CN114301529A - Volterra equalization method and system based on multi-symbol processing - Google Patents
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Abstract
The invention discloses a Volterra equalization method and a Volterra equalization system based on multi-symbol processing, and the method comprises the following specific steps: s1, carrying out normalization processing on the receiving end sampling signal Xt to obtain a receiving end sampling signal X normalized by the equalizer; s2, selecting a step length parameter a, and adjusting tap coefficients of the linear equalizer on a training set by using a self-adaptive algorithm to obtain a trained linear equalizer; and S3, inputting the signal to be equalized into the equalizer, and judging the output of the equalizer to realize channel equalization. The invention utilizes the characteristic of one symbol in the Volterra equalizer to generate the equalization result of a plurality of symbols, thereby reducing the repeated calculation in the equalization process. The invention can obviously reduce the computational complexity of the equalizer and can obtain the transmission performance equivalent to that of the traditional Volterra equalizer.
Description
Technical Field
The invention belongs to the technical field of optical communication, and particularly relates to a Volterra equalization method and system based on multi-symbol processing.
Background
The number of global internet users is continuously increasing, and network related services are rapidly developed, so that the bandwidth requirement and the speed requirement of the market on an optical fiber transmission system are improved, a high-speed optical network is rapidly developed in recent years, and an optical network with larger capacity, higher speed and lower cost is a main direction for development in the next years. However, due to the cost limitation, low-cost optoelectronic devices actually applied to the network may bring linear and nonlinear distortion, and interact with other channel noise to cause severe Inter Symbol Interference (ISI), which greatly damages the signal transmission quality. In order to solve this problem, it is necessary to introduce a Digital Signal Processing (DSP) technology to equalize the transmitted Signal so as to alleviate the damage to the Signal during transmission.
The DSP technique at the receiving end mainly uses an equalization algorithm to compensate for the signal impairments such as attenuation, dispersion, and nonlinear effects, and the signal equalization process is a necessary technique for implementing a low-cost high-rate optical network. As known from the research in the prior art, the conventional Equalization schemes include a Feed-Forward Equalization filter (FFE), a Decision Feedback Equalizer (DFE), a Volterra Non-linear Equalizer (VNLE), etc. But for severe intersymbol interference and nonlinear effects, the FFE and DFE are not sufficient to meet the equalization requirements of the system (DSP enabled next generation 50G TDM-PON, published in the Journal of Optical Communications and Networking in 2020). The VOLTERRA equalizer is an effective tool for compensating signal linear and nonlinear impairments, but the computational complexity increases rapidly with the increase of the introduced order, and several hundred features may be needed to achieve satisfactory performance in practical system applications. With the rapid development of machine learning related algorithms and the powerful performance of Neural Networks (NN) in fitting nonlinear functions, Neural Network-based equalization schemes are receiving wide attention in the field of optical fiber communication. However, the existing scheme for equalizing the nonlinear interference based on the Machine Learning algorithm has high complexity, and cannot simultaneously meet the requirements of low cost and low power consumption (An Overview on Application of Machine Learning technologies in Optical Networks, published in IEEE Communications & Networks in 2019). In order to obtain an equalization scheme with lower system complexity and computational complexity while maintaining higher decision accuracy, an improvement on the existing equalization scheme is needed.
Due to the excellent performance of the Volterra equalizer in compensating for signal linear and non-linear impairments, experts focus on reducing the complexity of the Volterra equalizer. Most of the simplified schemes proposed at present based on the Volterra equalizer are to cut off the taps that contribute less to performance optimization during the equalization process, for example, Wei Jinlong et al propose to set a threshold and remove the taps with tap coefficients below the threshold (Low Complexity DSP for High Speed Optical Access Networking, published in Applied Sciences), the selection of the threshold in the scheme has a large impact on performance and no exact algorithm selects a proper threshold, an excessive threshold will result in a large number of taps being cut off, sufficient features cannot be reserved for signal classification, and an insufficient threshold cannot reduce the computational Complexity. In 2020 Yukui Yu et al (Low-complex Nonlinear Equalizer Based on Absolute Operation for C-band IM/DD systems, published in Opt Express and Nonlinear Equalizer Based on Absolute Operation for IM/DD systems Using DML, published in IEEE Photonic technologies Letters) and Qianwu Zhang team (An Improved Nonlinear Equalizer for 50Gb/sPAM4 IM/DD Transmission with 10G-Class Optics, published in ACP) all propose to convert the product Operation in VOLTERRA Equalizer to Absolute value Operation, but this approach leads to a reduction in equalization performance. Yukui Yu et al also propose to leave only the diagonal taps and remove all other taps, but this scheme removes many of the original features, resulting in inaccurate equalization results. In 2021, Yang Zheng et al proposed that a Principal Component Analysis (PCA) algorithm was used to map features to other vector spaces, and then taps with larger contribution degrees were reserved (Optimized Volterra filter based on weighted Principal Component Analysis, published in Opt let), however, the PCA algorithm is an unsupervised learning algorithm, and the class of the sample is not considered in the process of mapping the sample, which easily results in that the sample is not easily classified after being mapped.
