CN117675009B - A dispersion compensation method based on reserve pool calculation - Google Patents

Abstract

The present invention relates to a dispersion compensation method based on reserve pool calculation, which belongs to the field of optical communication technology, including: generating a signal and sampling it, and pulse shaping the sampled signal through a root raised cosine filter; modulating the signal through an ideal intensity optical modulator, converting the electrical signal into an optical signal, and injecting the optical signal into an optical channel composed of a standard single-mode optical fiber; converting the optical signal into an electrical signal at the receiving end through a photoelectric detector square rate detection, and converting the signal into a digital domain through an analog-to-digital converter, and then matching filtering through a root raised cosine filter; using a trained reserve pool to compensate for dispersion to obtain an output signal, and performing hard judgment on the processed signal. The present invention enables the reserve pool to have short-term memory capability through random connections between neurons in a hidden layer, and the reserve pool has very rich dynamic characteristics inside, and the two characteristics of the reserve pool are used to compensate for dispersion, thereby restoring the original signal.

Description

A dispersion compensation method based on reserve pool calculation

Technical Field

The present invention relates to the field of optical communication technology, and in particular to a dispersion compensation method based on reserve pool calculation.

Background technique

Intensity modulated direct detection (IMDD) has the advantages of simple structure and low power consumption in short-distance optical transmission. However, a serious limitation of IMDD systems is dispersion, because phase information will be lost after direct detection. In addition, large signal bandwidth and long fiber transmission length will lead to RF power fading effect in IMDD systems. For IMDD transmission, dispersion compensation technology mainly includes optical domain and electrical domain technology. Traditional optical technology requires optical devices such as dispersion compensating fiber, chirped fiber Bragg grating and ring resonator. Since optical domain dispersion compensation is either costly or greatly affected by nonlinear effects caused by ambient temperature and optical power, it has not been widely used in short-distance optical transmission. Compared with optical technology, the advantage of electrical domain dispersion compensation technology is that it does not require changing the structure of the transmitter and receiver, and does not introduce optical loss. The most common equalizers in the electrical domain are feedforward equalizer (FFE) and decision feedback equalizer (DFE). FFE is a linear equalizer, but its compensation performance is poor. In direct detection systems, due to square-law detection, linear optical distortion becomes nonlinear damage in the electrical domain, and linear FFE cannot compensate for these nonlinear distortions. DFE adds a prediction filter to FFE to reduce the interference variance at the equalizer output, thereby improving the bit error rate performance. However, a major problem faced by DFE is that they also suffer from error propagation when erroneous equalization decisions are passed to the feedback process.

Summary of the invention

The purpose of the present invention is to overcome the shortcomings of the prior art and provide a dispersion compensation method based on reserve pool calculation to solve the shortcomings of the prior art.

The object of the present invention is achieved by the following technical solution: a dispersion compensation method based on reserve pool calculation, the dispersion compensation method comprising:

Generate an OOK signal, sample each symbol of the OOK signal, and perform pulse shaping on the sampled OOK signal through a root raised cosine filter;

Modulating the signal through 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 optical signal is converted into an electrical signal at the receiving end through square rate detection of a photodetector, and after the signal is converted into a digital domain through an analog-to-digital converter ADC, matched filtering is performed through a root raised cosine filter;

The trained reserve pool is used to compensate for dispersion to obtain an output signal, and a hard decision is performed on the processed signal to obtain an OOK signal.

The reserve pool is a neural network based on a recurrent neural network, which replaces the hidden layer of the traditional recurrent neural network with a large-scale sparse randomly connected network. By training part of the weights of the network, the training process of the algorithm is greatly simplified, overcoming the shortcomings of the traditional recurrent neural network structure that is difficult to determine and the training process that is too complicated. Since the reserve pool has a feedback-connected neural network architecture, it can learn and memorize past observations by forming an information loop structure, enabling it to compensate for nonlinear effects, namely the dispersion effect in the IMDD system;

The reserve pool includes an input layer, a reservoir and an output layer; a weight matrix ^Win connecting the input layer and the reservoir is obtained from a uniform distribution U(-1,1), and the dimension is (N+b)×M; the probability of interconnection of neurons in the reservoir is obtained from a binary distribution, and a weight matrix W ^res connecting neurons in the reservoir is set according to a standard normal distribution N(0,1), and the dimension is M×M, and the state equation of the reserve pool is obtained as x[n]=α·f(W ⁱⁿ ·u[n]+W ^res ·x[n-1])+(1-α)·x[n-1], wherein α represents a leakage rate, f represents an activation function, u[n] represents an input signal, N represents an input of the network, b represents a bias component, and M represents the number of neurons in the reservoir;

use Represents the weight matrix connecting the reservoir and the output, with a dimension of M×L,/> Represents the weight matrix connecting the input layer and the output layer, with a dimension of (N+b)×L. The output signal is obtained by changing the state x[n] of the reservoir and the input signal u[n]/> Among them, L represents the output of the network.

