A field recovery iterative aided nonlinear channel equalization method

Abstract

This invention proposes a field recovery-assisted iterative nonlinear channel equalization method for use in intensity modulation direct detection (IM / DD) fiber optic transmission systems. The method cascades the Gerchberg-Saxton (GS) iterative algorithm with a Volterra decision feedback equalizer (VDFE) in a digital receiver, forming a GS-VDFE equalizer. The GS iterative module proceeds first, iteratively updating the optical field by inferring the phase from the optical intensity signal, initially compensating for fiber dispersion and increasing the power at fading frequencies. The VDFE module follows, employing a simplified structure of a second-order feedforward Volterra and a first-order feedback DFE, to perform nonlinear equalization on the GS output signal to eliminate residual distortion. GS preprocessing eliminates the need for high-order nonlinear compensation in the VDFE, reducing equalizer complexity and noise sensitivity. The VDFE handles residual compensation, reducing the number of GS iterations to below 20, thus lowering processing latency. This invention effectively recovers high-speed digital signals in high-dispersion channels and mitigates spectral fading and self-reflection interference without altering the existing system structure.

Description

Technical Field

[0001] This invention relates to direct detection fiber optic transmission technology, and particularly to nonlinear waveform distortion recovery technology applicable to direct detection fiber optic transmission systems. Background Technology

[0002] The rapid development of artificial intelligence, 5G / 6G mobile communication, and intelligent computing center interconnection technologies has placed higher demands on the data carrying capacity of optical fiber transmission systems. In transmission scenarios with link lengths of tens of kilometers, such as high-speed passive optical networks, intensity modulation direct detection (IM / DD) optical fiber transmission architecture is widely used due to its advantages of simple structure, low cost, and low power consumption. According to the ITU-T standard, the 50G high-speed passive optical network (HSP) is still based on the IM / DD architecture. As the next generation of HSP evolves towards 100G / 200G, if the IM / DD system continues to be used, signal transmission will be further limited by fiber dispersion, and the degree of performance degradation will be proportional to the square of the transmission rate. In the frequency domain, this degradation manifests as an increasing number of frequency-selective deep fading points and optical field signal self-backlash interference (SSBI) within the frequency band. The performance of the IM / DD system is approaching its theoretical limit, and to achieve error-free data transmission, a highly complex nonlinear equalizer is generally required.

[0003] Common nonlinear equalization methods include nonlinear Volterra feedforward equalization, Volterra-nonlinear decision feedback equalization, and Tomlinson-Harashima precoding (THP). Volterra feedforward equalization improves nonlinear characterization by simultaneously considering both linear and nonlinear components in the received signal; however, its signal compensation capability is limited when one or more frequency-selective deep fading points exist within a frequency band. While Volterra-nonlinear decision feedback equalization can match frequency-selective fading in IM / DD high-dispersion channels, its algorithm complexity is extremely high, and error propagation is a serious problem at low signal-to-noise ratios. THP precoding, while offering high noise tolerance, increases transmitter algorithm complexity. Furthermore, the maximum likelihood sequence detection (MLSD) method theoretically obtains the optimal solution under the condition of equal probability prior transmission symbols, but its complexity increases sharply with channel memory length and modulation order, making it only suitable for IM / DD transmission systems that have not yet reached power fading zeros; therefore, it is not suitable for transmission links with large cumulative dispersion.

[0004] Fiber optic transmission systems can be mathematically described as partial differential equations governing electromagnetic field transmission. The Gerchberg-Saxton (GS) iterator solves for signals through numerical iteration, utilizing the evolution of high-speed signal light fields in standard single-mode fiber. It also constrains the iterative process using modulation characteristics and digital signal features, thus effectively addressing the challenges of IM / DD transmission in high-dispersion channels. However, this method also suffers from local optima, requires a large number of iterations for convergence, and introduces significant digital signal processing delays. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a solution for improving the tolerance of existing intensity modulation direct detection IM / DD fiber optic transmission systems to fiber chromatic dispersion by using digital filtering methods to improve the severe waveform distortion and frequency selective deep fading problems that occur during broadband signal transmission.

