A method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems using geometric shaping

Abstract

This invention discloses a method for noise optimization in discrete spectrum nonlinear frequency division multiplexing (DSP) systems using geometric shaping, belonging to the field of communication technology. The method includes: considering ASE noise and establishing a channel model under noisy conditions; based on the channel model under noisy conditions, designing an olive-shaped 32QAM in the DSP system; and by optimizing the geometric distribution of constellation points, mapping the optical signal to the point distribution of the olive-shaped 32QAM, reducing the probability of high-power points and minimizing the impact of accumulated spontaneous emission noise (ASE) and phase noise, thereby improving the signal's noise immunity and system transmission stability.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, specifically relating to a method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems using geometric shaping. Background Technology

[0002] With the explosive growth of global information volume, optical fiber communication, as a core technology of backbone networks, faces unprecedented challenges in bandwidth and transmission distance. Traditional optical fiber communication suffers from nonlinear effects over long transmission distances, leading to signal distortion and performance degradation. These nonlinear effects severely limit the transmission capacity and distance of optical fiber communication. To address these issues, researchers have proposed various nonlinear compensation techniques, among which Nonlinear Frequency Division Multiplexing (NFDM) technology, with its utilization of channel nonlinear characteristics, has shown great application potential. NFDM systems use inverse nonlinear Fourier transform (INFT) to map the spectrum of the optical signal onto a nonlinear spectrum. Unlike traditional linear optical fiber transmission, NFDM systems can transform unfavorable nonlinear effects in the fiber into favorable signal transmission mechanisms, enabling stable signal transmission on the nonlinear spectrum. This technology generates a special soliton pulse by solving the nonlinear Schrödinger equation (NLSE), utilizing the self-stabilizing properties of the soliton pulse to achieve long-distance distortion-free transmission without loss or noise. Nonlinear spectra can be divided into discrete spectra (DS) and continuous spectra (CS). Among them, discrete spectrum NFDM (DS-NFDM) is more suitable for high-order modulation formats and long-distance fiber optic transmission due to its stability. However, under actual transmission conditions, fiber optic links are inevitably affected by factors such as spontaneous emission noise (ASE), phase noise, and amplifier non-ideals.

[0003] ASE noise not only interferes with the amplitude and phase of the signal but also reduces the demodulation accuracy at the receiver. Phase noise, mainly introduced by the laser, causes phase jitter and shift in the transmitted signal, leading to an increase in the bit error rate (BER) of the demodulated signal. The presence of these noise factors makes it difficult for NFDM systems to maintain ideal performance, thus affecting the stability and data throughput of long-distance transmission. To improve the noise immunity of NFDM systems, researchers have proposed various noise immunity optimization schemes. For example, Kalman filtering can effectively reduce the interference of random noise on the system, while neural network models can learn the characteristics of noise's impact on the system through training on a large amount of historical data, thereby combating noise in the system. However, neural network and other schemes have high computational complexity and require high equipment resources for practical applications, making them difficult to adapt to low-cost and high real-time requirements. Regarding high-order modulation formats, 32QAM has received widespread attention due to its good bandwidth utilization. However, under high-order modulation conditions, the signal is more sensitive to phase and amplitude noise, and existing schemes struggle to maintain system stability while ensuring high transmission distances. Therefore, how to enhance noise tolerance in NFDM systems by optimizing modulation formats and phase recovery techniques remains one of the key issues that urgently need to be addressed. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems using geometric shaping, thereby solving the problems in existing technologies.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for noise optimization of discrete-spectrum nonlinear frequency division multiplexing systems using geometric shaping includes the following steps:

[0007] Considering ASE noise, establish a channel model under noisy conditions;

[0008] Based on the channel model under noisy conditions, an olive-shaped 32QAM is designed in a discrete spectrum nonlinear frequency division multiplexing system. By optimizing the geometric distribution of constellation points, the optical signal is mapped to the point distribution of the olive-shaped 32QAM.