The reserve pool is trained through an equalization process, which includes equalizing the number of reservoir neurons, the spectral radius and the leakage rate, three key parameters that determine the reservoir structure, so that the reserve pool achieves the best effect.

The balancing process for training the reserve pool includes:

The weight matrix W ⁱⁿ connecting the input layer and the storage layer is obtained from the uniform distribution U(-1,1). According to the size of sparsity, a reservoir weight matrix W ^res of binary distribution is generated. The non-zero elements of the reservoir weight matrix W ^res are replaced by the normal distribution N(0,1). According to the size of the spectral radius, the reservoir weight matrix W ^res is rescaled.

According to the input signal u[n], the state equation of the reservoir is used to obtain the state of the reservoir x[n] = α·f(W ⁱⁿ ·u[n]+W ^res ·x[n-1])+(1-α)·x[n-1], and according to the formula The weight matrix connecting the reservoir and the output layer is trained using the state x[n] of the reservoir, the input signal u[n] and the target signal y[n]/> and the weight matrix connecting the input layer and the output layer Among them,/> b represents the bias term, λ is the ridge regularization factor, I is an identity matrix of size M+N+1;

Input signal u[n], according to the formula x[n] = α·f(W ⁱⁿ ·u[n]+W ^res ·x[n-1])+(1-α)·x[n-1] and The output signal y[n] is calculated.

The present invention has the following advantages: a dispersion compensation method based on reserve pool calculation, which enables the reserve pool to have short-term memory capability through random connections between neurons in the hidden layer, and has very rich dynamic characteristics inside the reserve pool. These two characteristics of the reserve pool are used to compensate for dispersion, thereby restoring the original signal.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is a schematic diagram of the process of the present invention;

FIG2 is a comparative schematic diagram of the changes of three key parameters with the fiber length, wherein (a) shows the change of the bit error rate with the fiber length under different numbers of neurons in the reserve pool; (b) shows the change of the bit error rate with the fiber length under different spectral radii; (c) shows the change of the bit error rate with the fiber length under different leakage rates;

FIG3 is a schematic diagram of the curves showing the change of the bit error rate of a 32Gbaud OOK signal after 10km SSMF transmission with different equalization technologies as the received optical power improves;

FIG. 4 is a schematic diagram showing a curve of the received optical power sensitivity cost versus optical fiber length for different equalization technologies when the bit error rate is 10 ^-3 .

Detailed ways

In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of the present application provided below in conjunction with the drawings is not intended to limit the scope of protection of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present application. The present invention is further described below in conjunction with the drawings.

As shown in FIG1 , the present invention specifically relates to a dispersion compensation method based on reserve pool calculation, which specifically includes the following contents:

Step 1: Generate an OOK signal with a bandwidth of 32 GBaud, and sample 8 samples for each symbol of the OOK signal.

Step 2: The sampled OOK signal is pulse shaped by passing it through a root raised cosine filter (SRRC) with a roll-off factor of 0.1.

Step 3: Modulate the signal through an ideal intensity optical modulator to convert the electrical signal into an optical signal.

Step 4: Inject the optical signal into an optical channel composed of a standard single-mode optical fiber (SSMF), with a dispersion parameter of D=16.4ps/nm/km. Since a short distance is considered, the SSMF model does not include nonlinearity.

Step 5: At the receiving end, a photodetector (PD) square-rate detection converts the optical signal into an electrical signal.

Step 6: The signal is converted into the digital domain through an analog-to-digital converter (ADC), and then matched filtered through a root raised cosine filter (SRRC).

Step 7: Compensate for dispersion using the reserve pool calculation method.

Step 8: Finally, perform hard decision (DEC) on the processed signal to obtain the OOK signal.

Furthermore, the reservoir is mainly composed of three parts, the input layer, the hidden layer called the reservoir, and the output layer. The weights (W ⁱⁿ ) connecting the input layer and the reservoir are drawn from the uniform distribution U(-1,1). The probability of interconnection between neurons in the reservoir is drawn 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 according to the standard normal distribution N(0,1) and remain fixed. Sparsity represents the proportion of non-zero elements in the reservoir matrix to the total elements, and here the sparsity is set to 0.9. The neurons in the reservoir are leaky integrating 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 leakage rate, which controls the state of the reservoir at the last moment. f represents the activation function, and the hyperbolic tangent function is selected here. In the output layer, the network reading y[n] is obtained by linearly changing the state x[n] of the reservoir and the input signal u[n]:

The evolution of the state of the reservoir depends only on the input, and training is only used to optimize the output weights This optimization does not require complex and computationally expensive backpropagation through the entire network as in RNNs (backpropagation through time). Training can be performed with a single linear regression operation. Mean squared error (MSE) is used as the objective 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 treated as a pseudo-inverse problem.

The number of reservoir neurons, spectral radius and leakage rate are key parameters for determining the reservoir structure. Therefore, these parameters need to be explored to find the best balance effect. In the simulation process, the principle of the control variable method is adopted, and the default values of these three parameters are selected as 300, 0.8 and 0.9 respectively, and the transmission performance under different fiber distances is examined.