[0006] The technical solution adopted by this invention to solve the above problems is a field recovery iterative-assisted nonlinear channel equalization method, comprising:

[0007] In the digital receiver, after the received signal is resampled and frame synchronized, the synchronized data is input to the GS-VDFE iteratively assisted VDFE equalizer for equalization processing.

[0008] The GS-VDFE is composed of a cascaded GS iteration module and a VDFE module.

[0009] The GS iteration module is used to infer the low-pass equivalent phase from the optical intensity signal, and recover the optical field phase through iterative updates to initially compensate for fiber dispersion.

[0010] The VDFE module is a Volterra decision feedback equalizer, used to perform nonlinear equalization on the signal output by the GS iteration module, eliminate residual distortion, and make a decision output.

[0011] Specifically, the implementation process of the GS iteration module includes:

[0012] Step S1: Construct the receiving optical field based on the detected intensity signal and the assumed initial phase, and perform linearization dispersion compensation on the optical field in the digital domain to obtain the estimated transmitting optical field.

[0013] Step S2: Update the phase of the modulator output based on the modulation prior information of the intensity modulator;

[0014] Step S3: Apply the fiber dispersion transfer function to the phase-updated optical field signal to obtain a new receiving optical field;

[0015] Step S4: Update the new receiving optical field by calculating the phase angle of the optical field signal and replacing the calculated optical field intensity with the original intensity signal detected by the photodetector.

[0016] Step S5: Repeat step S4 until the preset number of iterations is reached, and output the final iterated signal to the VDFE module.

[0017] Specifically, the VDFE module consists of a feedforward section and a feedback section; the feedforward section is a second-order Volterra equalizer, and the feedback section is a first-order decision feedback equalizer (DFE).

[0018] This invention places the GS iterative algorithm before the VDFE equalizer, adding a GS preprocessing module before adaptive equalization. The VDFE only requires a second-order feedforward Volterra and a first-order feedback DFE structure with fewer taps. When an IM / DD fiber optic transmission system transmits broadband high-speed signals in a non-zero dispersion band, and one or more frequency-selective fading points occur in the spectrum due to dispersion, if traditional Volterra equalization, Volterra-VDFE equalization, and maximum likelihood sequence detection methods cannot effectively recover the signal, the GS-assisted VDFE equalizer proposed in this invention can achieve better dispersion compensation performance and lower equalizer complexity. This invention does not require changes to the existing IM / DD system structure or equalizer adaptive algorithm, nor does it require channel precompensation.

[0019] The beneficial effects of this invention are that, through the synergistic design of GS and VDFE, performance improvements are achieved in two aspects:

[0020] 1. Reduce GS iteration latency

[0021] When used alone, the GS iteration is slow to converge and has a large time delay. This invention feeds the GS output into a VDFE, which handles the residual nonlinearity compensation. This eliminates the need for the GS to iterate until full convergence, reducing the number of iterations to less than 20, thereby reducing the GS processing delay.

[0022] 2. Reduce the implementation complexity of VDFE

[0023] When used alone, a VDFE requires a high-order Volterra and a long memory length to handle channels with high dispersion, resulting in high complexity. This invention uses GS to perform linearization preprocessing on the channel, increasing the power at fading frequencies, so that the subsequent VDFE can adopt a simplified structure (second-order feedforward Volterra + first-order feedback DFE), reducing implementation complexity while ensuring equalization performance.

[0024] In summary, this invention can effectively recover high-speed digital signals transmitted in IM / DD systems in high-dispersion channels, and mitigate the effects of spectral fading and signal self-recording interference (SSBI) caused by the combined effects of dispersion and square-law detection. It is particularly suitable for high-speed passive optical network (PON) scenarios with transmission rates greater than 100 Gbit / s. Attached Figure Description

[0025] Figure 1 This is a flowchart of the IM / DD fiber optic transmission system and DSP of the present invention. Wherein, DSP: Digital Signal Processing; AWG: Arbitrary Waveform Generator; ECL: External Cavity Laser; RFA: Radio Frequency Amplifier; MZM: Mach-Zehnder Modulator; SSMF: Standard Single-Mode Fiber; VOA: Adjustable Optical Attenuator; PD: Photodetector; GS-VDFE: Equalizer as described in this invention.

