CN117675009B - Dispersion compensation method based on reserve pool calculation - Google Patents
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Abstract
The invention relates to a dispersion compensation method based on reserve pool calculation, which belongs to the technical field of optical communication and comprises the following steps: generating and sampling signals, and carrying out pulse shaping on the sampled signals through a root raised cosine filter; modulating the signal by an ideal intensity optical modulator, converting the electrical signal into an optical signal, and injecting the optical signal into an optical channel consisting of a standard single-mode optical fiber; the method comprises the steps of detecting the square rate of a photoelectric detector, converting an optical signal into an electric signal at a receiving end, converting the electric signal into a digital domain through an analog-to-digital converter, and carrying out matched filtering through a root raised cosine filter; and compensating the chromatic dispersion by using a trained reserve pool to obtain an output signal, and performing hard decision on the processed signal. The invention enables the reserve tank to have short-term memory capacity through random connection among neurons of the hidden layer, and the interior of the reserve tank has very rich dynamics characteristics, and the two characteristics of the reserve tank are utilized to compensate dispersion, so that the original signal is recovered.
Description
Technical Field
The invention relates to the technical field of optical communication, in particular to a dispersion compensation method based on reservoir calculation.
Background
Intensity Modulation Direct Detection (IMDD) has the advantages of simple structure and low power consumption in short-distance optical transmission, however, the serious limitation of the IMDD system is chromatic dispersion, because phase information is lost after direct detection, and in addition, the radio frequency power fading effect in the IMDD system can be caused by large signal bandwidth and long optical fiber transmission length; for IMDD transmission, the dispersion compensation technology mainly comprises an optical domain technology and an electrical domain technology, and the traditional optical technology needs optical devices such as a dispersion compensation optical fiber, a chirped apodized fiber Bragg grating, a ring resonator and the like; optical domain dispersion compensation is not widely used in short-range optical transmission because it is either costly or is greatly affected by nonlinear effects caused by ambient temperature and optical power. The advantage of the electrical domain dispersion compensation technique over optical techniques is that it does not require changes in the structure of the transmitter and receiver, nor introduces optical losses. The most common equalizers in the electrical domain are Feed Forward Equalizer (FFE) and Decision Feedback Equalizer (DFE). FFE is a linear equalizer, but its compensation performance is poor. In a direct detection system, linear optical distortions can become nonlinear impairments in the electrical domain due to square-law detection, and linear FFE cannot compensate for these nonlinear distortions. The DFE is to add a prediction filter based on FFE to reduce the interference variance at the equalizer output, thereby improving the bit error rate performance. One major problem faced by DFEs is that they also suffer from error propagation when false equalization decisions are passed to the feedback process.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a dispersion compensation method based on reservoir calculation, and solves the defects in the prior art.
The aim of the invention is achieved by the following technical scheme: a dispersion compensation method based on reservoir calculation, the dispersion compensation method comprising:
Generating an OOK signal, sampling each symbol of the OOK signal, and pulse shaping the sampled OOK signal through a root raised cosine filter;
Modulating the signal by an ideal intensity optical modulator, converting the electrical signal into an optical signal, and injecting the optical signal into an optical channel consisting of a standard single-mode optical fiber;
The method comprises the steps of detecting the square rate of a photoelectric detector, converting an optical signal into an electric signal at a receiving end, converting the electric signal into a digital domain through an analog-to-digital converter ADC, and performing matched filtering through a root raised cosine filter;
and compensating chromatic dispersion by using the trained reserve pool to obtain an output signal, and performing hard decision on the processed signal to obtain an OOK signal.
