmission performance, but also increases the tolerance of the fiber optic transmission system to optical signal-to-noise ratio degradation and the achievable transmission distance, realizing high-performance KK direct detection reception in complex nonlinear environments.

[0005] This disclosure provides a method for eliminating nonlinear impairments in a KK receiver, including: After the optical signal is transmitted through the optical fiber link, it is converted into a corresponding photocurrent signal, and the photocurrent signal is sampled to obtain the corresponding sampling and receiving power signal. The sampled received power signal is recovered into a recovered field signal using the Cramer-Kronig relation. In the digital domain, the recovered field signal is combined with the reference pilot signal to mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier field signal within the transmission system's frequency band. This yields a modeling expression for the nonlinear damaged signal, and the reconstructed nonlinear damaged signal is determined based on the modeling expression. The reconstructed nonlinear damage signal is combined with the measured damage signal, and the normalization factor used for amplitude normalization of the reconstructed nonlinear damage signal is calculated by the least squares method. The reconstructed nonlinear damage signal is scaled using the normalization factor, and the scaled reconstructed nonlinear damage signal is subtracted from the sampled received power signal to determine the photocurrent signal after nonlinear damage elimination. The step of repeatedly using the Cramer-Kronig relation to recover the sampled received power signal into a recovered field signal is used to gradually reduce the error signal in an iterative feedback manner until the residual nonlinear impairment in the recovered field signal approaches zero.

[0006] In one optional implementation, the optical signal is transmitted via an optical fiber link and then converted into a corresponding photocurrent signal, and the photocurrent signal is sampled to obtain a corresponding sampling and receiving power signal, specifically including: The optical signal, which contains the low-frequency pilot signal from the automatic bias control device, is transmitted through the optical fiber link of a preset distance, and then undergoes photoelectric conversion by a photodetector at the receiving end to obtain the photocurrent signal. The photocurrent signal is sampled using an oscilloscope to obtain the sampled received power signal. The sampled received power signal undergoes preprocessing including at least filtering, noise reduction, and normalization.

[0007] In an optional implementation, after recovering the sampled received power signal into a recovered field signal using the KK relationship, the method further includes: Digital domain dispersion compensation is performed on the recovered field signal, and equalization technology is used to compensate for channel distortion to determine the equalized symbol sequence; A symbol decision is performed on the symbol sequence to determine the QAM symbol after the decision, and the QAM symbol is remodulated to obtain a service signal that does not contain pilot beat frequency interference. The channel response obtained during the equalization process is applied to the service signal, and the inverse process of digital domain dispersion compensation is performed to obtain a reconstructed field signal with less beat frequency interference.

[0008] In one optional implementation, the recovered field signal is combined with the reference pilot signal in the digital domain to mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier signal within the system frequency band, specifically including: Based on the photocurrent mathematical model after incorporating the reference pilot signal, the frequency components of the carrier field signal, the transmission field signal, and the reference pilot signal are expanded into multiplication terms. From the multiplication terms, select the pilot and transmission field signal beat frequency components and the pilot and carrier signal beat frequency components that fall within the effective signal frequency band of the system as the constituent components of the nonlinear damage signal; Ignore the second-order terms of the pilot signal and the beat frequency components that are outside the effective frequency band; The constituent components are weighted and linearly superimposed according to the phase and amplitude relationship in the photocurrent mathematical model to obtain the modeling expression with the carrier field signal, the transmission field signal and the pilot frequency component as independent variables and undetermined coefficients as parameters, which serves as the mathematical model for reconstructing the nonlinear damage signal.

[0009] In one optional implementation, the reconstructed nonlinear damage signal is combined with the measured damage signal, and a normalization factor for amplitude normalization of the reconstructed nonlinear damage signal is calculated using the least squares method, specifically including: With the goal of minimizing the energy difference between the reconstructed nonlinear damage signal and the measured damage signal within a preset time window, the initial normalization factor is determined using a least-squares fitting method. A parameter scanning range with a preset step size is selected near the initial normalization factor, and the optimal normalization factor is determined based on the criterion that the preset performance index of the transmission system reaches its optimum. In each subsequent iteration, the optimal normalization factor is used to scale the amplitude of the reconstructed nonlinear damage signal.

[0010] In one optional implementation, the step of repeatedly using the KK relationship to recover the sampled received power signal into a recovered field signal, and gradually reducing the error signal through iterative feedback, specifically includes: In each iteration, the DC component of the photocurrent signal obtained in the current iteration after nonlinear damage elimination is filtered out to obtain the updated sampled received power signal; By repeatedly performing the steps of recovering the field signal, nonlinear damage modeling, normalization factor scaling, and damage signal elimination using the updated sampled received power signal, a new error signal is obtained. When the change in the mean square value of the error signal relative to the previous iteration is lower than a preset threshold, or when the number of iterations reaches a preset maximum number of iterations, the iteration is determined to be converged, and the updated sampled received power signal is used as the final photocurrent signal after nonlinear damage elimination.

[0011] This disclosure also provides an apparatus for eliminating nonlinear impairments in a KK receiver, comprising: The optical signal conversion module is used to convert the optical signal transmitted through the optical fiber link into the corresponding photocurrent signal, and to sample the photocurrent signal to obtain the corresponding sampling and receiving power signal. The nonlinear damage modeling module is used to recover the sampled received power signal into a recovered field signal using the Cramer-Kronig relation, combine the recovered field signal with the reference pilot signal in the digital domain, mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier field signal within the transmission system frequency band, obtain the modeling expression of the nonlinear damage signal, and determine the reconstructed nonlinear damage signal based on the modeling expression. The normalization factor determination module is used to combine the reconstructed nonlinear damage signal with the measured damage signal and calculate the normalization factor used for amplitude normalization of the reconstructed nonlinear damage signal using the least squares method. The damage elimination module is used to scale the reconstructed nonlinear damage signal using the normalization factor and subtract the scaled reconstructed nonlinear damage signal from the sampled received power signal to determine the photocurrent signal after nonlinear damage elimination. The iterative feedback module is used to repeatedly utilize the Cramer-Kronig relation to recover the sampled received power signal into a recovered field signal, and gradually reduce the error signal in an iterative feedback manner until the residual nonlinear damage in the recovered field signal approaches zero.

[0012] In an optional embodiment, the apparatus further includes a field signal reconstruction module, the field signal reconstruction module being used for: Digital domain dispersion compensation is performed on the recovered field signal, and equalization technology is used to compensate for channel distortion to determine the equalized symbol sequence; A symbol decision is performed on the symbol sequence to determine the QAM symbol after the decision, and the QAM symbol is remodulated to obtain a service signal that does not contain pilot beat frequency interference. The channel response obtained during the equalization process is applied to the service signal, and the inverse process of digital domain dispersion compensation is performed to obtain a reconstructed field signal with less beat frequency interference.

[0013] This disclosure also provides an electronic device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform steps in any of the possible implementations of the above-described method for eliminating nonlinear impairments in a KK receiver, or the above-described method for eliminating nonlinear impairments in a KK receiver.

[0014] This disclosure also provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of any possible implementation of the method for eliminating nonlinear impairments in a KK receiver described above, or the method for eliminating nonlinear impairments in a KK receiver described above.

