A Nonlinear Equalization Method for MZM Based on LM-BP Algorithm

Abstract

The present invention discloses an MZM non - linear equalization compensation method based on the LM - BP neural network algorithm, belonging to the field of communication. First, at the transmitting end of the system, the generation of random signals and the modulation of PAM4 signals are implemented in Matlab. A PAM4 signal IM / DD back - to - back transmission system is built using the VPI simulation platform to simulate the non - linear damage caused by MZM and transmit the signals. The signal data after transmission is collected, and digital signal processing is performed through Matlab after going offline. The compensation algorithm of the present invention is to put the offline data into the neural network model, generate a large amount of empirical data through learning and exploration of the data to train the model, and finally extract the trained neural network model to verify the data signal. This method has an extremely fast operation speed, high accuracy after training, low scheme cost, good effect, can ensure the stability of the IM / DD system transmission, achieve precise compensation for MZM; and while not increasing the algorithm complexity, reduce the transmission error rate and improve the transmission efficiency of the system.

Description

Technical Field

[0001] The present invention belongs to the field of communications, and relates to digital signal processing in an IM-DD optical fiber communication system based on PAM4 signals. Specifically, the present invention relates to a method for compensating MZM non-linear equalization based on the LM-BP neural network algorithm. Background Art

[0002] For short-distance optical links, considering cost and performance, the current mainstream technology is IM / DD. The traditional IM / DD optical communication system implemented using the NRZ format is difficult to meet the requirements of continuously increasing transmission rates. Therefore, many advanced modulation formats are used in IM / DD systems, such as four-level pulse amplitude modulation, carrierless amplitude-phase modulation, and discrete multi-tone modulation. Among them, considering power consumption and implementation complexity, the IM / DD system based on the PAM4 modulation format is widely applied in practice.

[0003] In the IM / DD system based on PAM4, at the transmitting end, digital signal processing is required for the transmitted signal, which mainly includes techniques such as channel coding, oversampling, and PAM4 symbol mapping. Subsequently, the PAM4 signal enters the optical modulator through a digital-to-analog converter (DAC). Currently, the common modulation methods for IM / DD systems are internal modulation and external modulation. Internal modulation mainly includes electro-absorption modulated lasers and directly modulated lasers, while external modulation is mainly the Mach-Zehnder modulator.

[0004] In the short-range optical link based on PAM4 modulation, the signal impairments caused by the system also pose a great challenge to digital signal processing, such as linear and non-linear impairments. Linear impairments mainly include two aspects. One is the pulse broadening effect caused by fiber dispersion, and the other is caused by insufficient bandwidth of devices (such as DAC, ADC, etc.). Non-linear impairments are mainly caused by insufficient linearity of optoelectronic devices. For example, the modulation curve of the MZM has non-linear characteristics.

[0005] Compared with NRZ signals, PAM4 signals have higher requirements for the linearity of optoelectronic devices. As one of the mainstream modulators in the IM / DD system, the signal non-linear distortion caused by the modulation characteristics of the MZM itself is an inevitable problem in the IM / DD system based on PAM4. In summary, there is an urgent need to provide an equalization method for compensating MZM non-linearity. Summary of the Invention

[0006] In order to compensate for the non - linear damage caused by the modulation characteristics of the MZM itself and improve the transmission efficiency of the signal, the present invention provides a non - linear equalization method for MZM based on the LM - BP algorithm. The non - linear equalization method of the present invention uses the joint simulation of Matlab and VPI to simulate the IM / DD back - to - back transmission system based on PAM4. In the whole system, the modulation and demodulation of the PAM4 signal and digital signal processing are implemented by Matlab, and the optoelectronic conversion, digital - to - analog conversion, etc. of the PAM4 signal are implemented by VPI.

[0007] First, at the sending end of the system, the generation of random signals and the modulation of PAM4 signals are implemented in Matlab. A PAM4 signal IM / DD back - to - back transmission system is built using the VPI simulation platform, simulating the non - linear damage caused by the MZM and transmitting the signal. The signal data after transmission is collected and, after going offline, digital signal processing is performed through Matlab. The digital signal processing is the LM - BP neural network equalization compensation algorithm of the present invention. The offline data is put into the neural network model, and a large number of empirical data are generated through learning and exploration of the data to train the model. Finally, the trained neural network model is extracted to verify the data signal. The present invention uses the DSP method of machine - learning neural network to equalize and compensate for the non - linear damage caused by the modulation characteristics of the MZM itself, improve the transmission distance, and increase the signal transmission efficiency.

