A bandwidth restriction and electrical dispersion cooperative pre-compensation method based on improved GS algorithm

Abstract

The application relates to a bandwidth restriction and electric dispersion cooperative pre-compensation method based on an improved GS algorithm, and belongs to the technical field of optical fiber communication and compensation. The method designs a filter for balancing bandwidth restriction and integrates the filter into an improved GS pre-EDC method, and specifically comprises the following steps: step 1, using the improved GS pre-EDC at a transmitting end and using FFE post-equalization at a receiving end, wherein the tap coefficient of the FFE is stored as h BL ; step 2, initializing a signal; step 3, performing receiving end restriction on the amplitude of odd samples of the signal; step 4, converting the signal to the transmitting end through an inverse dispersion frequency domain transmission function and an inverse filter; step 5, performing transmitting end restriction on the phase of the signal; step 6, converting the signal back to the receiving end through a dispersion frequency domain transmission function and a filter; and step 7, repeatedly performing steps 3-6 to complete N iterations. The pre-compensation performance of the method is superior to that of the improved GS pre-EDC method, the bandwidth requirement of optoelectronic devices in a high-speed system is reduced, and post-equalization is not needed.

Description

Technical Field

[0001] This invention relates to a method for coordinated pre-compensation of bandwidth limitation and electrodispersion based on an improved GS algorithm, belonging to the field of optical fiber communication and compensation technology. Background Technology

[0002] Driven by applications such as big data, cloud computing, artificial intelligence, and short videos, data center interconnect traffic is growing exponentially. Intensity Modulation / Direct Detection (IM / DD) systems are widely used in cost-sensitive short-distance optical interconnects due to their low cost, low power consumption, and simple structure. However, in the context of high-speed transmission, the bandwidth limitation (BL) of low-cost devices leads to the loss of high-frequency information in the signal, causing intersymbol interference (ISI). Furthermore, the periodic power fading caused by the combined effect of chromatic dispersion (CD) in the fiber and square-law detection at the receiver can severely distort the signal. Therefore, bandwidth limitation and dispersion-induced impairments remain major challenges to improving C-band transmission performance in IM / DD systems.

[0003] Recently, electronic dispersion pre-compensation (pre-EDC) based on the Gerchberg-Saxton (GS) algorithm has become a research hotspot. Basic GS pre-EDC treats the amplitude at the transmitter and the phase information before direct detection at the receiver as degrees of freedom, using the GS iterative algorithm to generate a pre-distorted signal with anti-dispersion capabilities. Building upon this, the modified GS pre-EDC method introduces amplitude and phase errors, as well as related error inversion factors, to accelerate algorithm convergence and improve performance. One pre-EDC method based on a polynomial nonlinear filter (PNLF) designs a PNLF to replace the modified GS pre-EDC to achieve signal pre-distortion. At the receiver, it needs to be combined with a feed-forward equalizer (FFE) for post-equalization. This method uses only odd-numbered sample information of the signal during the pre-compensation process. To fully utilize the degrees of freedom in the improved GS pre-EDC method, a pre-EDC method based on trained dual finite impulse response (FIR) filters is proposed to further enhance compensation performance by designing FIR filters separately for odd and even samples. However, few studies have investigated the impact of bandwidth limitations on the improved GS pre-EDC.

[0004] This invention designs an equalized bandwidth-limited filter and integrates it into an improved GS pre-EDC method. The invention aims to achieve bandwidth limitation and electro-dispersion coordinated pre-compensation (pre-BL-EDC) based on an optimized GS algorithm, thereby improving the compensation performance of the improved GS pre-EDC in bandwidth-limited systems. Summary of the Invention

[0005] The purpose of this invention is to address the bandwidth limitation problem in improved GS pre-EDC, and to propose a bandwidth limitation and electro-dispersion co-compensation method (pre-BL-EDC) based on an improved GS algorithm. This method, building upon the improved GSpre-EDC, introduces a filter to equalize the bandwidth limitation, performing bandwidth limitation and electro-dispersion co-pre-distortion on the signal. Specifically, it consists of two stages.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0007] The bandwidth limiting and electrodispersion coordinated predistortion method includes the following steps (where step 1 is stage one, and steps 2-7 are stage two):

[0008] Step 1: At the transmitting end, a modified GS pre-EDC is used to predistort the signal; at the receiving end, FFE is used for post-equalization, and the tap coefficients of FFE are stored as h. BL ;

[0009] Step 2: Initialize the signal. Initialize the signal amplitude to the target amplitude A. Target The phase is initialized to zero. The target amplitude A... Target It is the amplitude of the on-off keying (OOK) signal after being shaped by a raised cosine (RC) filter with a roll-off factor of 1.0;

