Low-complexity nonlinear equalization method based on cosine polynomial

Abstract

The invention relates to the technical field of optical communication, in particular to a low-complexity nonlinear equalization method based on a cosine polynomial. A cross beat frequency item in a traditional diagonal clipping Volterra decision feedback equalizer (DP-VDFE) is replaced by an item composed of two input samples and a cosine value, so that the calculation complexity is remarkably reduced, and meanwhile, the equalization performance similar to that of the DP-VDFE is kept.

Description

Technical Field

[0001] The present invention relates to the field of optical communication technologies, and more specifically, to a low-complexity non-linear equalization method based on cosine polynomials. Background Art

[0002] With the continuous growth of data traffic in wireless communication and data center applications, there is an urgent need to implement cost-effective optical transmission systems that can operate at rates of 100 Gb / s and above. Compared with coherent systems, intensity modulation and direct detection (IM / DD) systems, which have significant advantages such as small size, low cost, and low power consumption, have received extensive attention. Among various spectrally efficient modulation formats, four-level pulse amplitude modulation (PAM-4) has low complexity and can be better applied to IM / DD systems. Currently, PAM-4 has been standardized in 400G Ethernet and is expected to be an ideal solution for the next-generation 800G Ethernet. However, cost-effective PAM-4 systems are vulnerable to fiber dispersion, limited system bandwidth, and various non-linear effects related to modulation and detection, which significantly limit the transmission distance and capacity of the system. In addition, the interaction between dispersion and square-law detection also causes severe frequency-selective power fading, ultimately limiting the available bandwidth of the signal and hindering high-speed transmission of the signal over long-distance optical fibers.

[0003] Among existing dispersion and non-linear compensation technologies, non-linear decision feedback equalizers (VDFEs) based on Volterra series and non-linear equalizers based on neural networks can effectively compensate for system dispersion and non-linear impairments. However, the equalization scheme based on neural networks cannot achieve good performance when the training data scale is insufficient, and even performs worse than traditional linear equalizers. VDFE requires a long equalizer memory length, resulting in a high number of real-number multiplications. Therefore, this equalization method requires a large number of multipliers in practical applications and is difficult to apply to IM / DD short-distance optical fiber communication systems. To reduce the number of real-number multiplications of VDFE, some cross-beat frequency terms with large delays can be pruned, and this method is called the diagonal pruning-based Volterra decision feedback equalizer (DP-VDFE), but it still has the problem of excessive complexity. Summary of the Invention

[0004] The object of the present invention is to overcome the deficiency that the prior art cannot ensure high equalization performance of VDFE while reducing its computational complexity, and provide a low-complexity non-linear equalization method based on cosine polynomials. Compared with the traditional diagonal pruning-based Volterra decision feedback equalizer (DP-VDFE), the method proposed by the present invention significantly reduces the computational complexity while maintaining an equalization performance similar to that of the traditional DP-VDFE method.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0006] Provide a non-linear equalizer based on cosine polynomial. The model establishment of the non-linear equalizer CTDFE based on cosine polynomial includes: replacing the cross-beat frequency term in the diagonal clipped Volterra decision feedback equalizer DP-VDFE with the cosine term of the sum of two input samples, introducing a non-linear adjustment factor at the same time, and establishing a pre-lookup table related to the parameters, directly mapping the input signal term to the corresponding cosine function output term.

[0007] A non-linear equalizer based on cosine polynomial provided by the present invention significantly reduces the computational complexity by replacing the cross-beat frequency term in the traditional diagonal clipped Volterra decision feedback equalizer (DP-VDFE) with a term composed of the cosine values of the sum of two input samples, while maintaining an equalization performance similar to that of DP-VDFE.