[0008] The present invention is realized through the following technical solutions:

[0009] The present invention provides a non - linear equalization method for MZM based on the LM - BP algorithm, including the following steps:

[0010] Step A: Collect the PAM4 signal data after transmission;

[0011] Step B: Training of the BP neural network model based on machine learning, including:

[0012] Step B1: Determine the topological structure of the BP neural network;

[0013] Step B2: Use the LM algorithm to train the BP neural network model;

[0014] Step C: Use the trained BP neural network model for testing.

[0015] Further, step A is specifically as follows:

[0016] Step A1: First, generate a segment of random binary digital signals in Matlab, and then map the random signals into the PAM4 signal format. At this time, each symbol of the signal can provide 2 bits of information, and the generated PAM4 digital signal is resampled to two samples per symbol;

[0017] Step A2: Upload the generated PAM4 signal to the VPI simulation software for transmission, propagation, and reception.

[0018] Step A3: Acquire the output signal and construct a sample data set.

[0019] Construct a sample data set from the input and output data, and divide the sample data set into a training set and a test set.

[0020] Furthermore, the transmission process of building a PAM4 signal IM / DD back-to-back transmission system based on the VPI simulation platform in Step A2 is as follows:

[0021] (1) The digital PAM4 signal enters the digital-to-analog converter (DAC) module.

[0022] (2) The PAM4 electrical signal is loaded onto the optical signal through a Mach-Zehnder modulator (MZM).

[0023] (3) The optical signal is converted into an electrical signal through a PIN photodetector.

[0024] (4) The electrical signal enters the analog-to-digital converter (ADC) to achieve analog-to-digital conversion.

[0025] (5) Receive the digital PAM4 signal.

[0026] Furthermore, the determination of the topological structure of the BP neural network described in Step B1 consists of three layers of neurons: an input layer, a hidden layer, and an output layer. Among them, the input layer is the data input end of the entire neural network, consisting of multiple neuron input nodes; the hidden layer is the data operation and processing layer, connected to the input layer and the output layer respectively; the output layer outputs and represents the data processing results of the hidden layer.

[0027] Furthermore, the network training and learning process described in Step B2 is as follows:

[0028] At each output neuron in the input layer, the input data is summed through a weighted method, and the operation result is compared with the threshold set in the output layer. If the deviation between the two is greater than or equal to the pre-set parameter value, the input layer and the hidden layer will correct the weight value according to the LM algorithm error function, and so on, until the deviation between the weighted fusion result and the set threshold is less than the pre-set parameter, and finally the network training and learning is completed.

[0029] Furthermore, the specific training steps of Step B2 are as follows:

[0030] (1) Input the sample data and calculate the output value.

[0031] The calculation formula for the output signal y(n) is Neural network weight w ij and w i respectively represent the connection weight from the j-th node in the input layer to the i-th node in the hidden layer and the weight from the i-th node in the hidden layer to the output layer; the bias b i and b respectively represent the bias of the i-th node in the hidden layer and the bias of the output node in the output layer; the integers m and r respectively represent the number of nodes in the input layer and the hidden layer; the vector x(n) represents the input signal; the functions f(·) and σ(·) respectively represent the activation functions of the hidden layer and the output layer, where the activation function of the hidden layer adopts the sigmoid function, that is is a continuous unipolar S-shaped non-linear activation function from the real number field R to the closed set [0, 1], and at the same time has the boundedness and differentiability of a complex function; the activation function of the output layer adopts a linear function;

[0032] (2), Set the allowable value ε of the training error, the constants μ and β (0 < β < 1), and initialize the weight and threshold vectors, and let the iteration number k = 0;

[0033] (3), Calculate the error function E(w k );

[0034] In the formula, Y i is the expected network output vector, Y i ' is the actual network output vector, P is the number of samples, w is the vector composed of network weights and thresholds, and e i (w k ) is the error between the expected network output and the network output of the k-th iteration;

[0035] (4), Calculate the weight increment Δw;

[0036] w k represents the vector composed of the weights and thresholds of the k-th iteration, and the vector w k+1 = w k + Δw, and the calculation formula of the weight increment Δw is Δw = [J T (w)J(w) + μI] -1 J T (w)e(w), in the formula, I is the identity matrix; μ is the user-defined learning rate; J(w) is the Jacobian matrix;

[0037] (5), According to the relationship between the error value and the allowable error value, judge whether the learning is over;

[0038] If E(w k ) < ε, the training learning ends;

[0039] (6), If E(wk ) ≥ ε, then use w k+1 = w k + Δw as the weight and threshold vector, calculate the error function. If E(w k+1 ) < E(w k ), then let k = k + 1, μ = μβ, and repeat (3); otherwise μ = μ / β, and repeat (4);

[0040] (7) Training is completed.

