Signal phase holding method and system in optical fiber communication

Abstract

The invention relates to a signal phase keeping method and system in optical fiber communication, when coherent detection of received signals is carried out, the received signals are balanced in combination with frequency offset estimation (FOE), carrier phase recovery (CPR) and a plurality of neural networks, the carrier phase recovery is realized based on a Viterbi-Viterbi algorithm, and meanwhile, the plurality of neural networks provided by the invention can be used for carrying out coherent detection on the received signals. An input value, a neural node and an output value are complex numbers, and in a wireless channel equalization network, a CReLU activation function is used for complex value calculation for the first time. Compared with the prior art, the method is suitable for a complex signal generated by a QAM modulation format or coherent detection, the bit error rate performance more reliable than that of a real number neural network is achieved, and the method has the advantages of being low in complexity, reliable in bit error rate performance, high in sensitivity and the like.

Description

[0001] This application is a divisional application. The original application was entitled "A Nonlinear Equilibrium System and Method Based on Complex Neural Networks", with application number 202211529457.2 and application date of November 30, 2022. Technical Field

[0002] This invention relates to the field of digital signal processing technology, and in particular to a nonlinear equalization system and method based on complex neural networks. Background Technology

[0003] Currently, high-frequency millimeter-wave bands from 100 GHz to terahertz (300 GHz-10 THz) are considered effective candidate solutions for alleviating the problems of Beyond 5G (B5G) and future 6G mobile networks, with advantages in terms of large bandwidth. D-band millimeter waves (mm-wave) have attracted considerable research attention due to their atmospheric transmission window bandwidth of approximately 26 GHz. High-frequency optical fiber radio (ROF) can generate high-capacity millimeter-wave signals.

[0004] For nonlinear noise generated by optical fibers and optoelectronic devices, current solutions include equalization, lookup table predistortion, and artificial intelligence (AI) from the Volterra series. AI includes methods such as artificial neural networks (ANN), deep neural networks (DNN), convolutional neural networks (CNN), and recurrent neural networks (RNN). However, these real-valued NN equalizers are limited to models that construct complex channels; that is, traditional NN equalization models are not suitable for complex signals generated by QAM modulation formats or coherent detection. While Volterra equalizers can extend to both the real and imaginary parts of QAM signals, they neglect the relationship between the real and imaginary parts, thus ignoring potential phase information. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art by providing a nonlinear equalization system and method based on complex neural networks.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A nonlinear equalization system based on complex neural networks is applied to an optical fiber link communication system, including a pre-amplifier module, a frequency offset estimation module, a carrier phase recovery module, a CVNN equalizer module, and a discrimination module.

[0008] The pre-amplifier module is used to generate a D-band PAM-4 signal. The PAM-4 signal is then down-converted and resampled to obtain a resampled signal.

[0009] The frequency offset estimation module is used to estimate the frequency offset of the resampled signal to obtain the frequency offset-estimated signal;

[0010] The carrier phase recovery module is used to perform carrier phase recovery on the frequency offset estimated signal to obtain a carrier phase recovery signal.

[0011] The CVNN equalizer module is used to perform equalization on the carrier phase recovery signal to obtain a complex signal;

[0012] The discrimination module is used to identify the complex-valued signal and calculate the bit error rate.

[0013] Furthermore, the CVNN equalizer module is implemented based on a complex neural network;

[0014] The complex neural network is a multi-layer network structure consisting of an input layer, a hidden layer, and an output layer.

[0015] The number of neurons in the input layer-hidden layer-output layer of the complex neural network is 371-260-1;

[0016] The weights of the complex neural network are initialized to complex numbers;

[0017] The activation function of the complex neural network is the CReLU function;

[0018] The error of the backpropagation of the complex neural network is a complex number;

[0019] The output value of the output layer of the complex neural network is also a complex number.

[0020] Furthermore, the training operation of the complex neural network is achieved by updating the weights of the complex number, the activation function of the complex number, and the backpropagation error of the complex number;

[0021] The complex neural network is updated through complex neural nodes and continuously trained with complex inputs until the complex error function converges, thus completing the training of the complex neural network.