In summary, a new technical scheme needs to be explored in the research direction of reducing the voltage equalizer, and a voltage equalizer which has stable equalization performance on signal linear and nonlinear impairments and lower complexity is developed, so that the voltage equalizer is an important solution for supporting the construction of an optical network with higher speed and lower cost.
Disclosure of Invention
The invention aims to provide a Volterra equalization method and system based on multi-symbol processing aiming at the defects of the prior art.
The invention provides a Volterra equalization method and a Volterra equalization system based on multi-symbol processing. Therefore, the invention proposes to use the characteristics of one symbol to generate the equalization result of a plurality of symbols, thereby reducing the repeated calculation in the equalization process. The Volterra equalization method based on multi-symbol processing can significantly reduce the computational complexity of the equalizer and obtain the same transmission performance as the traditional Volterra equalizer.
In order to achieve the purpose, the invention adopts the following technical scheme:
the Volterra equalization method based on multi-symbol processing can be applied to equalization of linear and nonlinear damages in an optical fiber communication system, and comprises the following specific steps:
s1, carrying out normalization processing on the receiving end sampling signal Xt to obtain a receiving end sampling signal X normalized by the equalizer;
s2, selecting a step length parameter a, and adjusting tap coefficients of the Volterra equalizer on a training set by using a self-adaptive algorithm to obtain a well-trained Volterra equalizer;
and S3, inputting the signal to be equalized into the equalizer, and judging the output of the equalizer to realize the effect of channel equalization.
The invention provides an equalization result of a plurality of symbols generated by utilizing the characteristics of one symbol, thereby reducing repeated calculation in the equalization process. The Volterra equalization method based on multi-symbol processing can significantly reduce the computational complexity of the equalizer and obtain the same transmission performance as the traditional Volterra equalizer.
Preferably, in step S1, the transmitting-end signal is a pseudo random code generated based on the metson rotation algorithm.
Preferably, in step S1, the signal is normalized by calculating a mean value of the signal sequence and subtracting the calculated mean value from each signal in the signal sequence,
X(i)＝Xt(i)-Xt,mean (2)
in the formula, Xt(i) For the i-th signal value, X, of the received sampled signalt,meanAnd (2) obtaining a normalized receiving end characteristic sequence X by subtracting the signal mean value obtained by the formula (1) from each sampling signal of the receiving end, wherein cnt is the receiving end signal mean value, and X (i) is the characteristic value of the ith signal corresponding to the normalized receiving end characteristic sequence.