[0009] Furthermore, when establishing the channel model under noisy conditions, in a noise-free environment, the fiber transmission process follows lossless NLSE, and the eigenvalues ​​of each soliton pulse remain unchanged. However, if ASE noise is present, the NLSE envelope electric field function is:

[0010] iq z -q tt -2|q| 2 q = η(z,t)

[0011] Where z and t are the normalized distance of the optical fiber and the normalized delay time in the envelope synchronous motion frame, respectively, q represents the complex envelope of the optical signal, and η(z,t) represents the zero-mean circular symmetric additive white Gaussian noise term.

[0012] Furthermore, in the presence of ASE noise, the eigenvalue λ of each soliton pulse i It will be distorted and become λ d =λ i +Δλ; Eigenvalue distortion causes noise in the spectral amplitude. This spectral amplitude disturbance accumulates with increasing propagation distance, manifesting as:

[0013]

[0014]

[0015] In the formula, log is the logarithm operation. Let q represent the result of the NFT, and Δλ be the distorted value of the eigenvalue.

[0016] Furthermore, during optical signal transmission, accumulated ASE noise will affect the signal. The output discrete-time channel model Y is set as the square root of the output signal amplitude A, and its conditional probability density function is:

[0017]

[0018] in, I1(g) is the normalized cumulative ASE noise variance, and I1(g) is the first-type modified Bessel function.

[0019] Furthermore, the constellation points of the olive-shaped 32QAM are distributed in a symmetrical structure, and three elliptical rings with different radii are set to distribute different power points.

[0020] Furthermore, the constellation diagram of the olive-shaped 32QAM is divided into four parts:

[0021] The first part consists of 8 symmetrically distributed points on the imaginary axis, with the relative positions of the constellation points being (±1+1i). 2 ,(±3+3i) 2 ,(±5+5i) 2 ,(±7+7i) 2 ;

[0022] The second to fourth parts are three elliptical rings from the inside out, with the innermost ring E1 containing four ideal constellation points (1+3i). 2 ,(-1+3i) 2 ,(3+i) 2 ,(-3+i) 2The intermediate ring E2 has 8 ideal points (-1+5i). 2 (1+5i) 2 ,(-5+i) 2 ,(5+i) 2 (-3+5i) 2 (3+5i) 2 (5+3i) 2 (-5+3i) 2 The outermost ring E3 has 12 ideal constellation points (-1 + 7i). 2 (1+7i) 2 ,(-7+i) 2 ,(7+i) 2 (-3+7i) 2 (3+7i) 2 (7+3i) 2 (-7+3i) 2 ,(-5+7i) 2 (5+7i) 2 (7+5i) 2 .

[0023] Furthermore, in a noise-free environment, the optical signal of the discrete spectrum nonlinear frequency division multiplexing system is mapped from the nonlinear spectrum to the time domain through inverse nonlinear Fourier transform.

[0024] A computer storage medium storing a readable program, which, when executed, can perform the aforementioned method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems using geometric shaping.

[0025] An electronic device includes: a processor, a memory, a communication interface, and a communication bus, wherein the processor, the memory, and the communication interface communicate with each other through the communication bus;

[0026] The memory is used to store at least one executable instruction, which causes the processor to perform the operation corresponding to the above-mentioned geometric shaping method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems.

[0027] A computer program product includes computer instructions that instruct a computing device to perform operations corresponding to the above-described geometric shaping method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems.

[0028] The beneficial effects of this invention are:

[0029] 1. This invention, through the design of an olive-shaped 32QAM constellation distribution, significantly enhances the noise immunity of discrete-spectrum nonlinear frequency division multiplexing systems against spontaneous emission noise (ASE) and phase noise. Under this geometric shaping scheme, the constellation points of the olive-shaped 32QAM are arranged in a symmetrical geometric structure, effectively reducing the noise impact from high-power signal points and making signal transmission more stable. Under the same bit error rate requirement (BER = 3.8 × 10⁻⁶), [the system achieves this]. -3 Under the condition of ), the olive-shaped 32QAM scheme improves the OSNR gain by about 1.7dB compared with the traditional 32QAM under OSNR conditions, and at the same time improves the transmission distance by 157 kilometers compared with the traditional 32QAM scheme.