[0008] Furthermore, the model of the improved non-linear equalizer CTDFE is:

[0009]

[0010] In the formula, x(2n) is the received signal at an interval of 1 / 2 symbol period, and d(n) is the output after the signal is hard-decided; h m and w m are the filter tap coefficients of the feedforward equalization part and the decision feedback equalization part respectively; N m and D m are the filter memory lengths of the feedforward equalization part and the decision feedback equalization part respectively. It is stipulated that N m = 2L m +1 must be an odd number, where m = 1 or 2, and L m is a positive integer; k is the index value of the filter memory length; Q and U are the non-linear truncation factors of the feedforward equalization part and the decision feedback equalization part respectively, and q and u are the index values corresponding to the non-linear truncation factors; cos(·) represents the cosine operator; α and β are the non-linear adjustment factors of the feedforward equalization part and the decision feedback equalization part respectively; x(2n–k) and x(2n–k–q) are the received signals at the previous k and previous k+q moments respectively; d(n–k) and d(n–k–q) are the decision feedback signals at the previous k and previous k+q moments respectively; y(n) is the equalization output signal at the current moment.

[0011] The present invention provides a low-complexity non-linear equalization method based on cosine polynomial, which uses the non-linear equalizer CTDFE based on cosine polynomial described above to compensate for dispersion and non-linear impairments, including the following steps:

[0012] S1. Equalizer CTDFE Coefficient Initialization: Determine the tap coefficients h of the equalizer based on Y training symbols using the recursive least squares algorithm m and w m ;

[0013] S2. Parameter Initial Setting: Set initial values for the filter memory length N m and D m , truncation factors Q and U, and non - linear adjustment factors α and β;

[0014] S3. Equalization Operation: Perform summation, function mapping, and multiplication operations on the input signal x(2n–k) according to Equation (1), and perform weighted addition with the decision - feedback signal d(n–k) at the previous moment to obtain the equalized output y(n) at the current moment;

[0015] S4. Feedback Update: Use the hard - decision signal of the equalized output y(n) at the current moment as the decision - feedback signal d(n–1) at the next moment for subsequent calculations;

[0016] S5. Bit Error Rate Calculation: Perform the operations in steps S3 - S4 on all input signals to obtain the equalized output result, and compare it with the transmitted - end signal to obtain the bit error rate BER of the equalized system;

[0017] S6. Structural Parameter Optimization: Optimize the parameters of the filter memory length N m and D m as well as the truncation factors Q and U;

[0018] S7. Non - linear Factor Optimization: Optimize the non - linear adjustment factors α and β to determine the optimal values;

[0019] S8. Equalization Implementation: Equalize the input signal under the optimal parameter configuration to achieve the best equalization performance.

[0020] Furthermore, in step S6, use the traversal method to search, and select the corresponding value when the system bit error rate is the smallest as the optimal setting.

[0021] Furthermore, in step S7, use the traversal method to search, and select the corresponding value when the system bit error rate is the smallest as the optimal setting.

[0022] Furthermore, the step S6 includes:

[0023] Optimize N1 and D1: Set N2 = D2 = 0 in DP-VDFE. At this time, DP-VDFE only includes linear feedforward equalization terms and linear decision feedback equalization terms. Set the value ranges and step sizes of N1 and D1, traverse all value cases, and obtain the curve of the bit error rate varying with coefficients N1 and D1. After balancing the equalizer performance and computational complexity, find the optimal parameters N1' and D1'.

[0024] Optimize N2 and Q: Set N1 = N1', D1 = D1', D2 = 0 in DP-VDFE. At this time, DP-VDFE does not include second-order decision feedback equalization terms. Set the value of N2. Under this condition, set the value range and step size of Q, traverse all value cases, and obtain the curve of the bit error rate varying with coefficient Q. From the curve, it can be obtained that when Q > Q', the bit error rate does not improve, and the optimal value Q = Q' is obtained. Fix Q = Q', set the value range and step size of N2, traverse all cases, and obtain the optimal value N2'.

[0025] Optimize D2 and U: Set N1 = N1', N2 = N2', Q = Q', D1 = D1' in DP-VDFE. Set the value of D2. Under this condition, set the value range and step size of U, traverse all value cases, and obtain the curve of the bit error rate varying with coefficient U. From the curve, it can be obtained that when U > U', the bit error rate does not improve, and the optimal value U = U' is obtained. Fix U = U', set the value range and step size of D2, traverse all cases, and obtain the optimal value D2'.