[0041] Furthermore, step C is specifically as follows:

[0042] (1) Randomly extract input and output data from the test set and test the trained BP neural network;

[0043] (2) Make a judgment and calculate the bit error rate.

[0044] Compared with the prior art, the advantages of the present invention are as follows:

[0045] The present invention proposes an MZM nonlinear equalization method based on the LM - BP algorithm. Specifically, this method is a nonlinear equalization method for training a BP neural network with the LM algorithm, which does not require a complex modeling process, has an extremely fast operation speed, a high accuracy rate after training, a low cost of the scheme, a good effect, can ensure the stability of the IM / DD system transmission, and achieve precise compensation for the MZM. Moreover, compared with the classical nonlinear equalization method, without increasing the algorithm complexity, it reduces the transmission bit error rate and improves the transmission efficiency of the system; BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0047] Figure 1 is the flowchart of the MZM nonlinear equalization method based on the LM - BP algorithm of the present invention;

[0048] Figure 2 is the structure diagram of the IM / DD system based on PAM4 of the present invention;

[0049] Figure 3 is the BP neural network model diagram of the present invention;

[0050] Figure 4 is the BP neural network flowchart of the present invention;

[0051] Figure 5 is the flowchart of the LM algorithm of the present invention;

[0052] Figure 6 Training effect diagram for Example 1;

[0053] Figure 7 Result eye diagram for Example 1;

[0054] Among them, a) is the system input eye diagram, b) is the system output eye diagram, and c) is the eye diagram after algorithm correction. Detailed implementation manners

[0055] To clearly and completely describe the technical solution of the present invention and its specific working process, in combination with the accompanying drawings of the specification, the specific implementation manners of the present invention are as follows:

[0056] In the description of this specification, the description referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0057] Example 1

[0058] As Figure 1 shown, this embodiment provides a nonlinear equalization method for MZM based on the LM-BP algorithm, including the following steps:

[0059] Step A: Collect the PAM4 signal data after transmission;

[0060] Step A1: First, generate a segment of random binary digital signal in Matlab, and then map the random signal into the PAM4 signal format. At this time, each symbol of the signal can provide 2 bits of information, and the generated PAM4 digital signal is resampled to two samples per symbol;

[0061] Step A2: Upload the generated PAM4 signal to the VPI simulation software for sending, transmitting, and receiving;

[0062] As Figure 2 shown, the transmission process of building a PAM4 signal IM / DD back-to-back transmission system based on the VPI simulation platform in Step A2 is as follows:

[0063] (1), The digital PAM4 signal enters the digital-to-analog converter (DAC) module;

[0064] (2), The PAM4 electrical signal is loaded onto the optical signal through a Mach-Zehnder modulator (MZM);

[0065] (3), The optical signal is converted into an electrical signal by a PIN photodetector;

[0066] (4), The electrical signal enters an analog-to-digital converter (ADC) to achieve analog-to-digital conversion;

[0067] (5), Receive the digital PAM4 signal;

[0068] Step A3: Collect the output signal and construct a sample data set;

[0069] Construct a sample data set from the input and output data, and divide the sample data set into a training set and a test set;

[0070] Step B: Training of a BP neural network model based on machine learning, including:

[0071] Step B1: Determine the topological structure of the BP neural network;

[0072] As Figure 3 shown, the determination of the topological structure of the BP neural network described in Step B1 consists of three layers of neurons: an input layer, a hidden layer, and an output layer; among them, the input layer is the data input end of the entire neural network, consisting of multiple neuron input nodes; the hidden layer is the data operation and processing layer, connected to the input layer and the output layer respectively; the output layer outputs and represents the data processing result of the hidden layer. In this example, a 3-10-1 network topological structure is adopted, that is, 3 nodes in the input layer, 10 nodes in the hidden layer, and 1 node in the output layer;

