A volterra nonlinear equalization method and system

Abstract

The application relates to a Volterra nonlinear equalization method and system, which comprises the following steps: obtaining an input signal; inputting the input signal into an improved Volterra equalizer after a pre-DSP step, and outputting an equalization result; when the improved Volterra equalizer is designed, the traditional algorithm in the prior art, in which all training sequences are directly used for training in sequence, is improved into a new algorithm in which the training sequences are grouped, intercepted and shuffled, the training set and the test set are divided, and training is carried out in two stages. Compared with the prior art, the application effectively solves the invisible and uncontrollable problem of overfitting during equalizer training while improving the training efficiency of the equalizer, thereby improving the compensation effect, and the application has good universality.

Description

Technical Field

[0001] This invention relates to the field of optical fiber communication, and in particular to a Volterra nonlinear equalization method and system. Background Technology

[0002] With the continuous development and advancement of science and technology, new technologies such as big data, cloud computing, and artificial intelligence are constantly emerging. These developments have tangibly improved people's lives and created enormous commercial value; consequently, they have led to a significant increase in global bandwidth demand. High capacity and high speed have become the primary goals in developing next-generation fiber optic transmission systems. In fiber optic communication systems, nonlinear impairments have a significant impact on system performance, greatly hindering the improvement of capacity and speed. On the hardware side, various optical / electrical devices in existing fiber optic communication systems, such as Mach-Zehnder modulators (MZMs), photodiodes (PDs), amplifiers, and lasers, all introduce nonlinear impairments; the nonlinear impairments introduced by optical fibers also become significant over long distances. It is difficult to achieve breakthroughs in reducing nonlinear impairments in these hardware components in the short term; therefore, nonlinear compensation algorithms at the receiver end are particularly important.

[0003] The Volterra equalization algorithm is an excellent nonlinear compensation method that effectively compensates for both linear and nonlinear impairments in a system. This algorithm is based on multi-order Volterra series and uses training sequences for iterative training to obtain tap coefficients. In the paper [M. Kong, K. Wang, J. Ding, J. Zhang, W. Li, J. Shi, F. Wang, L. Zhao, C. Liu, Y. Wang, W. Zhou, and J. Yu, “640-Gbps / carrier WDM Transmission over 6,400km Based on PS-16QAM at 106Gbaud Employing Advanced DSP,” Journal of Lightwave Technology, pp. 1-1, 2020], the authors used four independent Volterra equalizers for the four PS-PAM4 signals (i.e., X / Y polarized in-phase / quadrature components) in the PS-16QAM signal. They trained the linear and nonlinear tap coefficients of the four PAM signals respectively based on the PS-16QAM training sequence, and then used the trained tap coefficients for actual transmission.

[0004] However, the process of iteratively training a set of training sequences that are much shorter than the actual transmission sequences not only allows the Volterra equalizer to learn the inherent linear and nonlinear characteristics of the channel, but also to fit some stochastic processes. A Volterra equalizer based solely on the bit error rate results of the equalization training sequences cannot determine whether overfitting has occurred during training or the degree of overfitting. The inability to effectively avoid overfitting during parameter tuning and training leads to a discrepancy between the equalizer's performance and the theoretical performance obtained during training when the trained tap coefficients are used in actual transmission. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a Volterra nonlinear equalizer for use in fiber optic communication systems. This invention not only has the compensation function of the traditional Volterra algorithm for linear and nonlinear impairments, but also improves training efficiency and effectively solves the problem of invisible and uncontrollable overfitting when training the Volterra equalizer.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A Volterra nonlinear equilibrium method includes the following steps:

[0008] S1. Acquire the input signal;

[0009] S2. The input signal is fed into the improved Volterra equalizer after passing through the pre-DSP step.