[0022] Furthermore, the complex neural network structure includes:

[0023] An input layer consists of a real part and an imaginary part, which are operated on by activation functions for complex numbers.

[0024] There are two hidden layers. The hidden layers receive complex data and error function values ​​from the input layer, and perform calculations using a complex activation function according to certain weights.

[0025] An output layer consists of a real part and an imaginary part. The real part and the imaginary part are calculated separately and passed through a complexlogits layer to obtain the error function value.

[0026] Furthermore, the expression for the CReLU function is:

[0027] CReLU=ReLU(real)+i·ReLU(imaginary)=max(0,real)+i·max(0,imaginary)

[0028] Its derivative is:

[0029]

[0030] Where real represents the real part of the input variable, imaginary represents the imaginary part of the input variable, and i represents the imaginary unit.

[0031] Furthermore, the expression for the error function is:

[0032]

[0033] in For the target complex signal, Let yr be the complex-valued signal output from the CVNN equalizer, and t be the real part of the complex-valued signal output from the CVNN equalizer. r Let yi be the real part of the target complex signal, yi be the imaginary part of the complex signal output from the CVNN equalizer, and t be the real part of the target complex signal. i Let i be the imaginary part of the target complex signal, and i be the imaginary unit.

[0034] Furthermore, the frequency offset estimation module uses mathematical methods to estimate the carrier frequency offset based on the characteristics of the resampled signal, and performs frequency compensation on the resampled signal.

[0035] Furthermore, the carrier phase recovery module is implemented based on the Viterbi-Viterbi algorithm. The carrier phase recovery module performs nonlinear transformation on the frequency offset estimated signal to process the phase noise generated during transmission, compensate for phase loss, and reduce nonlinear distortion.

[0036] Furthermore, the front-end module generates a D-band PAM-4 signal based on optical heterodyne beat frequency.

[0037] A nonlinear equalization method based on a complex neural network, characterized in that it is applied to a nonlinear equalization system based on a complex neural network as described in any one of claims 1-9, and includes the following steps:

[0038] The D-band PAM-4 signal generated by the front-end module is received. After down-conversion and resampling, the PAM-4 signal is used to obtain a resampled signal.

[0039] The frequency offset of the resampled signal is estimated to obtain the frequency offset-estimated signal;

[0040] Carrier phase recovery is performed on the frequency offset estimated signal to obtain the carrier phase recovered signal;

[0041] The carrier phase recovery signal is subjected to equalization to obtain a complex signal;

[0042] Identify the complex-valued signal and calculate the bit error rate.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] 1. When performing coherent detection of the received signal, this invention combines frequency offset estimation (FOE), carrier phase recovery (CPR), and complex neural network to equalize the received signal. Among them, since the carrier phase recovery is based on the Viterbi-Viterbi algorithm, frequency and phase noise are mitigated, making the signal after frequency offset estimation and carrier phase recovery easier to demodulate. This not only enables the recovery of complex signals but also effectively reduces the amount of complex computation and improves sensitivity.

[0045] 2. Since the received signal uses coherent detection, it inevitably generates complex signals, while real-valued neural network equalizers are limited to models that construct complex channels. Therefore, traditional neural network equalization models are not suitable for complex signals inherently generated by QAM modulation formats or coherent detection. While Volterra equalizers can extend to both the real and imaginary parts of QAM signals, this ignores the relationship between the real and imaginary parts, thus neglecting potential phase information. Therefore, compared to real-valued neural networks, this invention is more practical for complex signals generated by QAM modulation formats or coherent detection.

[0046] 3. The complex neural network proposed in this invention has complex input values, neural nodes, and output values. Furthermore, this invention is the first to use the CReLU activation function for complex value computation in a wireless channel equalization network. Through this design, a more reliable bit error rate performance is achieved compared to real-number neural networks.