[0026] Figure 2 This refers to the GS-VDFE equalizer proposed in this invention.

[0027] Figure 3 The spectrum is shown after GS iteration and VDFE equalization under frequency-selective fading. Detailed Implementation

[0028] Figure 1 The diagram shows an intensity modulation direct detection IM / DD fiber optic transmission system. The specific implementation steps are as follows:

[0029] Step 1. The IM / DD fiber optic transmission system consists of a digital transmitter, an optical transmission system, and a digital receiver.

[0030] Step 2. In the digital transmitter DSP, the binary pseudo-random bit sequence is first PAM symbol mapping, then upsampled by 2 times and Nyquist pulse shaping is performed. Then, it is adjusted to the specified transmission rate through resampling, and then converted into an analog electrical signal output by a high-speed DAC.

[0031] Step 3. The electrical signal output by the transmitter DSP is first converted from digital to analog by a 128-GSa / s AWG digital-to-analog converter, and then output as an analog electrical signal. This analog signal is then amplified by a broadband radio frequency amplifier (RFA) to drive the modulator. The external cavity laser (ECL) generates a continuous light wave. The intensity modulator receives the amplified electrical signal and the light wave, and uses the electrical signal to modulate the light wave. The intensity modulator can be a Mach-Zehnder intensity modulator (MZM), a direct modulated laser (DML), or an electroabsorption modulated laser (EML). Figure 1The MZM (Medium-Zero Dispersion Array) is used. Light waves can be emitted from zero-dispersion (O-band) light sources or from non-zero-dispersion (C-band) light sources. The optical signal output from the MZM is transmitted through a standard single-mode fiber optic cable (SSMF), and then the optical power entering the photodetector (PD) is controlled by an adjustable optical attenuator (VOA), ensuring the PD operates within its optimal receiving range. The optical signal is converted into a baseband electrical signal by the photodetector, and finally, high-speed data acquisition is performed using a 256-GSa / s oscilloscope. After completing the analog-to-digital (ADC) conversion of the electrical signal, the data is output to the digital receiver (DSP).

[0032] Step 4. In the digital receiver DSP, the photocurrent generated by the detector is converted into a digital signal by a high-speed ADC. After resampling to an integer multiple of the symbol rate, frame synchronization is performed using a synchronization header. The synchronized data is input to the GS-VDFE iteratively assisted VDFE equalizer, and the output of the GS-VDFE is used for symbol demapping and decoding operations.

[0033] The GS-VDFE equalizer, assisted by GS iteration, consists of a GS iteration module and a VDFE module. The GS iteration module recovers phase from intensity, provides initial dispersion compensation, and enhances power at fading frequencies. The VDFE is a cascaded Volterra decision feedback equalizer (DFE) used for nonlinear equalization, eliminating residual distortion, and providing a decision output. The VDFE consists of two parts: a second-order Volterra equalizer for the feedforward section and a first-order decision feedback equalizer (DFE) for the feedback section.

[0034] The specific operating steps for GS-VDFE are as follows:

[0035] Step S1. In the GS-iterative-assisted VDFE equalization, the input signal is first subjected to GS iterative processing, and then the iterated signal is sent to the VDFE equalizer. The GS iteration refers to the process of inversely deriving the low-pass equivalent phase from the light intensity signal: first, the receiving optical field is constructed by the detected intensity signal and the assumed initial phase, then the optical field is linearized and dispersion compensated in the digital domain, and the compensated complex signal is regarded as the optical field output by the transmitting intensity modulator.

[0036] Step S2. Based on known modulation prior information, such as the MZM output signal having zero-phase chirp, the DML output having frequency modulation and phase modulation effects, and the EML output having phase modulation effects, update the phase of the modulator output.