[0026] Furthermore, the step S7 includes: Set N1 = N1', N2 = N2', Q = Q', D1 = D1', D2 = 0 in CTDFE. Set the value range and step size of α, traverse all value cases, and obtain the curve of the bit error rate varying with coefficient α, and obtain α = α' under the optimal bit error rate. Set N1 = N1', N2 = N2', Q = Q', α = α', D1 = D1', D2 = D2', U = U', set the value range and step size of β, traverse all value cases, and obtain the curve of the bit error rate varying with coefficient β, and obtain β = β' under the optimal bit error rate.

[0027] The present invention provides a digital signal processing method, including the following steps:

[0028] At the transmitting end: The signal is input into an arbitrary waveform generator. The generated signal is amplified by an electrical amplifier and input into a Mach-Zehnder modulator for dual-side electro-optic conversion. An external cavity laser provides the light source. After the signal is transmitted through a standard single-mode fiber, without dispersion compensation, the received optical power of the signal is adjusted by an adjustable optical attenuator. An erbium-doped fiber amplifier and an optical bandpass filter are used to boost the signal power and then input it into a photodetector. The signal is then subjected to analog-to-digital conversion by a real-time oscilloscope.

[0029] At the receiving end: Offline digital signal processing is performed, including resampling, synchronization, equalization using the above-mentioned non-linear equalizer CTDFE based on cosine polynomials, symbol decision, PAM demapping, and bit error rate calculation.

[0030] The present invention provides a computer device, including a processor and a memory. The memory stores a computer program. When the processor executes the computer program, the steps of the above-mentioned low-complexity non-linear equalization method based on cosine polynomials are implemented.

[0031] The present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned low-complexity non-linear equalization method based on cosine polynomials are implemented.

[0032] Compared with the prior art, the beneficial effects of the present invention are:

[0033] A non-linear equalizer based on cosine polynomials and a low-complexity non-linear equalization method based on cosine polynomials of the present invention significantly reduce the computational complexity by replacing the cross-beat frequency terms in the traditional diagonal clipping Volterra decision feedback equalizer (DP-VDFE) with terms composed of the cosine values of the sum of two input samples, while maintaining an equalization performance similar to that of the DP-VDFE. Description of the Drawings

[0034] Figure 1 It is the digital signal processing block diagram in Embodiment 3;

[0035] Figure 2 It is the curve of the bit error rate (BER) varying with the non-linear adjustment factor α and the non-linear adjustment factor β in Embodiment 2, where (a) represents the curve varying with the non-linear adjustment factor α, and (b) represents the curve varying with the non-linear adjustment factor β;

[0036] Figure 3 It is the curve of the bit error rate (BER) varying with the received optical power (ROP) after 60 km of single-mode fiber transmission in Embodiment 3. Detailed Embodiments

[0037] The present invention will be further described below in conjunction with specific embodiments. Among them, the drawings are only for illustrative purposes, showing only schematic diagrams rather than physical diagrams, and should not be construed as limiting the present invention; in order to better illustrate the embodiments of the present invention, some components in the drawings will be omitted, enlarged or reduced, which do not represent the dimensions of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0038] In the drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", etc. indicating the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, it is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0039] Embodiment 1

[0040] This embodiment is an embodiment of a non-linear equalizer based on a cosine polynomial. In this embodiment, by replacing the cross-beat frequency term in the traditional diagonal clipped Volterra decision feedback equalizer (DP-VDFE) with a term composed of the cosine value of the sum of two input samples, the computational complexity is significantly reduced while maintaining an equalization performance similar to that of the DP-VDFE.