[0047] 4. The CVNN equalization method of this invention combines frequency offset estimation (FOE) and carrier phase recovery (CPR) algorithms, effectively reducing complexity compared to purely data-driven CVNN methods. This invention solves the problem that the complex baseband signal generated after down-conversion cannot be recovered by a real-valued equalizer, while also alleviating problems such as complex weights and time delays caused by the introduction of I and Q components. Compared to purely data-driven complex neural network equalizers, real-valued deep neural network nonlinear equalizers, and Volterra nonlinear equalizers, this invention significantly improves receiver sensitivity and enhances the reliability of communication systems. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating the implementation of an embodiment of the present invention;

[0049] Figure 2 This is a schematic diagram of the specific structure of the CVNN equalizer in the flowchart of this invention;

[0050] Figure 3 This is a schematic diagram of the optical fiber link communication system structure used in this invention;

[0051] Figure 4 In this embodiment of the invention, the constellation diagram after CVNN equalization is used when combining FOE and CPR.

[0052] Figure 5 This is a graph showing the relationship between the bit error rate of various nonlinear equalizers and optical power in embodiments of the present invention;

[0053] Figure 6 This is a graph showing the relationship between the bit error rate of a CVNN equalizer combining FOE and CPR and the number of neurons in the hidden layer, as described in an embodiment of the present invention. Detailed Implementation

[0054] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0055] For the transmission of PAM-4 signals in the D-band, this invention employs a combination of purely data-driven CVNN (Complex-valued neural networks), frequency-offset estimator (FOE), and carrier phase recovery (CPR) methods. The complex neural network proposed in this invention has complex input values, neural nodes, and output values, as shown in the appendix. Figure 1As shown, this invention also applies the complex ReLU function, i.e., the CReLU activation function, to wireless channel equalization. Through the above design, a more reliable bit error rate performance is achieved than that of real-number neural networks.

[0056] This embodiment provides a nonlinear equalization system based on complex neural networks, applied to an optical fiber link communication system, including a pre-amplifier module, a frequency offset estimation module, a carrier phase recovery module, a CVNN equalizer module, and a discrimination module;

[0057] The preamplifier module is used to generate the D-band PAM-4 signal. After down-conversion and resampling, the PAM-4 signal is used to obtain the resampled signal.

[0058] The frequency offset estimation module is used to estimate the frequency offset of the resampled signal to obtain the frequency offset-estimated signal;

[0059] The carrier phase recovery module is used to recover the carrier phase of the signal after frequency offset estimation to obtain the carrier phase recovery signal;

[0060] The CVNN equalizer module includes a CVNN equalizer, which is used to perform equalization on the carrier phase recovery signal to obtain a complex-valued signal; the discrimination module is used to identify the complex-valued signal and calculate the bit error rate.

[0061] like Figure 1 As shown, based on this system, a nonlinear equilibrium method based on complex neural networks can be implemented, including the following steps:

[0062] S1. Receive the D-band PAM-4 signal generated by the front-end module. After the PAM-4 signal undergoes down-conversion and resampling processing, a resampled signal is obtained.

[0063] S2. Perform frequency offset estimation on the resampled signal to obtain the frequency offset estimated signal;

[0064] S3. Perform carrier phase recovery on the frequency offset estimated signal to obtain the carrier phase recovered signal;

[0065] S4. Perform equalization on the carrier phase recovery signal to obtain a complex signal;

[0066] S5. Identify complex-valued signals and calculate the bit error rate.

[0067] In this embodiment, the CVNN equalizer module is implemented based on a complex neural network (CVNN);

[0068] like Figure 2 As shown, a complex neural network is a multi-layer network structure consisting of an input layer, a hidden layer, and an output layer; in this embodiment, the number of neurons in the input layer-hidden layer-output layer of the complex neural network is 371-260-1.

[0069] The weights of a complex neural network are initialized to complex numbers;

[0070] The activation function for complex neural networks is the complex ReLU function, or CReLU function;

[0071] The error of backpropagation in a complex neural network is a complex number;

[0072] The output value of the output layer of a complex neural network is also a complex number.