[0010] Step 3: Apply receiver constraints to the amplitudes of the odd-numbered samples of the signal, i.e., use A Target(odd) (n)-α·error(n) is used instead. Here, α is the amplitude error inversion factor, with a value range of 0≤α≤1, error is the amplitude error of odd-numbered samples, and n is the sample index;

[0011] Step 4: Using the inverse dispersive frequency domain transfer function and inverse filter Convert the signal to the transmitting end;

[0012] Step 5: Apply transmitter constraints to the phase of the signal, i.e., use... Instead. Where β is the phase error reversal factor, with a value range of 0 ≤ β ≤ 1;

[0013] Step 6: Utilize the dispersive frequency domain transfer function H CD and filter H BL Convert the signal back to the receiving end;

[0014] Step 7: Repeat steps 3-6 to complete N iterations. The signal amplitude A in step 5... Tx (n) is the final output after the algorithm iteration is completed. This predistorted signal can offset the damage caused by bandwidth limitation and dispersion, eliminating the need for equalization after using FFE at the receiver.

[0015] Among them, the dispersive frequency domain transfer function H CD Represented as:

[0016]

[0017] Where D is the dispersion coefficient; λ is the optical carrier wavelength; ω is the angular frequency; l is the transmission distance; and c is the speed of light in a vacuum. Filter H BL The Z-domain expression is:

[0018]

[0019] Where k is the number of taps.

[0020] Beneficial effects

[0021] This invention provides a bandwidth limiting and electrodispersion co-compensation method based on an improved GS algorithm, which achieves bandwidth limiting and electrodispersion co-compensation in cost-sensitive IM / DD fiber optic transmission systems. Compared with the improved GS pre-EDC method, it has the following advantages:

[0022] 1. The method described above has a higher tolerance for system bandwidth limitations;

[0023] 2. The method described above improves the achievable symbol rate under limited system bandwidth;

[0024] 3. The method described above can improve compensation performance, enhance receiver sensitivity, and eliminates the need for post-equalization. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of a bandwidth limitation and electrodispersion co-compensation method based on an improved GS algorithm according to the present invention. Figure 1 (a) is a schematic diagram of the overall principle. Figure 1 (b) is a schematic diagram of Phase One. Figure 1 (c) is a schematic diagram of Phase Two;

[0026] Figure 2This invention presents a comparison of the spectra of predistorted signals generated by a bandwidth limitation and electrodispersion co-compensation method based on an improved GS algorithm and an improved GS pre-EDC method.

[0027] Figure 3 This invention presents a comparison of the spectrum of received signals between a bandwidth limitation and electrodispersion co-compensation method based on an improved GS algorithm and an improved GS pre-EDC method.

[0028] Figure 4 This is a schematic diagram and a flowchart of digital signal processing (DSP) for a C-band 20 / 28 / 32 Gbit / s 50km OOK IM / DD experimental system, as shown in Embodiment 1 of the present invention, which describes a bandwidth limitation and electro-dispersion co-compensation method based on an improved GS algorithm. The inset shows the frequency response of the optical back-to-back channel.

[0029] Figure 5 This is a compensation result diagram at different baud rates for Embodiment 1 of the present invention, which is a bandwidth limitation and electro-dispersion co-compensation method based on an improved GS algorithm.

[0030] Figure 6 This is a diagram showing the receiver sensitivity results at different baud rates for Embodiment 1 of the present invention, which is a bandwidth limitation and electrodispersion co-compensation method based on an improved GS algorithm. Figure 6 (a) is 20 Gbit / s. Figure 6 (b) is 28 Gbit / s. Figure 6 (c) is 32 Gbit / s. Detailed Implementation

[0031] The present invention will now be described in conjunction with the accompanying drawings and specific embodiments. The following embodiments are only for illustrating the present invention in more detail, but are not intended to limit the scope of application of the bandwidth limiting and electrodispersion co-compensation method based on the improved GS algorithm.

[0032] Example 1

[0033] In practical implementation, for example, some operators interconnect data centers in Haidian District and Yizhuang District of Beijing, which may encounter signal distortion problems due to device bandwidth limitations and fiber dispersion effects. Our method can effectively improve signal quality, reduce the bit error rate, and ensure that high-speed data transmission meets design requirements. In a 50km fiber optic transmission system, OOK signals of 20Gbit / s, 28Gbit / s, and 32Gbit / s were transmitted respectively. All transmitted signals employed the bandwidth limitation and electro-dispersion co-compensation method based on an improved GS algorithm according to this invention. The pre-compensation method consists of two stages, and the flowchart is attached. Figure 1As shown. The specific implementation steps are as follows:

[0034] Step 1: At the transmitting end, a modified GS pre-EDC is used to predistort the signal; at the receiving end, FFE is used for post-equalization, and the tap coefficients of FFE are stored as h. BL ;