[0010] S3, Improved Volterra equalizer output equalization result;

[0011] The acquisition of the improved Volterra equalizer includes the following steps:

[0012] (1) Obtain the signal sequence x from the transmitting end;

[0013] (2) Generate a training sequence and transmit the training sequence through the channel to obtain the receiving end signal sequence; pass the receiving end signal sequence through the pre-processing DSP step to obtain the Volterra equalizer input signal sequence y;

[0014] (3) The Volterra equalizer input signal sequence y is divided into groups and truncated to obtain the input signal sequence fragment set G;

[0015] (4) The set of input signal sequence fragments is matched one-to-one with the signal sequence x at the transmitting end to obtain a set of fragment pairs P;

[0016] (5) Randomize the elements in the fragment set to obtain a randomized set P.shuffled ;

[0017] (6) The disordered set P shuffled Split into training set P train and test set P test ;

[0018] (7) The training set P train The signal sequence segments in the middle and the corresponding signal sequence segments from the transmitting end are input into the Volterra equalizer to calculate the training loss value and perform error backpropagation to update the weight coefficients.

[0019] (8) The test set P test The signal sequence segments in the middle and the corresponding signal sequence segments from the transmitting end are input into the Volterra equalizer to calculate the test loss value. The error is not backpropagated. The test loss value is compared with the training loss value obtained in step (7), and the system error performance is calculated at the same time.

[0020] (9) If the system error rate performance does not meet the preset requirements, adjust the parameters of the second-order Volterra equalizer and repeat steps (7) and (8); otherwise, proceed to the next step.

[0021] (10) Input the signal sequence segments in the test set and the corresponding transmitter signal sequence segments into the Volterra equalizer, calculate the loss value and backpropagate the error, update the weight coefficients, and obtain the weight coefficients after training is completed.

[0022] (11) Initialize the Volterra equalizer with the trained weight coefficients to obtain the improved Volterra equalizer.

[0023] Further, in step (3), the Volterra equalizer input signal sequence y is grouped and truncated to obtain the input signal sequence fragment set G, including the following steps:

[0024] Define the number of taps for grouping as n. taps Its expression is:

[0025] n taps =max(N) i ), i = 1, 2, 3, ...

[0026] Where, N i This refers to the i-th order kernel size of the Volterra equalizer;

[0027] The expression for the input signal sequence fragment set is:

[0028] G = [g1, g2, ..., g] n ]

[0029]

[0030] Among them, y i Let n be the i-th element in the input signal sequence y, and n be the total number of segments in the input signal sequence. n is determined by the input signal sequence y and the number of taps. taps A joint decision.

[0031] Furthermore, in step (6), specifically based on the training set ratio coefficient r train Ratio coefficient r of the test set test The disordered set P shuffled Split into training set P train and test set P test .

[0032] Furthermore, the training set ratio coefficient r train Ratio coefficient r of the test set test The following relationship exists:

[0033] r train +r test =1

[0034] And the length of the training set is: r train ·n;

[0035] The length of the test set is: r test ·n.

[0036] Furthermore, in steps (7) and (8), the formulas for calculating the test loss value and the training loss value are as follows:

[0037]

[0038] in, Let x be the error function, where x = [x1, x2, ... x]. i ..., x n [ ] represents the signal sequence transmitted from the transmitting end.

[0039] Furthermore, the Volterra equalizer includes a first-order part and a second-order part, wherein the first-order part stores a signal sequence σ1 of length N1:

[0040]

[0041] The second-order part stores a signal sequence σ2 of length N2:

[0042]

[0043] σ1 and σ2 are respectively derived from P train and P test The signal sequence fragment set Gtrain and G test It was intercepted.

[0044] Furthermore, the first-order portion includes a first-order kernel, which is composed of a single stored signal and is used to compensate for linear impairments. The number of first-order kernels is M1 = N1, and the expression for the first-order kernel vector is:

[0045]

[0046] The second-order part includes a second-order kernel, which is composed of the product of any two stored signals and is used to compensate for nonlinear impairments. The number of second-order kernels is M² = N². N The expression for the second-order kernel vector is: (1+1) / 2.

[0047]

[0048] Furthermore, the first-order kernel and the second-order kernel each correspond to a set of weighting coefficients, and the weighting coefficients of the first-order kernel... Represented as:

[0049]

[0050] The weighting coefficients of the second-order kernel Represented as:

[0051]

[0052] The weighting coefficient and The initial value is 0.

