CN109039472B - Data center optical communication dispersion estimation and management method based on deep learning - Google Patents

Data center optical communication dispersion estimation and management method based on deep learning Download PDF

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CN109039472B
CN109039472B CN201810754897.5A CN201810754897A CN109039472B CN 109039472 B CN109039472 B CN 109039472B CN 201810754897 A CN201810754897 A CN 201810754897A CN 109039472 B CN109039472 B CN 109039472B
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瞿国庆
瞿国亮
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Abstract

The invention discloses a data center optical communication dispersion estimation and management method based on deep learning, wherein an equalizer based on an artificial neural network is divided into two stages, the first stage adopts pulse response data of an optical channel to train the artificial neural network, optimizes model parameters of the artificial neural network and establishes a nonlinear response model of the artificial neural network; and in the second stage, the transmission data of the optical channel is processed by adopting a trained artificial neural network equalizer to realize the estimation and compensation of chromatic dispersion of the optical channel. Simulation experiments are carried out according to the optical network scheme of the data center, and results show that the equalizer based on the artificial neural network improves the optical signal-to-noise ratio of optical communication and prolongs the transmission distance of the optical communication.

Description

Data center optical communication dispersion estimation and management method based on deep learning
Technical Field
The invention relates to a data center optical communication dispersion estimation and management method based on deep learning.
Background
With the development of cloud computing, the scale of a data center is rapidly increased, and an optical network is a main communication mode of the data center at present. The optical fiber has dispersion phenomenon, which causes linear or nonlinear distortion in the propagation process of the optical wave. In a coherent optical communication system, a linear equalizer can be used to directly compensate for dispersion, but a linear equalizer scheme cannot be adopted in a direct detection system, and the dispersion phenomenon causes obvious errors because phase information of symbols is lost in the detection process of the direct detection system. In all equalizer techniques, MLSE (maximum likelihood receiver) has the best equalization performance, but its computation cost for each symbol is proportional to the inter-symbol interference, resulting in a scenario where MLSE is not suitable for high-speed symbol transmission. The transmission distance of the data center is mostly several kilometers to several tens of kilometers, and the transmission speed is higher than 10Gbps, so the data center needs to increase a modulation technology and a digital signal processing technology. Optical networks in data centers typically use directly modulated lasers and directly detected receivers, and as the bit rate of data transmission increases, the transmission distance of such networks is limited mainly by the dispersion problem of optical communications. In order to achieve equalization performance close to that of the MLSE equalizer and lower calculation cost, an equalization scheme based on an ANN (artificial neural network) model is designed. The ANN is a nonlinear and self-adaptive information processing system formed by interconnection of a large number of processing units, and the learning capability of the ANN is utilized to realize prediction and compensation of the optical communication dispersion problem.
The maximum likelihood estimation is the most accurate estimation algorithm of optical communication dispersion, but the calculation cost of the maximum likelihood estimation for each symbol is in direct proportion to the inter-symbol interference, and in the case of high-speed optical communication, the interference between optical communication symbols is extremely large, so the calculation complexity of the maximum likelihood estimation for the high-speed optical communication is extremely high, and the practicability is low. The data center light rate of cloud computing is generally higher than 10Gbps, in which case the computation cost of maximum likelihood estimation is extremely large.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a data center optical communication dispersion estimation and management method based on deep learning.
In order to solve the technical problems, the invention provides the following technical scheme:
the invention provides a data center optical communication dispersion estimation and management method based on deep learning, which is characterized by comprising the following steps of:
s1, training the ANN by using the impulse response data of the optical channel, optimizing model parameters of the ANN, and establishing a nonlinear response model of the ANN;
and S2, processing the transmission data of the optical channel by adopting the trained ANN equalizer to realize the estimation and compensation of the chromatic dispersion of the optical channel.