[0041] The expression of the traditional DP-VDFE is shown in Equation (1), where x(2n) is the received signal at an interval of 1 / 2 symbol period, and d(n) is the output after hard decision of the signal; h m and w m are the filter tap coefficients of the feedforward equalization part and the decision feedback equalization part respectively; N m and D m are the filter memory lengths of the feedforward equalization part and the decision feedback equalization part respectively. It is stipulated that N m = 2L m +1 must be an odd number, where m = 1 or 2, and L mis a positive integer; k is the index value of the filter memory length; Q and U are the non - linear truncation factors of the feed - forward equalization part and the decision - feedback equalization part respectively, and q and u are the index values corresponding to the non - linear truncation factors; x(2n–k) and x(2n–k–q) are the received signals at the previous k and previous k + q moments respectively; d(n–k) and d(n–k–q) are the decision - feedback signals at the previous k and previous k + q moments respectively; y(n) is the equalization output signal at the current moment. Due to the existence of cross - beat frequency terms in the second - order feed - forward equalization and second - order decision - feedback equalization, the number of real - number multiplications (RNRM) of this method is shown in Equation (2).

[0042] The CTDFE expression of the non - linear equalizer based on cosine polynomial proposed in this embodiment is shown in Equation (3), where cos(·) represents the cosine operator. To enhance the non - linear fitting ability, two parameters α and β are introduced, which represent the non - linear adjustment factors of the feed - forward equalization part and the decision - feedback equalization part respectively, and their value ranges are both from 0 to 1. The meanings of the remaining parameters are the same as those in Equation (1). In CTDFE, by replacing the cross - beat frequency term in DP - VDFE with the cosine term of the sum of two input samples and establishing a pre - lookup table related to these parameters, CTDFE can directly map the input signal terms to the corresponding cosine function output terms. The number of real - number multiplications (RNRM) required by this method is shown in Equation (4). Compared with DP - VDFE, CTDFE significantly reduces the required number of real - number multiplications.

[0043]

[0044] RNRM DP-VDFE = N1 + Q(2N2 - Q + 1)+D1 + U(2D2 - U + 1) (2)

[0045]

[0046] RNRM CTDFE = N1 + Q(2N2 - Q + 1) / 2+D1 + U(2D2 - U + 1) / 2 (4)

[0047]

[0048] Equation (5) is the Taylor expansion of cos(α(x(2n - k)+x(2n - k - q))), where (·)! represents the factorial operation. Since the expansion of the cosine term contains various even - order non - linear terms of different orders, CTDFE can effectively compensate for the system non - linear effect and frequency - selective fading, achieving an equalization performance similar to that of DP - VDFE.

[0049] Embodiment 2

[0050] This embodiment is an embodiment of a low-complexity non-linear equalization method based on a cosine polynomial. The non-linear equalizer CTDFE based on the cosine polynomial described in Embodiment 1 is used to compensate for dispersion and non-linear impairments, including the following steps:

[0051] S1. Initialization of the coefficients of the equalizer CTDFE: The tap coefficients h m and w of the equalizer are determined based on 10,000 training symbols using the recursive least squares algorithm, where m = 1 or 2;

[0052] S2. Initial setting of parameters: Set initial values for the filter memory length N m and D m , the truncation factors Q and U, and the non-linear adjustment factors α and β;

[0053] S3. Equalization operation: Perform summation, function mapping, and multiplication operations on the input signal x(2n–k) according to formula (3) in Embodiment 1, and perform weighted addition with the decision feedback signal d(n–k) at the previous moment to obtain the equalized output y(n) at the current moment;

[0054] S4. Feedback update: Use the hard decision signal of the equalized output y(n) at the current moment as the decision feedback signal d(n–1) at the next moment for subsequent calculations;

[0055] S5. Bit error rate calculation: Perform the operations in steps S3 to S4 on all input signals to obtain the equalized output result, and compare it with the transmitted signal to obtain the bit error rate BER of the equalized system;

[0056] S6. Optimization of structural parameters: Optimize the filter memory length N m and D m and the truncation factors Q and U; Use the traversal method to search and select the corresponding values when the system bit error rate is the smallest as the optimal settings;

[0057] S7. Optimization of non-linear factors: Optimize the non-linear adjustment factors α and β to determine the optimal values; Use the traversal method to search and select the corresponding values when the system bit error rate is the smallest as the optimal settings;

[0058] S8. Equalization implementation: Equalize the input signal under the optimal parameter configuration to achieve the best equalization performance.