[0035] Step 2: Initialize the signal. Initialize the signal amplitude to the target amplitude A. Target The phase is initialized to zero. The target amplitude A... Target It is the amplitude of the on-off keying (OOK) signal after being shaped by a raised cosine (RC) filter with a roll-off factor of 1.0;

[0036] Step 3: Apply receiver constraints to the amplitudes of the odd-numbered samples of the signal, i.e., use A Target(odd) (n)-α·error(n) is used instead. Here, α is the amplitude error inversion factor, with a value range of 0≤α≤1, error is the amplitude error of odd-numbered samples, and n is the sample index;

[0037] Step 4: Using the inverse dispersive frequency domain transfer function and inverse filter Convert the signal to the transmitting end;

[0038] Step 5: Apply transmitter constraints to the phase of the signal, i.e., use... Instead. Where β is the phase error reversal factor, with a value range of 0 ≤ β ≤ 1;

[0039] Step 6: Utilize the dispersive frequency domain transfer function H CD and filter H BL Convert the signal back to the receiving end;

[0040] Step 7: Repeat steps 3-6 to complete N iterations. The signal amplitude A in step 5... Tx (n) is the final output after the algorithm iteration is completed. This predistorted signal can offset the damage caused by bandwidth limitation and dispersion, eliminating the need for equalization after using FFE at the receiver.

[0041] Among them, the dispersive frequency domain transfer function H CD Represented as:

[0042]

[0043] Where D is the dispersion coefficient; λ is the optical carrier wavelength; ω is the angular frequency; l is the transmission distance; and c is the speed of light in a vacuum. Filter H BL The Z-domain expression is:

[0044]

[0045] Where k is the number of taps.

[0046] Appendix Figure 2 and attached Figure 3 The spectra of the predistorted signal and the received signal generated by the bandwidth-limited and electro-dispersion-coordinated pre-compensation method based on the improved GS algorithm of this invention were compared with those of the improved GS pre-EDC method. The improved GS pre-EDC method requires post-equalization at the receiver using FFE to compensate for the loss caused by bandwidth limitation, which also amplifies high-frequency noise. However, the predistorted signal generated by the bandwidth-limited and electro-dispersion-coordinated pre-compensation method of this invention has slightly higher high-frequency frequencies than that of the improved GS pre-EDC method. This mitigates the impact of system bandwidth limitation, resulting in a flatter received signal spectrum and eliminating the need for post-equalization.

[0047] In practice, an experimental system will be built, as shown in the attached document. Figure 4 As shown. The system bandwidth is fixed, therefore different system bandwidth limits are achieved by changing the baud rate of the OOK signal. At the transmitting end, firstly 2 15A random data stream is mapped to OOK symbols using Gray coding, upsampled by a factor of 2, and pulse-shaped using a raised cosine filter with a roll-off factor of 1. Then, a bandwidth-limiting and electro-dispersion co-compensation method based on an improved GS algorithm, according to this invention, is used to pre-distort the signal. The pre-distorted digital signal is sequentially fed into a 65GSa / s arbitrary waveform generator (AWG) with a bandwidth of 20GHz, an electrical amplifier (EA) with a gain of 19dB and a bandwidth of 12GHz, and a Mach-Zehnder modulator (MZM) with a bandwidth of 40GHz. A 1500nm linewidth and 10MHz optical carrier is generated by an external cavity laser (ECL). The first erbium-doped optical fiber amplifier (EDFA) amplifies the optical power of the signal to 5 dBm. After transmission through 50 km of optical fiber, a second EDFA is used to compensate for transmission loss and filters out out-of-band noise using a 0.4 nm bandwidth optical bandpass filter (OBPF). The received optical power is adjusted by a variable optical attenuator (VOA). Subsequently, the signal passes through a 40 GHz bandwidth photodiode with a transimpedance amplifier (TIA) and a 36 GHz bandwidth digital phosphor oscilloscope (DPO). Finally, the signal undergoes offline DSP processing, including resampling, frame synchronization, downsampling, OOK demapping, and bit error rate (BER) calculation. The illustration shows the frequency response of the optical back-to-back channel, revealing that the system's 3dB bandwidth is approximately 9 GHz and its 10dB bandwidth is approximately 16 GHz. This indicates insufficient available bandwidth for 20 Gbit / s, 28 Gbit / s, and 32 Gbit / s OOK signals.