Further, in step S1, an optical communication system model is established, where the short-distance optical communication model mainly consists of a sending module, an optical channel, and a receiving module; the sending module consists of a direct modulation laser or an external modulation laser; assuming that the noise of the transmitter is white gaussian noise, the generalized transmit module outputs:
Figure BDA0001726495070000021
in the formula akFor independent and equally distributed input symbols, N is the total number of transmitted symbols, T-1Is the symbol rate, F (t) is the pulse shape; f (t) of DML is defined as:
Figure BDA0001726495070000022
where P (t) is the distribution of output energy,
Figure BDA0001726495070000023
the phase (t) is equal to the result of the DML frequency chirp, defined as integral[6]：
Figure BDA0001726495070000024
In which alpha is a linear factor, KvThe first term and the second term of the formula (3) represent transient chirp and adiabatic chirp, respectively; the F (t) of EML is defined as:
Figure BDA0001726495070000025
assuming that the optical channel is a linear Single Mode Fiber (SMF), the transfer function is:
Figure BDA0001726495070000026
in the formula beta2Is the group velocity dispersion coefficient, L is the fiber length; the optical fiber output signal has a bandwidth BoThe receiving signal of the receiver can be expressed as follows:
r(t)＝(x(t)*hf(t))*ho(t) (6)
in the formula, the operator "+" represents the convolution operation, hf(t) and ho(t) the impulse responses of the fiber and the filter, respectively;
noise n of receivere(t) includes shot noise and thermal noise; because the direct photoelectric detection scheme is simple to implement and low in cost, the direct photoelectric detection scheme is generally adopted in short-distance communication; the output signal of the output end low-pass filter is:
y(t)＝(|r(t)|2+ne(t))*he(t) (7)
in the formula he(t) is the impulse response of the low pass filter;
in the process of converting a received optical signal r (t) into an electrical signal y (t), nonlinear distortion occurs, mainly because the received signal loses phase information; therefore, there is a need to add an equalizer to the digital signal processing module of the receiver, which should effectively compensate for the distortion of the signal.
Further, in step S2, the artificial neural network-based equalizer is used to effectively compensate for nonlinear optical communication distortion, assuming that the input vector of the neural network is
Figure BDA0001726495070000031
Y is the input vector of the equalizer, Y represents the received distorted data, and the output vector is
Figure BDA0001726495070000032
Assuming that n represents the number of taps required for the equalizer, an ANN-based nonlinear feedforward equalizer structure is employed, which has three layers: the device comprises an input layer, a hidden layer and an output layer, wherein the hidden layer and the output layer are respectively provided with m nodes and l nodes.
Further, assume that the non-linear activation function of the hidden layer is fh() And processing the sum of each hidden layer node by adopting an activation function, wherein the output result can be expressed as the following form:
Figure BDA0001726495070000033
in the formula
Figure BDA0001726495070000034
Representing the weight assigned to the connection between the ith input node and the jth hidden node; outputting z for hidden layerjAssigning different weights and obtaining the activation function f of the output layero() Can be defined as follows:
Figure BDA0001726495070000035
in the formula
Figure BDA0001726495070000036
Is the weight assigned to the connection between the jth hidden node and the output node; defining a weight vector
Figure BDA0001726495070000037
Wherein Wh
Figure BDA0001726495070000038
Set of weights for input node to hidden node connection, Wo
Figure BDA0001726495070000039
The weight set is the weight set of the connection of the hidden node and the output node;
to determine the response function of the equalizer, the ANN is first trained using known input-output data, and the weighting parameters of the ANN model are optimized.