[0059] In this embodiment, under the condition that the received optical power is -10 dBm, the structural parameters and non-linear factors are optimized. Among them, step S6 includes:

[0060] Optimize N1 and D1: Set N2 = D2 = 0 in DP-VDFE. At this time, DP-VDFE only contains linear feed-forward equalization terms and linear decision feedback equalization terms. Set the value range of N1 to be from 45 to 125, and the value range of D1 to be from 20 to 34, with a step of 4. Traverse all value cases to obtain the curve of the bit error rate varying with the coefficients N1 and D1. The curve shows a trend of first decreasing and then remaining unchanged. After balancing the equalizer performance and computational complexity, the optimal parameters are found to be N1 = 109 and D1 = 32;

[0061] Optimize N2 and Q: Set N1 = 109, D1 = 32, and D2 = 0 in DP-VDFE. At this time, DP-VDFE does not contain second-order decision feedback equalization terms. Set a relatively large value N2 = 77. Under this condition, set the value range of Q to be from 5 to 25, with a step of 2. Traverse all value cases to obtain the curve of the bit error rate varying with the coefficient Q. The curve shows a trend of first decreasing and then remaining unchanged. When Q > 17, the bit error rate hardly improves, and the optimal value Q = 17 is obtained. Fix Q = 17, set the value range of N2 to be from 31 to 79, with a step of 4. Traverse all cases to obtain the optimal value N2 = 59;

[0062] Optimize D2 and U: Set N1 = 109, N2 = 59, Q = 17, and D1 = 32 in DP-VDFE. Set a relatively large value D2 = 32. Under this condition, set the value range of U to be from 1 to 17, with a step of 2. Traverse all value cases to obtain the curve of the bit error rate varying with the coefficient U. The curve shows a trend of first decreasing and then remaining unchanged. When U > 13, the bit error rate hardly improves, and the optimal value U = 13 is obtained. Fix U = 13, set the value range of D2 to be from 12 to 32, with a step of 2. Traverse all cases to obtain the optimal value D2 = 24.

[0063] In step S7, optimize α and β: Set N1 = 109, N2 = 59, Q = 17, D1 = 32, and D2 = 0 in CTDFE. Set the value range of α to be from 0 to 1, with a step of 0.1. Traverse all value cases to obtain the curve of the bit error rate varying with the coefficient α. The curve shows a trend of first decreasing and then increasing, and the α = 0.3 under the optimal bit error rate is obtained. Set N1 = 109, N2 = 59, Q = 17, α = 0.3, D1 = 32, D2 = 24, and U = 13. Optimize β in the same way to obtain β = 0.7 under the optimal bit error rate. Figure 2 The curves of the bit error rate of CTDFE varying with the coefficients α and β are shown.

[0064] Embodiment III

[0065] This embodiment is an embodiment of a digital signal processing method, as Figure 1 shown:

[0066] At the transmitting end: A 50-GBaud PAM-4 signal is input into an arbitrary waveform generator. The generated signal is amplified by an electrical amplifier and input into a Mach-Zehnder modulator for dual-side electro-optic conversion. A light source with a central wavelength of 1550.12 nm is provided by an external cavity laser. After the signal is transmitted through a 60-kilometer standard single-mode fiber, without dispersion compensation, the received optical power of the signal is adjusted by an adjustable optical attenuator. An erbium-doped fiber amplifier and an optical bandpass filter are used to boost the signal power to 7 dBm and input it into a photodetector. The signal is then subjected to analog-to-digital conversion through a real-time oscilloscope.

[0067] At the receiving end: Offline digital signal processing is performed, including resampling, synchronization, equalization using the above-mentioned CTDFE based on cosine polynomial, symbol decision, PAM demapping, and bit error rate calculation.