[0015] This disclosure also provides a computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps of any possible implementation of the method for eliminating nonlinear impairments in a KK receiver described above, or the method for eliminating nonlinear impairments in a KK receiver described above.

[0016] This disclosure provides a method and apparatus for eliminating nonlinear impairments in a KK receiver. The method involves transmitting an optical signal via an optical fiber link, converting it into a corresponding photocurrent signal, and sampling the photocurrent signal to obtain a corresponding sampled received power signal. The sampled received power signal is then used to recover a restored field signal using the Cramer-Kronig (KK) relation. In the digital domain, the recovered field signal is combined with a reference pilot signal to mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier field signal within the transmission system's frequency band. This yields a modeling expression for the nonlinear impairment signal, and the reconstructed nonlinear impairment signal is determined based on the modeling expression. The reconstructed nonlinear impairment signal is combined with the measured impairment signal, and a normalization factor for amplitude normalization of the reconstructed nonlinear impairment signal is calculated using the least squares method. The reconstructed nonlinear impairment signal is then amplitude-scaled using the normalization factor, and the scaled reconstructed nonlinear impairment signal is subtracted from the sampled received power signal to determine the photocurrent signal after nonlinear impairment elimination. The step of recovering the recovered field signal from the sampled received power signal using the Cramer-Kronig relation is repeated, iteratively reducing the error signal until the residual nonlinear impairment in the recovered field signal approaches zero. This method enables accurate modeling and reconstruction of the beat frequency process between the pilot and transmitted field signals, and between the pilot and carrier field signals, within the digital domain of the KK receiver. Combined with least squares normalization and iterative feedback mechanisms, it effectively eliminates the nonlinear impairment introduced by pilot beat frequency from the sampled received power signal, significantly reducing the residual nonlinear distortion in the recovered field signal. This not only reduces the system's requirements for transmitter bias stability and device linearity, improving bit error rate performance and Q factor, but also increases the fiber optic transmission system's tolerance to optical signal-to-noise ratio degradation and achievable transmission distance, enabling high-performance KK direct detection reception in complex nonlinear environments.

[0017] To make the above-mentioned objects, features and advantages of this disclosure more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the accompanying drawings used in the embodiments will be briefly described below. These drawings are incorporated in and constitute a part of this specification. They illustrate embodiments conforming to this disclosure and, together with the specification, serve to explain the technical solutions of this disclosure. It should be understood that the following drawings only show some embodiments of this disclosure and should not be considered as limiting the scope. Those skilled in the art can obtain other related drawings based on these drawings without creative effort.

[0019] Figure 1A flowchart of a method for eliminating nonlinear impairments in a KK receiver, provided by an embodiment of this disclosure, is shown. Figure 2 A block diagram illustrating the principle of a method for eliminating nonlinear impairments in a KK receiver according to an embodiment of this disclosure is shown. Figure 3 A schematic diagram of an apparatus for eliminating nonlinear impairments in a KK receiver, provided by an embodiment of this disclosure, is shown. Figure 4 A schematic diagram of an electronic device provided in an embodiment of the present disclosure is shown. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. The components of the embodiments of this disclosure described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this disclosure provided in the accompanying drawings is not intended to limit the scope of the claimed disclosure, but merely represents selected embodiments of this disclosure. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without inventive effort are within the scope of protection of this disclosure.

[0021] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0022] In this document, the term "and / or" merely describes a relationship, indicating that three relationships can exist. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Furthermore, the term "at least one" in this document means any combination of at least two of any one or more elements. For example, including at least one of A, B, and C can mean including any one or more elements selected from the set consisting of A, B, and C.

[0023] Research has shown that the commonly used single-sideband (SSB) signal implementation scheme is optical SSB transmission based on IQ modulators, which has advantages such as simple structure, high signal quality, and a wide range of carrier-signal power ratio (CSPR) adjustment. IQ modulators typically require three bias controllers to stabilize the bias voltage and employ pilot-based ABC (Analog-Based Array) to eliminate bias voltage drift caused by temperature, mechanical vibration, and other external environmental changes. However, the double-sideband pilots introduced by the ABC device violate the minimum phase condition, leading to a degraded KK receiver performance. Furthermore, due to the square-law detection of the single-ended photodetector, beat frequency interference between the pilot and the signal cannot be completely eliminated by the KK receiver, thus significantly impacting system performance.

[0024] Based on the above research, this disclosure provides a method and apparatus for eliminating nonlinear impairments in a KK receiver. The method involves transmitting an optical signal via an optical fiber link, converting it into a corresponding photocurrent signal, and sampling the photocurrent signal to obtain a corresponding sampled received power signal. The sampled received power signal is then used to recover a restored field signal using the KK relation. In the digital domain, the recovered field signal is combined with a reference pilot signal to mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier field signal within the transmission system's frequency band, obtaining a modeling expression for the nonlinear impairment signal. The reconstructed nonlinear impairment signal is then determined based on this modeling expression. The reconstructed nonlinear impairment signal is combined with a measured impairment signal, and a normalization factor for amplitude normalization of the reconstructed nonlinear impairment signal is calculated using the least squares method. The reconstructed nonlinear impairment signal is then amplitude-scaled using the normalization factor, and the scaled reconstructed nonlinear impairment signal is subtracted from the sampled received power signal to determine the photocurrent signal after nonlinear impairment elimination. The step of recovering the sampled received power signal from the sampled received power signal using the KK relation is repeated, iteratively reducing the error signal until the residual nonlinear impairment in the recovered field signal approaches zero. This method enables accurate modeling and reconstruction of the beat frequency process between pilot and transmitted field signals, and between pilot and carrier field signals, within the digital domain of the KK receiver. By combining least-squares normalization and iterative feedback mechanisms, it effectively eliminates the nonlinear impairment introduced by pilot beat frequency from the sampled received power signal, significantly reducing residual nonlinear distortion in the recovered field signal. This not only reduces the system's requirements for transmitter bias stability and device linearity, improving bit error rate performance and Q-factor, but also increases the fiber optic transmission system's tolerance to optical signal-to-noise ratio degradation and the achievable transmission distance, realizing high-performance KK direct detection reception in complex nonlinear environments.

[0025] To facilitate understanding of this embodiment, a method for eliminating nonlinear impairments in a KK receiver, as disclosed in this disclosure, will first be described in detail. The execution entity of this method for eliminating nonlinear impairments in a KK receiver is generally a computer device with certain computing capabilities. This computer device may include, for example, a terminal device, a server, or other processing equipment. The terminal device can be a user equipment (UE), mobile device, user terminal, terminal, cellular phone, cordless phone, personal digital assistant (PDA), handheld device, computing device, vehicle-mounted device, wearable device, etc. In some possible implementations, this method for eliminating nonlinear impairments in a KK receiver can be implemented by a processor calling computer-readable instructions stored in memory.

[0026] See Figure 1 and Figure 2 As shown, Figure 1 A flowchart of a method for eliminating nonlinear impairments in a KK receiver, provided by an embodiment of this disclosure, is included in the method, comprising steps S101 to S105. Figure 2 A principle block diagram of a method for eliminating nonlinear impairments in a KK receiver provided in this disclosure embodiment, wherein: S101. After the optical signal is transmitted through the optical fiber link, it is converted into a corresponding photocurrent signal, and the photocurrent signal is sampled to obtain the corresponding sampling and receiving power signal.