[0048] Appendix Figure 5The BER performance of three methods at different baud rates was compared: a method without pre-equalization, an improved GS pre-EDC method, and a bandwidth-limited and electro-dispersion-coordinated pre-compensation method based on an improved GS algorithm proposed in this invention. The methods without pre-equalization and the improved GS pre-EDC method require post-equalization with FFE, and the number of FFE taps is optimized based on the BER. For the method without pre-equalization, signals at all baud rates fail to reach the Hard-Decision Forward Error Correction (HD-FEC) threshold. The improved GS pre-EDC method can reduce BER, but for a 32 Gbit / s signal, due to more severe bandwidth limitations, the BER cannot reach the HD-FEC threshold. However, the bandwidth-limited and electro-dispersion-coordinated pre-compensation method based on an improved GS algorithm proposed in this invention exhibits better BER performance, enabling a 32 Gbit / s signal to meet the HD-FEC threshold without post-equalization. The results show that in bandwidth-constrained IM / DD systems, the bandwidth-limited and electro-dispersion-coordinated pre-compensation method based on an improved GS algorithm proposed in this invention improves the achievable symbol rate.

[0049] Appendix Figure 6 The receiver sensitivity of the three methods at different baud rates was further compared. (For the appendix...) Figure 6 As shown in Figure a, for the 20 Gbit / s signal, it can be observed that compared to the improved GS pre-EDC method, the bandwidth limiting and electrodispersion co-compensation method based on the improved GS algorithm of this invention provides a 1.0 dB gain in receiver sensitivity at the HD-FEC threshold. For the attached... Figure 6 The 28 Gbit / s signal shown in b presents a severe bandwidth limitation for the system, yet the bandwidth limitation and electrodispersion co-compensation method based on the improved GS algorithm of this invention still maintains a 1.0 dB advantage in receiver sensitivity. (For the attached...) Figure 6 For the 32 Gbit / s signal shown in c, the improved GS pre-EDC method can barely reach the HD-FEC threshold, while the bandwidth limiting and electrodispersion co-compensation method based on the improved GS algorithm of this invention can reach the HD-FEC threshold at a ROP of -8.0 dBm, providing a 2.0 dB gain in receiver sensitivity. The results show that the bandwidth limiting and electrodispersion co-compensation method based on the improved GS algorithm of this invention significantly reduces the bandwidth requirements of optoelectronic devices in high-speed systems.

[0050] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A bandwidth limiting and electro-dispersion co-compensation method based on an improved GS algorithm, comprising a designed equalized bandwidth limiting filter, which is incorporated into an improved GS pre-EDC, and the generated pre-distortion signal co-compensates for bandwidth limiting and electro-dispersion, characterized in that: Includes the following steps: Step 1: At the transmitting end, a modified GS pre-EDC is used to predistort the signal; at the receiving end, FFE is used for post-equalization, and the tap coefficients of FFE are stored as h. BL ; Step 2: Initialize the signal by setting its amplitude to the target amplitude A. Target The phase is initialized to zero; Step 3: Apply receiver constraints to the amplitudes of the odd-numbered samples of the signal, i.e., use A Target(odd) (n)-α·error(n) is used instead, where α is the amplitude error inversion factor, error is the amplitude error of odd-numbered samples, and n is the sample index; Step 4: Using the inverse dispersive frequency domain transfer function and inverse filter Convert the signal to the transmitting end; Step 5: Apply transmitter constraints to the phase of the signal, i.e., use... Instead, where β is the phase error inversion factor; Step 6: Utilize the dispersive frequency domain transfer function H CD and filter H BL Convert the signal back to the receiving end; Step 7: Repeat steps 3-6 to complete N iterations.

2. The bandwidth limiting and electrodispersion co-compensation method based on the improved GS algorithm according to claim 1, characterized in that: In step 2, the target amplitude A Target It is the amplitude of the OOK signal after being shaped by a raised cosine filter with a roll-off factor of 1.

0.

3. The bandwidth limiting and electrodispersion co-compensation method based on the improved GS algorithm according to claim 1, characterized in that: In step 3, the value of α is in the range of 0 ≤ α ≤ 1.

4. The method for coordinated pre-compensation of bandwidth limitation and electrodispersion based on an improved GS algorithm according to claim 1, characterized in that: In step 5, the value of β is in the range of 0 ≤ β ≤ 1.

5. The bandwidth limiting and electrodispersion co-compensation method based on the improved GS algorithm according to claim 1, characterized in that: In step 6, the dispersive frequency domain transfer function H CD Represented as: Where D is the dispersion coefficient, λ is the optical carrier wavelength, ω is the angular frequency, l is the transmission distance, and c is the speed of light in a vacuum.

6. The method for coordinated pre-compensation of bandwidth limitation and electrodispersion based on an improved GS algorithm according to claim 1, characterized in that: In step 6, filter H BL The Z-domain expression is: Where k is the number of taps.

7. The method for coordinated pre-compensation of bandwidth limitation and electrodispersion based on an improved GS algorithm according to claim 1, characterized in that: In step 5, the signal amplitude A Tx (n) is the final output after the algorithm iteration. This predistorted signal can offset the damage caused by bandwidth limitation and dispersion, eliminating the need for equalization after using FFE at the receiver.

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