Further, step S1 is specifically:
ANN model training is a potential optimization problem with the goal of achieving an optimal ANN weight set W*The required equalization mapping is efficiently implemented:
Figure BDA00017264950700000310
can be explained as follows: the goal of the ANN equalizer training is to model the inverse response of the optical channel; assume that the training set of the ANN is NtrOne input-output set { Yk,Xk}，k＝1,2,…,NtrWherein Y iskIs the input to the kth equalizer and is denoted as
Figure BDA00017264950700000311
XkIs a delayed version of the time offset τ, i.e. XkX (kT- τ); converting the problem of model training into an optimization problem:
Figure BDA00017264950700000312
error in the equation
Figure BDA0001726495070000041
Representing the training error of the ANN for the k symbol, wherein the error of the expression (10) adopts the square of the Euclidean distance as a measurement index;
to ensure the performance of the equalizer, the length of the input vector Y and the required number of training data N should be selected appropriatelytr(ii) a Optical length L and compensation parameter beta thereof2A modulation-dependent format; the number of taps of the equalizer can be estimated by convergence analysis: firstly, selecting the minimum possible value n to be 3 to train an ANN model, testing the performance of an equalizer, and then gradually reducing the value of n until the BER value reaches convergence;
after the input-output training data is selected, the optimal ANN weight W can be determined by solving the formula (10)*Solving the formula (10) by using a levenberg-marquardt algorithm; the calculation method of levenberg-marquardt algorithm comprises the following steps[7]：
W(i+1)＝W(i)-(H(i)+μI)-1▽f(i),i＝0,1,2,… (11)
V in formula(i)And H(i)Respectively, a gradient vector and a Hessian matrix of the objective function f (W), mu is a positive scalar, and I is an identity matrix; (11) formula (v) requires calculation of first and second derivative forms, i.e. + -(i)And H(i)The two derivatives are relatively expensive to calculate, and in order to increase the calculation speed, the partial derivative of the objective function f with respect to W is modified to be calculated[7]The calculation method comprises the following steps:
Figure BDA0001726495070000042
the ANN outputs a gradient vector of the result with respect to W of
Figure BDA0001726495070000043
In the formula
Figure BDA0001726495070000044
Figure BDA0001726495070000045
(j＝1,2,…,m)；
Figure BDA0001726495070000046
About weight
Figure BDA0001726495070000047
And
Figure BDA0001726495070000048
the partial derivatives of (a) are:
Figure BDA0001726495070000049
Figure BDA00017264950700000410
f in formula (II)'h(. o) and f'0Denotes the first derivative of the hidden and output layer activation functions respectively,
Figure BDA00017264950700000413
the analytic formula of the Hessian matrix H is approximated as:
H＝JTJ (15)
where J is the Jacobian matrix calculated as:
Figure BDA00017264950700000414
further, step S2 is specifically: after the optimal weight of the ANN model is obtained through model training, the data transmission is realized by using an equalizer; the input vector of the ANN model is represented as:
Yk＝[y-K+k,y-K+k+1…yk…yK+k-1,yK+k]T,k＝0,1,2…， (17)
in the formula ykK is the number of expected interference symbols for the transmission symbol of the kth time slot;
for each input vector Yk
Figure BDA0001726495070000051
The ANN model equalizer outputs the dispersion compensation symbol of the k time slot transmission symbol
Figure BDA0001726495070000052
Then, the corresponding transmission symbols are estimated by a decision rule
Figure BDA0001726495070000053
The symbol is the actual symbol akAn estimated value of (d);
because of the difference in environmental conditions, the dispersion values of the optical fibers also differ; the ANN model can adaptively adjust the weight value of the model by retraining the ANN model, thereby solving the problem of dispersion compensation under different environmental conditions; output of decision rule of the invention
Figure BDA0001726495070000054
The error that can be used to calculate the estimate is defined as:
Figure BDA0001726495070000055
the invention has the following beneficial effects:
the invention adopts the artificial neural network technology (belonging to the deep learning technology) to estimate the chromatic dispersion of optical communication, the calculation cost of the artificial neural network is mainly in the training stage, and the calculation cost in the prediction stage is lower. And the artificial neural network also has higher prediction accuracy, so the invention uses the artificial neural network to replace the maximum likelihood estimation, and aims to keep higher optical communication dispersion prediction accuracy and realize higher calculation speed.
The equalizer based on the ANN is divided into two stages, the first stage adopts the impulse response data of an optical channel to train the ANN, optimizes the model parameters of the ANN and establishes a nonlinear response model of the ANN; and in the second stage, the trained ANN equalizer is adopted to process the transmission data of the optical channel, so as to realize the estimation and compensation of the chromatic dispersion of the optical channel. Finally, simulation experiments are carried out according to the optical network scheme of the cloud computing data center, and results show that the equalizer based on the ANN improves the optical signal-to-noise ratio of optical communication and expands the maximum transmission distance of the optical communication.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a diagram of a short-distance optical communication model;
FIG. 2 is a schematic diagram of an ANN based nonlinear feedforward equalizer structure;
FIG. 3 is a graph of the effect of whether equalization has been performed on the received BER metric for different transmission distances (a)10km of fiber, (b)15km of fiber, and (c)20km of fiber;
fig. 4 is a graph of OSNR (optical signal to noise ratio) required for BER 10 "3 versus fiber length.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
The equalizer based on the ANN is divided into two stages, the first stage adopts the impulse response data of an optical channel to train the ANN, optimizes the model parameters of the ANN and establishes a nonlinear response model of the ANN; and in the second stage, the trained ANN equalizer is adopted to process the transmission data of the optical channel, so as to realize the estimation and compensation of the chromatic dispersion of the optical channel. Finally, simulation experiments are carried out according to the optical network scheme of the cloud computing data center, and results show that the equalizer based on the ANN improves the optical signal-to-noise ratio of optical communication and expands the maximum transmission distance of the optical communication.
