CN113612707A - IM/DD-OFDM/OQAM-PON system channel estimation method based on ANN _ LS - Google Patents

Abstract

The invention discloses an IM/DD-OFDM/OQAM-PON system channel estimation method based on ANN _ LS, which comprises the steps of firstly collecting time domain data and using the time domain data to carry out forward propagation; then, a gradient descent algorithm is used for back propagation, so that W and b of the algorithm are continuously adjusted, the sum of squares of errors of the whole algorithm is minimized, a Transfer Function (TF) of the system is further obtained, and finally channel estimation is carried out in a frequency domain by LS. Simulation results show that when the optical fiber transmission distance is long, compared with an ANN-based channel estimator algorithm, the ANN-LS algorithm can obtain higher CE precision and has better system optimization performance.

Description

IM/DD-OFDM/OQAM-PON system channel estimation method based on ANN _ LS

Technical Field

The invention belongs to the technical field of optical communication, and particularly relates to a channel estimation method of an IM/DD-OFDM/OQAM-PON system.

Background

The OFDM-PON with Cyclic Prefix (CP) can effectively reduce Inter-Symbol Interference (ISI) caused by Dispersion (CD) and Inter-Polarization crosstalk (PMD) induced by Polarization Mode Dispersion (PMD) in a fiber communication system. In addition, the sub-carriers in the system are orthogonal to each other, Interference-free superposition of different frequency spectrums is realized, and Inter-Carrier Interference (ICI) can be effectively resisted. But the insertion of the CP reduces the spectrum utilization of the system. Aiming at the defects existing in the OFDM-PON system, orthogonal frequency division multiplexing/offset quadrature amplitude modulation (OFDM/OQAM) is proposed in optical communication, and is considered to be a good alternative solution for the traditional OFDM-PON technology.

Compared with OFDM, OFDM/OQAM adopts a prototype filter with good time-frequency focusing characteristics to suppress ISI and ICI, and does not need to insert CP or guard interval, thereby effectively improving the frequency spectrum utilization rate of the system and reducing out-of-band radiation. In recent years, the OFDM/OQAM system has become one of the alternatives in wireless area network, coherent optical communication, intensity modulation and direct detection (IM/DD) transmission systems, provides a good solution for high-speed and long-distance transmission, and has a strong development potential.

Because the OFDM/OQAM system is only orthogonal in the real number domain, Intrinsic Imaginary Interference (IMI) is generated when the system transmits a real number symbol, thereby affecting the performance of the system, and these characteristics make the optical OFDM/OQAM system require accurate Channel Estimation (CE) to suppress the influence of the IMI. In the channel estimation algorithm based on the ANN, the neural network has three layers including two hidden layers, and the calculation workload is large. Compared with the method based on the ANN channel estimation algorithm, the method based on the ANN _ LS algorithm has the advantage of low computational complexity. In the channel estimation algorithm based on the ANN _ LS, the neural network has only two layers except the input layer, and the number of hidden layers is changed into 1, so that the calculation complexity is greatly reduced. The complexity is lower as the number of layers is smaller, the complexity of the forward/backward propagation of the neural network is proportional to the quantity of parameters, and the quantity of the parameters is the sum of all the weights (W) and all the thresholds (b).

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides an IM/DD-OFDM/OQAM-PON system channel estimation method based on ANN _ LS, which comprises the steps of firstly collecting time domain data and using the time domain data for forward propagation; then, a gradient descent algorithm is used for back propagation, so that W and b of the algorithm are continuously adjusted, the sum of squares of errors of the whole algorithm is minimized, a Transfer Function (TF) of the system is further obtained, and finally channel estimation is carried out in a frequency domain by LS. Simulation results show that when the optical fiber transmission distance is long, compared with an ANN-based channel estimator algorithm, the ANN-LS algorithm can obtain higher CE precision and has better system optimization performance.

