A method for nonlinear impairment equalization for a mode division multiplexing communication system

Abstract

The application discloses a nonlinear impairment equalization method for a mode division multiplexing (MDM) communication system, and belongs to the optical fiber communication field. The method is implemented as follows: an optical amplitude modulation (OAM)-MDM optical fiber communication system transmits and receives a pulse amplitude modulation (PAM) signal sequence, and a data feature vector is constructed by using received PAM data symbols; a training data set is used to train an equalizer; a test data set is input into an AffinityNet equalizer to obtain a predicted value of a signal, and high-accuracy data recovery is realized. The AffinityNet uses a "small sample" to establish an accurate nonlinear model and has a high generalization ability to predict the random characteristic nonlinearity of the OAM-MDM. The AffinityNet nonlinear equalizer can effectively compensate the random nonlinearity in the OAM-MDM system through the nonlinear model learned by the small sample. The application has a lower calculation complexity, can efficiently recover the data symbols transmitted in the OAM system, and compensates the system nonlinearity of the OAM optical communication system.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of optical fiber communication and relates to an OAM mode division multiplexing emphasis direct detection PAM transmission nonlinear compensation method based on an AffinityNet neural network. BACKGROUND

[0002] Data center networks have become an indispensable infrastructure of modern Internet and cloud computing, carrying data traffic communication for service providers such as Google, Microsoft, Alibaba, etc. Short-range intensity modulation direct-detection (IM / DD) optical communication systems are typical applications of data center optical fiber interconnection. Short-range optical communication systems require high speed, low power consumption and high reliability to meet the data transmission requirements within data centers. In recent years, with the rapid development of the Internet industry, the transmission capacity demand of short-range optical interconnection data centers has increased exponentially. Therefore, it is urgent to expand the capacity of short-range optical communication systems. Mode division multiplexing (MDM) allows multiple independent communication channels to be used for data transmission at the same time and frequency resources, and these channels are orthogonal in space. In traditional MDM optical fiber communication systems, data can be loaded onto multiple mutually orthogonal polarization modes. The orthogonality between modes ensures independent transmission of each mode without crosstalk. The increase in orthogonal modes can significantly improve the capacity of the system.

[0003] Orbital angular momentum (OAM) multiplexing technology is an emerging MDM technology. In this multiplexing technology, data is loaded onto mutually orthogonal vortex beams with different topological charges and transmitted through a weakly coupled ring-core fiber (RCF). Since different orders of OAM modes are mutually orthogonal, OAM-MDM technology can greatly expand the performance of optical communication systems. Therefore, OAM-MDM technology has become an important research topic to break through the capacity limit of short-range optical communication systems in data centers.

[0004] Nonlinear impairment is an important factor affecting the transmission performance of OAM-MDM optical communication systems. Compared with traditional optical fiber communication systems, OAM-MDM uses a large number of optoelectronic devices, which introduces serious nonlinear impairment. On the one hand, the nonlinear impairments generated by different optical devices such as spatial light modulators (SLM), Mach-Zehnder modulators (MZM), and photodetectors (PD) are coupled with each other, resulting in extremely complex nonlinear models of OAM-MDM systems. On the other hand, the random mode coupling in OAM-MDM systems leads to strong randomness of the nonlinear impairment in the system. In traditional single mode fiber (SMF) communication systems, deterministic nonlinear models are usually established to mitigate nonlinear impairment, such as Volterra series equalizer, digital predistortion (DPD) method, and lookup table (LUT) method. However, due to the complexity and randomness of the nonlinear model of the OAM MDM system, these methods cannot accurately fit the nonlinear model. Therefore, it is very important to propose a new nonlinear equalizer to compensate for the random nonlinear impairment of the OAM-MDM optical fiber communication system.