[0053] Furthermore, based on the first-order kernel vector, the second-order kernel vector, and the weight coefficients... and Get the output of the Volterra equalizer Its expression is:

[0054]

[0055] A Volterra nonlinear equalization system is provided to implement the Volterra nonlinear equalization method described above, including a group truncation module, a signal alignment module, a disordered ordering module, a data segmentation module, and a Volterra equalizer module.

[0056] The grouping and truncation module is used to divide the equalizer input signal sequence y into groups according to the number of taps n. taps The input signal sequence fragments are truncated to obtain a set G.

[0057] The signal alignment module is used to map the input signal sequence fragment set G to the transmitting signal sequence one by one, and encapsulate and store them to obtain the fragment pair set P;

[0058] The scrambling module is used to scramble the fragment pair set to obtain a scrambled set P. shuffled ;

[0059] The data segmentation module is based on the training set ratio coefficient r. train Ratio coefficient r of the test set test The disordered set P shuffled Split into training set P train and test set P test ;

[0060] The Volterra equalizer module is used to equalize the input signal according to weighting coefficients of each order; and the Volterra equalizer module can use a reference signal to calculate the error of the equalization result and feed the error back to optimize the weighting coefficients.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] 1. In designing the Volterra equalizer, this invention improves upon the traditional algorithm that inputs data sequentially and uses all training sequences directly for training. It introduces a new algorithm that groups and shuffles the data, divides it into training and test sets, and performs training in two stages. The improved Volterra equalizer proposed in this invention can effectively identify overfitting during training and achieve ideal results through parameter tuning. This keeps the gap between the ideal performance achieved by the equalizer during training and its actual transmission performance within a small range, effectively solving the overfitting problem during training and achieving better compensation.

[0063] 2. This invention has good versatility. At the algorithm level, the data preprocessing and training methods proposed in this invention are also applicable to other equalization algorithms that require training sequences. In terms of application scenarios, this invention is suitable for nonlinear equalization in various scenarios such as long-distance single-carrier coherent optical transmission, short-distance intensity modulation direct detection (IM-DD) systems, and fiber-to-the-wire (ROF) systems. This invention can flexibly change the Volterra order of the equalizer, the number of taps at each order, and the loss function, etc., according to the situation. Attached Figure Description

[0064] Figure 1 This is a schematic diagram of the process in an embodiment of the present invention.

[0065] Figure 2 This is a schematic diagram of the improved Volterra equalizer training section in an embodiment of the present invention;

[0066] Figure 3 This is a schematic diagram of the second-order Volterra equalizer used in an embodiment of the present invention.

[0067] The labels in the diagram have the following meanings:

[0068] 1 — Transmitter signal sequence x;

[0069] 2—Channel and Volterra Equalizer Pre-DSP Process;

[0070] 3—Volterra equalizer input signal sequence y;

[0071] 4—Input signal sequence fragment set G;

[0072] 5 — Signal alignment operation;

[0073] 6 — Set of fragment pairs P;

[0074] 7 — Element reordering operation;

[0075] 8—Disordered set P shuffled ;

[0076] 9—Training set ratio coefficient r train ;

[0077] 10 — Test set ratio coefficient r test ;

[0078] 11 — Training set P obtained from segmentation train ;

[0079] 12 — The test set P obtained by segmentation test ;

[0080] 13—Volterra equalizer input signal sequence;

[0081] 14 — The signal sequence stored in the first-order part of the equalizer;

[0082] 15 — First-order kernel vector;

[0083] 16 — Weighting coefficient of the first-order partial tap of the equalizer;

[0084] 17—The signal sequence stored in the second-order part of the equalizer;

[0085] 18—Second-order kernel vector;

[0086] 19 — Weighting coefficients of the second-order partial taps of the equalizer;

[0087] 20 — Volterra equalizer output value

[0088] 21 — Signal reference value for the corresponding location;

[0089] 22—The loss function used to calculate the difference between the output value and the reference value;

[0090] 23—Volterra equalizer, the dotted line section is broken in process 27 during the equalizer usage and training phases;

[0091] 24 - Using P train Loss value L during training train ;

[0092] 25—Training process in the first phase of training, error backpropagation, and the dotted line in 23 connecting the two points;

[0093] 26 - Using P test Loss value L during training test ;

[0094] 27—Testing process in the first phase of training, error is not propagated back, the dotted line in 23 is broken;

[0095] 28—Judgment criteria: Has the system performance largely met the standards?