[0030] 2. This optimization scheme improves the system's tolerance to signal amplitude and phase shift by adjusting the constellation point distribution, providing an efficient noise reduction method for long-distance optical fiber transmission and significantly enhancing the system's transmission performance under low signal-to-noise ratio conditions. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is the olive-shaped 32QAM design drawing of the present invention;

[0033] Figure 2 This is a simulation flowchart of the present invention;

[0034] Figure 3 This invention relates to the constellation diagram and three-dimensional kernel density diagram of 32APSK, 32QAM, and Olive-32QAM.

[0035] Figure 4 This is a graph showing the relationship between OSNR, BER, and maximum kernel density for different modulation and transmission schemes of this invention;

[0036] Figure 5 The BER performance of the 32APSK, 32QAM and olive-shaped 32QAM of this invention under different OSNRs;

[0037] Figure 6 This is a graph showing the BER performance of the 32APSK, 32QAM, and Olive-32QAM of this invention under different LW conditions. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] Example 1

[0040] A method for noise optimization of discrete-spectrum nonlinear frequency division multiplexing systems using geometric shaping includes the following steps:

[0041] S1. Considering ASE noise, establish a channel model under noisy conditions;

[0042] Assuming the system is noise-free, the optical signal in a discrete-spectrum NFDM system is mapped from the nonlinear spectrum to the time domain via an inverse nonlinear Fourier transform (NFT). In this case, the fiber transmission process follows the lossless nonlinear Schrödinger equation (NLSE). In a noise-free environment, the NLSE is completely integrable, meaning that the eigenvalues ​​of each soliton pulse remain unchanged, and the optical signal can propagate stably. However, practical single-mode fibers cannot provide a lossless and noise-free transmission environment. Assuming the presence of ASE noise, the NLSE envelope electric field function can be written as:

[0043] iq z -q tt -2|q| 2 q=η(z,t)(1)

[0044] Where z and t are the normalized distance of the optical fiber and the normalized delay time in the envelope synchronous motion frame, respectively, q represents the complex envelope of the optical signal, and η(z,t) represents the zero-mean circular symmetric additive white Gaussian noise term.

[0045] Ideally, NLSE is integrable, meaning that every eigenvalue in the multi-soliton signal remains unchanged during transmission. However, in the presence of ASE noise, the eigenvalue λ... i It will be distorted and become λ d =λ i +Δλ. The distortion of eigenvalues ​​introduces noise in the spectral amplitude, and these spectral amplitude perturbations accumulate with increasing propagation distance z, manifesting as:

[0046]

[0047]

[0048] In the formula, log is the logarithm operation. Let q represent the result of the NFT, and Δλ be the distorted value of the eigenvalue.

[0049] During optical signal transmission, accumulated ASE noise will affect the signal; the output discrete-time channel model Y is set as the square root of the output signal amplitude A, and its conditional probability density function is expressed as:

[0050]

[0051] in, I1(g) is the normalized cumulative ASE noise variance, and I1(g) is the modified Bessel function of the first kind. This probability distribution function (PDF) is actually a non-central chi-square distribution with four degrees of freedom, thus exhibiting non-Gaussian statistical properties. According to formula (4), in the NFDM system, ASE noise is affected by the signal amplitude. This is because the signal amplitude directly affects its power, and the power is related to the degree of accumulation of ASE noise. Higher amplitude leads to higher peak power, increasing the impact of ASE noise.

[0052] S2, based on the channel model under noisy conditions established in S1, designs an olive-shaped 32QAM to replace the traditional 32QAM in the discrete spectrum nonlinear frequency division multiplexing system. By optimizing the geometric distribution of constellation points, the optical signal is mapped to the constellation point distribution of the olive-shaped 32QAM, reducing the probability of high-power points and the impact of accumulated spontaneous emission noise (ASE) and phase noise, thereby improving the noise immunity of the signal and the transmission stability of the system.