[0005] In recent years, machine learning algorithms have been widely used in nonlinear impairment compensation in optical fiber communication due to their strong nonlinear fitting ability, such as convolutional neural network (CNN), artificial neural network based on transfer learning, and waveform regression. Therefore, machine learning-based nonlinear equalizers can compensate for serious nonlinear impairment in OAM-MDM optical fiber communication. However, these machine learning-based nonlinear equalizers also have a major drawback in compensating for nonlinear impairment in OAM-MDM systems. Although these machine learning algorithm-based equalizers have improved performance compared to traditional equalizers, they cannot overcome the strong randomness of nonlinearities in OAM-MDM. Therefore, these equalizers are not suitable for high-speed OAM-MDM optical fiber communication systems. SUMMARY

[0006] The application aims to provide a nonlinear impairment equalization method for a mode division multiplexing communication system, an OAM-MDM optical fiber communication system transmits and receives a pulse amplitude modulation (PAM) signal sequence, and a data feature vector is constructed according to the received PAM data symbol; a training data set is used to train an equalizer; a test data set is input into an AffinityNet equalizer to obtain a predicted value of the signal, and high-accuracy data recovery is realized. The AffinityNet uses a "small sample" to establish an accurate nonlinear model and has a high generalization ability to predict the random feature nonlinearities of the OAM-MDM. Therefore, although there is a large difference between the training signal and the test signal due to the random nonlinear impairment, the AffinityNet nonlinear equalizer can effectively compensate the random nonlinearities in the OAM-MDM system through the nonlinear model learned by the small sample. The application has a lower calculation complexity and can efficiently recover the data symbol transmitted in the OAM system, thereby compensating the system nonlinearities of the OAM optical communication system.

[0007] The application aims to achieve the above-mentioned purposes through the following technical solutions.

[0008] The application discloses a nonlinear impairment equalization method for a mode division multiplexing communication system, and comprises the following steps.

[0009] Step one: build a high-speed OAM-MDM optical fiber communication system. Orthogonal OAM modes are used for mode multiplexing to realize an integer times expansion of the communication system capacity.

[0010] Step two: prepare binary data bits with a length of 2 raised to the power as training data, and the data bits are sent after PAM symbol mapping, resampling and pulse shaping at the sending end in the OAM-MDM optical fiber communication system and are input into the OAM-MDM communication system for transmission.

[0011] The received signal y is expressed as:

[0012] y(n)=H(x(n))+noise(n)

[0013] Wherein, y(n)=[y1,y2,...,y n ] represents a sequence composed of PAM received symbols; H represents a channel response; x(n)=[x1,x2,...,x n ] represents PAM original symbols sent by the sending end; and noise(n) represents additive Gaussian noise in the high-speed OAM-MDM system.

[0014] Step 3: Due to random nonlinear damage during transmission, the data symbol size is distorted. After the received data symbol is clock recovered, the PAM symbol y is converted into n Together with the adjacent symbols, the data set is formed. n The combination of the L symbols before and after it is the characteristic vector of the symbol, that is, [y n-L ,…,y n-1 ,y n ,y n+1 ,…,y n+L ]. Distorted signal y(n) = [y1, y2, ..., y n ] is converted into (n-2L) feature vectors of length M (M=2L+1):

[0015]

[0016] Step 4: Use the AffinityNet equalizer to compensate for the PAM data symbols. A fully connected neural network is used to calculate the sample feature vectors to derive an estimate of the input sample, which is the PAM data symbol after nonlinear equalization. During training, parameters are updated using a backpropagation gradient descent algorithm. During testing, the distorted signal is equalized.

[0017] Divide the dataset Y into training set Y P =[Y1, Y2, ..., Y p ] and the test set Y Q =[Y1, Y2, ..., Y q ].

[0018] First, the feature vector Y in the training set i (i=1,2,...,p) is used as input to train the equalizer parameters. In the feature attention layer, the input training sample Y i Perform bit-by-bit multiplication with the feature attention vector w to perform weighted calculation on the features of the training sample:

[0019] h i =w⊙Y i

[0020] Where h i represents the output of the feature attention layer; ⊙ represents the bitwise multiplication operator; the feature attention vector w is defined as The feature attention layer performs feature enhancement on the feature vector through bit-by-bit multiplication.

[0021] Then, the kNN attention pooling layer containing k (k < p) feature vectors of length M is used for h i to be processed.