[0037] Step S3. Apply the fiber dispersion transfer function to the updated optical field signal to obtain the receiving optical field.

[0038] Step S4. Perform an iterative update on the receiving end optical field. The update method is as follows: calculate the phase angle of the optical field signal and replace the calculated optical field intensity with the intensity signal detected by the photodetector.

[0039] Step S5. Repeat the iterative process described in step S4. The number of iterations depends on the algorithm configuration before and after. In GS-assisted VDFE, the number of iterations can be reduced to less than 20.

[0040] In step S6, the output signal of the GS iteration is fed into the input of the VDFE equalizer. The equalizer tap coefficients converge by transmitting the error between the training sequence and the VDFE output sequence. The feedforward section of the equalizer uses a second-order Volterra equalizer, and the feedback section uses a DFE. Because the preceding GS iteration plays a role in system linearization, the subsequent feedback equalizer does not employ a higher-order nonlinear compensation structure. When other nonlinearities such as modulator nonlinearity exist, using a higher-order feedforward nonlinear equalizer can further reduce the bit error rate.

[0041] To effectively compensate for dispersion damage, this invention employs a GS-VDFE joint equalization structure. The internal principle and signal flow of this equalizer are as follows: Figure 2 As shown.

[0042] Traditional IM / DD fiber optic transmission systems using Volterra FFE+Volterra DFE channel equalizers employ adaptive filtering of the synchronized sequence using a training sequence. In high-dispersion IM / DD channels, the equalizer not only needs to calculate higher-order tap coefficients but also requires a longer memory length. Even so, it remains difficult to compensate for deep fading impairments in spectral power at low signal-to-noise ratios. The GS-VDFE nonlinear compensation technique leverages the complementary advantages of both field recovery iteration and nonlinear equalization techniques.

[0043] Let the signal vector input to the GS-VDFE at time n be... , For time indexing, Let represent the input signal value at time n-1, and let the phase of the signal vector input to the GS-VDFE at time n be . , , Phase value from time 0 to n-1 All values ​​are initialized to 0, and the receiving end optical field vector corresponding to time n is constructed. exp is an exponential function with the natural constant as its base, and j represents the imaginary unit; then fiber dispersion compensation is performed to obtain the estimated transmitted optical field at the nth time. .in, Represents the time-domain impulse response of the fiber dispersion at time n of the inverse system. , Indicates Fourier transform, Indicates fiber dispersion parameters, Indicates fiber optic transmission distance, These represent the signal's center wavelength, speed of light, and frequency, respectively. Discard the calculated values. And retain ,according to Given the modulator type, estimate the phase of the modulator output optical field, where abs represents the complex modulus (amplitude) and angle represents the complex phase (argument), in radians. Taking MZM as an example, the updated transmitter optical field phase at time n. Thus, the transmitter output light field at the nth time moment is obtained. The estimated value of the transmitted signal at time n can be obtained by taking the square of the modulus of the output optical field and removing the DC, that is:

[0044] ;

[0045] in, This indicates taking the square modulo 1. This indicates taking the arithmetic mean of the sequence, used to remove the DC component of the signal.

[0046] On the reconstructed transmitting optical field, estimate the low-pass equivalent phase of the optical field at the nth moment in front of the receiving photodetector. , This represents the convolution operation, which yields the receiving optical field after one iteration. .

[0047] The output signal after several iterations is fed into the VDFE equalizer. The output of the Volterra equalizer at time n is... Represented as:

[0048] ;

[0049] in, This represents the first-order Volterra tap index, with time offset relative to the current time n. For the first Each first-order Volterra tap coefficient is delayed at time n. Input signal for one symbol period; The single-sided memory length of a second-order Volterra equalizer. These are all second-order Volterra tap indices, used to identify the two delay positions corresponding to the second-order nonlinear terms; These are second-order Volterra tap index pairs used to identify a specific second-order nonlinear term; For the corresponding index pair The second-order Volterra tap coefficient, limiting To avoid double counting of symmetric terms, The estimated transmission delay at time n VDFE input signal for one symbol period.

