CN114301529B - 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 a receiving end sampling signal Xt to obtain an equalizer normalized receiving end sampling signal X; s2, selecting a step length parameter a, and adjusting tap coefficients of the linear equalizer on a training set by utilizing an adaptive algorithm to obtain a trained linear equalizer; s3, inputting the signals to be equalized into the equalizer, and judging the equalizer output 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 remarkably reduce the calculation complexity of the equalizer and can obtain the equivalent transmission performance with 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 the global internet users is continuously increased, the related business of the network is rapidly developed, the improvement of the bandwidth requirement and the rate requirement of the market on the optical fiber transmission system is promoted, the high-speed optical network is rapidly developed in recent years, and the optical network with larger capacity, higher rate and lower cost is the main direction of development in the next few years. However, due to cost limitations, low cost opto-electronic devices actually used in networks can introduce linear and nonlinear distortions, which interact with other channel noise to cause severe intersymbol interference (Inter Symbol Interference, ISI), which can significantly impair signal transmission quality. In order to solve the problem, digital signal processing technology (Digital Signal Processing, DSP) is introduced to equalize the transmitted signals, so that it is necessary to relieve the damage suffered in the signal transmission process.
The DSP technology at the receiving end mainly utilizes an equalization algorithm to compensate for the damage of attenuation, dispersion, nonlinear effect and the like of signals, and the signal equalization process is a necessary technology for realizing a low-cost high-speed optical network. As known from prior art investigations, common equalization schemes are feedforward equalization filters (Feed-Forward Equalization, FFE), decision feedback Equalizer (Decision Feedback Equalization, DFE), volterra nonlinear Equalizer (VNLE), etc. But for severe intersymbol interference and nonlinear effects FFE and DFE are not sufficient to meet the equalization requirements of the system (DSP enabled next generation G TDM-PON,2020 published in Journal of Optical Communications and Networking). The VOLTERRA equalizer is an effective tool for compensating for linear and nonlinear impairments of signals, but the computational complexity increases rapidly with increasing introduced orders, and hundreds of features may be required to achieve satisfactory performance in practical system applications. With the vigorous development of machine learning related algorithms and the powerful performance of Neural Networks (NNs) in fitting nonlinear functions, neural Network-based equalization schemes have received widespread attention in the field of fiber optic communications. However, the existing solutions for balancing nonlinear interference based on machine learning algorithms have high complexity, and cannot meet the requirements of low cost and low power consumption (An Overview on Application of Machine Learning Techniques in Optical Networks,2019 published in IEEE Communications Surveys & Tutorials). In order to obtain an equalization scheme with lower system complexity and calculation complexity on the premise of keeping higher decision accuracy, the existing equalization scheme needs to be improved.
Due to the excellent performance of Volterra equalizers in compensating for signal linear impairments and nonlinear impairments, expert students have focused their attention on reducing the complexity of Volterra equalizers. Most of the simplified schemes based on Volterra equalizer that have been proposed so far are to cut out taps that contribute less to performance optimization in the equalization process, for example Wei Jinlong et al propose that by setting a threshold and removing 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 great influence on performance and does not have an exact algorithm to select a suitable threshold, and too large a threshold can result in a large number of taps being cut down, enough features cannot be retained for signal classification, and too small a threshold cannot reduce computational complexity. In 2020, yukui Yu et al (Low-complexity 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 System Using DML, published in IEEE Photonics Technology Letters) and Qianwu Zhang team (An Improved Volterra Nonlinear Equalizer for Gb/sPAM4 IM/DD Transmission with 10G-Class Optics, published in ACP) proposed the conversion of the product operation in the VOLTERRA equalizer to an absolute value operation, but this method resulted in reduced equalization performance. Yukui Yu et al also propose to leave only the diagonal taps off of all other taps, but this approach removes many of the original features, resulting in inaccurate equalization results. 2021, yang Zheng et al proposed that a principal component analysis (Principal Component Analysis, PCA) algorithm was used to map features to other vector spaces and then retain a tap with a greater contribution (Optimized Volterra filter equalizer based on weighted principal component analysis for IM-DD transmission, published in Opt Lett), whereas PCA algorithm is an unsupervised learning algorithm, and in the process of mapping samples, the classification of samples is not considered, which easily results in a result that the samples are mapped and are rather less prone to classification.