[0022]

[0023] where h i (j = 1, 2,..., p, j≠i) represents the k nearest neighbors of the feature vector h i ; a(·, ·) represents the spatial distance between the feature vector h i and h j calculated by the Gaussian kernel function; the parameter σ represents the Gaussian kernel smoothing factor; N(i) represents the set of the k nearest neighbors of the sample h i ; ||h i -h j || 2 represents the Euclidean distance between the feature vector h i and h i . However, the power operation leads to a high complexity in the calculation of the Euclidean distance. By replacing the Euclidean distance with the Manhattan operator, the above formula is rewritten as:

[0024]

[0025] The kNN attention pooling layer outputs a new feature vector representing the sample Y i by using the spatial distance between the feature vectors:

[0026]

[0027] The kNN attention pooling layer calculates the spatial distance between the samples, and generates a new feature vector representing the sample by using the spatial distance, thereby realizing the clustering of the samples, shortening the spatial distance between the feature vectors, and making the samples belonging to the same class close to each other in the feature space.

[0028] The fully connected neural network layer performs a regression fitting operation on the sample feature vectors, which is represented as:

[0029] h″ i = ReLU(W2(ReLU(W1h′ i +B1))+B2)

[0030] where W1 and W2 represent the weight matrices of the fully connected layer; B1 and B2 represent the bias matrices of the fully connected layer.

[0031] The output neuron of the output layer calculates and outputs the fitting result of the sample Y i , which is represented as:

[0032]

[0033] where W3 and B3 represent the weight and bias matrices, respectively. After obtaining the fitting result After that, the AffinityNet equalizer uses the mean square error loss function to calculate the loss value of the fitting result, and uses the Adam gradient descent algorithm to update the equalizer parameters. When the equalizer loss reaches the set threshold, the training process ends, and the test sample set is input into the equalizer to obtain the nonlinear equalized PAM symbol.

[0034] Step five: using the minimum Euclidean distance, mapping the equalized PAM symbol to the integer symbol position, and inversely mapping it to the binary data bit, comparing the equalization result with the transmitted symbol, demapping to obtain the bit error rate, and compensating the system nonlinearity of the OAM optical communication system according to the bit error rate.

[0035] Advantages:

[0036] 1. The nonlinear damage equalization method for a mode division multiplexing communication system disclosed in the application is used for transmitting and receiving a pulse amplitude modulation (PAM) signal sequence of an OAM-MDM optical fiber communication system, and a data feature vector is constructed from the received PAM data symbol; the equalizer is trained by using a training data set; the test data set is input into the AffinityNet equalizer to obtain the predicted value of the signal, and high-accuracy data recovery is realized. The application is used for 400Gbit / s 4-mode transmission of intensity modulation direct detection (IM / DD) OAM-MDM optical fiber communication, and significantly improves the transmission capacity in the IM / DD OAM-MDM transmission.

[0037] 2. The nonlinear damage equalization method for a mode division multiplexing communication system disclosed in the application adopts a nonlinear equalizer realized based on an Affinity network model, and the equalizer clusters the feature vectors of the training samples with the same label in the feature space. Through clustering, the AffinityNet nonlinear equalizer can learn the nonlinear features of the "one type" signal level instead of the "average point" of the signal level in the traditional equalizer, and the generalization ability of the equalizer is significantly improved.

[0038] 3. The nonlinear damage equalization method for a mode division multiplexing communication system disclosed in the application realizes small sample learning by using the AffinityNet equalizer, and regards the training data symbol as a "small sample" and the test data symbol as a "large target". The AffinityNet equalizer based on small sample learning can learn the accurate OAM-MDM model, and due to its high generalization ability, can effectively compensate for random nonlinear damage. DETAILED DESCRIPTION

[0039] Figure 1 It is a flowchart of the nonlinear damage equalization method for a mode division multiplexing communication system disclosed in the application.