[0096] 29—Second stage training process, error backpropagation, dotted line in 23 connected. Detailed Implementation

[0097] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0098] This invention relates to nonlinear compensation in the field of optical fiber communication, specifically to an improved Volterra nonlinear equalization method and system for optical fiber communication systems. This invention effectively solves the problems of multi-order interference and I / Q imbalance between in-phase and quadrature components while compensating for the linear and nonlinear impairments of the in-phase and quadrature components.

[0099] A Volterra nonlinear equilibrium method includes the following steps:

[0100] S1. Acquire the input signal;

[0101] S2. The input signal is fed into the improved Volterra equalizer after passing through the pre-DSP step.

[0102] S3, Improved Volterra equalizer output equalization result;

[0103] Specifically, the pre-processing DSP steps in this embodiment typically include sequential steps such as dispersion compensation, clock recovery, constant mode algorithm, frequency offset compensation, and phase offset compensation in relevant optical communication systems. These are common methods for signal processing in this field and will not be elaborated upon in this embodiment.

[0104] like Figure 1 As shown, obtaining the improved Volterra equalizer includes the following steps:

[0105] (1) Obtain the signal sequence x from the transmitting end;

[0106] (2) Generate a training sequence and transmit the training sequence through the channel to obtain the receiving end signal sequence; pass the receiving end signal sequence through the pre-processing DSP step to obtain the Volterra equalizer input signal sequence y;

[0107] (3) The Volterra equalizer input signal sequence y is divided into groups and truncated to obtain the input signal sequence fragment set G;

[0108] (4) Match the set of input signal sequence fragments with the signal sequence x at the transmitting end to obtain the set of fragment pairs P;

[0109] (5) Randomize the elements in the fragment pair set to obtain the disordered set P. shuffled ;

[0110] (6) Disordered set P s，huffled Split into training set P train and test set P test ;

[0111] (7) The training set P train The signal sequence segments in the middle and the corresponding signal sequence segments from the transmitting end are input into the Volterra equalizer to calculate the training loss value and perform error backpropagation to update the weight coefficients.

[0112] (8) Test set P test The signal sequence segments in the middle and the corresponding signal sequence segments from the transmitting end are input into the Volterra equalizer to calculate the test loss value. The error is not backpropagated. The test loss value is compared with the training loss value obtained in step (7), and the system error performance is calculated at the same time.

[0113] (9) If the system error rate performance does not meet the preset requirements, adjust the parameters of the second-order Volterra equalizer and repeat steps (7) and (8); otherwise, proceed to the next step.

[0114] (10) Input the signal sequence segments in the test set and the corresponding transmitter signal sequence segments into the Volterra equalizer, calculate the loss value and backpropagate the error, update the weight coefficients, and obtain the weight coefficients after training.

[0115] (11) Initialize the Volterra equalizer with the trained weight coefficients to obtain the improved Volterra equalizer.

[0116] In step (3), the Volterra equalizer input signal sequence y is grouped and truncated to obtain the input signal sequence fragment set G, including the following steps:

[0117] Define the number of taps for grouping as n. taps Its expression is:

[0118] n taps =max(N) i ), i = 1, 2, 3, ...

[0119] Where, N i This refers to the i-th order kernel size of the Volterra equalizer;

[0120] The expression for the input signal sequence fragment set is:

[0121] G = [g1, g2, ..., g] n ]

[0122]

[0123] Among them, y i Let n be the i-th element in the input signal sequence y, and n be the total number of segments in the input signal sequence. n is determined by the input signal sequence y and the number of taps. taps A joint decision.