The technical scheme adopted by the invention for solving the technical problem comprises the following steps:

step 1: constructing an ANN neural network;

the ANN neural network comprises an input layer, a hidden layer and an output layer; the number of the neurons of the input layer and the output layer is n, and the number of the neurons of the hidden layer is p;

step 2: initializing all weights and biases in the ANN neural network;

and step 3: collecting training data { x⁽¹⁾，x⁽²⁾，…，x⁽ⁿ⁾}；

After the binary sequence is modulated, IFFT transformed and filtered, the target data is collected and is marked as { y⁽¹⁾，y⁽²⁾，…，y⁽ⁿ⁾}; then the target data is sampled and distinguished through a Mach-Zehnder modulator, an optical fiber and photoelectric conversion, and then the target data is collected as training data and marked as { x⁽¹⁾，x⁽²⁾，…，x⁽ⁿ⁾In which x^(j)And y^(j)One-to-one correspondence, j 1, 2.., n;

and 4, step 4: forward propagation;

step 4-1: the feedforward of the ANN neural network is to obtain output according to input; input training data as { x⁽¹⁾，x⁽²⁾，…，x⁽ⁿ⁾H represents the output vector of the hidden layer_jThen the output of the hidden layer is represented as:

h_j＝f(z_j)

wherein, ω is_ijIs the weight between the ith neuron of the input layer and the jth neuron of the hidden layer, b_jIs the bias of the jth neuron of the hidden layer; f (-) its activation function, choose tanh function, its expression is

Step 4-2: the optimal estimated value of the output layer is represented as y_predExpressed as:

wherein, ω is_jkIs the connection weight between the jth neuron of the hidden layer and the kth neuron of the output layer, b_kIs the deviation of the kth neuron of the output layer;

step 4-3: a feedforward loss function;

the squared error function is used as a feedforward loss function and is expressed as:

lose＝mean(square(y-y_pred))

calculating an error between the predicted data and the target data using a loss function;

and 5: a back propagation algorithm;

step 5-1: using SGD as back propagation, and continuously adjusting the weight and deviation of the network;

step 5-2: the back propagation loss function comprises a plurality of multivariate functions of weights and thresholds, represented as:

L(ω_ij，ω_jk，b_j，b_k)

the derivative of the loss function with respect to weight and bias is expressed as:

wherein the content of the first and second substances,

is the gradient of the jth neuron of the first hidden layer;

step 5-3: the update of the weights and biases is represented as:

wherein, the negative sign represents gradient decrease, eta and n are constants; eta is the learning rate and determines the training speed of the network; n is the batch size;

step 6: evaluating the model;

the accuracy is obtained through the estimation of the R party, so that the effect of the ANN neural network training is judged, namely:

and 7: performing channel estimation in a frequency domain by using LS;

step 7-1: will predict data y_predRemoving the filter, and then performing FFT to obtain:

Y＝XH+W

h is a frequency domain channel matrix, X is a frequency domain transmitting signal matrix, Y is a frequency domain receiving signal matrix, and W is a Gaussian noise matrix;

step 7-2: the channel estimation for the frequency domain LS is:

wherein, X_PAnd Y_PIndicating the transmitted and received data, respectively, for the pilot locations.

Preferably, n is 10 and p is 10.

The invention has the following beneficial effects:

1. compared with an ANN-based channel estimator algorithm, the method of the invention can obtain higher CE precision and better system optimization performance based on the ANN-LS algorithm when the optical fiber transmission distance is longer.

2. The method of the invention carries out feedforward on training data, and then uses a random gradient descent algorithm to continuously adjust the weight and the deviation, thereby reducing the mean square error of predicted data and target data to the maximum extent, and proving that the complexity of the channel estimation algorithm based on ANN LS is lower.

Drawings

Fig. 1 is a schematic diagram of the uplink transmission of the OFDM/OQAM-PON according to the present invention.

FIG. 2 is a diagram of the ANN and ANN _ LS of the present invention, (a) a schematic diagram of the ANN architecture, and (b) a system block diagram of the ANN _ LS based algorithm.

Fig. 3 is a BER curve over transmission distance for an ANN-based CE algorithm and an ANN _ LS-based CE algorithm according to an embodiment of the present invention.

