Simplified second-order Volterra nonlinear equalization method and system based on weight screening
By simplifying the second-order Volterra nonlinear equalization algorithm, optimizing the weight coefficients, and removing some weights, the problem of high computational complexity of the Volterra equalizer is solved, achieving efficient signal equalization and cost reduction in communication systems.
Patent Information
- Application Number
- CN202511237133.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2022-11-17
- Publication Date
- 2025-12-09
AI Technical Summary
Existing Volterra equalizers have high computational complexity in communication systems, resulting in high power consumption and high cost, making them difficult to apply in practical systems, especially when compensating for nonlinear impairments.
A simplified second-order Volterra nonlinear equilibrium algorithm is adopted. Through three steps of training, simplification and equilibrium, the weight coefficients are optimized and some weights are removed to reduce computational complexity. This includes training the weight coefficient update and simplification process based on the second-order Volterra algorithm, and using the first-order and simplified second-order weight coefficients for equilibrium.
While reducing computational complexity and power consumption, it maintains good signal equalization performance, significantly reducing the cost of Volterra equalizers and making them suitable for cost-sensitive communication systems.
Smart Images
Figure CN121098672A_ABST
Abstract
Description
[0001] This application is a divisional application. The original application was entitled "A Simplified Second-Order Volterra Nonlinear Equalization Algorithm and Device", with application number 202211441206.9 and application date of November 17, 2022. Technical Field
[0002] This invention belongs to the field of communication technology, specifically relating to a simplified second-order Volterra nonlinear equalization algorithm and device for digital signal processing at the receiving end of a communication system. Background Technology
[0003] In communication systems, signals are subjected to varying degrees of impairment from the channel during transmission, resulting in distortion. Upon receiving the signal at the receiver, digital signal processing equalization can be used to recover a high-quality signal. Signal impairments in communication systems can be categorized as linear or nonlinear. Generally, a time-domain or frequency-domain linear equalizer with low computational complexity is sufficient to handle linear impairments in the channel. However, for some communication systems, nonlinear impairments in the channel are not negligible. For example, in high-speed, high-capacity fiber optic communication systems, nonlinear impairments caused by imperfect modulators, photodiodes, amplifiers, and other devices can have a significant impact; furthermore, for long-distance transmission, various nonlinear effects in the optical fiber are further amplified.
[0004] Volterra equalizers based on multi-order Volterra series can be used to simultaneously equalize linear and nonlinear impairments in a system. However, the computational complexity of Volterra equalizers is very high, and their high power consumption and cost are unacceptable for practical communication systems. Furthermore, higher computational complexity also implies greater time delays. To address this issue, this invention provides a simplified second-order Volterra nonlinear equalization algorithm that effectively solves the problem of high computational complexity in traditional Volterra nonlinear equalizers while compensating for linear and nonlinear impairments in communication systems. Summary of the Invention
[0005] In view of the above situation, the purpose of this invention is to provide a simplified second-order Volterra nonlinear equalization algorithm and device, which can effectively solve the problem of excessive computational complexity of traditional Volterra nonlinear equalizers while compensating for linear and nonlinear impairments in communication systems.
[0006] The simplified second-order Volterra equalizer provided by this invention can have its number of input and output interfaces selected according to specific circumstances. The following explanation uses a single-input single-output Volterra equalizer as an example. For multiple-input multiple-output systems with crosstalk between channels, the number of input and output interfaces of the Volterra equalizer can be increased to support MIMO equalization.
[0007] The simplified second-order Volterra nonlinear equalization algorithm with single input and single output described in this invention specifically includes three steps: training, simplification, and equalization, as detailed below:
[0008] (i) Training: Based on the second-order Volterra algorithm, the received data is balanced according to two sets of weight coefficients, first-order and second-order, and the error is calculated using the corresponding sent data as a reference; the error is then transmitted back to update and optimize each weight coefficient.
[0009] (ii) Simplification: Arrange the final optimized second-order nonlinear weight coefficients in descending order of their absolute magnitudes, remove the smaller 70% of the values, and use the remaining 30% as the simplified second-order nonlinear weight coefficients.
[0010] (iii) Equalization: Using the obtained first-order weight coefficients and simplified second-order weight coefficients, the effective data other than the training sequence are successively equalized and output.