[0073] Step B2: Use the LM algorithm to train the BP neural network model, and the training effect diagram is as Figure 6 , The training times reach the best performance at 3 times, and the mean square error (mse) is 4.8318e-19;

[0074] The network training and learning process described in Step B2 is: as Figure 4 shown, at each output neuron in the input layer, the input data is summed by weighting, and the operation result is compared with the threshold set in the output layer. If the deviation between the two is greater than or equal to the preset parameter value, the input layer and the hidden layer will correct the weights according to the LM algorithm error function, and so on, until the deviation between the weighted fusion result and the set threshold is less than the preset parameter, and finally complete the network training and learning;

[0075] Step C: Use the trained BP neural network model for testing and output the compensation result, specifically as follows:

[0076] (1) Randomly extract input and output data from the test set and test the trained BP neural network. The result is an eye diagram as shown in Figure 7 ;

[0077] (2) Make a judgment and calculate the bit error rate. It can be seen from a), b), and c) in Figure 7 that the bit error rate of the eye diagram after being corrected by the algorithm of the present invention is 0.

[0078] In this embodiment, as shown in Figure 5 , the steps of using the LM algorithm to train the BP neural network model in step B2 of this embodiment are introduced in detail. The specific training steps are as follows:

[0079] (1) Take a set of random samples as the input signal and calculate the output value of the output layer;

[0080] The calculation formula for the output signal y(n) is where the neural network weights w ij and w i respectively represent the connection weight from the j-th node in the input layer to the i-th node in the hidden layer and the weight from the i-th node in the hidden layer to the output layer; the biases b i and b respectively represent the bias of the i-th node in the hidden layer and the bias of the output node in the output layer; the integers m and r respectively represent the number of nodes in the input layer and the hidden layer; the vector x(n) represents the input signal; the functions f(·) and σ(·) respectively represent the activation functions of the hidden layer and the output layer. Among them, the activation function of the hidden layer uses the sigmoid function, that is It is a continuous unipolar S-shaped nonlinear activation function from the real number field R to the closed set [0,1], and at the same time has the boundedness and differentiability of a complex function; the activation function of the output layer uses a simple linear function.

[0081] (2) Set the allowable value ε of the training error, constants μ and β (0 < β < 1), and initialize the weight and threshold vectors, and let the iteration number k = 0;

[0082] (3) Calculate the error function E(w k ) of the network to correct the weights;

[0083] Among them, In the formula, Y i is the expected network output vector, Y i ' is the actual network output vector, P is the number of samples, w is the vector composed of network weights and thresholds, and e i (w k ) is the error between the expected network output and the network output of the k-th iteration;

[0084] (4) Calculate the weight increment Δw;

[0085] w k represents the vector composed of the weights and thresholds in the k-th iteration, and the vector w of the new weights and thresholds k+1 = w k + Δw. The calculation formula for the weight increment Δw is Δw = [J T (w)J(w) + μI] -1 J T (w)e(w), where I is the identity matrix; μ is the user-defined learning rate; J(w) is the Jacobian matrix;

[0086] (5) Judge whether the learning is over according to the relationship between the error value and the allowable error value;

[0087] If the deviation E(w k ) < ε, the algorithm ends;

[0088] (6) If the deviation E(w k ) ≥ ε, then use w k+1 = w k + Δw as the weight and threshold vector, calculate the error index function. If E(w k+1 ) < E(w k ), then let k = k + 1, μ = μβ, and repeat (3); otherwise μ = μ / β, and repeat (4);

[0089] (7) The training ends.

[0090] The preferred embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solutions of the present invention, and these simple modifications all fall within the protection scope of the present invention.

[0091] In addition, it should be noted that, in the above specific embodiments, the various specific technical features described can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not separately describe various possible combination methods.

[0092] Furthermore, any combination can be made between various different embodiments of the present invention as long as it does not violate the idea of the present invention, and it should also be regarded as the content disclosed by the present invention.