Figure 4 is a graph of BER versus transmission distance for different laser linewidths in accordance with an embodiment of the present invention.

Figure 5 is a graph of BER performance for different training times for embodiments of the invention at fiber lengths of 50km and 60 km.

Figure 6 is a graph of BER performance for different training set sizes for an embodiment of the present invention,

Detailed Description

The invention is further illustrated with reference to the following figures and examples.

An IM/DD-OFDM/OQAM-PON system channel estimation method based on ANN _ LS comprises the following steps:

step 1: constructing an ANN neural network;

the ANN neural network comprises an input layer, a hidden layer and an output layer; the number of the neurons of the input layer and the output layer is n, and the number of the neurons of the hidden layer is p;

step 2: initializing all weights and biases in the ANN neural network;

and step 3: collecting training data { x⁽¹⁾，x⁽²⁾，…，x⁽ⁿ⁾}；

After the binary sequence is modulated, IFFT transformed and filtered, the target data is collected and is marked as { y⁽¹⁾，y⁽²⁾，…，y⁽ⁿ⁾}; then the target data is sampled and distinguished through a Mach-Zehnder modulator, an optical fiber and photoelectric conversion, and then the target data is collected as training data and marked as { x⁽¹⁾，x⁽²⁾，…，x⁽ⁿ⁾In which x^(j)And y^(j)One-to-one correspondence, j 1, 2.., n;

and 4, step 4: forward propagation;

step 4-1: the feedforward of the ANN neural network is to obtain output according to input; input training data as { x⁽¹⁾，x⁽²⁾，…，x⁽ⁿ⁾H represents the output vector of the hidden layer_jThen the output of the hidden layer is represented as:

h_j＝f(z_j)

wherein, ω is_ijIs the weight between the ith neuron of the input layer and the jth neuron of the hidden layer, b_jIs the bias of the jth neuron of the hidden layer; f (-) its activation function, choose tanh function, its expression is

Step 4-2: the optimal estimated value of the output layer is represented as y_predExpressed as:

wherein, ω is_jkIs the connection weight between the jth neuron of the hidden layer and the kth neuron of the output layer, b_kIs the deviation of the kth neuron of the output layer;

step 4-3: a feedforward loss function;

the squared error function is used as a feedforward loss function and is expressed as:

lose＝mean(square(y-y_pred))

calculating an error between the predicted data and the target data using a loss function;

and 5: a back propagation algorithm;

step 5-1: using SGD as back propagation, and continuously adjusting the weight and deviation of the network;

step 5-2: the back propagation loss function comprises a plurality of multivariate functions of weights and thresholds, represented as:

L(ω_ij，ω_jk，b_j，b_k)

the derivative of the loss function with respect to weight and bias is expressed as:

wherein the content of the first and second substances,

is the gradient of the jth neuron of the first hidden layer;

step 5-3: the update of the weights and biases is represented as:

wherein, the negative sign represents gradient decrease, eta and n are constants; eta is the learning rate and determines the training speed of the network; n is the batch size;

step 6: evaluating the model;

the accuracy is obtained through the estimation of the R party, so that the effect of the ANN neural network training is judged, namely:

and 7: performing channel estimation in a frequency domain by using LS;

step 7-1: will predict data y_predRemoving the filter, and then performing FFT to obtain:

Y＝XH+W

h is a frequency domain channel matrix, X is a frequency domain transmitting signal matrix, Y is a frequency domain receiving signal matrix, and W is a Gaussian noise matrix;

step 7-2: the channel estimation for the frequency domain LS is:

wherein, X_PAnd Y_PIndicating the transmitted and received data, respectively, for the pilot locations.