[0053] In traditional 32QAM constellation designs, the density and distribution of constellation points can easily lead to significant shifts in high-power points under noise. To address this issue, this embodiment redesigns the 32QAM constellation, distributing it in an olive-shaped geometric structure (e.g., Figure 1 (As shown). The specific design is as follows:

[0054] 1) The constellation point distribution of the olive-shaped 32QAM is a symmetrical structure. By setting three elliptical rings with different radii to distribute different power points, the frequency of high power points is reduced, and the interference between signals is reduced.

[0055] 2) The constellation diagram of the olive-shaped 32QAM is divided into four parts. The first part consists of eight symmetrically distributed points on the imaginary axis. The relative positions of the constellation points are (±1+1i). 2 ,(±3+3i) 2 ,(±5+5i) 2 ,(±7+7i) 2 The second to fourth parts are three elliptical rings from the inside out, with the innermost ring E1 containing four ideal constellation points (1+3i). 2 ,(-1+3i) 2 ,(3+i) 2,(-3+i) 2 The intermediate ring E2 has 8 ideal points (-1+5i). 2 (1+5i) 2 ,(-5+i) 2 ,(5+i) 2 (-3+5i) 2 (3+5i) 2 (5+3i) 2 (-5+3i) 2 The outermost ring E3 has 12 ideal constellation points (-1 + 7i). 2 (1+7i) 2 ,(-7+i) 2 ,(7+i) 2 (-3+7i) 2 (3+7i) 2 (7+3i) 2 (-7+3i) 2 ,(-5+7i) 2 (5+7i) 2 (7+5i) 2 This ensures the stability and anti-interference capabilities of the signal distribution.

[0056] 3) Adjusting the elliptical ring distribution ensures that the spacing between constellation points of different amplitudes is appropriate, reducing the cumulative impact of ASE noise and enhancing the constellation points' tolerance to phase noise.

[0057] Based on a similar inventive concept, embodiments of the present invention also provide a computer storage medium storing a readable program that, when the program is run, can execute the above-described geometric shaping method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems.

[0058] Based on a similar inventive concept, this invention provides an electronic device, including: a processor, a memory, a communication interface, and a communication bus, wherein the processor, the memory, and the communication interface communicate with each other through the communication bus;

[0059] The memory is used to store at least one executable instruction, which causes the processor to perform the operation corresponding to the above-mentioned geometric shaping method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems.

[0060] Based on a similar inventive concept, embodiments of the present invention also provide a computer program product, including computer instructions, which instruct a computing device to perform the operation corresponding to the above-described geometric shaping method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems.

[0061] Example 2

[0062] The performance of the olive-shaped 32QAM (Olive-32QAM) mentioned in Example 1 will be verified by simulation below;

[0063] like Figure 2 As shown, to verify the proposed Olive-32QAM performance, a 2Gbaud single-polarization DS-NFDM system was built in this embodiment, and the performance of the scheme was verified through two transmission scenarios: fiber optic link and BTB. At the transmitter, the data sequence is generated into Olive-32QAM symbols through symbol mapping. The system sets the characteristic value λ. k The value is 0.25i. Subsequently, the transmission characteristic pulse is generated through Darboux transform (i.e., inverse nonlinear Fourier transform). The center wavelength of the emitting laser is 1550 nm. For example... Figure 2 As shown in Figure I, in the BTB test scenario, additive white Gaussian noise (AWGN) is added using the software's built-in module "Set OSNR" to adjust the signal-to-noise ratio (OSNR) in order to test the impact of OSNR on the signal. In... Figure 2 In the fiber optic link transmission scenario of Part II, the input power of the DS-NFDM signal is set to 5.6 dBm. Each fiber loop includes a 50 km section of standard single-mode fiber (SSMF) and an EDFA with a noise figure of 6 dB. The dispersion, nonlinearity coefficient, and attenuation parameters of the fiber are set to 16.8 ps / (nm·km), 1.3 W / km, and 0.2 dB / km, respectively. Furthermore, a 39.2 GHz optical bandpass filter (OBPF) is used in this embodiment to filter out out-of-band noise. At the coherent receiver, the center wavelength of the local oscillator laser is set to 1550 nm. The received signal undergoes offline digital signal processing, mainly including algorithms such as normalization, NFT, channel equalization, frequency offset estimation, and carrier phase recovery. Then, through geometric shaping inverse mapping relative to the transmitter, the BER value of the system is finally obtained. The number of test symbols for each sample point is 2048, and the average value is obtained after 20 iterations.