[0011] Corresponding to the simplified second-order Volterra nonlinear equalization algorithm described above, this invention also relates to a simplified second-order Volterra nonlinear equalizer, comprising three modules: a training module, a simplification module, and an equalization module, which respectively perform the functions of the three steps described above.
[0012] This invention has good versatility and is applicable to digital signal processing at the receiving end of various communication systems. It has high application value, especially in cost-sensitive scenarios. Attached Figure Description
[0013] Figure 1 This is a simplified schematic diagram of a second-order Volterra equalizer with a single input and single output.
[0014] In the diagram, 1 represents the signal data X input to the Volterra equalizer, and 2 represents the data X stored in the linear section of the equalizer. L 3 represents the data X stored in the nonlinear part of the equalizer. N , 4 is the linear weighting coefficient h L 5 represents the second-order nonlinear weighting coefficient h. NN 6 represents the linear equalization output, 7 represents the non-linear equalization output, and 8 represents the output data Y of the Volterra equalizer. k9 represents the error E between the output value and the reference value, and 10 represents the reference value Y corresponding to the output term in the transmitted training sequence. k ', 11 are the second-order nonlinear weighting coefficients arranged according to the absolute value of their amplitudes, 12 are the nonlinear weighting coefficients with 70% of their absolute values removed, and 13 are the simplified nonlinear weighting coefficients h of the output. NN '. Detailed Implementation
[0015] The present invention will now be further described in detail with reference to the accompanying drawings:
[0016] The principles and complete process of the training and simplification sections are shown in the attached diagram.
[0017] (I) Training; First, extract and store the linear portion X of length L sequentially from the signal data X input from the Volterra equalizer. L And a nonlinear portion of length N stores the data X N L and N are both odd numbers, representing the first and second order storage lengths of the Volterra equalizer, respectively. X L and X N The middle position is X. k After that, X L and the corresponding first-order linear weighting coefficient h L Corresponding multiplication, and X N Multiply by any of its terms to get N 2 After that, add the second-order nonlinear weighting coefficient h. NN By multiplying the corresponding values and summing the results, we can obtain the output data Y of the Volterra equalizer. k The above process can be represented by matrix calculation formula (1):
[0018] Y k =h L X L H +X NN h NN X NN H (1)
[0019] Among them, X L XNN and h L All are row vectors, h NN For N 2 A two-dimensional matrix.
[0020] Then, in the sent training sequence, find the reference value Y corresponding to this output term. k And use the loss function shown in formula (2) to calculate the difference E between the output value and the reference value:
[0021] E=Y k '-Y k (2)
[0022] Then, based on the difference between the output value and the reference value, the two sets of weight coefficients are updated with step sizes μ1 and μ2 respectively using the feedback function shown in formula (3):
[0023] h L =h L +μ1EX L
[0024] h NN =h NN + μ2 EX NN H X NN (3)
[0025] Repeat the process shown in formulas (1), (2), and (3), and the signal will gradually converge. Finally, two sets of trained linear and nonlinear weight coefficients are obtained.
[0026] (ii) Simplification; After training, the second-order nonlinear weight coefficient h NN Each element is arranged in descending order of its absolute magnitude, and the smaller 70% are removed. The remaining values are used as simplified second-order nonlinear weighting coefficients h. NN '.
[0027] (III) Equilibrium; Finally, the simplified second-order nonlinear weighting coefficients h are obtained. NN 'and first-order linear weighting coefficient h L Together, these are used as fixed values to compensate for effective information other than the training sequence. The steps are the same as the training process described above, except that the loss function calculation error and the part that updates the weight coefficients are removed, that is, the above formula (1) is repeated continuously.
[0028] By using a simplified second-order Volterra equalizer, the computational complexity can be significantly reduced while ensuring sufficient online and nonlinear equalization performance at the receiver of the communication system. This invention can effectively reduce the power consumption and cost of Volterra equalizers in practical applications.
[0029] Taking long-distance coherent optical communication as an example, this paper illustrates the application and results of a simplified second-order Volterra equalization algorithm in digital signal processing at the receiver.