The reserve pool is based on a cyclic neural network, and a large-scale sparse random connection network is used for replacing a hidden layer of the traditional cyclic neural network. The training process of the algorithm is greatly simplified through the partial weight of the training network, and the defects that the traditional recurrent neural network structure is difficult to determine and the training process is too complex are overcome. Since the reserve tank has a neural network architecture with feedback connection, it can learn and memorize information observed in the past by forming a structure of information circulation, so that it can compensate nonlinear effects, namely, dispersion effects in IMDD systems;
The reserve tank comprises an input layer, a reservoir layer and an output layer; obtaining a weight matrix W in for connecting the input layer and the reservoir from the uniform distribution U (-1, 1), wherein the dimension is (N+b) multiplied by M; obtaining the probability of the interconnection of the neurons in the reservoir from the binary distribution, setting a weight matrix W res of the connected neurons in the reservoir according to the standard normal distribution N (0, 1), setting the dimension as MxM, and obtaining a state equation of a reservoir as x [ N ] =alpha.f (W in·u[n]+Wres.x [ N-1 ])+ (1-alpha). X [ N-1], wherein alpha represents the leakage rate, f represents the activation function, u [ N ] represents the input signal, N represents the input of the network, b represents the bias component, and M represents the number of the neurons in the reservoir;
By using Representing a weight matrix connecting the reservoir and the output, the dimension being MxL,/>Representing a weight matrix connecting the input and output layers, the dimension being (n+b) x L, the output signal/>, obtained by varying the state x [ N ] of the reservoir and the input signal u [ N ]Where L represents the output of the network.
Training the reservoir by an equalization process comprising equalizing the number of reservoir neurons, the spectral radius and the leak rate of three key parameters defining the reservoir structure to achieve the optimal effect of the reservoir.
The balancing process training the reserve tank includes:
Obtaining a weight matrix W in for connecting the input layer and the storage layer from uniform distribution U (-1, 1), generating a binary distribution reservoir weight matrix W res according to the sparsity, replacing non-zero elements of the reservoir weight matrix W res by normal distribution N (0, 1), and rescaling the reservoir weight matrix W res according to the size of the spectrum radius;
According to the input signal u [ n ], the state equation of the reserve tank is used to obtain the state x [ n ] =alpha.f (W in·u[n]+Wres. X [ n-1 ])+ (1-alpha) & x [ n-1] of the reserve tank, and according to the formula Training a weight matrix/>, connecting a reservoir and an output layer, using the state x [ n ] of the reservoir, the input signal u [ n ], and the target signal y [ n ]And a weight matrix connecting the input layer and the output layerWherein/> B represents the bias term and,Lambda is a ridge regularization factor, and I is an identity matrix with the size of M+N+1;
The input signal u [ n ] is expressed by the formula x [ n ] = α·f (W in·u[n]+Wres ·x [ n-1 ]) + (1- α) ·x [ n-1] and And calculating to obtain an output signal y [ n ].
The invention has the following advantages: a dispersion compensation method based on reservoir calculation, which enables the reservoir to have short-term memory capacity through random connection among neurons of a hidden layer, and the reservoir has very rich dynamics, and the dispersion is compensated by utilizing the two characteristics of the reservoir, so that an original signal is recovered.
Drawings
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 is a graph showing three key parameters as a function of fiber length, wherein (a) shows the change in bit error rate as a function of fiber length for different numbers of neurons in the reservoir; (b) The error rate is shown as a function of fiber length at different spectral radii; (c) The error rate is shown as a function of fiber length at different leak rates;
FIG. 3 is a graph showing the variation of bit error rate of a 32Gbaud OOK signal after SSMF transmission for 10km with the change of received optical power according to different equalization techniques;
fig. 4 is a graph showing the sensitivity cost of the received optical power according to the length of the optical fiber at the error rate of 10 -3 in different equalization technologies.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. The components of the embodiments of the present application generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Accordingly, the following detailed description of the embodiments of the application, as presented in conjunction with the accompanying drawings, is not intended to limit the scope of the application as claimed, but is merely representative of selected embodiments of the application. All other embodiments, which can be made by a person skilled in the art without making any inventive effort, are intended to be within the scope of the present application. The application is further described below with reference to the accompanying drawings.