[0124] In step (6), specifically based on the training set ratio coefficient r train Ratio coefficient r of the test set test , the disordered set P shuffled Split into training set P train and test set P test .

[0125] Training set ratio coefficient r train Ratio coefficient r of the test set test The following relationship exists:

[0126] r train +r test =1

[0127] And the length of the training set is: r train ·n;

[0128] The length of the test set is: r test ·n.

[0129] In steps (7) and (8), the formulas for calculating the test loss and training loss are as follows:

[0130]

[0131] in, Let x be the error function, where x = [x1, x2, ... x]. i ..., x n [ ] represents the signal sequence transmitted from the transmitting end.

[0132] The Volterra equalizer consists of a first-order part and a second-order part. The first-order part stores a signal sequence σ1 of length N1:

[0133]

[0134] The second-order part stores a signal sequence σ2 of length N2:

[0135]

[0136] σ1 and σ2 are respectively derived from P train and P test The signal sequence fragment set G train and G test It was intercepted.

[0137] The first-order part includes a first-order kernel, which consists of a single stored signal and is used to compensate for linear impairments. The number of first-order kernels is M1 = N1, and the expression for the first-order kernel vector is:

[0138]

[0139] The second-order part includes a second-order kernel, which is composed of the product of any two stored signals and is used to compensate for nonlinear impairments. The number of second-order kernels is M2 = N2(N1+1) / 2, and the expression for the second-order kernel vector is:

[0140]

[0141] The first-order kernel and the second-order kernel each correspond to a set of weighting coefficients. The weighting coefficients of the first-order kernel... Represented as:

[0142]

[0143] Weighting coefficients of the second-order kernel Represented as:

[0144]

[0145] Weighting coefficient and The initial value is 0.

[0146] Based on first-order kernel vector, second-order kernel vector, and weight coefficients and Get the output of the Volterra equalizer Its expression is:

[0147]

[0148] It is worth noting that the Volterra order of the Volterra equalizer in this invention can be selected according to specific circumstances. A first-order Volterra series can equalize linear responses, while second-order and higher-order Volterra series can equalize nonlinear damage. Considering both compensation effect and computational complexity, the Volterra equalizer typically uses a maximum of three orders. Furthermore, the number of taps for each order of Volterra equalizer can be different; in this invention, the maximum number of taps is simply set to n. taps When the number of taps is less than n taps The calculation discards the redundant parts on both sides. This embodiment uses a second-order Volterra equalizer as an example.

[0149] Meanwhile, the sampling rate of the input signal can be selected according to specific circumstances. For example, single sampling can be used in low-speed, short-distance transmission systems, while oversampling can be used for high-speed, long-distance applications, as long as signal alignment is ensured (i.e., each transmitting signal corresponds to a segment of Volterra equalizer input signal sequence, with its center at the Volterra equalizer input signal point corresponding to the transmitting signal). In this embodiment, the case where the Volterra equalizer input signal sequence is single-sampled (i.e., each input signal corresponds to one transmitting signal) is taken as an example.

[0150] The loss function used in the training section to calculate the difference between the training and reference values ​​can be selected according to specific circumstances. This manual uses the minimum mean square error function as an example.

[0151] This invention has strong universality. At the algorithm level, the data preprocessing and training methods proposed in this invention are also applicable to other equalization algorithms that require training sequences; in terms of application scenarios, this invention is applicable to nonlinear equalization in various scenarios such as long-distance single-carrier coherent optical transmission, short-distance intensity modulation direct detection (IM-DD) systems, and fiber-to-wireless (ROF) systems.

[0152] In practice, the Volterra order of the equalizer can be selected according to the specific situation. In this embodiment, a second-order Volterra equalizer is used as an example.

[0153] The improved Volterra equalizer described in this invention specifically includes three parts: "data preprocessing", "training", and "use".