[0027] In a specific implementation, the optical signal containing the low-frequency pilot signal from the automatic bias control device is transmitted through the optical fiber link of a preset distance, and then photoelectric conversion is performed by a photodetector at the receiving end to obtain the photocurrent signal; the photocurrent signal is sampled by an oscilloscope to obtain the sampled received power signal; and the sampled received power signal is preprocessed, including at least filtering, noise reduction and normalization.

[0028] Specifically, the optical signal, modulated by the IQ modulator and mixed with the low-frequency pilot signal from the automatic bias control device, is output from the transmitter and coupled into the optical fiber transmission link for transmission. Preferably, the optical fiber link uses standard single-mode fiber; in specific implementations, an 80 km length of standard single-mode fiber is selected to characterize typical medium-to-long-distance direct detection single-sideband transmission scenarios and ensure that the method of this invention can be verified for its effectiveness in eliminating nonlinear impairments under typical link conditions in actual engineering applications. After completing transmission over the 80 km standard single-mode fiber, the modulated optical signal reaches the receiver and enters the photoelectric conversion and sampling module.

[0029] Here, at the receiving end, a photodetector and a signal receiver electrically connected to it are provided to convert the optical signal transmitted through the optical fiber link into a corresponding photocurrent signal and complete high-speed sampling.

[0030] Specifically, the received single-sideband optical signal is first incident on a single-ended photodetector, which then converts the incident light power into a corresponding current signal for output.

[0031] In a preferred embodiment of the present invention, the single-sideband transmission signal is directly input to the sampling oscilloscope through a photodetector with a bandwidth of 50 GHz, ensuring sufficient receiving bandwidth for the spectral components of the 80 Gb / s single-sideband service signal, thereby avoiding additional amplitude and phase distortion due to insufficient receiver bandwidth.

[0032] Here, the photocurrent signal output by the photodetector is sent to a sampling oscilloscope (DSO) or an integrated optical module for discrete sampling. Under specific experimental conditions, the sampling rate of the sampling oscilloscope is 80 GSa / s. The photocurrent waveform over a continuous time period is sampled at equal time intervals to obtain a series of discrete sampling point data arranged in chronological order.

[0033] It should be noted that although the sampling rate of 80 GSa / s is somewhat different from the high sampling rate required by the theoretical KK receiver, in the system structure of this invention, this sampling rate is sufficient to completely record the amplitude change information of the optical signal after transmission through the optical fiber link and photoelectric conversion, providing sufficient raw data support for subsequent digital signal processing.

[0034] In this invention, the discrete-time series obtained by photodetector conversion and sampling oscilloscope or integrated optical module acquisition is collectively referred to as the sampled received power signal. In an optional implementation, the signal receiver may include a data acquisition card, integrated optical module, sampling oscilloscope, and other signal receiving devices with high-speed sampling capabilities, used to flexibly acquire photocurrent signals according to system configuration. Regardless of the specific hardware form used, the sampled received power signal that accurately reflects the link transmission and device characteristics is obtained by photoelectric conversion and high-speed sampling of the optical signal output from the fiber optic link, providing the basic input for subsequent preprocessing, field recovery, and nonlinear damage modeling and elimination steps in this invention.

[0035] Furthermore, after transmitting the optical signal via the optical fiber link and completing photoelectric conversion and sampling to obtain the sampled received power signal, the sampled received power signal is preprocessed to provide stable input data for subsequent KK field recovery, nonlinear damage modeling, and iterative feedback elimination algorithms.

[0036] Specifically, the present invention sets up a signal preprocessing unit in the digital signal processing module to perform a series of operations on the sampled received power signal, including at least filtering and normalization, so as to suppress high-frequency noise, measurement noise and distortion introduced by device bandwidth limitation in the sampled received power signal. At the same time, it unifies the sampled received power signals obtained under different experimental conditions to a preset amplitude and scale range, ensuring the convergence and comparability of subsequent processing.

[0037] In one embodiment of the present invention, the sampled received power signal is first input to a digital domain filtering module, where a reasonably designed digital filter is used to filter and denoise the signal. The filtering can be performed using low-pass filtering, band-pass filtering, or other equivalent digital filtering structures, depending on the system bandwidth and the spectral distribution of the transmitted signal. This retains useful components falling within the effective frequency band of the service signal while suppressing noise components exceeding the effective frequency band and spurious spectral components introduced by the limited sampling bandwidth of the oscilloscope. Through this filtering process, random fluctuations caused by photodetector thermal noise, oscilloscope quantization noise, and environmental electromagnetic interference are effectively reduced. Furthermore, the impact of sharp pulses or isolated anomalies caused by fiber optic link dispersion and device response on subsequent calculations is weakened, resulting in a pre-processed intermediate signal with a smoother waveform and a higher signal-to-noise ratio.

[0038] After filtering and denoising, the present invention further normalizes the sampled received power signal. Specifically, by statistically analyzing the amplitude distribution of the sampled received power signal within a preset time window, the signal is scaled up to a predetermined amplitude range. For example, using the average power or peak value of the photocurrent signal as a reference, the signal amplitude is mapped to a uniform numerical range. If necessary, the DC component of the signal can also be corrected to make its mean close to zero.

[0039] Thus, through the above normalization operation, on the one hand, the influence of differences in light source output power, photodetector gain, and sampling device range under different test conditions on the accuracy of subsequent KK field recovery and damage modeling can be avoided; on the other hand, it helps to improve the stability of numerical calculations and prevent overflow or underflow in steps such as exponential and integral operations. The sampled received power signal, after filtering, denoising, and normalization preprocessing, is used as the preprocessed photocurrent signal input to the KK receiver module for subsequent field recovery, nonlinear damage modeling, and iterative feedback elimination steps.

[0040] S102. The sampled received power signal is recovered into a recovered field signal using the KK relationship. In the digital domain, the recovered field signal is combined with the reference pilot signal to mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier field signal within the transmission system frequency band, thereby obtaining the modeling expression for the nonlinear damaged signal. The reconstructed nonlinear damaged signal is then determined based on the modeling expression.

[0041] In practice, after filtering, denoising and normalizing the sampled received power signal, the preprocessed sampled received power signal is first input into the KK receiver module, and the intensity signal is restored to the corresponding complex field signal using the KK relationship.

[0042] Specifically, the preprocessed sampled received power signal can be considered as the photocurrent waveform obtained after square-law detection by a single-ended photodetector, which has a definite functional relationship with the amplitude of the incident light field envelope. In the digital signal processing module, this invention performs normalization, logarithmic calculation, Hilbert transform, and exponential restoration on the photocurrent signal to obtain the recovered field signal E that satisfies the minimum phase condition assumption. s .

[0043] In practical implementation, the KK relationship recovery can be achieved through Matlab, Python or other data processing platforms. The above operation is performed on the photocurrent sample at each sampling time to obtain a series of discrete sequences of recovered field signals that correspond one-to-one with the sampled received power signals, providing an optical field information basis for subsequent pilot-based nonlinear damage modeling.