The specific embodiment is as follows:

as shown in fig. 1, an electrical signal generated by an OFDM/OQAM transmitting end is modulated on a specific subcarrier by IFFT, then a transmitting signal is modulated on an optical carrier by mach-zehnder, and the uplink OFDM/OQAM signals are coupled and transmitted to an optical fiber line for transmission. After the optical signal is transmitted through a standard single-mode optical fiber, the optical signal is received and demodulated at a receiving end in a mode of optical intensity modulation and direct detection. At the transmitting end, the input binary data stream is encoded into baseband symbols a_m，n，m＝0，1，2，…，M-1，n＝0，1，2，…，N_s-1 where M is the number of subcarriers, N_sThe number of baseband symbols. After QAM mapping, the real part and imaginary part of the data symbol are extracted. Through IFFT transformation and a prototype filter bank, data is converted into serial data flow, and then signals sent by an OFDM/OQAM-PON system at a transmitting end are obtained, wherein the expression is

Wherein, a_m，nAt the m < th >N-th real-valued symbol, g, transmitted on a subcarrier_m，n(t) represents the filter function at the time-frequency coordinate point (m, n), and g (t) is the basis function of the prototype filter. v. of₀And τ₀The sub-carrier interval and the time interval of transmitting signals of the OFDM/OQAM system are respectively satisfied

After transmission over the optical fiber, the received OFDM/OQAM signal can be expressed as

Where h (t) is the channel transmission response and η (t) is the Amplified Spontaneous Emission (ASE) noise.

In PON transmissions at a distance of 20-100km, the maximum delay spread Δ of the channel is usually small, and therefore:

therefore, the OFDM/OQAM signal can be rewritten as

In the formula

Definition of

Thus, it is further rewritten as

The above formula can be rewritten as:

wherein the content of the first and second substances,

is a purely imaginary term of the intrinsic imaginary part interference

Is the interference weight of the prototype filter, and represents the correlation degree of the OFDM/OQAM symbol at (m, n) and (m + p, n + q). Order to

The least squares channel estimation can be processed as

Fig. 2(a) is a schematic diagram of an ANN _ LS based CE algorithm, including an input layer, an output layer, and a hidden layer. The number of neurons in the hidden layer was 10, respectively. The neural network includes neurons having a nonlinear activation function in an input layer and a hidden layer, and neurons having a linear activation function in an output layer. (b) Is a system block diagram of an ANN _ LS based algorithm. The application of the algorithm considers three phases. Firstly, ANN is fitted with time domain data to obtain predicted data

The second stage is the LS channel estimation of the frequency domain prediction data. First mapping the binary sequence by QAM and then inserting the pilot data X_PWill valid data X_DAnd X_PAnd performing IFFT transformation and filtering to obtain target data. After sending data over the optical channel, training data and test data are collected. Second, the training data is fed forward and then the weights and biases are iteratively adjusted using a Steepest Gradient (SGD) method to minimize Mean Square Error (MSE) of the predicted and target data.And finally, performing frequency domain LS channel estimation on the predicted data after FFT.

In order to verify the prediction performance of the trained ANN algorithm, a group of test sets with about 10000 data are randomly collected, and after 2000 iterations, the iteration step length is 0.1, and the learning rate is 0.1. The mean square error of the raw data was 0.2363308099897791, with an accuracy of 0.053940237. The mean square error after the ANN training is 0.061629243 and the accuracy is 0.93331087. Therefore, the neural network model trained by the ANN can reduce the mean square error and improve the accuracy.

As shown in table 1, in the transmitter, 20Gbaud baseband OFDM/OQAM signals are generated in MATLAB, and then the virtual-real separation is converted into two analog streams by digital-to-analog converters (DACs), respectively. The OFDM/OQAM signal is converted to a Double Sideband (DSB) optical signal using a Mach-Zehnder modulator (MZM). The two optical signals are combined by the PC. An Isotropic Orthogonal Transformation Algorithm (IOTA) is used as a prototype filter and a filter bank is constructed. The pulse length of the prototype filter is 4, M is 1024, the total number of subcarriers is 256, and the number of symbols of each subcarrier is 40. And then through Standard Single Mode Fiber (SSMF). At the receiving end, the DSB optical OFDM/OQAM signal is divided by PS and detected by two photodiodes respectively. The analog signal is then converted to a discrete digital signal using an analog-to-digital converter (ADC). In MATLAB, the received electrical OFDM/OQAM signal is decoded offline.