As shown in fig. 1, the present invention relates to a dispersion compensation method based on reservoir calculation, which specifically includes the following steps:
step 1, generating an OOK signal with a bandwidth of 32GBaud, and sampling 8 samples for each symbol of the OOK signal.
And step 2, pulse shaping is carried out on the OOK signals after sampling through a root raised cosine filter (SRRC) with the roll-off factor of 0.1.
And 3, modulating the signal by an ideal intensity light modulator, and converting the electric signal into an optical signal.
Step 4, injecting an optical signal into an optical channel consisting of a Standard Single Mode Fiber (SSMF), wherein the dispersion parameter is d=16.4 ps/nm/km, and the SSMF model does not contain nonlinearity due to consideration of short distance.
And 5, at a receiving end, detecting the square rate of a Photoelectric Detector (PD) to convert the optical signal into an electric signal.
Step 6, converting the signal into a digital domain through an analog-to-digital converter ADC, and then performing matched filtering through a root raised cosine filter (SRRC).
And 7, compensating the chromatic dispersion by using a reserve pool calculation method.
And 8, finally, performing hard Decision (DEC) on the processed signal to obtain an OOK signal.
Further, the reservoir is mainly composed of three parts, an input layer, a hidden layer called reservoir, and an output layer. The weights (W in) connecting the input and reservoir are derived from the uniform distribution U (-1, 1). The probability of neuron interconnection in a reservoir is derived from a binary distribution. The weights (W res) between neurons in the reservoir determine the connectivity of the reservoir, and these non-zero weights (W res) are defined and remain fixed according to a standard normal distribution N (0, 1). Sparsity represents the proportion of non-zero elements in the reservoir matrix to total elements, where sparsity is set to 0.9. Neurons in the reservoir are leaky-integrate neurons, so the state equation of the reservoir is:
x[n]＝α·f(Win·u[n]+Wres·x[n-1])+(1-α)·x[n-1]
Where α is the leak rate, controlling the state of the reservoir at the last moment. f represents an activation function, here a hyperbolic tangent function is chosen. At the output level, the network reading y [ n ] is obtained by linearly changing the state of the reservoir x [ n ] and the input signal u [ n):
The evolution of the state of the pool depends only on the input and training is only used to optimize the output weights This optimization does not require complex and computationally expensive back propagation throughout the network as does RNN (time back propagation algorithm). Training may be performed by a single linear regression operation. The Mean Square Error (MSE) is used as the target loss function during the training phase and the least squares method is used to solve this linear regression problem. Computationally, this problem can be further handled as a pseudo-inverse problem.
The number of reservoir neurons, the spectral radius and the leak rate are key parameters in determining the reservoir structure, and therefore these parameters need to be explored to find the best equalization effect. In the simulation process, the principle of a control variable method is adopted, default values 300, 0.8 and 0.9 of the three parameters are respectively selected, and the transmission performance under different optical fiber distances is inspected.
As shown in fig. 2, the transmission variation of BER at different transmission distances is shown for a received optical power of-2 dBm. In order to be able to capture all sample features, the reservoir typically needs a sufficiently large network scale. As can be seen from graph (a) in fig. 2, reservoir performance increases with increasing number of neurons. It will be appreciated that the greater the number of neurons in the reservoir, the more neurons the signal will pass through, and the greater the nonlinear capability of the system. With the increasing number of neurons in the reservoir, the complexity of the network structure increases dramatically, and the phenomenon of "over-fitting" easily occurs, resulting in a decrease in the generalization ability of the network. Therefore, after increasing the number of neurons to 300, the system performance of 400 neurons and 500 neurons was hardly improved.
The spectrum radius is the maximum singular value of the connection weight matrix of the storage layer, and when the spectrum radius is smaller than 1 and larger than 0, the storage pool is guaranteed to have echo state characteristics. The spectral radius determines the storage capacity of the echo state network. Figure 2, panel (b), shows that the stability of the network is best at 0.8. In general, the greater the leak rate, the better the long-term memory capability of the network. As can be seen from fig. 2 (c), as the leak rate increases, the performance of the algorithm increases accordingly. When the leak rate exceeds 0.8, the performance of the reservoir tends to stabilize. Thus, the key parameter was chosen to be 300 neurons with a leak rate of 0.9 and a spectral radius of 0.8.