[0073] In this embodiment, the training operation of the complex neural network is achieved by updating the weights, activation function, and backpropagation error of the complex numbers. The complex neural network is continuously trained by updating the complex neural nodes and training the complex inputs until the complex error function converges, thus completing the training of the complex neural network.

[0074] Specifically, complex neural network structures include:

[0075] An input layer consists of a real part and an imaginary part. The real part and the imaginary part are respectively operated on by the activation function of complex numbers and propagated to the next layer node through their respective paths.

[0076] The network consists of two hidden layers. In each layer, real nodes connect to the real and imaginary nodes of the next layer, and vice versa. These interconnections form paths between nodes, each with a weight. The hidden layers receive complex data from the input layer and the output information, which is then backpropagated using the error function value. This process continuously updates the state of the complex neural network nodes. In essence, iterative training is achieved by continuously updating the weights of the neural network paths, the complex activation function, and the backpropagation error value. The path weights represent the connectivity strength between neural nodes.

[0077] An output layer consists of a real part and an imaginary part. The real part and the imaginary part are calculated separately and passed through a complex Logit function layer to obtain the error function value.

[0078] In this embodiment, the expression for the CReLU activation function of the complex neural network is:

[0079] CReLU = ReLU(real) + i·ReLU(imaginary) = max(0,real) + i·max(0,imaginary) and its derivative is:

[0080]

[0081] Where real represents the real part of the input variable, imaginary represents the imaginary part of the input variable, and i represents the imaginary unit.

[0082] The expression for the error function is:

[0083]

[0084] in For the target complex signal, Let yr be the complex-valued signal output from the CVNN equalizer, and t be the real part of the complex-valued signal output from the CVNN equalizer. r Let yi be the real part of the target complex signal, yi be the imaginary part of the complex signal output from the CVNN equalizer, and t be the real part of the target complex signal. i Let i represent the imaginary part of the target complex signal, where i is the imaginary unit. The frequency offset estimation module uses mathematical methods to estimate the carrier frequency offset based on the characteristics of the resampled signal and performs frequency compensation on the resampled signal.

[0085] The carrier phase recovery module is based on the Viterbi-Viterbi algorithm. It performs nonlinear transformation on the frequency offset estimated signal to process the phase noise generated during transmission, compensate for phase loss, and reduce nonlinear distortion.

[0086] Compared to existing technologies, this embodiment utilizes optical heterodyne beat frequency to generate a D-band PAM-4 signal. Furthermore, due to the coherent detection employed at the receiver, complex signals are inherently generated; therefore, a complex-valued neural network (CVNN) is essential, as it provides a more constrained system than real-valued training structures. Simultaneously, this invention is the first in wireless channel equalization networks to use the CReLU activation function for complex-valued computation.

[0087] like Figure 3 As shown, this invention is applied to an optical fiber link communication system, which includes a standard single-mode optical fiber and a wireless channel. In this embodiment, the front-end module includes:

[0088] (1) The sending end, which includes:

[0089] Two laser generators (ECL1, ECL2) generate optical carriers of a specific frequency to carry the modulation signal. The two optical carriers have different frequencies, and the frequency space between ECL1 and ECL2 is 135 GHz. This difference is the frequency of the electrical signal obtained after beat frequency.

[0090] An arbitrary waveform transmitter (AWG) is used to perform digital-to-analog conversion on baseband PAM-4 signals generated by offline Matlab software;

[0091] An electrical amplifier (EA) is used to amplify the baseband PAM-4 signal, which then enters the modulator to modulate the optical carrier.

[0092] A Mach-Zehnder intensity modulator (MZM) driven by a baseband PAM-4 signal boosted from an electrical amplifier has a 3dB optical bandwidth of 30 GHz, a 2.7-V half-wave voltage at 1 GHz, and a 5-dB insertion loss.

[0093] An erbium-doped fiber amplifier (EDFA) is used to amplify weak optical signals;

[0094] An optical coupler is used to couple the MZM-modulated signal to the signal generated by the laser generator ECL2.