Preferably, in step S2, every distance of step parameter a is a center symbol, the characteristic of the Volterra equalizer is input as the characteristic of the center symbol, and the equalization result is output as the center symbol and its preceding (a-1)/2 and following (a-1)/2 symbols, where step parameter a is 2i +1(i is 1,2, 3.). The input-output relationship of an nth order Volterra equalizer can be expressed as:
wherein x (k) is the normalized receiving end sampling signal, y (k) is the equalization result of the Volterra equalizer, w (l)1,l2,…,ln) The tap coefficient is of n orders, and Ln is the memory length of the tap of n orders. It can be seen that as the order of the Volterra equalizer increases, the number of taps of the Volterra equalizer increases rapidly. The number of taps of n steps can be calculated by adopting the following formula:
the number of first-order taps of the Volterra equalizer is L by substituting the formula1The number of taps of the second order term is L2(L2+1)/2, the number of taps of the third order term is L3(L3+1)(L3+2)/6. For a traditional Volterra equalizer, each first-order tap needs to be multiplied once in the process of realizing equalization of a first-order term, each second-order tap needs to be multiplied twice in the process of equalization of a second-order term, namely, multiplication between signals and multiplication between a tap coefficient and a second-order term of the signals, and so on, each n-order tap needs to be multiplied n times in the process of equalization of an m-order term, so the computational complexity of the n-order Volterra equalizer using the multiplication number measurement can be expressed as:
for the Volterra equalization method based on multi-symbol processing provided by the invention, the operation of obtaining the high-order form of the signal in the high-order equalization process is shared among a plurality of multi-output symbols, and the operation does not need to be re-operated in the same iteration, so that the calculation complexity of the n-order Volterra equalizer can be expressed as follows for the case of the step parameter a:
compared with the traditional scheme, the calculation complexity of the method is reduced along with the increase of the step parameter a on the premise that the order n is fixed. Wherein the ratio of the computational complexity of each stage of the multi-output equalization scheme to the conventional scheme can be expressed as:
preferably, in step S2, the feature weights are updated by an adaptive algorithm. The adaptive algorithm here may select a Least Mean Square algorithm (LMS), a Recursive Least Square algorithm (RLS), or the like.
Preferably, there are various adaptive algorithms that can be applied to the algorithm, the present invention preferably uses RLS as an example for analysis, and the specific process of updating the feature weight by the RLS adaptive algorithm is as follows:
s21, initializing a weight vector w (n);
s22, calculating an error vector e (n) according to the current weight vector and the training label:
e(i)＝d(i)-wT(i-1)x(n) (4)
where e (i) is the error vector at time i, d (i) is the label at time i;
s23, updating the gain vector k (n), the weight vector w (n) and the inverse matrix P (n) of the correlation matrix according to the error vector e (n) obtained in the step S22;
w(i)＝w(i-1)+k(i)e(i) (6)
where forget is a forgetting factor that affects the learning rate of the RLS algorithm, and p (n) is the inverse of the correlation matrix of the input signal. k (i) is the gain vector at time i, w (i) is the weight vector at time i;
and S24, repeating the steps S22 and S23 on the training set to obtain a final weight vector w (n).
Preferably, in step S3, a final equalization result is calculated according to the tap coefficients of each step obtained by training in step S2:
y(t)＝W1X1+W2X2+...+WnXn
wherein WnIs a matrix of tap coefficients of order n, XnIs a high-order signal characteristic of order n. And (d) judging the equalized signal y (t) to obtain a judgment result z (t).
The invention also discloses a Volterra equalization system based on multi-symbol processing, which specifically comprises the following modules:
a normalization processing module: the receiving end sampling signal Xt is subjected to normalization processing to obtain a receiving end sampling signal X normalized by an equalizer;
a channel equalization module: and adjusting tap coefficients of the Volterra equalizer on a training set by using a self-adaptive algorithm to obtain the well-trained Volterra equalizer, inputting a signal needing to be equalized into the Volterra equalizer, and judging the output of the Volterra equalizer to realize channel equalization.
An error rate calculation module: and comparing the equalization result with the signal of the sending end, and calculating the error rate by obtaining the proportion of the symbol with wrong judgment in the test set symbol.
Preferably, in the normalization processing module, the normalization processing is performed on the signals by calculating a mean value of the signal sequence and subtracting the calculated mean value from each signal in the signal sequence,
X(i)＝Xt(i)-Xt,mean (2)
in the formula, Xt(i) For the i-th signal value, X, of the received sampled signalt,meanIs the mean value of the signal at the receiving end, cnt is connectedAnd (3) the length of the receiving end signal, namely subtracting the signal mean value obtained by the formula (1) from each sampling signal of the receiving end to obtain a normalized receiving end characteristic sequence X, wherein X (i) is the characteristic value of the ith signal corresponding to the normalized receiving end characteristic sequence.
Preferably, in the channel equalization module, the feature weights are updated by an adaptive algorithm. The adaptive algorithm here may be selected from a least mean square algorithm, a recursive least squares algorithm, etc.