In summary, a new technical solution needs to be explored in the research direction of reducing the Volterra equalizer, and the development of the Volterra equalizer with stable equalization performance on signal linear impairment and nonlinear impairment and lower complexity is an important solution for supporting the construction of an optical network with higher speed and lower cost.
Disclosure of Invention
The invention aims at overcoming the defects of the prior art and provides a Volterra equalization method and a Volterra equalization system based on multi-symbol processing.
The invention provides a Volterra equalization method and a Volterra equalization system based on multi-symbol processing, wherein the traditional Volterra equalizer often generates an equalization result of one symbol in one iteration, and the repeated acquisition of the characteristics of adjacent symbols brings great calculation pressure to the equalizer due to the fact that the characteristics of the adjacent symbols have great similarity. The present invention therefore proposes to use the characteristics of one symbol to generate equalization results for a plurality of symbols, thereby reducing the repetition of the equalization process. The Volterra equalization method based on multi-symbol processing can significantly reduce the computational complexity of the equalizer and achieve the same transmission performance as the conventional Volterra equalizer.
In order to achieve the above purpose, the present 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 a receiving end sampling signal Xt to obtain an equalizer normalized receiving end sampling signal X;
s2, selecting a step length parameter a, and adjusting tap coefficients of the Volterra equalizer on a training set by utilizing an adaptive algorithm to obtain a trained Volterra equalizer;
s3, inputting the signals to be equalized into the equalizer, and judging the equalizer output to realize the effect of channel equalization.
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 achieve the same transmission performance as the conventional Volterra equalizer.
Preferably, in step S1, the transmitting-side signal is a pseudo-random code generated based on the meisen rotation algorithm.
Preferably, in step S1, the normalization of the signals is performed by calculating the mean value of the signal sequence, subtracting the calculated mean value from each signal in the signal sequence,
X(i)＝X t (i)-X t,mean (2)
wherein X is t (i) For the ith signal value of the receiving end sampling signal, X t,mean And (2) subtracting the signal average value obtained in the formula (1) from each sampling signal of the receiving end to obtain a normalized characteristic sequence X of the receiving end, wherein X (i) is the characteristic value of the ith signal corresponding to the normalized characteristic sequence of the receiving end.
Preferably, in step S2, the distance of the step parameter a is one center symbol, the characteristic of the input Volterra equalizer is the characteristic of the center symbol, and the output is the equalization result of the center symbol and the preceding (a-1)/2 and the following (a-1)/2 symbols, and the step parameter a=2i+1 (i=1, 2, 3.). The input-output relationship of an n-order Volterra equalizer can be expressed as:
wherein x (k) is a receiving end sampling signal after normalization processing, y (k) is an equalization result of the Volterra equalizer, and w (l) 1 ,l 2 ,…,l n ) For the tap coefficients of order n, ln is the memory length of the tap of order n. It can be seen that the number of taps of the Volterra equalizer increases rapidly as the order of the Volterra equalizer increases. Wherein the number of taps of the n-order can be calculated by the following formula:
substituting the formula to know that the number of first-order term taps of the Volterra equalizer is L 1 The tap number of the second order term is L 2 (L 2 +1)/2, the number of taps of the third-order term is L 3 (L 3 +1)(L 3 +2)/6. For a traditional Volterra equalizer, each first-order tap needs one multiplication operation in the process of realizing the equalization of a first-order term, and each second-order tap needs two multiplication operations in the process of realizing the equalization of a second-order term, namely one multiplication operation between signals and one multiplication operation between tapsOne multiplication of the coefficients and the second order term of the signal, and so on, each n-tap in the equalization of the m-order term requires n multiplication operations, so the computational complexity of an n-order Volterra equalizer using a multiplication count metric can be expressed as:
for the Volterra equalizing method based on multi-symbol processing, which is provided by the invention, the operation of obtaining the high-order form of the signal in the high-order equalizing process is shared among a plurality of symbols with multiple outputs, and no re-operation is needed in the same iteration, so that the calculation complexity of the n-order Volterra equalizer can be expressed as follows for the case of step-length parameter a:
compared with the traditional scheme, the calculation complexity of the method is reduced along with the increase of the step size parameter a on the premise of fixed order n. 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 herein may select a least mean square algorithm (Least Mean Square, LMS), a recursive least squares algorithm (Recursive Least Squares, RLS), or the like.