[0050] The signal after DFE filtering at time n Represented as:

[0051] ;

[0052] in, For DFE feedback tap count, This represents a first-order Volterra tap index. This indicates a DFE operation. The output delay of VDFE at time n A signal with one symbol period;

[0053] The output of VDFE at time n express:

[0054] ;

[0055] in, This indicates a symbolic decision operation.

[0056] To calculate the tap coefficients to be determined, error calculation is first required, specifically the error of VDFE at time n. Represented as:

[0057] ;

[0058] in The training sequence at time n. Based on the error signal, the tap coefficients can be solved using the Least Mean Squares (LMS) algorithm or the Recursive Least Squares (RLS) algorithm.

[0059] Figure 3 It gives in Figure 1 The 224 Gbit / s PAM4 signal transmitted in the system, after passing through 25 km of standard single-mode fiber, undergoes GS iteration and VDFE equalization. The resulting signal spectrum shows that GS iteration increases the power at fading frequencies, thus achieving the purpose of assisted equalization. This scheme can be used in high-dispersion IM / DD systems with ranges of tens of kilometers in 200G and hundreds of kilometers in 100G. The algorithm can reduce equalizer complexity with a relatively low number of GS iterations (<20 times), ultimately achieving efficient high-speed IM / DD system signal transmission.

Claims

1. A field recovery iterative-assisted nonlinear channel equalization method, applied to an intensity modulation direct detection (IM / DD) fiber optic transmission system, characterized in that, Includes the following steps: In the digital receiver, after the received signal is resampled and frame synchronized, the synchronized data is input to the GS-VDFE iteratively assisted VDFE equalizer for equalization processing. The GS-VDFE is composed of a cascaded GS iteration module and a VDFE equalization module. The GS iteration module is used to infer the low-pass equivalent phase from the optical intensity signal, and recover the optical field phase through iterative updates to initially compensate for fiber dispersion. The VDFE module is an adaptive decision feedback equalizer cascaded with Volterra feedforward equalizer, used to perform nonlinear equalization on the signal output by the GS iterative module, eliminate residual distortion, and make a decision output.

2. The method as described in claim 1, characterized in that, The specific implementation process of the GS iteration module includes: Step S1: Construct the receiving optical field based on the detected intensity signal and the assumed initial phase, and perform linearization dispersion compensation on the optical field in the digital domain to obtain the estimated transmitting optical field. Step S2: Update the phase of the modulator output based on the modulation prior information of the intensity modulator; Step S3: Apply the fiber dispersion transfer function to the phase-updated optical field signal to obtain a new receiving optical field; Step S4: Update the new receiving optical field by calculating the phase angle of the optical field signal and replacing the calculated optical field intensity with the original intensity signal detected by the photodetector. Step S5: Repeat step S4 until the preset number of iterations is reached, and output the final iterated signal to the VDFE module.

3. The method as described in claim 2, characterized in that, For high dispersion channels (typical value: 200 Gbit / s 25 km G.652 standard single-mode fiber C-band transmission), the preset number of iterations is less than 20.

4. The method as described in claim 1, characterized in that, The VDFE module consists of a feedforward section and a feedback section; The feedforward section is a second-order Volterra equalizer, and the feedback section is a first-order decision feedback equalizer (DFE).

5. The method as described in claim 4, characterized in that, The VDFE module drives the equalizer tap coefficients to converge through the error between the training sequence and the VDFE output sequence. Its adaptive algorithm adopts the least mean square algorithm (LMS) or the recursive least squares algorithm (RLS).

6. The method according to any one of claims 1 to 5, characterized in that, The intensity modulator is a Mach-Zehnder intensity modulator (MZM), a direct modulated laser (DML), or an electroabsorption modulated laser (EML).

7. The method according to any one of claims 1 to 5, characterized in that, The method is applicable to high-speed passive optical network (PON) scenarios with transmission rates greater than 100 Gbit / s and high-dispersion double-sideband IM / DD fiber optic transmission systems.

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