The optical fiber transmission system adopted by the invention comprises an arbitrary waveform generator, a laser, a variable optical attenuator, a photoelectric detector, a digital oscilloscope and an off-line DSP module, wherein the arbitrary waveform generator loads pseudo-random codes to obtain electric signals, the electric signals drive the laser to obtain optical signals, the optical signals are transmitted through a single-mode optical fiber, the optical signals are input into the variable optical attenuator, the optical signals are converted into the electric signals through the photoelectric detector, the received signals are sampled by the digital oscilloscope, the sampled signals are sent to the off-line DSP module, the off-line DSP module reconstructs a characteristic sequence, processes the signals by using a Volterra equalizer, and the Bit Error Rate (BER) calculation analysis algorithm performance is carried out on the equalized signals.
The invention utilizes the characteristic of one symbol to generate the equalization result of a plurality of symbols, thereby reducing the repeated calculation in the equalization process. The invention can significantly reduce the computational complexity of the equalizer and achieve the same transmission performance as a traditional Volterra equalizer.
Compared with the prior art, the method effectively reduces the repeated calculation of the Volterra equalizer when extracting the features, greatly reduces the calculated amount of the equalizer, and reduces the time cost and the calculation complexity of system processing.
Drawings
FIG. 1 is a schematic diagram of a fiber optic transmission system for use with the present invention;
fig. 2 is a flowchart of a Volterra equalization method based on multi-symbol processing according to an embodiment of the present invention;
fig. 3 is a graph comparing BER performance under different equalization algorithms when the optical fiber transmission system transmits NRZ signals according to the embodiment of the present invention;
fig. 4 is a graph comparing BER performances under different equalization algorithms when the PAM4 signal is transmitted by the optical fiber transmission system according to the embodiment of the present invention;
fig. 5 is a block diagram of a Volterra equalization system based on multi-symbol processing according to an embodiment of the present invention.
Detailed Description
The invention is further illustrated below with reference to preferred embodiments. The following preferred embodiments will help those skilled in the art to further understand the present invention. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention.
The invention provides a Volterra equalization method and system based on multi-symbol processing, which can be applied to equalizing linear and nonlinear damages in an optical fiber communication system. Conventional Volterra equalizers tend to produce an equalization result for one symbol in one iteration, and repeated acquisition of these characteristics can cause significant computational stress on the equalizer due to the large similarity of the characteristics of adjacent symbols. Therefore, the invention utilizes the characteristic of one symbol to generate the equalization result of a plurality of symbols, thereby reducing the repeated calculation in the equalization process. The Volterra equalization method based on multi-symbol processing can significantly reduce the computational complexity of the equalizer and obtain the same transmission performance as the traditional Volterra equalizer.
Fig. 1 shows a high-speed optical fiber transmission system according to an embodiment of the present invention. At a transmitting end of the Optical fiber transmission system, firstly, a pseudo-random code generated by a Meisen rotation algorithm is used for off-line loading to an Arbitrary Waveform Generator (AWG) to obtain an electric signal, the electric signal drives a 10GHz DML to obtain an Optical signal, the Optical signal is transmitted by a B2B/20km single-mode Optical fiber, and the Optical signal is input into a Variable Optical Attenuator (VOA) at a receiving end for adjusting the received Optical power to study the error rate conditions of different received Optical powers. After the optical signal is converted into an electrical signal by a photoelectric detector, a Digital Oscilloscope (DSO) samples the received signal, and the sampled signal is sent to an offline DSP module. And after the signals pass through the multi-output Volterra equalizer, the channel equalization is completed, and the equalized signals are analyzed for algorithm performance through a BER calculation module.
Specifically, as shown in fig. 2, the Volterra equalization method based on multi-symbol processing in the embodiment of the present invention includes the following steps:
the method comprises the following steps: the receiving end sampling signal Xt is subjected to normalization processing to obtain a receiving end sampling signal X normalized by an equalizer;
step two: selecting a step length parameter a, and adjusting tap coefficients of a Volterra equalizer on a training set by using a self-adaptive algorithm to obtain a well-trained Volterra equalizer;
step three: and inputting the signal to be equalized into the equalizer, and judging the output of the equalizer to realize the effect of channel equalization.
Each of the above steps is described in detail below:
in the first step: the received signal Xt is obtained as a column vector, Xt ═ Xt (1), Xt (2) … Xt (i)]TAnd Xt (i) represents the signal received by the receiving end of the optical fiber system at the moment i.