[0040] Figure 2 An OAM-MDM intensity direct-detection PAM transmission system is built for the embodiment;

[0041] Figure 3 An AffinityNet equalizer structure diagram suitable for OAM communication system symbol decision;

[0042] Figure 4 The bit error rate performance of the PAM symbols after being equalized by the AffinityNet equalizer is tested. DETAILED DESCRIPTION

[0043] In order to better illustrate the purposes and advantages of the present application, the content of the application is further described below in combination with the drawings and examples.

[0044] As Figure 1 shown, the embodiment discloses a nonlinear impairment equalization method for a mode division multiplexing communication system, and the specific implementation steps are as follows:

[0045] Step one: build a four-mode OAM-MDM intensity direct-detection communication system, as Figure 2 shown. In the transmitting end, the PAM-8 data symbols generated by the digital signal processing (DSP) are modulated into electrical signals by the arbitrary waveform generator (AWG), and the sampling rate is 99GSa / s. A laser with a wavelength of 1550nm is used to generate an optical carrier, and the electrical signal is modulated onto the optical carrier by the Mach-Zehnder modulator (MZM) to generate a double-sideband optical signal. In this way, the optical signal generated by the three optical couplers (OCs) is divided into four branches, and four erbium-doped fiber amplifiers (EDFAs) are used for signal optical power amplification. The four branches of the signal are respectively de-correlated by single-mode optical fibers with different lengths. Four polarization controllers (PCs) are used to adjust the polarization direction of the signal light, and a linear polarizer (LP) is used to adjust the polarization of the signal. All signals are subjected to OAM mode conversion (l=<2, 3, 4, 5>) by a phase-sensitive spatial light modulator (SLM). In this way, in the OAM-MDM IM / DD transmission, a 33GBaud PAM-8 signal per mode can achieve a total capacity of 400Gbit / s. Two OAM modes are phase-rotated by 90° through a half-wave plate (HWP). Four branches of beams are combined by a polarization-sensitive beam combiner (PBC) and a beam combiner (BC). Finally, the OAM mode beam is converted into circular polarization through a quarter-wave plate (QWP) and coupled into a ring core fiber (RCF) with a length of 2km.

[0046] At the receiving end, the mode multiplexed OAM beams are split into four beams by a beam splitter (BS) and converted into Gaussian beams by vortex phase plates (VPPs) with opposite topological charges. The four Gaussian beams are coupled into a single mode fiber (SMF) by a collimator (Col.) and converted into electronic signals by four photodetectors (PDs). The current waveforms are recorded by a real-time oscilloscope with a sampling rate of 256 GSa / s and processed by an offline DSP module. The DSP module adopts resampling, low-pass filter, clock recovery, AffinityNet equalizer and bit error rate calculation module. The performance of the proposed scheme is verified by calculating the bit error rate through bit-by-bit comparison.

[0047] Step two: prepare binary data bits with length of 2 17 . The data bits are mapped into PAM8 symbols, resampled and pulse-shaped, and then enter the OAM-MDM intensity direct detection communication system.

[0048] In this example, the received signal y can be represented as:

[0049] y(n) = H(x(n)) + noise(n)

[0050] where y(n) = [yl, y2,..., y n ] represents a sequence composed of PAM-8 received symbols; H represents the channel response; x(n) = [xl, x2,..., x n ], x n ∈ {-7, -5, -3, -1, +1, +3, +5, +7} represents the PAM-8 original symbols sent by the transmitting end; noise(n) represents the additive Gaussian noise in the high-speed OAM-MDM system.

[0051] Step three: combine the symbol y n and its front and back L symbols into the feature vector of the symbol, that is, [y n-L ,..., y n-1 , y n , y n+1 ,..., y n+L ]. The distorted signal y(n) = [yl, y2,..., y n ] is converted into (n-2L) feature vectors with length M (M = 2L+1):

[0052]

[0053] Step four: divide the data set Y into a training set Y P = [Yl, Y2,..., Y q ] and a test set Y Q = [Yl, Y2,..., Y q ].