Optical communication system model
The short-distance optical communication model mainly comprises a sending module, an optical channel and a receiving module, and a module diagram is shown in fig. 1.
The transmit module typically consists of a Directly Modulated Laser (DML) or an Externally Modulated Laser (EML). Assuming that the noise of the transmitter is white gaussian noise, the generalized transmit module outputs:
Figure BDA0001726495070000061
in the formula akFor independent and equally distributed input symbols, N is the total number of transmitted symbols, T-1F (t) is the symbol rate and the pulse shape. F (t) of DML is defined as:
Figure BDA0001726495070000062
where P (t) is the distribution of output energy,
Figure BDA0001726495070000063
the phase (t) is equal to the result of the DML frequency chirp, defined as integral[6]：
Figure BDA0001726495070000064
In which alpha is a linear factor, KvThe first term and the second term of the formula (3) represent transient chirp respectivelyAnd adiabatic chirp. The F (t) of EML is defined as:
Figure BDA0001726495070000065
assuming that the optical channel is a linear Single Mode Fiber (SMF), the transfer function is:
Figure BDA0001726495070000066
in the formula beta2Is the group velocity dispersion coefficient, and L is the fiber length. The optical fiber output signal has a bandwidth BoThe receiving signal of the receiver can be expressed as follows:
r(t)＝(x(t)*hf(t))*ho(t) (6)
in the formula, the operator "+" represents the convolution operation, hf(t) and ho(t) is the impulse response of the fiber and filter, respectively.
Noise n of receivere(t) includes shot noise and thermal noise. Direct photodetection schemes are generally employed in short-range communications because of their simplicity and low cost of implementation. The output signal of the output end low-pass filter is:
y(t)＝(|r(t)|2+ne(t))*he(t) (7)
in the formula he(t) is the impulse response of the low pass filter.
In the process of converting the received optical signal r (t) into the electrical signal y (t), nonlinear distortion occurs, mainly because the received signal loses phase information. Therefore, there is a need to add an equalizer to the digital signal processing module of the receiver, which should effectively compensate for the distortion of the signal.
Equalizer
The invention designs the equalizer based on the artificial neural network, and can effectively compensate nonlinear optical communication distortion. Assume that the input vector of the neural network is
Figure BDA0001726495070000071
Y is the input vector of the equalizer, Y represents the received distorted data, and the output vector is
Figure BDA0001726495070000072
Let n denote the number of taps required by the equalizer. The structure of the nonlinear feedforward equalizer based on the ANN is shown in FIG. 2, and comprises three layers: the device comprises an input layer, a hidden layer and an output layer, wherein the hidden layer and the output layer are respectively provided with m nodes and l nodes.
Assuming that the non-linear activation function of the hidden layer is fh() And processing the sum of each hidden layer node by adopting an activation function, wherein the output result can be expressed as the following form:
Figure BDA0001726495070000073
in the formula
Figure BDA0001726495070000074
Denoted as the weight assigned to the connection between the ith input node and the jth hidden node. Outputting z for hidden layerjAssigning different weights and obtaining the activation function f of the output layero() Can be defined as follows:
Figure BDA0001726495070000075
in the formula
Figure BDA0001726495070000076
Is the weight assigned to the connection between the jth hidden node and the output node. Defining a weight vector
Figure BDA0001726495070000077
Wherein Wh
Figure BDA0001726495070000078
For connecting input nodes with hidden nodesSet of weights of, Wo
Figure BDA0001726495070000079
Is the set of weights connecting the hidden node with the output node.