[0095] A 10km long optical fiber is used to transmit the coupled optical signal;

[0096] An optical attenuator is used to control the power of the transmitted optical signal so that the signal power can be received by the D-band photoelectric converter for beat frequency processing.

[0097] A photoelectric converter is used to beat the modulated ECL1 signal with the ECL2 signal to generate a low-frequency carrier electrical signal.

[0098] (2) The transmission section includes:

[0099] A pair of identical D-band horn antennas (HA) with a gain of 25 dBi are used to transmit 135 GHz signals;

[0100] A pair of lenses (Lens1 and Lens2) with diameters and focal lengths of 10cm and 20cm respectively are used to further amplify the 135GHz PAM-4 signal.

[0101] (3) The receiving end includes:

[0102] A commercial D-band mixer with 9.5dB conversion loss and 112GHz LO signal is used to downconvert a received 135GHz signal to an IF signal.

[0103] An electrical amplifier (EA) with a gain of 33dB is used to amplify signals for subsequent digital signal processing.

[0104] In practice, at the transmitting end, laser generator ECL1 generates a fixed-frequency optical carrier. This carrier undergoes intensity modulation at an optical modulator, with the modulation signal being a radio frequency signal generated by an arbitrary waveform generator (AWG). The modulated signal is amplified by a PM-EDFA. Simultaneously, another laser generator ECL2 generates an optical carrier at a different frequency. The signals from both locations are coupled at an optical coupler (OC). The coupled signal is then transmitted through a 10km-long standard single-mode fiber (SSMF). The power of the transmitted signal is adjusted by an attenuator (ATT) before entering a photodetector (PD) for beat frequency conversion, converting the optical signal into an electrical signal. This signal is a D-band PAM-4 signal.

[0105] The D-band PAM-4 signal is transmitted through an antenna to a 3m free space. Two terahertz lenses are placed in the free space to adjust the focal length of the signal. After passing through the lenses, the signal reaches the receiving antenna at the receiving end. The distance between the two antennas is 3m, and the distance between the two lenses and the antennas on both sides is 20cm.

[0106] At the receiving end, the receiving antenna receives the D-band PAM-4 signal and then performs down-conversion processing. The signal passes through a mixer and is mixed with a 117GHz down-converted signal. Since the down-converted signal output by the mixer is relatively weak, an electrical amplifier (EA) is used to amplify the signal. The time-domain waveform and spectrum of the signal are observed through an oscilloscope, and the sampled signal is processed offline by a DSP.

[0107] like Figure 1 As shown, since frequency offset estimation (FOE) and carrier phase recovery (CPR) are added before the complex neural network, the specific DSP processing flow is as follows: after the signal is down-converted, a resampling operation is performed, followed by frequency offset estimation, then carrier phase recovery, then equalization processing of the complex neural network, and then the PAM-4 level identification step, and finally the bit error rate is determined.

[0108] like Figure 4 As shown, the constellation chart changes after each step of processing. It can be seen that the constellation chart becomes clearer after each step of processing.

[0109] Since the receiver uses coherent detection, complex signals are inevitably generated, and real-valued NN equalizers are limited to models that construct complex channels. Therefore, traditional NN equalization models are not suitable for complex signals inherently generated by QAM modulation formats or coherent detection. For Volterra equalizers, although they can be extended to the real and imaginary parts of QAM signals, this ignores the relationship between the real and imaginary parts, thus ignoring potential phase information.

[0110] Therefore, compared to real-valued neural networks, this invention proposes complex deep neural networks, which are used to equalize signals, as shown in the appendix. Figure 1 As shown, this complex neural network employs a three-layer structure consisting of an input layer, a hidden layer, and an output layer, with the number of neurons in the input layer, hidden layer, and output layer being 371-260-1, respectively. This network has the following three main characteristics: 1. Weights are initialized with complex numbers; 2. The activation function is the complex ReLU function (CReLU); 3. The backpropagation error is a complex number.