[0030] In a wavelength division multiplexing (WDM) coherent optical communication system, a truncated probabilistically shaped 64th-order orthogonal amplitude modulation (64QAM) signal with a symbol rate of 100 Gbaud is transmitted within each 100 GHz wavelength interval. After transmission over a long distance of 2000 km in single-mode fiber, nonlinear distortion occurs. Following dual-polarization coherent reception at the receiver, offline digital signal processing is performed to recover the signal, including orthogonalization, dispersion compensation, clock recovery, CMA equalization, frequency offset estimation, and carrier phase recovery based on a blind phase search algorithm. A simplified second-order Volterra equalizer is used as the final step in the offline digital signal processing to reduce the influence of other factors on Volterra equalization training. The first-order linear part of the second-order equalizer uses a 2×2 complex-valued MIMO equalizer, and the second-order nonlinear part uses a real-valued Volterra equalizer. Furthermore, considering both performance and complexity, the first-order and second-order memory lengths are set to 149 and 99, respectively.
[0031] Since the transmitted signal is a polarization-multiplexed QAM signal, the input signal to the simplified second-order Volterra equalizer consists of four paths: two parts for X-polarization (I) and two parts for X-polarization (Q), and two parts for Y-polarization (I and Q). For the second-order Volterra equalization, these four sets of data are implemented with real values. Taking the X-polarized I signal as an example, 99 nonlinear components are extracted and stored sequentially, and the nonlinear weight coefficients are trained according to the above formula (1-3), where the reference value is also the corresponding value of the X-polarized I signal in the transmitted training sequence. The other three data paths are trained in the same way until convergence.
[0032] In the simplification phase, each of the four sets of trained weight coefficients is arranged in descending order of absolute amplitude, and the smaller values are removed, leaving the remaining values as simplified second-order nonlinear weight coefficients. Finally, these four simplified weight coefficients are used as fixed values to equalize another portion of the signal used for testing. Finally, the bit error rate is calculated together with the corresponding transmitted signal as a metric for evaluating the equalizer's performance.
[0033] In the simplification phase, the proportion of smaller weight coefficients removed was adjusted from 100% to 0%, and the final bit error rate (BER) was calculated. When 100% of the weight coefficients were removed, it was equivalent to completely removing the second-order Volterra nonlinear equalizer, thus degenerating it into a linear equalizer, with a BER of approximately 0.039. As the proportion of smaller weight coefficients removed gradually decreased, the effect of nonlinear equalization gradually increased, resulting in a rapid decrease in the BER. When the proportion of weight coefficients removed decreased to 70%, the BER had already decreased to approximately 0.035, indicating that the effect of nonlinear equalization was quite significant. Subsequently, the proportion of weight coefficients removed continued to decrease from 70%, at which point the rate of decrease in BER tended to level off. Finally, when all weight coefficients were retained, the BER was approximately 0.034. Considering both the equalization effect and computational complexity, a 70% removal rate of weight coefficients is a reasonable value. At this point, the computational complexity of the simplified second-order Volterra equalizer is reduced by approximately 70%, while the bit error rate performance of the equalized signal is very close to that of the complete second-order nonlinear equalizer. This result demonstrates that the simplified second-order Volterra nonlinear equalization algorithm is feasible and superior in practical communication systems for nonlinear compensation of received signals and reduction of computational complexity. Furthermore, for other specific systems, the proportion of weight coefficients removed in the second-order Volterra nonlinear equalizer can be flexibly adjusted according to the needs of the actual application scenario.