In the first step: the normalization process for the signals is obtained by calculating the mean of the signal sequence and subtracting the calculated mean from each signal in the signal sequence,
X(i)＝Xt(i)-Xt,mean (2)
in the formula, Xt(i) For the i-th signal value, X, of the received sampled signalt,meanAnd (2) obtaining a normalized receiving end sampling signal X by subtracting the signal mean value obtained by the formula (1) from each sampling signal of the receiving end, wherein cnt is the receiving end signal mean value, and cnt is the receiving end signal length, and the normalized receiving end sampling signal X is the characteristic value of the normalized receiving end sampling signal corresponding to the ith signal.
In the second step: every distance of the step parameter a is a center symbol, the characteristic of the input Volterra equalizer is the characteristic of the center symbol, the output is the equalization result of the center symbol and the front (a-1)/2 and the back (a-1)/2 symbols, and the step parameter a is 2i +1(i is 1,2, 3.).
In the second step: the feature weights are updated by an adaptive algorithm. The adaptive algorithm of the present embodiment may select LMS, RLS algorithm, etc. RLS is preferably used, and is described in detail below by way of example.
The RLS algorithm is an adaptive updating algorithm, aims to minimize the weighted sum of square errors between original data and estimated data, and has high convergence speed, stable performance and high estimation precision. Recursive estimation is adopted in the iteration process of the RLS algorithm, when a group of new data is obtained, the new data is used for correcting the result of the previous estimation on the basis of the previous iteration, the estimation error can be effectively reduced according to the recursive algorithm, the iteration times are increased along with the successive input of the training set data, and the parameter estimation is more accurate. The specific process of updating the feature weights by the RLS adaptive algorithm is as follows:
(1) initializing a weight vector w (n);
(2) calculating an error vector e (n) according to the current weight vector and the training label:
e(i)＝d(i)-wT(i-1)x(n) (6)
where e (i) is the error vector at time i, d (i) is the label at time i;
(3) updating the gain vector k (n), the weight vector w (n) and the inverse matrix P (n) of the correlation matrix according to the error vector e (n) obtained in the step (2);
w(i)＝w(i-1)+k(i)e(i) (8)
where forget is a forgetting factor that affects the learning rate of the RLS algorithm, and p (n) is the inverse of the correlation matrix of the input signal. k (i) is the gain vector at time i, w (i) is the weight vector at time i;
(4) and (5) repeating the steps (2) and (3) on the training set to obtain a final weight vector w (n).
In the third step: and calculating a final equalization result according to the tap coefficients of each order obtained by training in the step two:
y(t)＝W1X1+W2X2+...+WnXn
wherein WnIs a matrix of tap coefficients of order n, XnIs a high-order signal characteristic of order n.
In the third step: the decision process of obtaining the decision result z (t) after the decision of the equalized signal y (t) comprises the following specific steps:
(1) for NRZ signals: and calculating an average value m of the equalization result sequence, judging as a +1 signal when the equalization result is larger than or equal to the average value m, and judging as a-1 signal when the equalization result is smaller than the average value m.
(2) For PAM4 signal: calculating average value m of equalization result sequence1Taken to be greater than m1Average value m of the equalization results of (1)0And is less than m1Average value m of the equalization results of (1)2. The equalization result is less than m0When the average value is-3, the equalization result is m0And m1When m is in between, the judgment is-1, and the equalization result is m1And m2In between, the balance is judged to be 1, and the balance result is larger than m2If so, it is judged as 3.
Fig. 3 is a graph showing BER performance comparison based on different equalization algorithms after NRZ modulated signals are transmitted through optical fibers. The x-axis of the graph is the received optical power (dBm) and the y-axis is the BER magnitude. In the figure, "VNLE" represents a conventional Volterra equalizer scheme; in the figure, "a-3" represents the Volterra equalization scheme based on multi-symbol processing, and the step parameter a-3. Fig. 3(a) is a graph showing the experimental results of 25Gbps NRZ signals transmitted by using a 10G-class photoelectric device and B2B, and fig. 3(B) is a graph showing the experimental results of 25Gbps NRZ signals transmitted by using a 10G-class photoelectric device and 20 km. As can be seen from the figure, the Volterra equalization scheme based on multi-symbol processing obtains almost the same performance as the conventional Volterra equalizer scheme, and proves that the Volterra equalization scheme based on multi-symbol processing can reduce the computational complexity and maintain the excellent equalization performance of the Volterra equalizer.