[0044] Here, after obtaining the recovered field signal, the present invention introduces a reference pilot signal in the digital domain that is completely identical to the pilot used in the transmitter ABC. The reference pilot signal is a double-sideband low-frequency pilot with known frequency, amplitude, and phase characteristics, which is represented in the digital domain as a complex exponential form with two symmetrical frequency components, positive and negative, to accurately characterize the perturbation introduced by the ABC pilot in the photocurrent mathematical model.

[0045] In this invention, the recovered field signal and the reference pilot signal are multiplied in the digital domain. On the one hand, the beat frequency term between the pilot and the transmitted field signal can be explicitly constructed. On the other hand, the beat frequency term between the pilot and the carrier field signal can be constructed by combining the known amplitude and phase information of the carrier field signal, thereby reconstructing the beat frequency process corresponding to the nonlinear impairment in the actual receiving link in the digital domain.

[0046] Specifically, this invention provides a theoretical description of the photocurrent waveform at the receiving end based on a mathematical model of photocurrent with pilot signals added. After adding pilot signals, the photocurrent model can be expressed as: carrier field signal E0 and transmission field signal E... s The square-law combination includes the signal itself and the carrier-signal beat frequency component E0E. s Terms such as pilot-transmit signal beat frequency components and pilot-carrier beat frequency components, as well as second-order terms of the pilot signal itself.

[0047] It should be noted that the pilot used in this invention is a double-sideband pilot. During modeling, it is multiplied by the recovered field signal and the carrier field signal respectively to obtain a series of beat frequency components centered on the bandwidth of the service signal. Through spectral analysis of these beat frequency components, the pilot-transmission field signal beat frequency term and the pilot-carrier field signal beat frequency term falling within the effective signal band of the transmission system are selected as the main components of the nonlinear impairment signal. The second-order term of the pilot signal and the beat frequency components outside the effective band are considered as higher-order small quantities with minimal impact on system performance and are ignored in the mathematical modeling process, thereby simplifying the model and reducing computational complexity.

[0048] Based on this, according to the phase and amplitude relationships of each beat frequency component in the photocurrent mathematical model, this invention performs a weighted linear superposition of the aforementioned pilot-transmit field signal beat frequency components and pilot-carrier field signal beat frequency components according to predetermined coefficients, constructing a complete nonlinear damage signal modeling expression. This modeling expression uses the recovery field signal E... s Using the frequency and amplitude parameters of the carrier field signal E0 and the pilot signal as independent variables, and several undetermined coefficients used to characterize the nonlinear characteristics of the system and the device response as parameters, this invention can fit the multi-carrier beat frequency nonlinear impairment introduced by the ABC pilot within the transmission system's frequency band in the digital domain. In other words, by combining the recovered field signal with the reference pilot signal, this invention utilizes the known nonlinear impairment model and hybrid beat frequency model in the system to perform a unified mathematical modeling of the impairment signal, obtaining an analytical expression for the impairment signal that can be calculated at the sample level.

[0049] In actual operation, the digital signal processing module calls the above nonlinear damage modeling expression and substitutes the corresponding E for each recovery field signal sample point. s By taking the instantaneous values ​​of E0 and the reference pilot signal, the corresponding nonlinear damage estimate is calculated, thus obtaining a reconstructed nonlinear damage signal waveform that varies over time. This reconstructed nonlinear damage signal exhibits high consistency in statistical characteristics and spectral distribution with the nonlinear interference generated by pilot-signal beat frequencies and pilot-carrier beat frequencies in the actual photocurrent, and can be considered a mathematical fit to the real damage signal. Subsequently, by performing amplitude normalization matching between this reconstructed nonlinear damage signal and the measured damage signal, and subtracting it sample by sample from the sampled received power signal, the pilot-related nonlinear damage in the KK receiver can be gradually eliminated, providing accurate prior damage information for subsequent least-squares normalization and iterative feedback steps.

[0050] As one possible implementation, based on the photocurrent mathematical model after incorporating the pilot signal, the positive and negative frequency components of the carrier field signal, the transmission field signal, and the reference pilot signal are expanded into multiplication terms. From the multiplication terms, the beat frequency components of the pilot and transmission field signals and the beat frequency components of the pilot and carrier signals that fall within the effective signal band of the system are selected as the constituent components of the nonlinear damage signal. The second-order terms of the pilot signal and the beat frequency components that exceed the effective frequency band are ignored. The constituent components are weighted and linearly superimposed according to the phase and amplitude relationship in the photocurrent mathematical model to obtain a modeling expression with the carrier field signal, the transmission field signal, and the pilot frequency components as independent variables and undetermined coefficients as parameters, which serves as the mathematical model for reconstructing the nonlinear damage signal.

[0051] In a preferred embodiment of the present invention, in order to accurately reconstruct the nonlinear damage introduced by the pilot signal of the automatic bias control device in the digital domain, this scheme, based on the mathematical model of the received photocurrent, represents the carrier field signal, the transmission field signal, and the reference pilot signal in the frequency domain as a complex field envelope composed of several narrowband frequency components superimposed; wherein, the reference pilot signal has a double-sideband structure, which is further decomposed into mutually symmetrical positive and negative frequency components. Subsequently, the positive and negative frequency components of the carrier field signal, the transmission field signal, and the pilot signal are substituted into the mathematical model of the photocurrent containing the pilot, and all multiplication terms are expanded according to the square-law detection mechanism, thereby obtaining a series of beat frequency components containing different frequency centers and different bandwidths.

[0052] By performing spectral analysis on these multiplication terms and combining it with the effective signal bandwidth of the transmission system, the spectral position of each beat frequency component is determined: all pilot and transmission field signal beat frequency components, as well as pilot and carrier field signal beat frequency components whose spectra fall within the effective signal bandwidth of the system and are comparable to or partially overlap with the spectral width of the transmission service signal, are selected as components constituting the nonlinear impairment signal of this invention; while the second-order terms of the pilot itself have relatively small amplitudes and weak impact on system performance, so they are ignored in the modeling process. Similarly ignored are various high-frequency beat frequency components that are significantly outside the effective signal bandwidth, thereby reducing computational complexity while ensuring modeling accuracy.

[0053] After completing the above screening, this invention constructs a modeling expression for a nonlinear impairment signal by weighted linear superposition of the selected pilot and transmission field signal beat frequency components and the pilot and carrier field signal beat frequency components, based on the phase and amplitude relationships of each beat frequency component in the photocurrent mathematical model. This modeling expression uses the frequency components of the carrier field signal, transmission field signal, and pilot signal as independent variables, and several undetermined coefficients representing physical quantities such as the photodetector response coefficient, link gain, and nonlinear coupling strength as parameters. It can approximate and fit the nonlinear impairment caused by multi-carrier beat frequencies within the transmission system's frequency band in the digital domain.

[0054] Using this modeling expression, the recovered field signal obtained from the KK relationship and the known reference pilot signal are substituted into the actual calculation to calculate the reconstructed nonlinear damage signal waveform sample by sample.

[0055] As another possible implementation, after recovering the sampled received power signal into a recovered field signal using the KK relation, digital domain dispersion compensation is performed on the recovered field signal, and equalization technology is used to compensate for channel distortion to determine the equalized symbol sequence; symbol decision is performed on the symbol sequence to determine the decided QAM symbol, and the QAM symbol is remodulated to obtain a service signal that does not contain pilot beat frequency interference; the channel response obtained during the equalization process is applied to the service signal, and the inverse process of digital domain dispersion compensation is performed to obtain a reconstructed field signal with less beat frequency interference.