Preferably, there are a plurality of adaptive algorithms that can be applied to the algorithm, and the invention preferably uses RLS as an example for analysis, and the specific process of updating the feature weights 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)-w T (i-1)x(n) (4)
where e (i) is the error vector at time i and d (i) is the tag 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)
wherein forget is forgetting factor, affects learning rate of RLS algorithm, and P (n) is inverse matrix of input signal correlation matrix. k (i) is a gain vector at i time, and w (i) is a weight vector at i time;
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 each tap coefficient trained in step S2:
y(t)＝W 1 X 1 +W 2 X 2 +...+W n X n
wherein W is n For a matrix of n-tap coefficients, X n Is a higher order signal characteristic of order n. And 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 comprises the following modules:
normalization processing module: the receiving end sampling signal Xt is normalized to obtain an equalizer normalized receiving end sampling signal X;
and a channel equalization module: and (3) adjusting tap coefficients of the Volterra equalizer on a training set by utilizing an adaptive algorithm to obtain a trained Volterra equalizer, inputting signals to be equalized into the Volterra equalizer, judging the output of the Volterra equalizer, and realizing channel equalization.
And the error rate calculation module is used for: and comparing the equalization result with the signal of the transmitting end, and calculating the error rate by obtaining the proportion of the symbol with the decision error to the symbol of the test set.
Preferably, in the normalization processing module, the normalization processing of the signals is performed by calculating a mean value of the signal sequence, subtracting the calculated mean value from each signal in the signal sequence,
X(i)＝X t (i)-X t,mean (2)
wherein X is t (i) For the ith signal value of the receiving end sampling signal, X t,mean For the signal mean value of the receiving end, cnt is the signal length of the receiving end, the signal mean value obtained in the formula (1) is subtracted from each sampling signal of the receiving end, and the normalized characteristic sequence X of the receiving end is obtained, wherein X (i) is the characteristic value of the ith signal corresponding to the normalized characteristic sequence of the receiving end.
Preferably, in the channel equalization module, the feature weights are updated by an adaptive algorithm. The adaptive algorithm herein may select a least mean square algorithm, a recursive least squares algorithm, or the like.
The optical fiber transmission system 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 and input into the variable optical attenuator, the optical signals are converted into electric signals through the photoelectric detector, the digital oscilloscope samples received signals, the sampled signals are sent to the off-line DSP module, the off-line DSP module reconstructs a characteristic sequence and processes the signals through a Volterra equalizer, and the Error rate (BER) of the equalized signals is calculated and analyzed to obtain algorithm performance.
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 remarkably reduce the computational complexity of the equalizer and obtain the same transmission performance as the traditional Volterra equalizer.
Compared with the prior art, the invention effectively reduces the repeated calculation when the Volterra equalizer extracts the characteristics, greatly reduces the calculation amount of the equalizer, and reduces the time cost and the calculation complexity of the system processing.
Drawings
FIG. 1 is a schematic diagram of an optical fiber transmission system according to 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 showing BER performance under different equalization algorithms under the condition that an optical fiber transmission system transmits NRZ signals according to an embodiment of the present invention;
FIG. 4 is a graph showing BER performance under different equalization algorithms under the condition that an optical fiber transmission system according to an embodiment of the present invention transmits a PAM4 signal;
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 in connection with preferred embodiments. The following preferred embodiments will assist those skilled in the art in further understanding the present invention. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention.
The invention provides a Volterra equalization method and a Volterra equalization system based on multi-symbol processing, which can be applied to equalization of linear and nonlinear damages in an optical fiber communication system. Conventional Volterra equalizers tend to produce a symbol equalization result in one iteration, and because of the large similarity of the features of adjacent symbols, repeatedly taking these features can place a large computational burden on the equalizer. Thus, the invention utilizes 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 achieve the same transmission performance as the conventional Volterra equalizer.