[0154] (1) Data preprocessing, the principles of which are shown in the attached document. Figure 1 As shown, it includes the following steps:

[0155] Obtain the signal sequence x from the transmitting end;

[0156] A training sequence is generated and transmitted through a channel to obtain the receiving signal sequence. The receiving signal sequence is then processed through a pre-processing DSP step to obtain the Volterra equalizer input signal sequence y. The number of taps n for group truncation is defined. taps Considering that the kernel lengths of different orders in the Volterra equalizer are different, let's assume that the kernel size of order i is N. i ,have

[0157] n taps =max(N) i ), i = 1, 2, 3, ...

[0158] The Volterra equalizer input signal sequence y is grouped and truncated according to the number of taps. That is, the synchronized transmitter signal sequence x is mapped to the corresponding signal point in the Volterra equalizer input sequence y, and then extended left and right (n) at that point. taps -1) / 2 sample points, truncate these n... taps The Volterra equalizer input signal sequence y is processed sequentially on each sample point to obtain the Volterra equalizer input signal sequence fragment set G:

[0159] G = [g1, g2, ..., g] n ]

[0160]

[0161] Among them, y i Let y be the i-th element in the input signal sequence y, and n be the total number of segments in the input signal sequence.

[0162] The transmitted signal sequence x in the training sequence is compared with the grouped and truncated Volterra equalizer input signal sequence fragment set g. i A one-to-one correspondence is established, meaning that one transmitting signal corresponds to a set of signals of length n. taps Given the Volterra equalizer input sequence, we obtain a set P of segments between the transmitted signal and the Volterra equalizer input signal sequence. We then shuffle each element (i.e., the transmit / receive pair) in set P to obtain Ps. shuffled .

[0163] Based on the training set ratio coefficient r train Ratio coefficient r of the test set test , the disordered set Pshuffled Split into training set P train and test set P test .

[0164] r train +r test =1

[0165] And the length of the training set is: r train ·n;

[0166] The length of the test set is: r test ·n.

[0167] (2) Training section, the principle of which is attached. Figure 2-3 As shown.

[0168] Taking a second-order Volterra equalizer as an example, the storage lengths of the first-order and second-order parts of the Volterra equalizer are N1 and N2 respectively (both N1 and N2 are odd numbers), and the signals at the middle positions of the stored signals are kept to be the same. The signal sequences stored in both parts can be derived from P... train and P test The signal sequence fragment set G train and G test It was intercepted. It can be written as... A first-order kernel consists of a single stored signal, compensating for linear impairments, and has a number of kernels M1 = N1. A first-order kernel vector can be represented as... The second-order kernel is the product of any two stored signals, used to compensate for nonlinear impairments, and its number is M² = N²(N²+1) / 2. The second-order kernel vector can be represented as...

[0169] The first-order and second-order kernels each correspond to a set of weighting coefficients, which are used to multiply the first-order and second-order kernel vectors to obtain the equalized signal. The weighting coefficients of the first-order and second-order kernels can be expressed as follows: The initial values ​​of both sets of weighting coefficients are set to 0.

[0170] Based on the first and second order kernel vectors and weight coefficients, the output of the Volterra equalizer can be obtained. Given by formula (3):

[0171]

[0172] P obtained from data preprocessing train and P test It was used for training the first and second order Volterra equalizers, and the entire training process consists of two stages.

[0173] Phase 1, take P trainFor training, using P train The signal sequence fragment set in the input is used as the output value. Compared with the reference value, this embodiment selects P. train The transmitting end signal sequence x train As a reference value, the difference e between the output value and the reference value is calculated using the following formula. i :

[0174]

[0175] At the same time, the average training loss value for m iterations during the training process is calculated according to the loss function given below.

[0176]

[0177] Based on the difference between the output value and the reference value, the first-order kernel weight coefficients and the second-order kernel weight coefficients are updated with step sizes μ1 and μ2 respectively using the feedback function shown in formula (4):

[0178]

[0179]