TABLE 1 simulation system parameter Table

Parameter(s)	Value taking	Parameter(s)	Value taking
				Number of subcarriers	256	DAC/ADC rates	20Gsample/s
Prototype filter	IOTA	Bandwidth of	20GHz
				Laser output power	0dBm	Transmission distance		20 30 40 50 60 70 80 90 100km
Signal rate	20Gbaud	Optical fiber dispersion	16.75ps/km/nm
				Cyclic prefix length	0	Attenuation coefficient of optical fiber	0.2dB/km
Modulation system	QPSK	Optical fiber group velocity delay	0.2ps/km
				Laser wavelength	1550nm	Nonlinear coefficient of optical fiber	1.2W-1·km-1

Fig. 3 shows BER performance of an ANN-based CE algorithm and an ANN _ LS-based CE algorithm IM/DD-OFDM/OQAM system. As can be seen from the figure, as the transmission distance of the optical fiber increases, the BER gradually increases, which means that the CD and PMD interference to the channel will also increase. After SSMF transmission, the channel performance optimization of the CE algorithm based on ANN _ LS is obviously better than that of the CE algorithm based on ANN. The ANN _ LS based CE algorithm can optimize the system performance by an order of magnitude under certain conditions compared to the ANN based CE algorithm when the transmission distance of the optical fiber is between 20km and 100 km. The BER of the ANN based CE algorithm and the ANN _ LS based CE algorithm was 8.1055X 10-3 and 2.7344X 10-3, respectively, in the case of an optical fiber length of 40 km. The BER of the CE algorithm based on ANN _ LS was improved by 34% compared to the CE algorithm based on ANN. The CE algorithm based on ANN _ LS can effectively reduce the dispersion of the channel, and the robustness of the channel to the IMI effect is improved. The BER of the CE algorithm based on ANN _ LS is an order of magnitude better than that of the CE algorithm based on ANN with fiber lengths of 20km, 30km and 50 km. The BER of the ANN based CE algorithm and the ANN _ LS based CE algorithm was 5.8545X 10-2 and 5.1563X 10-2, respectively, in the case where the optical fiber length was 100 km. The optimization performance of the CE algorithm based on the ANN _ LS is slightly better than that of the CE algorithm based on the ANN. When the BER of the system is 10 "2, the transmission distance of the CE algorithm based on ANN _ LS can be increased by about 10km, compared to the CE algorithm based on ANN. Therefore, it can be concluded that the ANN _ LS based CE algorithm can effectively suppress the IMI and obtain a more accurate CE.

In fig. 4, the BER is plotted against transmission distance for different laser linewidths. The proposed ANN _ LS based CE algorithm has higher accuracy than the ANN based CE algorithm as the laser linewidth increases, indicating that the ANN _ LS based CE algorithm can improve the tolerance of the laser linewidth.

In fig. 5, the correlation between BER and training times of the CE algorithm based on ANN _ LS was studied. The fiber lengths of the OFDM/OQAM-PON systems were set to 50km and 60km, respectively. The BER of the system varies with the number of training times, which means that CE accuracy is affected by the number of training times. In the simulation of the present embodiment, the training effect of the CE algorithm based on ANN _ LS is optimal when the number of times of training is 2000. As shown in fig. 5, if the number of training times is insufficient (e.g., 200 and 800 times), the accuracy of CE may be reduced. Because of the small number of training times, the trained TF is not well generalized. Furthermore, if the number of training times is too large (e.g., 6000 and 10000 times), the system TF is overfit, and the accuracy of CE is reduced. Therefore, the system performance can be improved by reasonably selecting the training times.