As shown in fig. 1, a high-speed optical fiber transmission system according to an embodiment of the present invention is shown. At the transmitting end of the optical fiber transmission system, firstly, pseudo random codes are generated offline by utilizing a Mersen rotation algorithm and are loaded on any waveform generator (Arbitrary Waveform Generator, AWG) to obtain electric signals, the electric signals drive a 10GHz DML to obtain optical signals, the optical signals are transmitted through a B2B/20km single-mode optical fiber, and the optical signals are input into a variable optical attenuator (Variable Optical Attenuator, VOA) at the receiving end and are used for adjusting the received optical power to study the error rate conditions of different received optical powers. After the optical signals are converted into electric signals through the photoelectric detector, the digital oscilloscope (Digital Storage Oscilloscope, DSO) samples the received signals, and the sampled signals are sent to the off-line DSP module. After the multi-output Volterra equalizer is adopted, channel equalization is completed, and the equalized signal is 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 invention includes the following steps:
step one: the receiving end sampling signal Xt is normalized to obtain an equalizer normalized receiving end sampling signal X;
step two: selecting a step length parameter a, and adjusting tap coefficients of the Volterra equalizer on a training set by utilizing an adaptive algorithm to obtain a trained Volterra equalizer;
step three: and inputting the signals to be equalized into the equalizer, and judging the equalizer output to realize the effect of channel equalization.
Each of the above steps is described in detail below:
in the first step: obtainingIs a column vector, xt= [ Xt (1), xt (2) … Xt (i)] T Xt (i) represents a signal received by a receiving end of the optical fiber system at the moment i.
In the first step: the normalization of the signals is performed by calculating the mean value of the signal sequence, subtracting the calculated mean value from each signal in the signal sequence,
X(i)＝X t (i)-X t,mean (2)
wherein X is t (i) For the ith signal value of the receiving end sampling signal, X t,mean And (2) subtracting the signal average value obtained in the formula (1) from each sampling signal of the receiving end to obtain a normalized sampling signal X of the receiving end, wherein X (i) is the characteristic value of the normalized sampling signal of the receiving end corresponding to the ith signal.
In the second step: every other step parameter a is a center symbol, the characteristic of the input Volterra equalizer is the characteristic of the center symbol, and the output is the equalization result of the center symbol and the preceding (a-1)/2 and the following (a-1)/2 symbols, the step parameter a=2i+1 (i=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, or the like. RLS is preferably used, and will be described in detail below by way of example.
The RLS algorithm is an adaptive update algorithm, and aims to minimize the weighted sum of square errors between original data and estimated data, and has fast convergence speed, stable performance and high estimation accuracy. In the iteration process of the RLS algorithm, recursive estimation is adopted, and each time a new set of data is obtained, the result of the previous estimation is corrected by using the new data 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 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)-w T (i-1)x(n) (6)
where e (i) is the error vector at time i and d (i) is the tag 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)
wherein forget is forgetting factor, affects learning rate of RLS algorithm, and P (n) is inverse matrix of input signal correlation matrix. k (i) is a gain vector at i time, and w (i) is a weight vector at i time;
(4) Repeating the steps (2) and (3) on the training set to obtain a final weight vector w (n).
In the third step: calculating a final equalization result according to each tap coefficient obtained in the training in the step two:
y(t)＝W 1 X 1 +W 2 X 2 +...+W n X n
wherein W is n For a matrix of n-tap coefficients, X n Is a higher order signal characteristic of order n.
In the third step: the specific steps of the decision process for obtaining the decision result z (t) after deciding the equalized signal y (t) are as follows:
(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 the average value m of the equalization result sequence 1 Taking a value greater than m 1 Average value m of equalization results of (2) 0 And less than m 1 Average value m of equalization results of (2) 2 . The equalization result is less than m 0 When it is determined as-3, the equalization result is m 0 And m 1 When the balance is between the two values, the balance is judged to be-1, and the balance result is m 1 And m 2 When the balance is between the two values, the balance is judged to be 1, and the balance result is larger than m 2 In this case, 3 is determined.