[0180] Given a test period c, for P train For all reference values ​​- Volterra input sequence pairs, repeat the process of formulas (3) to (6). Every c repetitions, calculate the average training loss value for c repetitions. Simultaneously use P test The average test loss value is obtained by repeating formulas (3) to (5) for all reference values ​​and Volterra input sequence pairs. (Only calculate the loss value, do not update the weights). Iterate continuously, comparing... and The decline, if In the decline If the performance no longer decreases and the gap widens, it indicates that the training is heading towards overfitting, and the performance in practical applications has converged. Adjust the number of taps for each order of Volterra equalizer, the step size for updating weights during iterative training of each order of Volterra equalizer, and the number of iterations during training, and observe the comparison. and The equalizer is trained to avoid severe overfitting until the bit error rate performance (or loss value) roughly converges to the ideal position. This completes the first phase of training, determining the number of taps N for each order of the Volterra equalizer. i，i＝1，2，3，... The step size μ of weight updates i，i＝1，2，3，... And using P trainThe number of training iterations yielded the weight coefficients for the first stage of training. and

[0181] To fully utilize the data in the training sequence for the second stage of training, the number of taps N for each order of Volterra equalizer, which was determined in the first stage, is used. i，i＝1，2，3，... The step size μ of weight updates i，i＝1，2，3，... And parameters such as the number of training iterations, in P test The training data is fed into the equalizer and trained using formulas (4) and (6). The trained weight coefficients are then obtained. and

[0182] (3) “Usage” section:

[0183] The principles of the "Usage" section are attached. Figure 2 As shown ( Figure 2 (The dashed line is not connected).

[0184] The signal sequences stored in the first and second order kernels can be extracted from the signal input to the equalizer. Volterra equilibrium first-order kernel vector and second-order kernel vector Their quantities are M1 = N1 and M2 = N2(N2+1) / 2, respectively; the weight coefficients of the first and second order kernels obtained after training in two stages. The output value of this improved Volterra equalizer is obtained through transverse filtering. for:

[0185]

[0186] The improved Volterra equalizer proposed in this invention can effectively identify overfitting during training and achieve ideal results through parameter tuning. This keeps the gap between the ideal performance achieved by the equalizer during training and its actual performance in transmission within a small range, effectively solving the overfitting problem during training and achieving better compensation results.

[0187] This embodiment also provides a Volterra nonlinear equalization system for implementing the Volterra nonlinear equalization method described above, including a grouping and truncation module, a signal alignment module, a disordered ordering module, a data segmentation module, and a Volterra equalizer module;

[0188] The grouping and truncation module is used to divide the equalizer input signal sequence y into groups according to the number of taps n. taps The input signal sequence fragments are truncated to obtain a set G.

[0189] The signal alignment module is used to map the input signal sequence fragment set G to the transmitted signal sequence one by one, and encapsulate and store them to obtain the fragment pair set P;

[0190] The shuffle module is used to shuffle the set of fragment pairs to obtain a shuffled set P. shuffled ;

[0191] The data segmentation module is based on the training set ratio coefficient r. train Ratio coefficient r of the test set test , the disordered set P shuffled Split into training set P train and test set P test ;

[0192] The Volterra equalizer module is used to equalize the input signal according to weighting coefficients of each order; and the Volterra equalizer module can use a reference signal to calculate the error of the equalization result and feed the error back to optimize the weighting coefficients.