To determine the response function of the equalizer, the ANN is first trained using known input-output data, and the weighting parameters of the ANN model are optimized.
ANN model training phase
ANN model training is a potential optimization problem with the goal of achieving an optimal ANN weight set W*The required equalization mapping is efficiently implemented:
Figure BDA00017264950700000710
can be explained as follows: the goal of the ANN equalizer training is to model the inverse response of the optical channel. Assume that the training set of the ANN is NtrOne input-output set { Yk,Xk}，k＝1,2,…,NtrWherein Y iskIs the input to the kth equalizer and is denoted as
Figure BDA00017264950700000711
XkIs a delayed version of the time offset τ, i.e. XkX (kT- τ). Converting the problem of model training into an optimization problem:
Figure BDA0001726495070000081
error in the equation
Figure BDA0001726495070000082
Expressing the training error of the ANN for the k symbol, the error of the expression (10) adopts the square of the Euclidean distance as a measurement index.
To ensure the performance of the equalizer, the length of the input vector Y and the required number of training data N should be selected appropriatelytr. Optical length L and compensation parameter beta thereof2Depending on the format of the modulation. The number of taps of the equalizer can be estimated by convergence analysis: firstly, the methodThe minimum possible value n is selected to be 3, the ANN model is trained, the performance of the equalizer is tested, and then the value of n is gradually reduced until the BER value reaches convergence.
After the input-output training data is selected, the optimal ANN weight W can be determined by solving the formula (10)*Equation (10) is solved using the levenberg-marquardt algorithm. The calculation method of levenberg-marquardt algorithm comprises the following steps[7]：
W(i+1)＝W(i)-(H(i)+μI)-1▽f(i),i＝0,1,2,… (11)
V in formula(i)And H(i)The gradient vector and the Hessian matrix of the objective function f (W) are respectively, mu is a positive scalar, and I is an identity matrix. (11) Formula (v) requires calculation of first and second derivative forms, i.e. + -(i)And H(i)The two derivatives are relatively expensive to calculate, and in order to increase the calculation speed, the partial derivative of the objective function f with respect to W is modified to be calculated[7]The calculation method comprises the following steps:
Figure BDA0001726495070000083
the ANN outputs a gradient vector of the result with respect to W of
Figure BDA0001726495070000084
In the formula
Figure BDA0001726495070000085
Figure BDA0001726495070000086
(j＝1,2,…,m)。
Figure BDA0001726495070000087
About weight
Figure BDA0001726495070000088
And
Figure BDA0001726495070000089
the partial derivatives of (a) are:
Figure BDA00017264950700000810
Figure BDA00017264950700000811
f in formula (II)'h(. o) and f'0Denotes the first derivative of the hidden and output layer activation functions respectively,
Figure BDA00017264950700000814
the analytic formula of the Hessian matrix H is approximated as:
H＝JTJ (15)
where J is the Jacobian matrix calculated as:
Figure BDA00017264950700000815
data transmission phase
And after the optimal weight of the ANN model is obtained through model training, the equalizer is used for realizing data transmission. The input vector of the ANN model is represented as:
Yk＝[y-K+k,y-K+k+1…yk…yK+k-1,yK+k]T,k＝0,1,2…， (17)
in the formula ykK is the number of desired interference symbols for the transmission symbol of the K-th slot.
For each input vector Yk
Figure BDA0001726495070000091
The ANN model equalizer outputs the dispersion compensation symbol of the k time slot transmission symbol
Figure BDA0001726495070000092
Then, corresponding transmission is estimated through decision rulesSymbol input device
Figure BDA0001726495070000093
The symbol is the actual symbol akAn estimate of (d).
There will also be differences in the dispersion values of the fibers due to differences in environmental conditions. The ANN model can adaptively adjust the weight value of the model by retraining the ANN model, thereby solving the problem of dispersion compensation under different environmental conditions. Output of decision rule of the invention
Figure BDA0001726495070000094
The error that can be used to calculate the estimate is defined as:
Figure BDA0001726495070000095
simulation experiment and result analysis
Parameter and performance evaluation of simulation experiment
Two modulation formats, NRZ-OOK (non-return-to-zero OOK) and RZ-OOK (return-to-zero OOK), were used in the experiment. The experimental results of the model of the invention are compared with standard equalization techniques FFE (forward feedback equalization), DFE (decision feedback equalization) and MLSE (maximum likelihood sequence estimation equalization).