[0064] Kernel density estimation is applied to smooth the constellation distribution. In this embodiment, kernel density analysis, as an important nonparametric estimation method, is used to evaluate the distribution stability of the Olive-32QAM constellation under noisy conditions. Kernel density estimation smooths the discrete constellation point distribution into a continuous probability density curve by placing a kernel function around each data point, thereby effectively revealing the degree to which constellation points are affected by noise. This embodiment uses a Gaussian kernel as the analysis tool, and its formula is:

[0065]

[0066] in Let represent the estimated density function, n be the sample size, h be the smoothing parameter (i.e., bandwidth), and K be the kernel function. With a reasonably chosen bandwidth, kernel density analysis can balance noise smoothing and accuracy requirements, effectively characterizing the distribution characteristics of constellation points.

[0067] To verify the noise immunity of Olive-32QAM, this embodiment uses simulation to verify the constellation density distribution under different optical signal-to-noise ratios (OSNR). For example... Figure 3 (a), (b), and (c) are constellation diagram examples for 32APSK, 32QAM, and Olive-32QAM, respectively. Figure 3 (d), (e), and (f) in the diagram represent the kernel density maps for 32APSK, 32QAM, and Olive-32QAM, respectively. Under the condition of an OSNR of 12dB, the bit error rate (BER) of Olive-32QAM has reached the predetermined target (BER = 3.8 × 10⁻⁶). -3 While traditional 32QAM and 32APSK failed to meet the standard, this indicates that Olive-32QAM has better noise immunity at low OSNR. Furthermore, Olive-32QAM exhibits higher density clustering, with a more concentrated constellation point distribution and less susceptibility to noise. In contrast, the constellation point distribution of traditional 32QAM and 32APSK is more dispersed, with densities an order of magnitude lower than Olive-32QAM, demonstrating the significant advantage of the olive-shaped structure in combating amplitude and phase noise.

[0068] Figure 4 The BER and kernel density performance of three different transmission schemes under different OSNRs are shown. Figure 4 As shown on the left vertical axis of (a), the BER of all schemes decreases with increasing OSNR. The Olive-32QAM scheme consistently outperforms 32QAM and 32APSK within the test range, with the 32QAM modulation scheme performing the worst. Specifically, at an OSNR of 12dB, Olive-32QAM can achieve a BER of 3.8 × 10⁻⁶. -3 The threshold requirement is met, but 32QAM and 32APSK cannot fulfill the performance requirements. When the BER is 3.8 × 10⁻⁶... -3 At that time, Olive-32QAM can provide approximately 1 dB more OSNR gain than 32APSK, and approximately 1.7 dB more OSNR gain than 32QAM. For example... Figure 4 The curve of kernel density versus OSNR is shown on the right vertical axis of (a). The maximum kernel density of the constellation diagram under different OSNR conditions can be used to determine the noise impact on the constellation distribution. The larger the kernel density, the less affected by amplitude and phase noise, and the more concentrated the symbol distribution. Figure 4Figures (b)-(g) show the kernel density plots of 32QAM, 32APSK, and Olive-32QAM under 12dB and 14dB conditions, respectively. It can be seen that the relationship between the highest kernel density of the constellation points and OSNR shows an inverse trend compared to BER-OSNR, and the kernel density increases with increasing OSNR. Notably, the kernel density of Olive-32QAM is consistently higher than the other two modulation schemes under different OSNR conditions. Specifically, at an OSNR of 14dB, the BER of all modulation schemes has reached the threshold requirement. At this point, Olive-32QAM's highest kernel density is an order of magnitude higher than 32APSK's, and 32APSK's is an order of magnitude higher than 32QAM's. Therefore, under the same OSNR conditions, the Olive-32QAM modulation scheme can achieve a more concentrated constellation distribution than 32APSK and 32QAM, making it more efficient in combating amplitude and phase noise and maintaining a higher transmission capacity even at a relatively low BER. Conversely, the 32QAM and 32APSK modulation schemes are more sensitive to noise.