Claims

1. A non-linear equalization method for MZM based on the LM-BP algorithm, characterized in that, It includes the following steps: Step A: Collect the PAM4 signal data after transmission; Step B: Training of the BP neural network model based on machine learning, including: Step B1: Determine the topological structure of the BP neural network; Step B2: Train the BP neural network model using the LM algorithm; Step C: Use the trained BP neural network model for testing; Step A is specifically as follows: Step A1: First, generate a random binary digital signal in Matlab, and then map the random signal to the PAM4 signal format. At this time, each symbol of the signal can provide 2 bits of information, and the generated PAM4 digital signal is resampled to two samples per symbol; Step A2: Upload the generated PAM4 signal to the VPI simulation software for transmission, sending, and receiving; Step A3: Collect the output signal and construct a sample data set; Construct a sample data set from the input and output data, and divide the sample data set into a training set and a test set; The transmission process of the PAM4 signal IM / DD back-to-back transmission system based on the VPI simulation platform in Step A2 is specifically as follows: (1) The digital PAM4 signal enters the digital-to-analog converter DAC module; (2) The PAM4 electrical signal is loaded onto the optical signal through the Mach-Zehnder modulator MZM; (3) The optical signal is converted into an electrical signal through a PIN photodetector; (4) The electrical signal enters the analog-to-digital converter ADC to achieve analog-to-digital conversion; (5) Receive the digital PAM4 signal.

2. The MZM nonlinear equalization method based on the LM-BP algorithm according to claim 1, characterized in that, The determination of the topological structure of the BP neural network described in Step B1 is composed of three layers of neurons: the input layer, the hidden layer, and the output layer. Among them, the input layer is the data input end of the entire neural network, consisting of multiple neuron input nodes; the hidden layer is the data operation and processing layer, connected to the input layer and the output layer respectively; the output layer outputs and represents the data processing results of the hidden layer.

3. A non-linear equalization method for MZM based on the LM-BP algorithm according to claim 1, characterized in that, The network training and learning process in Step B2 is as follows: At each output neuron in the input layer, the input data is summed by weighting, and the operation result is compared with the threshold set in the output layer. If the deviation between the two is greater than or equal to the pre-set parameter value, the input layer and the hidden layer will correct the weight value according to the LM algorithm error function, and so on, until the deviation between the weighted fusion result and the set threshold is less than the pre-set parameter, and finally the network training and learning is completed.

4. The MZM nonlinear equalization method based on the LM-BP algorithm according to claim 1, wherein, The specific training steps of Step B2 are as follows: 1) Input sample data and calculate the output value; The calculation formula for the output signal y(n) is the neural network weights w ij and w i respectively represent the connection weight from the j-th node in the input layer to the i-th node in the hidden layer and the weight from the i-th node in the hidden layer to the output layer; the biases b i and b respectively represent the bias of the i-th node in the hidden layer and the bias of the output node in the output layer; the integers m and r respectively represent the number of nodes in the input layer and the hidden layer; the vector x(n) represents the input signal; the functions f(·) and σ(·) respectively represent the activation functions of the hidden layer and the output layer. Among them, the activation function of the hidden layer uses the sigmoid function, that is is a continuous unipolar S-shaped nonlinear activation function from the real number field R to the closed set [0, 1], and at the same time has the boundedness and differentiability of a complex function; the activation function of the output layer uses a linear function; (2) Set the allowable value ε of the training error, constants μ and β, 0 < β < 1, and initialize the weight and threshold vectors, and let the iteration number k = 0; (3) Calculate the error function E(w k ) for correcting the network weights; In the formula, Y i is the expected network output vector, Y i ' is the actual network output vector, P is the number of samples, w is the vector composed of network weights and thresholds, and e i (w k ) is the error between the expected network output and the network output of the k-th iteration; (4) Calculate the weight increment Δw; w k represents the vector composed of the weights and thresholds of the k-th iteration, and the vector w composed of the new weights and thresholds k+1 = w k + Δw. The calculation formula for the weight increment Δw is Δw = [J T (w)J(w) + μI] -1 J T (w)e(w), where I is the identity matrix; μ is the user-defined learning rate; J(w) is the Jacobian matrix; (5) Judge whether the learning is over according to the relationship between the error value and the error allowable value; If E(w k ) < ε, the training and learning are completed; (6) If E(w k ) ≥ ε, then use w k+1 = w k + Δw as the weight and threshold vector, calculate the error function. If E(w k+1 ) < E(w k ), then let k = k + 1, μ = μβ, and repeat (3); otherwise, μ = μ / β, and repeat (4); (7) The training is over.

5. The MZM nonlinear equalization method based on the LM-BP algorithm according to claim 1, wherein Step C is specifically as follows: (1) Randomly extract input and output data from the test set to test the trained BP neural network; (2) Calculate the bit error rate.

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