Further, the equalization process using the reservoir is:
training was performed using 20% of the symbol sequence, and 80% of the symbol sequence was used for testing.
The pool structure is initially set up. The weight matrix W in connecting the input layer and the storage layer is derived from the uniform distribution U (-1, 1). According to the sparsity, a binary distribution reservoir weight matrix W res is generated, and normal distribution N (0, 1) is used for replacing non-zero elements of the reservoir weight matrix W res. Finally, the reservoir weight matrix W res is rescaled according to the size of the spectral radius.
The pool structure is then trained.
The input signal is u n, and the state equation of the reserve tank is used to obtain the state x n of the reserve tank.
x[n]＝α·f(Win·u[n]+Wres·x[n-1])+(1-α)·x[n-1]
Training a weight matrix connecting the reservoir and the output layer using the state x [ n ], the input signal u [ n ], the target signal y [ n ] of the reservoir byAnd a weight matrix/>, connecting between the input layer and the output layer
Wherein the method comprises the steps ofB represents the bias term and, Lambda is a ridge regularization factor; i is an identity matrix of size M+N+1. Training may be performed by a single linear regression operation. This linear regression problem is solved using the Mean Square Error (MSE) as the target loss function and using the least squares method. Computationally, this problem can be further handled as a pseudo-inverse problem.
And finally, predicting the trained reserve pool. The input signal u n is calculated to obtain the output signal y n by the following two equations.
x[n]＝α·f(Win·u[n]+Wres·[n-1])+(1-α)·x[n-1]
To numerically compare the performance of reservoir dispersion compensation, a conventional Feed Forward Equalizer (FFE) and Decision Feedback Equalizer (DFE) were implemented in the receiver of the IMDD system. The number of taps of the FFE is set to 6, while the number of forward and reverse filter taps of the DFE are set to 4 and 2, respectively, and all of these taps are selected for optimal performance in the system. For both equalizers, the tap coefficients are adjusted using a Least Mean Square (LMS) algorithm. The equalizer is then modeled as a linear time invariant filter. The parameters of the reserve tank are set to the optimal parameters.
As shown in fig. 3, the relationship between the error rate and the received light power of three different equalization schemes at a transmission distance of 10km is shown. The reference system in the black curve represents the IMDD system without any dispersion compensation equalization. It can be seen that the reservoir equalizer is a better improvement over the other two equalization schemes at a fiber length of 10 km. The power loss of the receiver sensitivity has been reduced to-4 dBm at a bit error rate of 1 x 10 -3 compared to the reference system, which is increased by more than 1dB over the other two equalizers.
To study the effect of dispersion compensation over different fiber lengths, the received optical power sensitivity penalty is shown at bit error rates of 1x10 -3 over fiber lengths of 0km to 38km, as shown in fig. 4. It can be seen that the reservoir exhibits the lowest sensitivity penalty than the other two when the fiber length is less than 13 km. At fiber lengths of about 15km and 28km, the received optical power sensitivity of the reservoir had peaks indicating poor dispersion compensation in the system. This performance may be due to the limitation of the reservoir to compensate for dispersion at different transmission lengths, as shown by the PSD curves for different fiber lengths in fig. 1. The viable transmission distance of the reservoir can reach 38km in the range of 2dBm for the received optical power sensitivity penalty. When the length of the optical fiber exceeds 10km, the DFE exhibits better compensation performance than the FFE because the power attenuation is difficult to compensate with the linear equalizer.