[0068] Based on the optimal parameters obtained in the second embodiment, under the optimal parameter settings, the transmission performance of the system is evaluated based on the proposed CTDFE. Figure 3 Shows the relationship between the bit error rate of CTDFE and the received optical power when transmitting a 50-GBaud PAM-4 signal over a 60-kilometer standard single-mode fiber. For a 7% hard decision forward error correction threshold (HD-FEC) value of 3.8×10 -3 , compared with the traditional DP-VDFE, the receiver sensitivity of the proposed CTDFE is improved by about 0.3 dB, showing better performance. At the same time, it can be seen from Equation (2) and Equation (4) that after replacing the crossbeat term in DP-VDFE with the term composed of the cosine value of the sum of two input samples, the complexity of the proposed CTDFE is reduced by about 47% compared with DP-VDFE. The present invention proposes and implements a low-complexity non-linear equalization method based on cosine polynomial.

[0069] Embodiment 4

[0070] This embodiment provides a computer device, including a processor and a memory. The memory stores a computer program. When the processor executes the computer program, the steps of the above-mentioned low-complexity non-linear equalization method based on cosine polynomial are implemented.

[0071] Embodiment 5

[0072] The present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned low-complexity non-linear equalization method based on cosine polynomial are implemented.

[0073] In the specific content of the above specific embodiments, the technical features can be combined arbitrarily without contradiction. For the sake of concise description, not all possible combinations of the above technical features are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0074] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, rather than limitations on the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A non-linear equalizer based on cosine polynomials, characterized in that, The model establishment of the non - linear equalizer CTDFE based on cosine polynomial includes: replacing the cross - beat frequency term in the diagonal - clipped Volterra decision - feedback equalizer DP - VDFE with the cosine term of the sum of two input samples, introducing a non - linear adjustment factor at the same time, and establishing a pre - lookup table related to the parameters to directly map the input signal term to the corresponding cosine function output term.

2. The non-linear equalizer based on a cosine polynomial according to claim 1, characterized in that, The model of the improved non - linear equalizer CTDFE is: Where x(2n) is the received signal at intervals of half a symbol period, and d(n) is the output after hard decision of the signal; h m and w m are the filter tap coefficients of the feedforward equalization part and the decision feedback equalization part respectively; N m and D m are the filter memory lengths of the feedforward equalization part and the decision feedback equalization part respectively. It is stipulated that N m = 2L m +1 must be odd, where m = 1 or 2, and L m is a positive integer; k is the index value of the filter memory length; Q and U are the non-linear truncation factors of the feedforward equalization part and the decision feedback equalization part respectively, and q and u are the index values corresponding to the non-linear truncation factors respectively; cos(·) represents the cosine operator; α and β are the non - linear adjustment factors of the feed - forward equalization part and the decision - feedback equalization part respectively; x(2n–k) and x(2n–k–q) are the received signals at the previous k and previous k + q moments respectively; d(n–k) and d(n–k–q) are the decision - feedback signals at the previous k and previous k + q moments respectively; y(n) is the equalized output signal at the current moment.

3. A low-complexity non-linear equalization method based on cosine polynomials, characterized in that, Using the non - linear equalizer CTDFE based on cosine polynomial described in claim 2 to compensate for dispersion and non - linear impairments, including the following steps: S1. Initialization of equalizer CTDFE coefficients: Determine the tap coefficients h of the equalizer based on Y training symbols using the recursive least squares algorithm m and w m ; S2. Parameter Initial Setting: Set the initial values for the filter memory length N m and D m , the truncation factors Q and U, and the nonlinear adjustment factors α and β; S3. Equalization operation: Perform summation, function mapping, and multiplication operations on the input signal x(2n–k) according to formula (1), and perform weighted addition with the decision - feedback signal d(n–k) at the previous moment to obtain the equalized output y(n) at the current moment; S4. Feedback update: Use the hard - decision signal of the equalized output y(n) at the current moment as the decision - feedback signal d(n–1) at the next moment for subsequent calculations; S5. Bit - error rate calculation: Perform the operations of steps S3 - S4 on all input signals to obtain the equalized output result, and compare it with the transmitted - end signal to obtain the bit - error rate BER of the equalized system; S6. Structural parameter optimization: optimize the parameters of the filter memory length N m and D m as well as the truncation factors Q and U; S7. Non - linear factor optimization: Optimize the non - linear adjustment factors α and β to determine the optimal values; S8. Equalization implementation: Equalize the input signal under the optimal parameter configuration to achieve the best equalization performance.