[0056] In the implementation of this invention, after preprocessing the sampled received power signal and recovering it into a complex form using the KK relation, the recovered field signal is first subjected to dispersion compensation processing in the digital domain.

[0057] Specifically, by combining known fiber dispersion parameters and link length, dispersion compensation calculations are performed on the recovered field signal in the frequency domain to counteract the first-order or higher-order dispersion effects accumulated in the standard single-mode fiber during transmission. This results in the pulse broadening of the compensated field signal being compressed in the time domain and the inter-symbol crosstalk being significantly reduced, thereby recovering a waveform that is closer to that of the transmitter.

[0058] Subsequently, based on the recovered field signal after dispersion compensation, digital equalization technology is further introduced to compensate for linear channel distortion introduced by the fiber optic link, photodetector, and receiver front-end filtering. The equalization module can adopt structures such as decision feedback equalizers, linear equalizers, or frequency domain equalizers, and can adaptively update the equalization coefficients through training sequences or blind equalization algorithms to achieve a relatively ideal equalization effect under different link conditions and operating states. After the joint processing of dispersion compensation and equalization, field signal sampling points with significantly reduced waveform distortion are obtained, which can be demapped to form the equalized symbol sequence used for subsequent decision-making.

[0059] Here, after obtaining the equalized symbol sequence, the present invention performs a symbol decision operation on the symbol sequence, mapping each symbol sample to the nearest ideal QAM constellation point on its constellation diagram, thereby obtaining the decided QAM symbol sequence. Since this QAM symbol is an ideal discrete symbol recovered based on the prior information of the equalized post-field signal and modulation format, it can be regarded as an estimate of the original digital symbols at the transmitting end in a statistical sense.

[0060] Next, the QAM symbols after the decision are used as the information source and remodulated according to the modulation format and frame structure adopted by the transmitter. For example, in the implementation of multi-carrier orthogonal frequency division multiplexing, the QAM symbols after the decision can be remapped to each subcarrier, inverse fast Fourier transform is performed and a cyclic prefix is ​​added to obtain the service signal reconstructed in the digital baseband domain.

[0061] It should be noted that since this service signal has not undergone the ABC pilot injection and square law detection process in the actual physical link, it inherently does not contain beat frequency interference between the pilot and the transmission field signal, or between the pilot and the carrier field signal, and can be regarded as a service signal that does not contain pilot beat frequency interference.

[0062] Furthermore, to ensure that the reconstructed field signal approximates the linear distortion characteristics of the actual transmission link as closely as possible, this invention further utilizes the channel response estimated during the equalization process to process the aforementioned service signal. Specifically, when the equalization module solves for the equalization coefficients or constructs the frequency domain equalization filter, a channel response function H characterizing the overall linear transmission characteristics of the optical fiber link and the receiver can be obtained simultaneously.

[0063] This invention applies the channel response to the remodulated service signal, which is equivalent to performing a forward channel simulation on the ideal service signal in the digital domain, thereby re-superimposing linear distortions in amplitude and phase consistent with the actual transmission link. Subsequently, the service signal with the channel response applied is subjected to the inverse process of digital domain dispersion compensation, which is the opposite of the aforementioned dispersion compensation. That is, the frequency domain compensation transfer function originally used in the dispersion compensation stage is conjugate or inversely operated and applied to the service signal after channel response processing, thereby constructing a reconstructed field signal that matches the input conditions of the KK receiver and is basically free of pilot beat frequency interference.

[0064] It should be noted that the reconstructed field signal is denoted as E in this invention. s,remod Its time-domain waveform and spectral distribution can closely approximate the ideal state of the actual received field signal after removing pilot-related nonlinear interference, providing a high-fidelity field signal input for subsequent nonlinear damage beat frequency modeling and reconstruction in the digital domain by combining it with the reference pilot signal.

[0065] S103. Combine the reconstructed nonlinear damage signal with the measured damage signal, and calculate the normalization factor for amplitude normalization of the reconstructed nonlinear damage signal using the least squares method.

[0066] In a specific implementation, after obtaining the reconstructed nonlinear damage signal, the present invention further combines the reconstructed nonlinear damage signal with the measured damage signal, and calculates the normalization factor used to normalize the amplitude of the reconstructed nonlinear damage signal by the least squares method.

[0067] Specifically, a time window for fitting is first extracted in the digital signal processing module. Within this time window, the reconstructed nonlinear damage signal sequence obtained by mathematical modeling and the measured damage signal sequence obtained by processing the photocurrent signal acquired by the oscilloscope are recorded respectively.

[0068] The measured damage signal can be understood as the nonlinear interference component introduced by the beat frequency of the pilot and transmitted field signals, and the pilot and carrier field signals, in the sampled received power signal after removing the linear components. Then, an error signal sequence is constructed, where each sampling point is equal to the difference between the measured damage signal and the reconstructed nonlinear damage signal after the normalization factor α is applied at the same time. That is, the error signal is the measured damage minus α times the reconstructed damage.

[0069] In this way, by accumulating the power or mean square value of the error signal within the entire time window and taking the minimum mean square error as the optimization objective, the analytical solution of the optimal normalization factor in the least squares sense can be obtained, thereby achieving accurate estimation and matching of the amplitude of the reconstructed nonlinear damage signal.

[0070] In practical implementation, the present invention preferably uses the normalization factor obtained by the above least squares calculation as the initial normalization factor. With this initial value as the center, the normalization factor α is scanned within a preset step size and range. Under each candidate value of α, the operation of reconstructing the damaged signal scaling and subtracting the scaled reconstructed damaged signal from the sampled received power signal is performed once, and the performance index of the transmission system under the corresponding conditions is calculated.

[0071] For example, performance metrics may include bit error rate, Q factor, and / or error vector magnitude.

[0072] Furthermore, after comparing the system performance corresponding to each candidate α value, the α corresponding to the optimal performance index is selected as the final optimal normalization factor, and this optimal normalization factor is fixed and applied to the subsequent iterative feedback elimination process to perform amplitude normalization processing on the reconstructed nonlinear damage signal obtained in each iteration.

[0073] S104. The reconstructed nonlinear damage signal is scaled using the normalization factor, and the scaled reconstructed nonlinear damage signal is subtracted from the sampled received power signal to determine the photocurrent signal after nonlinear damage elimination.

[0074] In the implementation of this invention, after determining the normalization factor for amplitude normalization using the least squares method, the normalization factor is applied to the aforementioned reconstructed nonlinear damage signal to scale its amplitude, so as to obtain a reconstructed damage signal waveform that is consistent with the amplitude of nonlinear damage in the actual link.

[0075] Specifically, the reconstructed nonlinear damage signal obtained by the mathematical model of the beat frequency of the pilot and transmitted field signals and the pilot and carrier field signals is used as a reference. The amplitude of the signal is scaled up point by point by a normalization factor so that the scaled reconstructed nonlinear damage signal is as close as possible to the real nonlinear interference component introduced by the ABC pilot in the sampled received power signal in terms of amplitude and phase. In this way, a reconstructed damage current sequence that is highly consistent with the actual damage signal in the time domain is obtained.