[0069] The verification also revealed that as the OSNR increases, the kernel density distribution curve of Olive-32QAM changes smoothly, and the constellation points maintain a stable distribution structure. In contrast, the kernel density distribution of traditional 32QAM and 32APSK is more susceptible to noise, exhibiting a distinctly scattered pattern. These results demonstrate that kernel density analysis can clearly verify the superior noise immunity of olive-shaped 32QAM under conditions of spontaneous emission noise (ASE) and phase noise. This invention, by optimizing the constellation point distribution, improves signal concentration while reducing noise interference, providing a more robust solution for long-distance, high-efficiency fiber optic transmission.

[0070] like Figure 5As shown in the figure, the olive-shaped 32QAM was tested for ASE noise immunity in this embodiment. The OSNR test range was 11dB to 22dB. Points with a BER of 0 after taking the logarithm disappeared in the figure. The study shows that QAM modulation is significantly affected by noise during NFDM system transmission, and its transmission performance is worse than that of APSK modulation. Under the same OSNR, the BER of 32QAM, 32APSK, and olive-shaped 32QAM decreases sequentially. When the OSNR is 12dB, the 32APSK and 32QAM modulation schemes cannot reach below the BER threshold, while the olive-shaped 32QAM can already meet the performance requirements. At a BER of 3.8e-3, the olive-shaped 32APSK can provide an OSNR gain of approximately 1.1dB compared to 32APSK, and approximately 1.7dB compared to 32QAM. The olive-shaped 32APSK modulation scheme exhibits better transmission performance than 32QAM and 32APSK under low SNR conditions, indicating its higher tolerance to ASE noise.

[0071] In addition, the phase noise tolerance performance of the proposed olive-shaped 32QAM was tested in this embodiment. Figure 6 Images (a), (b), and (c) show the phase noise tests of the three modulation schemes under different OSNR conditions. To fully demonstrate the advantages and disadvantages of the modulation schemes, the BER was obtained without using any carrier phase recovery or equalization algorithms. As the OSNR increases, the tolerance of each modulation scheme to linewidth (LW) also increases. Figure 6 As shown in (a), at an OSNR of 12dB, the BER of 32QAM and 32APSK cannot meet the threshold requirement, but the olive-shaped 32QAM can tolerate a linewidth of approximately 1.1kHz. Figure 6 As shown in (b), when the OSNR is 17dB, the olive-shaped 32QAM tolerates approximately 3.2kHz more linewidth than the 32APSK and approximately 3.6kHz more linewidth than the 32QAM. Figure 6 As shown in (c), with the increase of OSNR, the difference in linewidth tolerance between the olive-shaped 32QAM and the other two schemes also increases. When the OSNR is 22dB, the proposed olive-shaped 32QAM can tolerate a linewidth of approximately 7.1kHz. Therefore, the Olive-32QAM has high tolerance for phase noise.

[0072] The methods of the present invention can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CD-ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code originally stored on a remote recording medium or a non-transitory machine-readable medium and subsequently stored on a local recording medium, downloaded via a network. Thus, the methods described herein can be processed by software stored on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that the computer, processor, microprocessor controller, or programmable hardware includes storage components (e.g., RAM, ROM, flash memory, etc.) capable of storing or receiving software or computer code that, when accessed and executed by the computer, processor, or hardware, implements the methods described herein. Furthermore, when a general-purpose computer accesses the code used to implement the methods shown herein, the execution of the code transforms the general-purpose computer into a dedicated computer for performing the methods shown herein.