[0054] First, the feature vector Y i (i = 1, 2,..., p) as input, the equalizer parameters are trained. In the feature attention layer, the input training sample Y i is multiplied bit by bit with the feature attention vector w:

[0055] h i = w ⊙ Y i

[0056] In the formula, h i represents the output of the feature attention layer; ⊙ represents the bit-by-bit multiplication operator; the feature attention vector w is defined as The feature attention layer performs feature enhancement on the feature vector through bit-by-bit multiplication.

[0057] Then, the kNN attention pooling layer containing k (k < p) feature vectors with length M processes h

[0058]

[0059] In the formula, h j (j = 1, 2,..., p, j ≠ i) represents the k nearest neighbor feature vectors of the feature vector h i ; a(·, ·) represents the spatial distance between the feature vectors h i and h j calculated using the Gaussian kernel function; the parameter σ represents the Gaussian kernel smoothing factor; N(i) represents the set of k nearest neighbors of the sample h i ; ||h i -h j || 2 represents the Euclidean distance between the feature vectors h i and h j . However, the power operation results in a high complexity in the calculation process of the Euclidean distance, so in the present application, the Manhattan operator is used to replace the Euclidean distance, and the above formula is rewritten as:

[0060]

[0061] The kNN attention pooling layer outputs a new feature vector representing the sample Y i using the spatial distance between the feature vectors:

[0062]

[0063] After the calculation of the kNN attention pooling layer, the spatial distance between the feature vectors is shortened, i.e., through the kNN clustering method, the samples belonging to the same class are close to each other in the feature space.

[0064] Then, two fully connected neural network layers are used to regress the sample feature vector, which is represented as:

[0065] h” i = ReLU(W2(ReLU(W1h i + B1)) + B2)

[0066] where W1, W2 represent the weight matrix of the fully connected layer; B1, B2 represent the bias matrix of the fully connected layer.

[0067] Finally, the output neuron of the output layer calculates and outputs the fitting result of the sample Y i , which is represented as:

[0068]

[0069] where W3 and B3 represent the weight and bias matrix respectively. After obtaining the fitting result , the AffinityNet equalizer uses the mean square error loss function to calculate the loss value of the fitting result, and uses the Adam gradient descent algorithm to update the equalizer parameters. When the equalizer loss reaches the set threshold, the training process is completed, and the test sample set is input into the equalizer to obtain the PAM-8 symbol after nonlinear equalization.

[0070] Step five: using the minimum Euclidean distance, the equalized PAM-8 symbol is mapped to the integer symbol position and inversely mapped to the binary data bit. The estimated PAM-8 data symbol is compared with the original PAM-8 sending symbol bit by bit to calculate the bit error rate. The bit error rate after using the AffinityNet equalizer is compared with the bit error rate after not using the equalizer, using the Volterra equalizer and the CNN equalizer, and the bit error rate comparison result is shown in Figure 4 . Compared with not using the equalizer, i.e. the minimum Euclidean distance decision (MED-decision), in the four OAM modes (l = <2, 3, 4, 5>), the AffinityNet equalizer respectively improves the receiver sensitivity by 2.3, 1.9, 4, 3.5 dB with a 15% FEC threshold; compared with the Volterra equalizer, the AffinityNet equalizer respectively improves the receiver sensitivity by 1.7, 1.8, 3, 3.3 dB; compared with the CNN equalizer, the AffinityNet equalizer respectively improves the receiver sensitivity by 0.8, 0.5, 0.9, 1.4 dB.