[0076] After obtaining the reconstructed nonlinear damage signal after normalization, the present invention performs point-to-point subtraction on it and the sampled received power signal acquired by the oscilloscope in the digital domain. That is, at each sampling time, the reconstructed nonlinear damage signal after normalization factor scaling is subtracted from the corresponding sampled received power signal, which is mathematically equivalent to canceling the pilot-related nonlinear interference component in the photocurrent.

[0077] Through the above calculations, the multi-carrier nonlinear crosstalk caused by the beat frequency of pilot and single-sideband service signals can be effectively eliminated, so that the remaining signal mainly contains the desired linear transmission components and unavoidable noise components.

[0078] It should be noted that the new photocurrent sequence obtained by this subtraction operation is defined in this invention as the photocurrent signal after nonlinear damage elimination. Its waveform and spectral characteristics are significantly improved compared with the original sampled received power signal, providing a cleaner and less distorted input basis for subsequent iterative feedback processing and KK field recovery, thereby significantly improving the performance and convergence effect of the entire transmission system.

[0079] S105. Repeat the step of using the KK relationship to recover the sampled received power signal into a recovered field signal, and gradually reduce the error signal in an iterative feedback manner until the residual nonlinear damage in the recovered field signal approaches zero.

[0080] In practice, after completing the field recovery based on the KK relationship, nonlinear damage modeling, normalization scaling, and subtracting the reconstructed nonlinear damage signal from the sampled received power signal, the signal processing flow is not directly ended. Instead, the photocurrent signal after nonlinear damage elimination is introduced as a new input signal into the KK receiver module for field recovery and subsequent digital signal processing.

[0081] Specifically, the photocurrent signal obtained from the previous round of damage elimination is first filtered to remove its DC component, and then preprocessing steps such as filtering, denoising, and normalization are repeated as needed. The updated photocurrent signal is then regarded as a new sampled received power signal, and the KK relationship is used to recover the new recovered field signal. Subsequently, the process of using the recovered field signal and the reference pilot signal to model the nonlinear damage signal, updating or calling the predetermined normalization factor through the least squares method, scaling the amplitude of the reconstructed nonlinear damage signal, and subtracting it from the updated sampled received power signal is repeated, thus forming a closed iterative feedback loop.

[0082] In this iterative feedback loop, the present invention defines an error signal that evolves with the number of iterations, used to characterize the deviation between the current recovered field signal and the ideal field signal, or to characterize the difference between the measured damage signal and the normalized reconstructed nonlinear damage signal.

[0083] Here, under the condition of no DC component, the error signal can be expressed as a function of the residual nonlinear damage component in the current iteration through the corresponding mathematical expression. Each complete iteration of KK field recovery—nonlinear damage modeling—normalization scaling—damage cancellation involves recalculating the error signal. By monitoring the power or mean square value of the error signal, it can be observed that the amplitude of the error signal gradually decreases with the increase of the iteration number, meaning that the residual nonlinear damage is weakened step by step. Mathematically, the iterative formula drives the recovered field signal to continuously converge towards an ideal field signal without nonlinear interference, until the error signal approaches zero.

[0084] Therefore, this invention repeatedly utilizes the KK relation to recover the updated sampled received power signal into a recovered field signal. After each round of recovery, it incorporates pilot-assisted nonlinear impairment modeling and reconstruction, normalization factor scaling, and subtraction of the reconstructed impairment signal from the received signal, forming an iterative feedback loop. This allows residual pilot-related nonlinear impairments in the recovered field signal to be gradually suppressed during continuous iteration. When the iteration reaches a certain round, if the mean square value of the error signal is less than a preset convergence threshold, or if further iterations improve the system's bit error rate, Q-factor, and other performance indicators negligible, the residual nonlinear impairments in the recovered field signal can be considered to have approached zero. At this point, the iteration process ends. The recovered field signal and corresponding photocurrent signal obtained from this round of iteration are used as the final signal after nonlinear impairment elimination for subsequent demodulation and performance evaluation, thereby achieving high-precision, low-complexity suppression of nonlinear impairments in KK receivers.

[0085] This disclosure provides a method for eliminating nonlinear impairments in a KK receiver. The method involves transmitting an optical signal via an optical fiber link, converting it into a corresponding photocurrent signal, and sampling the photocurrent signal to obtain a corresponding sampled received power signal. The sampled received power signal is then used to recover a complex field signal using the KK relation. In the digital domain, the recovered field signal is combined with a reference pilot signal to mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier field signal within the transmission system's frequency band, obtaining a modeling expression for the nonlinear impairment signal. Based on this modeling expression, a reconstructed nonlinear impairment signal is determined. The reconstructed nonlinear impairment signal is then combined with a measured impairment signal, and a normalization factor for amplitude normalization of the reconstructed nonlinear impairment signal is calculated using the least squares method. The reconstructed nonlinear impairment signal is then amplitude-scaled using the normalization factor, and the scaled reconstructed nonlinear impairment signal is subtracted from the sampled received power signal to determine the photocurrent signal after nonlinear impairment elimination. The step of recovering the recovered field signal from the sampled received power signal using the KK relation is repeated, iteratively reducing the error signal until the residual nonlinear impairment in the recovered field signal approaches zero. This method enables accurate modeling and reconstruction of the beat frequency process between pilot and transmitted field signals, and between pilot and carrier field signals, within the digital domain of the KK receiver. By combining least-squares normalization and iterative feedback mechanisms, it effectively eliminates the nonlinear impairment introduced by pilot beat frequency from the sampled received power signal, significantly reducing residual nonlinear distortion in the recovered field signal. This not only reduces the system's requirements for transmitter bias stability and device linearity, improving bit error rate performance and Q-factor, but also increases the fiber optic transmission system's tolerance to optical signal-to-noise ratio degradation and the achievable transmission distance, realizing high-performance KK direct detection reception in complex nonlinear environments.

[0086] The above scheme will now be described in conjunction with specific implementation methods.

[0087] The optical signal modulated by the IQ modulator is transmitted through an 80km optical fiber link. The photoelectric converter (PD) converts the received optical signal into a photocurrent signal (I) and then resamples it. The sampled photocurrent signal obtained after photoelectric conversion and resampling is then subjected to noise reduction and normalization preprocessing.

[0088] After preprocessing, the photocurrent signal is recovered into a field signal (E) using the KK relation. S The process involves digital domain dispersion compensation, followed by equalization to compensate for channel distortion, and finally symbol decision. The decided QAM symbols are then remodulated to obtain an OFDM signal free of pilot beat frequency interference. The channel response H obtained during equalization is applied to the remodulated OFDM signal, and then subjected to the inverse process of digital domain dispersion compensation to obtain an E signal with minimal beat frequency interference. s,remodE s,remod The beat frequency interference between the pilot signal and the signal within the spectral band is reconstructed using the pilot signal referenced in the digital domain, and the corresponding expression is obtained.

[0089] Next, the amplitude range of the reconstructed signal impairment is limited using a corresponding α scaling factor, and then the reconstructed beat frequency interference is subtracted from the received photocurrent signal I. DC is filtered out, and subsequent signal processing is the same as for a conventional KK receiver, with iterative loops performed until the system performance reaches its optimal level.