Fig. 3 is a graph showing BER performance comparison under different equalization algorithms after NRZ modulated signals are transmitted through an optical fiber. In the figure, the x-axis represents the received optical power (dBm), and the y-axis represents the BER. In the figure "VNLE" represents a conventional Volterra equalizer scheme; in the figure, "a=3" represents a Volterra equalization scheme based on multi-symbol processing, and the step size parameter a=3. Fig. 3 (a) is a graph of experimental results after transmission of 25Gbps NRZ signal through B2B using a 10G-class photoelectric device, and fig. 3 (B) is a graph of experimental results after transmission of 25Gbps NRZ signal through 20km using a 10G-class photoelectric device. As can be seen from the figure, the Volterra equalization scheme based on multi-symbol processing has almost the same performance as the conventional Volterra equalizer scheme, and it is proved that the Volterra equalization scheme based on multi-symbol processing can maintain excellent equalization performance of the Volterra equalizer while reducing computational complexity.
Fig. 4 is a graph showing BER performance comparison under different equalization algorithms after PAM4 modulated signals are transmitted through an optical fiber. In the figure, the x-axis represents the received optical power (dBm), and the y-axis represents the BER. In the figure "VNLE" represents a conventional Volterra equalizer scheme; in the figure, "a=3" represents a Volterra equalization scheme based on multi-symbol processing, and the step size parameter a=3. Fig. 4 (a) is an experimental result of transmitting 80gbps PAM4 signal through B2B using a 10G-stage photoelectric device, and fig. 4 (B) is an experimental result of transmitting 80gbps PAM4 signal through a 20km single mode fiber using a 10G-stage 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 even better, probably because errors of adjacent symbols are introduced 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 can be proved to be capable of maintaining excellent equalization performance of the Volterra equalizer while reducing computational complexity.
As shown in fig. 5, the Volterra equalizing system based on multi-symbol processing in this embodiment specifically includes the following modules connected in sequence:
normalization processing module: the receiving end sampling signal Xt is normalized to obtain an equalizer normalized receiving end sampling signal X;
and a channel equalization module: and (3) adjusting tap coefficients of the Volterra equalizer on a training set by utilizing an adaptive algorithm to obtain a trained Volterra equalizer, inputting signals to be equalized into the Volterra equalizer, judging the output of the Volterra equalizer, and realizing channel equalization.
And the error rate calculation module is used for: and comparing the equalization result with the signal of the transmitting end, and calculating the error rate by obtaining the proportion of the symbol with the decision error to the symbol of the test set.
In the normalization processing module of the present embodiment, the process of normalizing the signals is obtained by calculating the average value of the signal sequence, subtracting the calculated average value from each signal in the signal sequence,
X(i)＝X t (i)-X t,mean (2)
wherein X is t (i) For the ith signal value of the receiving end sampling signal, X t,mean For the signal mean value of the receiving end, cnt is the signal length of the receiving end, the signal mean value obtained in the formula (1) is subtracted from each sampling signal of the receiving end, and the normalized characteristic sequence X of the receiving end is obtained, wherein X (i) is the characteristic value of the ith signal corresponding to the normalized characteristic sequence of the receiving end.
In summary, the present invention relates to a Volterra equalization method and system based on multi-symbol processing, which uses the characteristics of one symbol to generate the equalization result of multiple symbols, so as to reduce the repeated computation in the equalization process. The Volterra equalization method based on multi-symbol processing can significantly reduce the computational complexity of the equalizer and achieve the same transmission performance as the conventional Volterra equalizer. Compared with the prior art, the invention effectively reduces the repeated calculation when the Volterra equalizer extracts the characteristics, greatly reduces the calculation amount of the equalizer, and reduces the time cost and the calculation complexity of the 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 characteristic of one symbol is utilized 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 remarkably reduce the calculation complexity of an equalizer and obtain the same transmission performance as the traditional Volterra equalizer.