Fig. 4 is a graph showing BER performance comparison based on different equalization algorithms after signals modulated by PAM4 are transmitted through an optical fiber. The x-axis of the graph is the received optical power (dBm) and the y-axis is the BER magnitude. In the figure, "VNLE" represents a conventional Volterra equalizer scheme; in the figure, "a-3" represents the Volterra equalization scheme based on multi-symbol processing, and the step parameter a-3. Fig. 4(a) is an experimental result of 80Gbps PAM4 signal transmission through B2B using a 10G-class photoelectric device, and fig. 4(B) is an experimental result of 80Gbps PAM4 signal transmission through 20km single-mode fiber using a 10G-class photoelectric device. As can be seen from the figure, the Volterra equalization scheme based on multi-symbol processing achieves almost the same performance as the conventional Volterra equalizer scheme or even better, which may be due to the introduction of errors of neighboring symbols when updating tap coefficients with an adaptive algorithm in the Volterra equalization scheme based on multi-symbol processing. The multi-output equalization scheme based on the Volterra equalizer proves to be capable of reducing the computational complexity and simultaneously keeping the excellent equalization performance of the Volterra equalizer.
As shown in fig. 5, the Volterra equalization system based on multi-symbol processing in this embodiment specifically includes the following modules connected in sequence:
a normalization processing module: the receiving end sampling signal Xt is subjected to normalization processing to obtain a receiving end sampling signal X normalized by an equalizer;
a channel equalization module: and adjusting tap coefficients of the Volterra equalizer on a training set by using a self-adaptive algorithm to obtain the well-trained Volterra equalizer, inputting a signal needing to be equalized into the Volterra equalizer, and judging the output of the Volterra equalizer to realize channel equalization.
An error rate calculation module: and comparing the equalization result with the signal of the sending end, and calculating the error rate by obtaining the proportion of the symbol with wrong judgment in the test set symbol.
In the normalization processing module of this embodiment, the normalization processing is performed on the signals by calculating the mean value of the signal sequence and subtracting the calculated mean value from each signal in the signal sequence,
X(i)＝Xt(i)-Xt,mean (2)
in the formula, Xt(i) For the i-th signal value, X, of the received sampled signalt,meanAnd (2) obtaining a normalized receiving end characteristic sequence X by subtracting the signal mean value obtained by the formula (1) from each sampling signal of the receiving end, wherein cnt is the receiving end signal mean value, and cnt is the receiving end signal length, and X (i) is the characteristic value of the normalized receiving end characteristic sequence corresponding to the ith signal.
In summary, the present invention relates to a Volterra equalization method and system based on multi-symbol processing, which utilizes the characteristics of one symbol to generate the equalization result of multiple symbols, thereby reducing the repeated calculation in the equalization process. The Volterra equalization method based on multi-symbol processing can significantly reduce the computational complexity of the equalizer and obtain the same transmission performance as the traditional Volterra equalizer. Compared with the prior art, the method effectively reduces the repeated calculation of the Volterra equalizer when extracting the features, greatly reduces the calculated amount of the equalizer, and reduces the time cost and the calculation complexity of system processing.
The invention discloses a Volterra equalization scheme based on multi-symbol processing for solving linear damage and nonlinear damage of an optical fiber transmission system, which is characterized in that: the characteristics of one symbol are used for generating the equalization result of a plurality of symbols, so that repeated calculation in the equalization process is reduced. The Volterra equalization method based on multi-symbol processing can obviously reduce the calculation complexity of the equalizer and obtain the same transmission performance as the traditional Volterra equalizer.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.
Claims (10)
1. The Volterra equalization method based on multi-symbol processing is characterized by comprising the following specific steps of:
s1, carrying out normalization processing on the receiving end sampling signal Xt to obtain a receiving end sampling signal X normalized by the equalizer;
s2, selecting a step length parameter a, and adjusting tap coefficients of the linear equalizer on a training set by using a self-adaptive algorithm to obtain a trained linear equalizer;
and S3, inputting the signal to be equalized into the equalizer, and judging the output of the equalizer to realize channel equalization.