Simulation experiments are carried out based on OptiSystems computer optical simulation software, and simulated communication channel parameters are respectively as follows: wavelength 1.55 μm, dispersion coefficient-21 ps2Km, modulation format OOK (On-Off Keying), transmission bit number 16384, sequence mode PRBS (pseudo random binary sequence) code stream 2101, an optical filter, an electrical filter, a Gaussian band-pass filter, a Gaussian low-pass filter, a load resistor, 1K omega and a temperature of 300K.
Shot noise and thermal noise are defined as follows[5]：
Figure BDA0001726495070000096
Figure BDA0001726495070000097
Wherein q is the charge, I is the average photocurrent, BeLow pass filter of 3dB bandwidth, KBIs Boltzmann constant, T is temperature, RLIs a load resistor.
The performance of the equalization scheme is evaluated using the bit error rate BER, which is defined as the following equation in a Gaussian noise channel[5]：
Figure BDA0001726495070000098
Where erfc () represents the error compensation function and Q is the quality factor, calculated as:
Q＝(I1-I0)/(σ1+σ0) (22)
where I and σ are the mean and standard deviation of the received signal, respectively, and the subscripts ("1" and "0") indicate the type of bit transmitted (bit 1 or 0).
Results and analysis of the experiments
Current data center fiber optic networks typically employ 28G baud fiber, either as a 28G baud serial link or as a 4 x 28G baud parallel link (100Gbps rate). The transmission distance of a data center is assumed to be dozens of kilometers, and an OOK modulation scheme is used[8]. Suppose the bandwidth of the optical and electrical filters is Bo100GHz and Be＝21GHz。
Simulation experiments are respectively carried out on the three transmission distances of 10km, 15km and 20km, whether the influence of equalization processing on the received BER index is tested, and the experimental result is shown in figure 3. The equalizer parameters of L-10 km and L-15 km are assumed to be n-5 and m-5; the equalizer parameter, L-20 km, is n-7 and m-6. When the length of the optical fiber is less than 10km, the intersymbol interference distortion has no influence on the transmission distance, whereas when the length of the optical fiber is 10km, in order to maintain the BER at 10-9The cost of optical signal to noise ratio can be significantly reduced with an ANN-based equalizer, as shown in fig. 3 (a). For long-haul fibers (15km and 20km), lightThe distortion caused by the fiber dispersion is obviously increased, the transmission performance without the equalizer is obviously influenced, at this time, the dispersion is compensated by using the equalizer based on the ANN, the transmission performance is improved, and the transmission distance limit is increased, as shown in fig. 3(b) (c), it can be seen that the equalizer based on the ANN can compensate the dispersion of the optical fiber, and the transmission distance of the optical fiber is increased to 20 km.
FIG. 4 shows that BER 10 is obtained-3Required OSNR (optical Signal to noise ratio) versus fiber length, relating ANN model performance to FFE[9]、DFE[10]And MLSE[11]The equalizers were compared. It can be seen that the performance of the ANN model is closer to MLSE. According to the literature[12]The computational complexity of MLSE is O (2)n) And n is the memory size of MLSE (ref.)[12]Set n to 7), the complexity of the ANN equalizer is O (n × m), and the per bit symbol transmitted computation cost MLSE is 27The algorithm is 6 × 7-42, 128 multiplications. The computational cost of the ANN equalizer is much less than the MLSE.