As shown in Figure 2, the transmission change of BER at different transmission distances when the received optical power is -2dBm is shown. In order to capture all sample features, the reserve pool usually requires a sufficiently large network scale. As can be seen from Figure (a) in Figure 2, the performance of the reserve pool increases with the increase in the number of neurons. It is not difficult to understand that the more neurons there are in the reserve layer, the more neurons the signal will pass through, and the stronger the nonlinear ability of the system will be. As the number of neurons in the reserve pool continues to increase, the complexity of the network structure increases dramatically, and the "overfitting" phenomenon is prone to occur, 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 has hardly improved.

The spectral radius is the maximum singular value of the connection weight matrix of the storage layer. When the spectral radius is less than 1 and greater than 0, the reserve pool is guaranteed to have echo state characteristics. The spectral radius determines the storage capacity of the echo state network. Graph (b) of Figure 2 shows that the stability of the network is best at 0.8. Generally speaking, the larger the leakage rate, the better the long-term memory capacity of the network. It can be seen from Graph (c) of Figure 2 that as the leakage rate increases, the performance of the algorithm also improves accordingly. When the leakage rate exceeds 0.8, the performance of the reserve pool tends to be stable. Therefore, the key parameters are selected as 300 neurons, a leakage rate of 0.9, and a spectral radius of 0.8.

Furthermore, the balancing process using the reserve pool is:

Use 20% of the symbol sequences for training and 80% of the symbol sequences for testing.

First, the reservoir structure is initialized. The weight matrix W in connecting the input layer and the storage layer is ^obtained from the uniform distribution U(-1,1). According to the size of the sparsity, the reservoir weight matrix W ^res of the binary distribution is generated, and the non-zero elements of the reservoir weight matrix W ^res are replaced by the normal distribution N(0,1). Finally, the reservoir weight matrix W ^res is rescaled according to the size of the spectral radius.

Then the reserve pool structure is trained.

The input signal is u[n], and the state equation of the reservoir is used to obtain the state of the reservoir x[n].

x[n]＝α·f( ^Win ·u[n]+ ^Wres ·x[n-1])+(1-α)·x[n-1]

The weight matrix connecting the reservoir and the output layer is trained using the state x[n] of the reservoir, the input signal u[n], and the target signal y[n] through the following formula: and the weight matrix connecting the input layer and the output layer/>

in b represents the bias term, λ is the ridge regularization factor; I is an identity matrix of size M+N+1. Training can be performed by a single linear regression operation. The mean squared error (MSE) is used as the objective loss function and the least squares method is used to solve this linear regression problem. Computationally, this problem can be further treated as a pseudo-inverse problem.

Finally, the trained reserve pool is predicted. The input signal u[n] is calculated by the following two equations to obtain the output signal y[n].

x[n]＝α·f( ^Win ·u[n]+ ^Wres ·[n-1])+(1-α)·x[n-1]

To numerically compare the performance of the reservoir dispersion compensation, a conventional feed-forward equalizer (FFE) and a decision feedback equalizer (DFE) were implemented in the receiver of the IMDD system. The number of taps of the FFE was set to 6, while the number of taps of the forward filter and the reverse filter of the DFE were set to 4 and 2, respectively, and all these taps were selected to obtain the best performance in this system. For both equalizers, the tap coefficients were adjusted using the least mean square (LMS) algorithm. The equalizers were then modeled as linear time-invariant electrical filters. The parameters of the reservoir were set to the optimal parameters.

As shown in Figure 3, the relationship between the bit error rate and the received optical power of three different equalization schemes at a transmission distance of 10 km is shown. The reference system in the black curve represents the IMDD system without any dispersion compensation equalization. It can be seen that the reserve pool equalizer has a better improvement than the other two equalization schemes at a fiber length of 10km. Compared with the reference system, the power loss of the receiver sensitivity at a bit error rate of 1× ^10-3 has been reduced to -4dBm, which is more than 1dB higher than the other two equalizers.

In order to study the dispersion compensation effect at different fiber lengths, as shown in Figure 4, the received optical power sensitivity penalty at a bit error rate of 1× ^10-3 at fiber lengths from 0km to 38km is shown. It can be seen that when the fiber length is less than 13km, the reserve pool shows the lowest sensitivity penalty than the other two. When the fiber length is about 15km and 28km, the received optical power sensitivity penalty of the reserve pool has some peaks, indicating that the dispersion compensation effect in the system is poor. This performance may be caused by the limitation of the reserve pool in dispersion compensation at different transmission lengths, as shown in the PSD curves of different fiber lengths in Figure 1. Within the range of 2dBm received optical power sensitivity penalty, the feasible transmission distance of the reserve pool can reach 38km. When the fiber length exceeds 10km, DFE shows better compensation performance than FFE, because power attenuation is difficult to compensate with a linear equalizer.

The above is only a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used for various other combinations, modifications and improvements, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge of the relevant field. The changes and modifications made by those skilled in the art do not deviate from the spirit and scope of the present invention, and should be within the scope of protection of the claims attached to the present invention.

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]+W^res.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]+W^res. 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]+W^res ·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.