[0111] like Figure 5 The figure shows the relationship between the bit error rate (BER) of several existing nonlinear equalizers and optical power. It illustrates the BER performance of these nonlinear equalizers when the optical signal enters the PD beat frequency converter. For transmitting a 45Gbaud PAM-4 signal, several nonlinear equalizers were combined using a 45-tap CMMA equalizer: a 151-2 tap Volterra and a 301-tap DDLMS structure; a DNN() structure with a softmax output layer; an end-to-end pure data-driven CVNN() structure; and a CVNN equalizer structure connected via FOE and CPR models. It is clear that the CVNN equalizer using the model connection after FOE and CPR exhibits a lower BER and more reliable performance compared to other methods.

[0112] According to the appendix Figure 6 It can be seen that in the CVNN equalizer method that combines FOE and CPR, the bit error rate gradually decreases as the number of nodes in the hidden layer increases.

[0113] This embodiment uses a 135GHz PAM-4 millimeter-wave ROF link as the basic framework, employing coherent detection to further improve receiver sensitivity. A complex DSP model is established more accurately through a complex neural network. This invention proposes a CVNN equalizer combining typical mathematical frequency offset estimation (FOE) and carrier phase recovery (CPR) algorithms, effectively reducing complexity compared to purely data-driven CVNN methods. This technical solution addresses the problem that the complex baseband signal generated after down-conversion cannot be recovered by a real-valued equalizer, while also mitigating issues such as complex weights and time delays caused by the introduction of I and Q components. Compared to purely data-driven complex neural network equalizers, real-valued deep neural network nonlinear equalizers, and Volterra nonlinear equalizers, this invention significantly improves receiver sensitivity and enhances the reliability of the communication system.

[0114] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A signal phase-preserving method in optical fiber communication, characterized in that, include: A D-band PAM-4 signal is generated, and the PAM-4 signal is down-converted and resampled to obtain a resampled signal. The resampled signal is subjected to frequency offset estimation and carrier phase recovery processing to compensate for linear phase noise, resulting in a carrier phase recovery signal; the carrier phase recovery processing is implemented based on the Viterbi-Viterbi algorithm. The carrier phase recovery signal is input into a complex neural network, which outputs a processed complex signal; wherein the complex neural network uses the CReLU activation function, and the derivative of the CReLU activation function is: Where real represents the real part of the input variable, imaginary represents the imaginary part of the input variable, and i represents the imaginary unit; The derivative function outputs a complex value containing the imaginary unit during the backpropagation process of the complex neural network, thus preserving the phase characteristics of the complex signal.

2. The method according to claim 1, characterized in that, The complex neural network is a multi-layer network structure consisting of an input layer, a hidden layer, and an output layer; the weights of the complex neural network are initialized to complex numbers; the activation function of the complex neural network is the CReLU function; the backpropagation error of the complex neural network is a complex number; and the output value of the output layer of the complex neural network is a complex number.

3. The method according to claim 1, characterized in that, The training operation of the complex neural network is achieved by updating the weights of the complex numbers, the activation function of the complex numbers, and the backpropagation error of the complex numbers. The complex neural network is updated through complex neural nodes and continuously trained with complex inputs until the complex error function converges, thus completing the training of the complex neural network.

4. A signal phase-preserving system for optical fiber communication, characterized in that, include: The signal generation module is used to generate a D-band PAM-4 signal. After down-conversion and resampling of the PAM-4 signal, a resampled signal is obtained. The phase noise compensation module is used to perform frequency offset estimation and carrier phase recovery processing on the resampled signal, compensate for linear phase noise, and obtain the carrier phase recovery signal; the carrier phase recovery processing is based on the Viterbi-Viterbi algorithm. A complex neural network processing module is used to input the carrier phase recovery signal into a complex neural network and output a processed complex signal; wherein, the complex neural network uses the CReLU activation function, and the derivative of the CReLU activation function is: Where real represents the real part of the input variable, imaginary represents the imaginary part of the input variable, and i represents the imaginary unit; The derivative function outputs a complex value containing the imaginary unit during the backpropagation process of the complex neural network, thus preserving the phase characteristics of the complex signal.

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