The foregoing describes specific embodiments of the present invention. It is to be understood that the invention is not limited to the particular embodiments described above, and that various changes or modifications may be made by those skilled in the art within the scope of the appended claims without affecting the spirit of the invention. The embodiments of the present application and features in the embodiments may be combined with each other arbitrarily without conflict.
Claims (4)
1. The Volterra equalization method based on multi-symbol processing is characterized by comprising the following specific steps:
s1, carrying out normalization processing on a receiving end sampling signal Xt to obtain an equalizer normalized receiving end sampling signal X;
s2, selecting a step length parameter a, and adjusting a tap coefficient, namely a characteristic weight, of the linear equalizer on a training set by utilizing an adaptive algorithm to obtain a trained linear equalizer;
s3, inputting the signals to be equalized into an equalizer, and judging the output of the equalizer to realize channel equalization;
in step S2, the distance of every step parameter a is a center symbol, the characteristic of the input Volterra equalizer is the characteristic of the center symbol, and the output is the equalization result of the center symbol and the front (a-1)/2 and the rear (a-1)/2 symbols thereof, the step parameter a=2i+1, i=1, 2,3 …;
in step S2, an RLS adaptive algorithm is selected, and the specific process of updating the feature weight 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)-w T (i-1)x(n) (5)
wherein e (i) is an error vector at time i, and d (i) is a 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 forgetting factor, P (i) is inverse of input signal correlation matrix; k (i) is a gain vector at i time, and w (i) is a weight vector at i time;
s24, repeating the steps S22 and S23 on the training set to obtain a final weight vector w (n).
2. The Volterra equalizing method based on multi-symbol processing according to claim 1, wherein in step S1, the specific process of normalizing the signal is: by calculating the mean value of the signal sequence, and subtracting the calculated mean value from each signal in the signal sequence,
X(i)＝X t (i)-X t,mean (2)
wherein X is t (i) For the ith signal value of the receiving end sampling signal, X t,mean For the signal mean value of the receiving end, cnt is the signal length of the receiving end, the signal mean value obtained in the formula (1) is subtracted from each sampling signal of the receiving end, and the normalized characteristic sequence X of the receiving end is obtained, wherein X (i) is the characteristic value of the ith signal corresponding to the normalized characteristic sequence of the receiving end.
3. The Volterra equalization system based on multi-symbol processing is characterized by comprising the following modules:
normalization processing module: the receiving end sampling signal Xt is normalized to obtain an equalizer normalized receiving end sampling signal X;
and a channel equalization module: the self-adaptive algorithm is utilized to adjust the tap coefficient, namely the characteristic weight, of the Volterra equalizer on the training set, so as to obtain a trained Volterra equalizer, signals to be equalized are input into the Volterra equalizer, and decision is made on the output of the Volterra equalizer, so that channel equalization is realized;
and the error rate calculation module is used for: comparing the equalization result with a signal of a transmitting end, and calculating the error rate by obtaining the proportion of the symbol with the judgment error to the symbol of the test set;
every other distance of the step parameter a is a center symbol, the characteristic of the input Volterra equalizer is the characteristic of the center symbol, and the output is the equalization result of the center symbol and the front (a-1)/2 and the rear (a-1)/2 symbols, and the step parameter a=2i+1, i=1, 2,3 …;
in the channel equalization module, an RLS self-adaptive algorithm is selected, and the specific process of updating the characteristic weight 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)-w T (i-1)x(n) (5)
wherein e (i) is an error vector at time i, and d (i) is a 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 forgetting factor, P (i) is inverse of input signal correlation matrix; k (i) is a gain vector at i time, and w (i) is a weight vector at i time;
s24, repeating the steps S22 and S23 on the training set to obtain a final weight vector w (n).
4. The Volterra equalization system based on multi-symbol processing of claim 3, 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)＝X t (i)-X t,mean (4)
wherein X is t (i) For the ith signal value of the receiving end sampling signal, X t,mean For the signal mean value of the receiving end, cnt is the signal length of the receiving end, the signal mean value obtained in the formula (1) is subtracted from each sampling signal of the receiving end, and the normalized characteristic sequence X of the receiving end is obtained, wherein X (i) is the characteristic value of the ith signal corresponding to the normalized characteristic sequence of the receiving end.
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