4. The low-complexity non-linear equalization method based on cosine polynomials according to claim 3, characterized in that, In step S6, the traversal method is used for searching, and the corresponding value is selected when the bit - error rate of the system is the smallest as the optimal setting.

5. The low-complexity non-linear equalization method based on cosine polynomial according to claim 3, characterized in that In step S7, the traversal method is used for searching, and the corresponding value is selected when the bit - error rate of the system is the smallest as the optimal setting.

6. The low-complexity non-linear equalization method based on a cosine polynomial according to claim 3, characterized in that The said step S6 includes: S61. Optimize N1 and D1: Set N2 = D2 = 0 in DP - VDFE. At this time, DP - VDFE only includes the linear feed - forward equalization term and the linear decision - feedback equalization term; set the value range and step size of N1 and D1, traverse all value cases, and obtain the curve of the bit - error rate varying with the coefficients N1 and D1; after balancing the equalizer performance and computational complexity, find the optimal parameters N1' and D1'; S62. Optimize N2 and Q: Set N1 = N1', D1 = D1', D2 = 0 in DP-VDFE. At this time, DP-VDFE does not include the second-order decision feedback equalization term. Set the value of N2. Under this condition, set the value range and step size of Q, traverse all value cases, and obtain the curve of the bit error rate varying with the coefficient Q. From the variation curve, it is obtained that when Q > Q', the bit error rate does not improve, and the optimal value Q = Q' is obtained. Fix Q = Q', set the value range and step size of N2, traverse all cases, and obtain the optimal value N2'. S63. Optimize D2 and U: Set N1 = N1', N2 = N2', Q = Q', D1 = D1' in DP-VDFE. Set the value of D2. Under this condition, set the value range and step size of U, traverse all value cases, and obtain the curve of the bit error rate varying with the coefficient U. From the variation curve, it is obtained that when U > U', the bit error rate does not improve, and the optimal value U = U' is obtained. Fix U = U', set the value range and step size of D2, traverse all cases, and obtain the optimal value D2'.

7. The low-complexity non-linear equalization method based on cosine polynomial according to claim 6, wherein The step S7 includes: Set N1 = N1', N2 = N2', Q = Q', D1 = D1', D2 = 0 in CTDFE. Set the value range and step size of α, traverse all value cases, and obtain the curve of the bit error rate varying with the coefficient α, and obtain α = α' under the optimal bit error rate. Set N1 = N1', N2 = N2', Q = Q', α = α', D1 = D1', D2 = D2', U = U', set the value range and step size of β, traverse all value cases, and obtain the curve of the bit error rate varying with the coefficient β, and obtain β = β' under the optimal bit error rate.

8. A digital signal processing method, characterized in that, It includes the following steps: At the transmitting end: The signal is input into an arbitrary waveform generator. The generated signal is amplified by an electrical amplifier and input into a Mach-Zehnder modulator for dual-sideband electro-optical conversion. And a light source is provided by an external cavity laser. After the signal is transmitted through a standard single-mode fiber, without dispersion compensation, the received optical power of the signal is adjusted by an adjustable optical attenuator. The signal power is boosted by using an erbium-doped fiber amplifier and an optical bandpass filter and then input into a photodetector. Subsequently, the signal undergoes analog-to-digital conversion through a real-time oscilloscope. At the receiving end: Perform offline digital signal processing, including resampling, synchronization, equalization using the CTDFE-based nonlinear equalizer according to claim 2, symbol decision, PAM demapping, and bit error rate calculation.

9. A computer device, comprising a processor and a memory, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 3 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 3 to 7.

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