The transmission distance of a data center is mostly several kilometers to several tens of kilometers, and the transmission speed is higher than 10Gbps, an optical network of the data center generally uses a direct modulation laser and a direct detection receiver, and the transmission distance of the network is mainly limited by the dispersion problem of optical communication along with the improvement of the data transmission bit rate. The invention adopts the artificial neural network technology to learn the dispersion phenomenon in the optical communication process, models the nonlinear distortion caused by dispersion quadrants, and adopts the equalizer based on the artificial neural network to estimate and automatically compensate the dispersion in the optical communication process. Simulation experiments are carried out according to the optical network scheme of the cloud computing data center, and results show that the distortion caused by long-distance optical fiber dispersion is large, the transmission performance of a non-equalizer is obviously influenced, the dispersion can be compensated by using the equalizer based on the artificial neural network, and the transmission performance is improved. The performance of the artificial neural network equalizer is closer to the MLSE, but the computation cost of the artificial neural network model is far less than that of the MLSE.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (4)

1. A data center optical communication dispersion estimation and management method based on deep learning is characterized by comprising the following steps:
s1, training the ANN by using the impulse response data of the optical channel, optimizing model parameters of the ANN, and establishing a nonlinear response model of the ANN;
s2, processing the transmission data of the optical channel by adopting a trained ANN equalizer to realize the estimation and compensation of optical channel dispersion;
step S1 specifically includes:
ANN model training is a potential optimization problem with the goal of achieving an optimal ANN weight set W*The required equalization mapping is efficiently implemented:
Figure FDA0002918056180000011
can be explained as follows: the goal of the ANN equalizer training is to model the inverse response of the optical channel; assume that the training set of the ANN is NtrOne input-output set { Yk,Xk}，k＝1,2,…,NtrWherein Y iskIs the input to the kth equalizer and is denoted as
Figure FDA0002918056180000012
XkIs a delayed version of the time offset τ, i.e. XkX (kT- τ); converting the problem of model training into an optimization problem:
Figure FDA0002918056180000013
error in the equation
Figure FDA0002918056180000014
Representing the training error of the ANN for the k symbol, wherein the error of the expression (10) adopts the square of the Euclidean distance as a measurement index;
to ensure the performance of the equalizer, the length of the input vector Y and the required number of training data N should be selected appropriatelytr(ii) a Optical length L and compensation parameter beta thereof2A modulation-dependent format; the number of taps of the equalizer can be estimated by convergence analysis: firstly, selecting the minimum possible value n to be 3 to train an ANN model, testing the performance of an equalizer, and then gradually reducing the value of n until the BER value reaches convergence;
after the input-output training data is selected, the optimal ANN weight W can be determined by solving the formula (10)*Solving the formula (10) by using a levenberg-marquardt algorithm; the calculation method of levenberg-marquardt algorithm comprises the following steps[7]：
Figure FDA0002918056180000015
In the formula
Figure FDA0002918056180000016
And H(i)Respectively, a gradient vector and a Hessian matrix of the objective function f (W), mu is a positive scalar, and I is an identity matrix; (11) the equations require the calculation of first and second derivative forms, i.e.
Figure FDA0002918056180000017
And H(i)The two derivatives are relatively expensive to calculate, and in order to increase the calculation speed, the partial derivative of the objective function f with respect to W is modified to be calculated[7]The calculation method comprises the following steps:
Figure FDA0002918056180000021
the ANN outputs a gradient vector of the result with respect to W of
Figure FDA0002918056180000022
In the formula
Figure FDA0002918056180000023
Figure FDA0002918056180000024
Figure FDA0002918056180000025
About weight
Figure FDA0002918056180000026
And
Figure FDA0002918056180000027
the partial derivatives of (a) are:
Figure FDA0002918056180000028
Figure FDA0002918056180000029
f in formula (II)'h(.) and f'0(.) represent the first derivative of the hidden and output layer activation functions respectively,
Figure FDA00029180561800000210
the analytic formula of the Hessian matrix H is approximated as:
H＝JTJ (15)
where J is the Jacobian matrix calculated as:
Figure FDA00029180561800000211
step S2 specifically includes: after the optimal weight of the ANN model is obtained through model training, the data transmission is realized by using an equalizer; the input vector of the ANN model is represented as:
Yk＝[y-K+k,y-K+k+1…yk…yK+k-1,yK+k]T,k＝0,1,2…， (17)
in the formula ykK is the number of expected interference symbols for the transmission symbol of the kth time slot;
for each input vector Yk
Figure FDA00029180561800000212