[0073] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for noise optimization of discrete-spectrum nonlinear frequency division multiplexing systems using geometric shaping, characterized in that: Includes the following steps: Considering ASE noise, establish a channel model under noisy conditions; Based on the channel model under noisy conditions, an olive-shaped 32QAM is designed in a discrete spectrum nonlinear frequency division multiplexing system. By optimizing the geometric distribution of constellation points, the optical signal is mapped to the point distribution of the olive-shaped 32QAM. When establishing a channel model under noisy conditions, in a noise-free environment, the fiber transmission process follows lossless NLSE, and the eigenvalues ​​of each soliton pulse remain unchanged. However, if ASE noise is present, the NLSE envelope electric field function is: iq z -q tt -2|q| 2 q=η(z,t) Where z and t are the normalized distance of the optical fiber and the normalized delay time in the envelope synchronous motion frame, respectively, q represents the complex envelope of the optical signal, and η(z,t) represents the zero-mean circular symmetric additive white Gaussian noise term. The constellation diagram of the olive-shaped 32QAM is divided into four parts: The first part consists of 8 symmetrically distributed points on the imaginary axis, with the relative positions of the constellation points being (±1+1i). 2 ,(±3+3i) 2 ,(±5+5i) 2 ,(±7+7i) 2 ; The second to fourth parts are three elliptical rings from the inside out, with the innermost ring E1 containing four ideal constellation points (1+3i). 2 ,(-1+3i) 2 ,(3+i) 2 ,(-3+i) 2 The intermediate ring E2 has 8 ideal points (-1+5i). 2 (1+5i) 2 ,(-5+i) 2 ,(5+i) 2 (-3+5i) 2 (3+5i) 2 (5+3i) 2 (-5+3i) 2 The outermost ring E3 has 12 ideal constellation points (-1 + 7i). 2 (1+7i) 2 ,(-7+i) 2 ,(7+i) 2 (-3+7i) 2 (3+7i) 2 (7+3i) 2 (-7+3i) 2 ,(-5+7i) 2 (5+7i) 2 (7+5i) 2 .

2. The method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems using geometric shaping according to claim 1, characterized in that, In the presence of ASE noise, the eigenvalue λ of each soliton pulse i It will be distorted and become λ d =λ i +Δλ; Eigenvalue distortion causes noise in the spectral amplitude. This spectral amplitude disturbance accumulates with increasing propagation distance, manifesting as: In the formula, log is the logarithm operation. Let q represent the result of the NFT, and Δλ be the distorted value of the eigenvalue.

3. The method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems using geometric shaping according to claim 2, characterized in that, During optical signal transmission, accumulated ASE noise will affect the signal. The output discrete-time channel model Y is set as the square root of the output signal amplitude A, and its conditional probability density function is: in, I1(·) is the normalized cumulative ASE noise variance, and I1(·) is the first-type modified Bessel function.

4. The method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems using geometric shaping according to claim 1, characterized in that, The constellation points of the olive-shaped 32QAM are distributed in a symmetrical structure, and three elliptical rings with different radii are set to distribute different power points.

5. The method for noise optimization of discrete-spectrum nonlinear frequency division multiplexing systems using geometric shaping according to claim 1, characterized in that, In a noise-free environment, the optical signal of a discrete spectrum nonlinear frequency division multiplexing system is mapped from the nonlinear spectrum to the time domain through an inverse nonlinear Fourier transform.

6. A computer storage medium storing a readable program, characterized in that, When the program runs, it can execute the method for noise optimization of discrete spectrum nonlinear frequency division multiplexing system by geometric shaping as described in any one of claims 1-5.

7. An electronic device, characterized in that, include: The processor, memory, communication interface, and communication bus are provided, wherein the processor, memory, and communication interface communicate with each other via the communication bus. The memory is used to store at least one executable instruction, which causes the processor to perform the operation corresponding to the method for noise optimization of discrete spectrum nonlinear frequency division multiplexing system by geometric shaping as described in any one of claims 1-5.

8. A computer program product comprising computer instructions, characterized in that, The computer instructions instruct the computing device to perform the operation corresponding to the method for noise optimization of discrete spectrum nonlinear frequency division multiplexing systems using geometric shaping as described in any one of claims 1-5.

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