Claims
1. A simplified second-order Volterra nonlinear equilibrium method based on weighted selection, characterized in that, include: Training: Extract and store linear portions of length L from the input signal data X in sequence. L And a nonlinear portion of length N stores the data X N L and N are both odd numbers, representing the first and second order storage lengths of the Volterra equalizer, respectively. X L and X N The middle position is X. k ; After that, X L and the corresponding first-order linear weighting coefficient h L Corresponding multiplication, and X N Multiply by any of its terms to get N 2 The term, plus the second-order nonlinear weighting coefficient h NN By multiplying the corresponding products and summing the values of both products, we obtain the output data Y. k The above process is illustrated by matrix calculation formula (1): Y k =h L X L H +X NN h NN X NN H (1) Among them, X L X NN and h L All are row vectors, h NN For N 2 A two-dimensional matrix; Then, in the sent training sequence, find the reference value Y corresponding to this output term. k And use the loss function shown in formula (2) to calculate the difference E between the output value and the reference value: E=Y k '-Yk (2) Then, based on the difference between the output value and the reference value, the two sets of weight coefficients are updated with step sizes μ1 and μ2 respectively using the feedback function shown in formula (3): h L =h L +μ1EX L h NN =h NN + μ2 EX NN H X NN (3) Repeat the process shown in formulas (1), (2), and (3), and the signal will gradually converge; finally, two sets of trained linear and nonlinear weight coefficients are obtained. Simplification: The second-order nonlinear weight coefficients h obtained after training NN All elements are sorted in descending order of their absolute magnitude. From the sorted results, a predetermined proportion of elements and their positions in the original matrix are selected to construct a simplified second-order nonlinear weighting coefficient matrix h. NN The preset ratio is the proportion of computational complexity that is reduced to the maximum extent possible after joint bit error rate-complexity testing in the target communication system, ensuring that the bit error rate performance loss is below a preset threshold. Specifically, it involves deleting 70% of the elements with the smallest absolute values in the sorting result, and using the remaining 30% of the elements and their position information in the original matrix to form a simplified second-order nonlinear weighting coefficient h. NN ; Equalization: Fix the first-order weight coefficients and the simplified second-order weight coefficients, and perform equalization calculations on the effective data other than the training sequence and output the results. The method is applied to a polarization multiplexed optical communication system, where training, simplification, and equalization steps are performed independently on four in-phase and orthogonal signals of X-polarization and Y-polarization, respectively.
2. The algorithm according to claim 1, characterized in that, The specific process of the equalization process is as follows: the obtained simplified second-order nonlinear weighting coefficients h NN 'and first-order linear weighting coefficient h L As a fixed value, it is used to compensate for effective information other than the training sequence. The equalization process is completed by repeatedly applying formula (1).
3. A simplified second-order Volterra nonlinear equilibrium system based on weighted selection, characterized in that, include: The training module is used to extract and store linear portions of length L from the input signal data X in sequence. L And a nonlinear portion of length N stores the data X N L and N are both odd numbers, representing the first and second order storage lengths of the Volterra equalizer, respectively. X L and X N The middle position is X. k ; After that, X L and the corresponding first-order linear weighting coefficient h L Corresponding multiplication, and X N Multiply by any of its terms to get N 2 The term, plus the second-order nonlinear weighting coefficient h NN By multiplying the corresponding products and summing the values of both products, we obtain the output data Y. k The above process is illustrated by matrix calculation formula (1): Y k =h L X L H +X NN h NN X NN H (1) Among them, X L X NN and h L All are row vectors, h NN For N 2 A two-dimensional matrix; Then, in the sent training sequence, find the reference value Y corresponding to this output term. k And use the loss function shown in formula (2) to calculate the difference E between the output value and the reference value: E=Y k '-Yk (2) Then, based on the difference between the output value and the reference value, the two sets of weight coefficients are updated with step sizes μ1 and μ2 respectively using the feedback function shown in formula (3): h L =h L +μ1EX L h NN =h NN + μ2 EX NN H X NN (3) Repeat the process shown in formulas (1), (2), and (3), and the signal will gradually converge; finally, two sets of trained linear and nonlinear weight coefficients are obtained. A simplification module is used to convert the second-order nonlinear weight coefficients h obtained after training. NN All elements are sorted in descending order of their absolute magnitude. From the sorted results, a predetermined proportion of elements and their positions in the original matrix are selected to construct a simplified second-order nonlinear weighting coefficient matrix h. NN The preset ratio is the proportion of computational complexity that is reduced to the maximum extent possible after joint bit error rate-complexity testing in the target communication system, ensuring that the bit error rate performance loss is below a preset threshold. Specifically, it involves deleting 70% of the elements with the smallest absolute values in the sorting result, and using the remaining 30% of the elements and their position information in the original matrix to form a simplified second-order nonlinear weighting coefficient h. NN ; The equalization module is used to fix the first-order weight coefficients and the simplified second-order weight coefficients, and to perform equalization calculations and output the results for each valid data other than the training sequence. The system is applied to a polarization multiplexed optical communication system, where training, simplification, and equalization steps are performed independently on four in-phase and orthogonal signals of X-polarization and Y-polarization, respectively.