[0090] The mathematical model expression for the pilot signal is:

[0091] The mathematical model expression for the photocurrent with the pilot signal added is:

[0092] Among them, E s For the transmitted signal, E0 is the carrier field signal, E0Es is the carrier-signal beat frequency signal, and E... dither The frequency components of the pilot signal. E s cos( ω d t () is the beat frequency signal of the pilot-transmission signal, E0E dither For the carrier pilot beat frequency signal, the last term in the formula is the second-order term of the pilot signal, which is usually small and can be ignored.

[0093] In this case, the mathematical expression for the recovered signal is:

[0094] The mathematical expression for the error signal:

[0095] The mathematical expression for the reconstructed damage signal is:

[0096] In the absence of a DC component, the mathematical expression for iterative damage elimination in the algorithm is:

[0097] Through continuous iteration, the field signal E in the recovered signal is continuously reduced until the error signal D approaches 0, achieving the best algorithm recovery effect.

[0098] Those skilled in the art will understand that, in the above-described method of the specific implementation, the order in which each step is written does not imply a strict execution order and does not constitute any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

[0099] Based on the same inventive concept, this disclosure also provides an apparatus for eliminating nonlinear impairments in a KK receiver, corresponding to the method for eliminating nonlinear impairments in a KK receiver. Since the principle of the apparatus in this disclosure for solving the problem is similar to the method for eliminating nonlinear impairments in a KK receiver described above, the implementation of the apparatus can refer to the implementation of the method, and repeated details will not be repeated.

[0100] Please see Figure 3 , Figure 3 This is a schematic diagram of an apparatus for eliminating nonlinear impairments in a KK receiver, provided as an embodiment of this disclosure. Figure 3 As shown in the illustration, the apparatus 300 for eliminating nonlinear impairments in a KK receiver provided in this embodiment includes: The optical signal conversion module 310 is used to convert the optical signal into a corresponding photocurrent signal after transmission through the optical fiber link, and to sample the photocurrent signal to obtain the corresponding sampling and receiving power signal.

[0101] The nonlinear damage modeling module 320 is used to recover the sampled received power signal into a recovered field signal using the Cramer-Kronig relation, combine the recovered field signal with the reference pilot signal in the digital domain, mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier field signal within the transmission system frequency band, obtain the modeling expression of the nonlinear damage signal, and determine the reconstructed nonlinear damage signal based on the modeling expression.

[0102] The normalization factor determination module 330 is used to combine the reconstructed nonlinear damage signal with the measured damage signal and calculate the normalization factor used to normalize the amplitude of the reconstructed nonlinear damage signal by least squares method.

[0103] The damage elimination module 340 is used to scale the reconstructed nonlinear damage signal using the normalization factor and subtract the scaled reconstructed nonlinear damage signal from the sampled received power signal to determine the photocurrent signal after nonlinear damage elimination.

[0104] The iterative feedback module 350 is used to repeatedly utilize the Cramer-Kronig relation to recover the sampled received power signal into a recovered field signal, and gradually reduce the error signal in an iterative feedback manner until the residual nonlinear damage in the recovered field signal approaches zero.

[0105] The processing flow of each module in the device and the interaction flow between each module can be referred to the relevant descriptions in the above method embodiments, and will not be detailed here.

[0106] This disclosure provides an apparatus for eliminating nonlinear impairments in a KK receiver. The apparatus converts an optical signal transmitted via an optical fiber link into a corresponding photocurrent signal, and samples the photocurrent signal to obtain a corresponding sampled received power signal. Using the KK relation, the sampled received power signal is recovered to a restored field signal. In the digital domain, the restored field signal is combined with a reference pilot signal to mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier field signal within the transmission system's frequency band, obtaining a modeling expression for the nonlinear impairment signal. Based on this modeling expression, a reconstructed nonlinear impairment signal is determined. The reconstructed nonlinear impairment signal is combined with a measured impairment signal, and a normalization factor for amplitude normalization of the reconstructed nonlinear impairment signal is calculated using the least squares method. The normalization factor is used to scale the amplitude of the reconstructed nonlinear impairment signal, and the scaled reconstructed nonlinear impairment signal is subtracted from the sampled received power signal to determine the photocurrent signal after nonlinear impairment elimination. The step of recovering the sampled received power signal to a restored field signal using the KK relation is repeated, iteratively reducing the error signal until the residual nonlinear impairment in the restored field signal approaches zero. This method enables accurate modeling and reconstruction of the beat frequency process between pilot and transmitted field signals, and between pilot and carrier field signals, within the digital domain of the KK receiver. By combining least-squares normalization and iterative feedback mechanisms, it effectively eliminates the nonlinear impairment introduced by pilot beat frequency from the sampled received power signal, significantly reducing residual nonlinear distortion in the recovered field signal. This not only reduces the system's requirements for transmitter bias stability and device linearity, improving bit error rate performance and Q-factor, but also increases the fiber optic transmission system's tolerance to optical signal-to-noise ratio degradation and the achievable transmission distance, realizing high-performance KK direct detection reception in complex nonlinear environments.

[0107] Corresponding to Figure 1 The present disclosure also provides an electronic device 400 for eliminating nonlinear impairments in a KK receiver, as described in the method for eliminating nonlinear impairments in a KK receiver. Figure 4 The diagram shown is a structural schematic of an electronic device 400 provided in an embodiment of this disclosure, including: Processor 41, memory 42, and bus 43; memory 42 is used to store execution instructions, including main memory 421 and external memory 422; the main memory 421, also called internal memory, is used to temporarily store the computational data in processor 41, as well as the data exchanged with external memory 422 such as hard disk. Processor 41 exchanges data with external memory 422 through main memory 421. When the electronic device 400 is running, processor 41 and memory 42 communicate through bus 43, enabling processor 41 to execute... Figure 1 The steps of the method for eliminating nonlinear impairments in a KK receiver.

[0108] This disclosure also provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of the method for eliminating nonlinear impairments in a KK receiver as described in the above-described method embodiments. The storage medium can be a volatile or non-volatile computer-readable storage medium.

[0109] This disclosure also provides a computer program product, which includes computer instructions. When the computer instructions are executed by a processor, they can perform the steps of the method for eliminating nonlinear impairments in the KK receiver described in the above method embodiments. For details, please refer to the above method embodiments, which will not be repeated here.

[0110] The aforementioned computer program product can be implemented through hardware, software, or a combination thereof. In one optional embodiment, the computer program product is specifically embodied in a computer storage medium; in another optional embodiment, the computer program product is specifically embodied in a software product, such as a software development kit (SDK), etc.

[0111] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the device described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here. In the several embodiments provided in this disclosure, it should be understood that the disclosed device and method can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Another point is that the displayed or discussed mutual coupling or direct coupling or communication connection may be through some communication interfaces; the indirect coupling or communication connection of devices or units may be electrical, mechanical, or other forms.

[0112] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0113] In addition, the functional units in the various embodiments of this disclosure can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0114] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this disclosure, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this disclosure. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0115] Finally, it should be noted that the above-described embodiments are merely specific implementations of this disclosure, used to illustrate the technical solutions of this disclosure, and not to limit it. The protection scope of this disclosure is not limited thereto. Although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this disclosure. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this disclosure, and should all be covered within the protection scope of this disclosure. Therefore, the protection scope of this disclosure should be determined by the protection scope of the claims.