2. The Volterra equalization method based on multi-symbol processing as claimed in claim 1, wherein in step S1, the specific process of normalizing the signal is as follows: obtained by calculating the mean of the signal sequence and subtracting the calculated mean from each signal in the signal sequence,
X(i)＝Xt(i)-Xt,mean (2)
in the formula, Xt(i) For the i-th signal value, X, of the received sampled signalt,meanAnd (2) obtaining a normalized receiving end characteristic sequence X by subtracting the signal mean value obtained by the formula (1) from each sampling signal of the receiving end, wherein cnt is the receiving end signal mean value, and cnt is the receiving end signal length, and X (i) is the characteristic value of the normalized receiving end characteristic sequence corresponding to the ith signal.
3. The Volterra equalization method based on multi-symbol processing according to claim 1 or 2, wherein in step S2, every distance of step parameter a is a center symbol, the input Volterra equalizer is characterized by the center symbol, and the output is the equalization result of the center symbol and its preceding (a-1)/2 and following (a-1)/2 symbols, and the step parameter a is 2i +1(i is 1,2, 3.).
4. The multi-symbol processing based Volterra equalization method of claim 3 wherein in step S2, the feature weights are updated by an adaptive algorithm.
5. The multi-symbol processing-based Volterra equalization method of claim 4, wherein in step S2, said adaptive algorithm selects a least mean square algorithm or a recursive least square algorithm.
6. The Volterra equalization system based on multi-symbol processing is characterized by specifically comprising the following modules:
a normalization processing module: the receiving end sampling signal Xt is subjected to normalization processing to obtain a receiving end sampling signal X normalized by an equalizer;
a channel equalization module: adjusting tap coefficients of a Volterra equalizer on a training set by using a self-adaptive algorithm to obtain a trained Volterra equalizer, inputting a signal to be equalized into the Volterra equalizer, and judging the output of the Volterra equalizer to realize channel equalization;
an error rate calculation module: and comparing the equalization result with the signal of the sending end, and calculating the error rate by obtaining the proportion of the symbol with wrong judgment in the test set symbol.
7. The multi-symbol processing-based Volterra equalization system as claimed in claim 6, wherein the normalization processing module normalizes the signals by calculating a mean value of the signal sequence and subtracting the calculated mean value from each signal in the signal sequence,
X(i)＝Xt(i)-Xt,mean (4)
in the formula, Xt(i) For the i-th signal value, X, of the received sampled signalt,meanAnd (2) obtaining a normalized receiving end characteristic sequence X by subtracting the signal mean value obtained by the formula (1) from each sampling signal of the receiving end, wherein cnt is the receiving end signal mean value, and cnt is the receiving end signal length, and X (i) is the characteristic value of the normalized receiving end characteristic sequence corresponding to the ith signal.
8. The Volterra equalization system based on multi-symbol processing according to claim 6 or 7, wherein the distance of every step parameter a is a center symbol, the input features of VNLE are features of the center symbol, the output is the equalization result of the center symbol and its front (a-1)/2 and back (a-1)/2 symbols, and the step parameter a is 2i +1(i is 1,2, 3.).
9. The multi-symbol processing based Volterra equalization system of claim 8 wherein the channel equalization module updates the feature weights by an adaptive algorithm.
10. The multi-symbol processing-based Volterra scale system of claim 9 wherein the RLS adaptive algorithm is selected and used in the channel equalization module, and the specific process of updating the feature weights is as follows:
s21, initializing a weight vector w (n);
s22, calculating an error vector e (n) according to the current weight vector and the training label:
e(i)＝d(i)-wT(i-1)x(n) (5)
where e (i) is the error vector at time i, d (i) is the label at time i;
s23, updating the gain vector k (n), the weight vector w (n) and the inverse matrix P (n) of the correlation matrix according to the error vector e (n) obtained in the step S22;
w(i)＝w(i-1)+k(i)e(i) (7)
wherein forget is a forgetting factor, and P (n) is an inverse matrix of the correlation matrix of the input signal; k (i) is the gain vector at time i, w (i) is the weight vector at time i;
and S24, repeating the steps S22 and S23 on the training set to obtain a final weight vector w (n).
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