[0071] The above detailed description of the specific description, the purpose, technical scheme and beneficial effects of the application are further described in detail, it should be understood that the above description is only a specific embodiment of the present application, and does not limit the protection scope of the present application, any modification, replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A nonlinear impairment equalization method for a mode division multiplexing communication system, characterized by: The steps include: Step 1: Build a high-speed OAM-MDM optical fiber communication system; use mutually orthogonal OAM modes for mode multiplexing to achieve integer multiple expansion of the communication system capacity; Step 2: Prepare binary data bits with a length of a power of 2 as training data. After the data bits undergo PAM symbol mapping, resampling, and pulse shaping, they are sent from the transmitting end of the OAM-MDM optical fiber communication system and transmitted into the OAM-MDM communication system. The received signal y is expressed as: y(n)=H(x(n))+noise(n) Where y(n)=[y1,y2,...,y n ] represents the sequence of PAM received symbols; H represents the channel response; x(n)=[x1,x2,...,x n ] represents the original PAM symbol sent by the transmitter; noise(n) represents the additive Gaussian noise in the high-speed OAM-MDM system; Step 3: Due to random nonlinear damage during transmission, the data symbol size is distorted; after clock recovery of the received data symbol, the PAM symbol y is converted into n Together with adjacent symbols, form a data set; symbol y n The combination of the L symbols before and after it is the characteristic vector of the symbol, that is, [y n-L ,...,y n-1 ,y n ,y n+1 ,...,y n+L ]; the sequence of PAM received symbols y(n)=[y1,y2,...,y n ] is converted into (n-2L) feature vectors of length M, where M=2L+1: Step 4: Use the AffinityNet equalizer to compensate for the PAM data symbols. A fully connected neural network is used to operate on the sample feature vectors to obtain an estimate of the input sample, i.e., the PAM data symbols after nonlinear equalization. During training, the backpropagation gradient descent algorithm is used to update the parameters. During testing, the distorted signal is equalized. Step 5: Use the minimum Euclidean distance to map the equalized PAM symbols to integer symbol positions and inversely map them to binary data bits. Compare the equalization results with the transmitted symbols, demap them, and calculate the bit error rate. Use the bit error rate to compensate for the system nonlinearity of the OAM optical communication system.

2. The nonlinear impairment equalization method for a mode division multiplexing communication system according to claim 1, wherein: The implementation method of step 4 is: Divide the dataset Y into training set Y P =[Y1,Y2,...,Y p ] and the test set Y Q =[Y1,Y2,...,Y q ]; First, the feature vector Y in the training set i As input, i=1,2...,p, the equalizer parameters are trained; in the feature attention layer, the input training sample Y i Perform bit-by-bit multiplication with the feature attention vector w to perform weighted calculation on the features of the training sample: h i =w⊙Y i Where h i represents the output of the feature attention layer; ⊙ represents the bitwise multiplication operator; the feature attention vector w is defined as w=(w1,w2,…,w M ), The feature attention layer performs feature enhancement on the feature vector through bit-by-bit multiplication; The kNN attention pooling layer contains k feature vectors of length M for h i Processing, k<p; Where h j Represents the eigenvector h i The k nearest neighbor eigenvectors of , j = 1, 2, ..., p, j ≠ i; a(·,·) represents the eigenvector h calculated using the Gaussian kernel function i With h j The spatial distance between them; parameter σ represents the Gaussian kernel smoothing factor; N(i) represents the sample h i The set of k nearest neighbors of ||h i -h j || 2 Represents the eigenvector h i With h j However, the power operation makes the calculation process of Euclidean distance more complex. Using Manhattan operator to replace Euclidean distance, the above formula is rewritten as: The kNN attention pooling layer uses the spatial distance between feature vectors and outputs the representation of sample Y i The new eigenvector of : The spatial distance between samples is calculated through the kNN attention pool layer, and a new feature vector representing the sample is generated using the spatial distance to achieve sample clustering, shortening the spatial distance between feature vectors so that samples belonging to the same class are close to each other in the feature space; The fully connected neural network layer performs regression fitting on the sample feature vector. The process is expressed as: h″ i =ReLU(W2(ReLU(W1h' i +B1))+B2) Where W1, W2 represent the weight matrix of the fully connected layer; B1, B2 represent the bias matrix of the fully connected layer; The output neurons of the output layer calculate and output the sample Y i The fitting result of , the process is expressed as: Where W3 and B3 represent weight and bias matrices respectively; Finally, the AffinityNet equalizer uses the mean square error loss function to calculate the loss value of the fitting result and uses the Adam gradient descent algorithm to update the equalizer parameters; when the equalizer loss reaches the set threshold, the training process ends, and the test sample set is input into the equalizer to obtain the PAM symbol after nonlinear equalization.

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