Claims

1. A method for eliminating nonlinear impairments in a KK receiver, characterized in that, include: After the optical signal is transmitted through the optical fiber link, it is converted into a corresponding photocurrent signal, and the photocurrent signal is sampled to obtain the corresponding sampling and receiving power signal. The sampled received power signal is recovered into a recovered field signal using the Cramer-Kronig relation. In the digital domain, the recovered field signal is combined with the reference pilot signal to mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier field signal within the transmission system's frequency band. This yields a modeling expression for the nonlinear damaged signal, and the reconstructed nonlinear damaged signal is determined based on the modeling expression. The reconstructed nonlinear damage signal is combined with the measured damage signal, and the normalization factor used for amplitude normalization of the reconstructed nonlinear damage signal is calculated by the least squares method. The reconstructed nonlinear damage signal is scaled using the normalization factor, and the scaled reconstructed nonlinear damage signal is subtracted from the sampled received power signal to determine the photocurrent signal after nonlinear damage elimination. The step of repeatedly using the Cramer-Kronig relation to recover the sampled received power signal into a recovered field signal is used to gradually reduce the error signal in an iterative feedback manner until the residual nonlinear impairment in the recovered field signal approaches zero.

2. The method according to claim 1, characterized in that, After the optical signal is transmitted through the optical fiber link, it is converted into a corresponding photocurrent signal, and the photocurrent signal is sampled to obtain the corresponding sampling and receiving power signal, specifically including: The optical signal, which contains the low-frequency pilot signal from the automatic bias control device, is transmitted through the optical fiber link of a preset distance, and then undergoes photoelectric conversion by a photodetector at the receiving end to obtain the photocurrent signal. The photocurrent signal is sampled using an oscilloscope to obtain the sampled received power signal. The sampled received power signal undergoes preprocessing including at least filtering, noise reduction, and normalization.

3. The method according to claim 1, characterized in that, After recovering the sampled received power signal into a recovered field signal using the KK relationship, the method further includes: Digital domain dispersion compensation is performed on the recovered field signal, and equalization technology is used to compensate for channel distortion to determine the equalized symbol sequence; A symbol decision is performed on the symbol sequence to determine the QAM symbol after the decision, and the QAM symbol is remodulated to obtain a service signal that does not contain pilot beat frequency interference. The channel response obtained during the equalization process is applied to the service signal, and the inverse process of digital domain dispersion compensation is performed to obtain a reconstructed field signal with less beat frequency interference.

4. The method according to claim 1, characterized in that, In the digital domain, the recovered field signal is combined with the reference pilot signal to mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier signal within the system's frequency band. Specifically, this includes: Based on the photocurrent mathematical model after incorporating the reference pilot signal, the frequency components of the carrier field signal, the transmission field signal, and the reference pilot signal are expanded into multiplication terms. From the multiplication terms, select the pilot and transmission field signal beat frequency components and the pilot and carrier signal beat frequency components that fall within the effective signal frequency band of the system as the constituent components of the nonlinear damage signal; Ignore the second-order terms of the pilot signal and the beat frequency components that are outside the effective frequency band; The constituent components are weighted and linearly superimposed according to the phase and amplitude relationship in the photocurrent mathematical model to obtain the modeling expression with the carrier field signal, the transmission field signal and the pilot frequency component as independent variables and undetermined coefficients as parameters, which serves as the mathematical model for reconstructing the nonlinear damage signal.

5. The method according to claim 1, characterized in that, The reconstructed nonlinear damage signal is combined with the measured damage signal, and a normalization factor for amplitude normalization of the reconstructed nonlinear damage signal is calculated using the least squares method. Specifically, this includes: With the goal of minimizing the energy difference between the reconstructed nonlinear damage signal and the measured damage signal within a preset time window, the initial normalization factor is determined using a least-squares fitting method. A parameter scanning range with a preset step size is selected near the initial normalization factor, and the optimal normalization factor is determined based on the criterion that the preset performance index of the transmission system reaches its optimum. In each subsequent iteration, the optimal normalization factor is used to scale the amplitude of the reconstructed nonlinear damage signal.

6. The method according to claim 1, characterized in that, The step of repeatedly using the KK relationship to recover the sampled power signal into a recovered field signal, and gradually reducing the error signal through iterative feedback, specifically includes: In each iteration, the DC component of the photocurrent signal obtained in the current iteration after nonlinear damage elimination is filtered out to obtain the updated sampled received power signal; By repeatedly performing the steps of recovering the field signal, nonlinear damage modeling, normalization factor scaling, and damage signal elimination using the updated sampled received power signal, a new error signal is obtained. When the change in the mean square value of the error signal relative to the previous iteration is lower than a preset threshold, or when the number of iterations reaches a preset maximum number of iterations, the iteration is determined to be converged, and the updated sampled received power signal is used as the final photocurrent signal after nonlinear damage elimination.

7. An apparatus for eliminating nonlinear impairments in a KK receiver, characterized in that, include: The optical signal conversion module is used to convert the optical signal transmitted through the optical fiber link into the corresponding photocurrent signal, and to sample the photocurrent signal to obtain the corresponding sampling and receiving power signal. The nonlinear damage modeling module is used to recover the sampled received power signal into a recovered field signal using the Cramer-Kronig relation, combine the recovered field signal with the reference pilot signal in the digital domain, mathematically model the beat frequency process between the pilot and the transmitted field signal, and between the pilot and the carrier field signal within the transmission system frequency band, obtain the modeling expression of the nonlinear damage signal, and determine the reconstructed nonlinear damage signal based on the modeling expression. The normalization factor determination module is used to combine the reconstructed nonlinear damage signal with the measured damage signal and calculate the normalization factor used for amplitude normalization of the reconstructed nonlinear damage signal using the least squares method. The damage elimination module is used to scale the reconstructed nonlinear damage signal using the normalization factor and subtract the scaled reconstructed nonlinear damage signal from the sampled received power signal to determine the photocurrent signal after nonlinear damage elimination. The iterative feedback module is used to repeatedly utilize the Cramer-Kronig relation to recover the sampled received power signal into a recovered field signal, and gradually reduce the error signal in an iterative feedback manner until the residual nonlinear damage in the recovered field signal approaches zero.

8. The apparatus according to claim 7, characterized in that, The device further includes a field signal reconstruction module, which is used for: Digital domain dispersion compensation is performed on the recovered field signal, and equalization technology is used to compensate for channel distortion to determine the equalized symbol sequence; A symbol decision is performed on the symbol sequence to determine the QAM symbol after the decision, and the QAM symbol is remodulated to obtain a service signal that does not contain pilot beat frequency interference. The channel response obtained during the equalization process is applied to the service signal, and the inverse process of digital domain dispersion compensation is performed to obtain a reconstructed field signal with less beat frequency interference.

9. An electronic device, characterized in that, include: The device includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is in operation, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of the method for eliminating nonlinear impairments in a KK receiver as described in any one of claims 1 to 6.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the method for eliminating nonlinear impairments in a KK receiver as described in any one of claims 1 to 6.

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