In fig. 6, the correlation between BER and training set size of the CE algorithm based on ANN _ LS was studied. The fiber lengths of the OFDM/OQAM-PON systems were set to 50km and 60km, respectively. The BER of the system varies with the training set size, which means that CE accuracy is affected by the training set size. The results show that the training effect of the ANN _ LS based CE algorithm is optimal when the number of subcarriers of the training set is 256, and further increasing the training set size does not reduce the BER of the system. As shown in FIG. 6, if the training set size is insufficient (e.g., 64 and 128 sizes), the accuracy of the CE may be reduced because the features of the smaller training set do not generalize well to the test set. Therefore, a reasonable selection of training set size may improve system performance.

On the basis of the specific embodiment, the method is realized by carrying out combined simulation on Python, Matlab and Optisystem software, the performance of the method is evaluated by simulation, and the feasibility of the method is proved by analysis.

Claims (2)

1. An IM/DD-OFDM/OQAM-PON system channel estimation method based on ANN _ LS is characterized by comprising the following steps:

step 1: constructing an ANN neural network;

the ANN neural network comprises an input layer, a hidden layer and an output layer; the number of the neurons of the input layer and the output layer is n, and the number of the neurons of the hidden layer is p;

step 2: initializing all weights and biases in the ANN neural network;

and step 3: collecting training data { x⁽¹⁾，x⁽²⁾，…，x⁽ⁿ⁾}；

After the binary sequence is modulated, IFFT transformed and filtered, the target data is collected and is marked as { y⁽¹⁾，y⁽²⁾，…，y⁽ⁿ⁾}; then the target data is sampled and distinguished through a Mach-Zehnder modulator, an optical fiber and photoelectric conversion, and then the target data is collected as training data and marked as { x⁽¹⁾，x⁽²⁾，…，x⁽ⁿ⁾In which x^(j)And y^(j)One-to-one correspondence, j 1, 2.., n;

and 4, step 4: forward propagation;

step 4-1: the feedforward of the ANN neural network is to obtain output according to input; input training data as { x⁽¹⁾，x⁽²⁾，…，x⁽ⁿ⁾H represents the output vector of the hidden layer_jThen the output of the hidden layer is represented as:

h_j＝f(z_j)

wherein, ω is_ijIs the weight between the ith neuron of the input layer and the jth neuron of the hidden layer, b_jIs the bias of the jth neuron of the hidden layer; f (-) its activation function, choose tanh function, its expression is

Step 4-2: the optimal estimated value of the output layer is represented as y_predExpressed as:

wherein, ω is_jkIs the connection weight between the jth neuron of the hidden layer and the kth neuron of the output layer, b_kIs the deviation of the kth neuron of the output layer;

step 4-3: a feedforward loss function;

the squared error function is used as a feedforward loss function and is expressed as:

lose＝mean(square(y-y_pred))

calculating an error between the predicted data and the target data using a loss function;

and 5: a back propagation algorithm;

step 5-1: using SGD as back propagation, and continuously adjusting the weight and deviation of the network;

step 5-2: the back propagation loss function comprises a plurality of multivariate functions of weights and thresholds, represented as:

L(ω_ij，ω_jk，b_j，b_k)

the derivative of the loss function with respect to weight and bias is expressed as:

wherein the content of the first and second substances,

is the gradient of the jth neuron of the first hidden layer;

step 5-3: the update of the weights and biases is represented as:

wherein, the negative sign represents gradient decrease, eta and n are constants; eta is the learning rate and determines the training speed of the network; n is the batch size;

step 6: evaluating the model;

the accuracy is obtained through the estimation of the R party, so that the effect of the ANN neural network training is judged, namely:

and 7: performing channel estimation in a frequency domain by using LS;

step 7-1: will predict data y_predRemoving the filter, and then performing FFT to obtain:

Y＝XH+W

h is a frequency domain channel matrix, X is a frequency domain transmitting signal matrix, Y is a frequency domain receiving signal matrix, and W is a Gaussian noise matrix;

step 7-2: the channel estimation for the frequency domain LS is:

wherein, X_PAnd Y_PIndicating the transmitted and received data, respectively, for the pilot locations.

2. The channel estimation method of claim 1, wherein n-10 and p-10 are used for IM/DD-OFDM/OQAM-PON system channel estimation based on ANN _ LS.

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