The ANN model equalizer outputs the dispersion compensation symbol of the k time slot transmission symbol
Figure FDA00029180561800000213
Then, the corresponding transmission symbols are estimated by a decision rule
Figure FDA00029180561800000214
The symbol is the actual symbol akAn estimated value of (d);
because of the difference in environmental conditions, the dispersion values of the optical fibers also differ; the ANN model can adaptively adjust the weight value of the model by retraining the ANN model, thereby solving the problem of dispersion compensation under different environmental conditions; output of decision rule of the invention
Figure FDA00029180561800000215
The error that can be used to calculate the estimate is defined as:
Figure FDA00029180561800000216
2. the deep learning-based data center optical communication dispersion estimation and management method according to claim 1, wherein in step S1, an optical communication system model is established, and the short-distance optical communication model mainly comprises a transmitting module, an optical channel and a receiving module; the sending module consists of a direct modulation laser or an external modulation laser; assuming that the noise of the transmitter is white gaussian noise, the generalized transmit module outputs:
Figure FDA0002918056180000031
in the formula akFor independent and equally distributed input symbols, N is the total number of transmitted symbols, T-1Is the symbol rate, F (t) is the pulse shape; f (t) of DML is defined as:
Figure FDA0002918056180000032
where P (t) is the distribution of output energy,
Figure FDA0002918056180000033
the phase (t) is equal to the result of the DML frequency chirp, defined as the integral form [6 ]]：
Figure FDA0002918056180000034
In which alpha is a linear factor, KvThe first term and the second term of the formula (3) represent transient chirp and adiabatic chirp, respectively; the F (t) of EML is defined as:
Figure FDA0002918056180000035
assuming that the optical channel is a linear Single Mode Fiber (SMF), the transfer function is:
Figure FDA0002918056180000036
in the formula beta2Is the group velocity dispersion coefficient, L is the fiber length; the optical fiber output signal has a bandwidth BoThe receiving signal of the receiver can be expressed as follows:
r(t)＝(x(t)*hf(t))*ho(t) (6)
in the formula, the operator "+" represents the convolution operation, hf(t) and ho(t) the impulse responses of the fiber and the filter, respectively;
noise n of receivere(t) includes shot noise and thermal noise; because the direct photoelectric detection scheme is simple to implement and low in cost, the direct photoelectric detection scheme is generally adopted in short-distance communication; the output signal of the output end low-pass filter is:
y(t)＝(|r(t)|2+ne(t))*he(t) (7)
in the formula he(t) is the impulse response of the low pass filter;
in the process of converting a received optical signal r (t) into an electrical signal y (t), nonlinear distortion occurs, mainly because the received signal loses phase information; therefore, there is a need to add an equalizer to the digital signal processing module of the receiver, which should effectively compensate for the distortion of the signal.
3. The method for estimating and managing chromatic dispersion in optical communication of data center based on deep learning of claim 1, wherein in step S2, the equalizer based on artificial neural network is used to effectively compensate nonlinear optical communication distortion, and the input vector of the neural network is assumed to be
Figure FDA0002918056180000041
Y is the input vector of the equalizer, Y represents the received distorted data, and the output vector is
Figure FDA0002918056180000042
Assuming that n represents the number of taps required for the equalizer, an ANN-based nonlinear feedforward equalizer structure is employed, which has three layers: the device comprises an input layer, a hidden layer and an output layer, wherein the hidden layer and the output layer are respectively provided with m nodes and l nodes.
4. The deep learning-based data center optical communication dispersion estimation and management method according to claim 3, wherein the nonlinear activation function of the hidden layer is assumed to be fh() And processing the sum of each hidden layer node by adopting an activation function, wherein the output result can be expressed as the following form:
Figure FDA0002918056180000043
in the formula
Figure FDA0002918056180000044
Representing the weight assigned to the connection between the ith input node and the jth hidden node; outputting z for hidden layerjAssigning different weights and obtaining the activation function f of the output layero() Can be defined as follows:
Figure FDA0002918056180000045
in the formula
Figure FDA0002918056180000046
Is the weight assigned to the connection between the jth hidden node and the output node; defining a weight vector
Figure FDA0002918056180000047
Wherein Wh
Figure FDA0002918056180000048
For connecting input nodes to hidden nodesSet of weights, Wo
Figure FDA0002918056180000049
The weight set is the weight set of the connection of the hidden node and the output node;
to determine the response function of the equalizer, the ANN is first trained using known input-output data, and the weighting parameters of the ANN model are optimized.
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