[0193] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A Volterra nonlinear equalization method, characterized in that, Includes the following steps: S1. Acquire the input signal; S2. The input signal is fed into the improved Volterra equalizer after passing through the pre-DSP step. S3, Improved Volterra equalizer output equalization result; The acquisition of the improved Volterra equalizer includes the following steps: 1) Obtain the signal sequence from the transmitting end. ; 2) Generate a training sequence and transmit it through the channel to obtain the receiving signal sequence; process the receiving signal sequence through a pre-processing DSP step to obtain the Volterra equalizer input signal sequence. ; 3) Input the Volterra equalizer signal sequence Grouping and segmenting yields a set of input signal sequence fragments G; 4) Combine the input signal sequence fragment set with the transmitted signal sequence. A one-to-one correspondence is obtained to obtain the set of fragment pairs P; 5) Randomize the elements in the fragment set to obtain a randomized set. ; 6) The disordered set Split into training set and test set ; 7) Transfer the training set The signal sequence segments in the middle and the corresponding signal sequence segments from the transmitting end are input into the Volterra equalizer to calculate the training loss value and perform error backpropagation to update the weight coefficients. 8) The test set The signal sequence segments in the middle and the corresponding signal sequence segments from the transmitting end are input into the Volterra equalizer to calculate the test loss value. The error is not backpropagated. The test loss value is compared with the training loss value obtained in step 7), and the system bit error rate performance is calculated at the same time. 9) If the system error rate performance does not meet the preset requirements, adjust the parameters of the second-order Volterra equalizer and repeat steps 7) and 8); otherwise, proceed to the next step. 10) Input the signal sequence segments in the test set and the corresponding transmitter signal sequence segments into the Volterra equalizer, calculate the loss value and backpropagate the error, update the weight coefficients, and obtain the weight coefficients after training is completed. 11) Initialize the Volterra equalizer using the trained weight coefficients to obtain the improved Volterra equalizer; In step 3), the Volterra equalizer input signal sequence is... The input signal sequence fragment set G is obtained by grouping and truncating the signal, including the following steps: Define the number of taps for grouping as Its expression is: in, For the Volterra equalizer Core size; The expression for the set of input signal sequence fragments is: in, For the input signal sequence The first in One element, The total number of segments in the input signal sequence; In steps 7) and 8), the formulas for calculating the test loss and training loss are as follows: in, Let be the error function. This is the signal sequence from the transmitting end.

2. The Volterra nonlinear equalization method according to claim 1, characterized in that, In step 6), specifically based on the training set ratio coefficient... Ratio coefficient of test set The disordered set Split into training set and test set .

3. The Volterra nonlinear equalization method according to claim 2, characterized in that, Training set ratio coefficient Ratio coefficient of test set The following relationship exists: And the length of the training set is: ; The length of the test set is: , This represents the total number of segments in the input signal sequence.

4. The Volterra nonlinear equalization method according to claim 1, characterized in that, The Volterra equalizer includes a first-order part and a second-order part. The first-order part stores data of length [length missing]. signal sequence : The second-order portion stores a length of signal sequence : and Each by and Set of signal sequence fragments and It was intercepted.

5. The Volterra nonlinear equalization method according to claim 4, characterized in that, The first-order portion includes first-order kernels, each consisting of a single stored signal, used to compensate for linear impairments. The number of first-order kernels is [number missing]. The expression for the first-order kernel vector is: The second-order part includes second-order kernels, which are composed of the product of any two stored signals and are used to compensate for nonlinear impairments. The number of second-order kernels is... The expression for the second-order kernel vector is: 。 6. The Volterra nonlinear equalization method according to claim 5, characterized in that, The first-order kernel and the second-order kernel each correspond to a set of weighting coefficients, the weighting coefficients of the first-order kernel... Represented as: The weighting coefficients of the second-order kernel Represented as: The weighting coefficient and The initial value is 0.

7. The Volterra nonlinear equalization method according to claim 6, characterized in that, Based on first-order kernel vector, second-order kernel vector, and weight coefficients and To obtain the output of the Volterra equalizer Its expression is: 。 8. A Volterra nonlinear equalization system, characterized in that, The method for implementing a Volterra nonlinear equalization method as described in any one of claims 1-7 includes a group truncation module, a signal alignment module, a disordered order module, a data segmentation module, and a Volterra equalizer module. The grouping and truncation module is used to extract the input signal sequence of the equalizer. According to the number of taps The input signal sequence is truncated to obtain a set of fragments. ; The signal alignment module is used to align the input signal sequence fragments. Each segment is individually mapped to a sequence of signals transmitted from the sending end, and then encapsulated and stored to obtain a set of segment pairs. ; The scrambling module is used to scramble the fragment pair set to obtain a scrambled set. ; The data segmentation module is based on the training set ratio coefficient. Ratio coefficient of test set The disordered set Split into training set and test set ; The Volterra equalizer module is used to equalize the input signal according to weighting coefficients of each order; Furthermore, the Volterra equalizer module can use a reference signal to calculate the error of the equalization result and feed the error back to optimize the weighting coefficients.

Images