The foregoing is merely a preferred embodiment of the invention, and it is to be understood that the invention is not limited to the form disclosed herein but is not to be construed as excluding other embodiments, but is capable of numerous other combinations, modifications and adaptations, and of being modified within the scope of the inventive concept described herein, by the foregoing teachings or by the skilled person or knowledge of the relevant art. And that modifications and variations which do not depart from the spirit and scope of the invention are intended to be within the scope of the appended claims.
Claims (2)
1. A dispersion compensation method based on reservoir calculation, characterized by: the dispersion compensation method comprises the following steps:
Generating an OOK signal, sampling each symbol of the OOK signal, and pulse shaping the sampled OOK signal through a root raised cosine filter;
Modulating the signal by an ideal intensity optical modulator, converting the electrical signal into an optical signal, and injecting the optical signal into an optical channel consisting of a standard single-mode optical fiber;
The method comprises the steps of detecting the square rate of a photoelectric detector, converting an optical signal into an electric signal at a receiving end, converting the electric signal into a digital domain through an analog-to-digital converter ADC, and performing matched filtering through a root raised cosine filter;
compensating chromatic dispersion by using a trained reserve pool to obtain an output signal, and performing hard decision on the processed signal to obtain an OOK signal;
The reserve tank replaces a hidden layer of a traditional circulating neural network with a large-scale sparse random connection network, the training process is simplified by training partial weights of the network, the reserve tank is provided with a neural network framework with feedback connection, and information observed in the past is learned and memorized by forming an information circulation structure, so that nonlinear effects, namely, chromatic dispersion effects in a IMDD system can be compensated;
The reserve tank comprises an input layer, a reservoir layer and an output layer; obtaining a weight matrix W in for connecting the input layer and the reservoir from the uniform distribution U (-1, 1), wherein the dimension is (N+b) multiplied by M; obtaining the probability of the interconnection of the neurons in the reservoir from the binary distribution, setting a weight matrix W res of the connected neurons in the reservoir according to the standard normal distribution N (0, 1), setting the dimension as MxM, and obtaining a state equation of a reservoir as x [ N ] =alpha.f (W in·u[n]+Wres.x [ N-1 ])+ (1-alpha). X [ N-1], wherein alpha represents the leakage rate, f represents the activation function, u [ N ] represents the input signal, N represents the input of the network, b represents the bias component, and M represents the number of the neurons in the reservoir;
By using Representing a weight matrix connecting the reservoir and the output, the dimension being MxL,/>Representing a weight matrix connecting the input and output layers, the dimension being (n+b) x L, the output signal/>, obtained by varying the state x [ N ] of the reservoir and the input signal u [ N ]Wherein L represents the output of the network;
training the reserve pool through the equalization process includes:
Obtaining a weight matrix W in for connecting the input layer and the storage layer from uniform distribution U (-1, 1), generating a binary distribution reservoir weight matrix W res according to the sparsity, replacing non-zero elements of the reservoir weight matrix W res by normal distribution N (0, 1), and rescaling the reservoir weight matrix W res according to the size of the spectrum radius;
According to the input signal u [ n ], the state equation of the reserve tank is used to obtain the state x [ n ] =alpha.f (W in·u[n]+Wres. X [ n-1 ])+ (1-alpha) & x [ n-1] of the reserve tank, and according to the formula Training a weight matrix connecting the reservoir and the output layer using the state x n of the reservoir, the input signal u n and the target signal y nAnd a weight matrix/>, connecting between the input layer and the output layerWherein/> B represents a bias term,/>Lambda is a ridge regularization factor, and I is an identity matrix with the size of M+N+1;
The input signal u [ n ] is expressed by the formula x [ n ] = α·f (W in·u[n]+Wres ·x [ n-1 ]) + (1- α) ·x [ n-1] and And calculating to obtain an output signal y [ n ].
2. A reservoir-based calculated dispersion compensation method as claimed in claim 1, wherein: training the reservoir by an equalization process comprising equalizing the number of reservoir neurons, the spectral radius and the leak rate of three key parameters defining the reservoir structure to achieve the optimal effect of the reservoir.
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