CN112887028A

CN112887028A - GS-QAM constellation-based decision decoding method in optical fiber access network

Info

Publication number: CN112887028A
Application number: CN202110102445.0A
Authority: CN
Inventors: 迟楠; 李忠亚
Original assignee: Zhuhai Fudan Innovation Research Institute
Current assignee: Zhuhai Fudan Innovation Research Institute
Priority date: 2021-01-26
Filing date: 2021-01-26
Publication date: 2021-06-01

Abstract

The invention belongs to the technical field of optical fiber communication, and particularly relates to a GS-QAM constellation-based decision decoding method in an optical fiber access network. The method for judging the constellation points of the GS-QAM signal comprises the steps that an optimal interface, namely a hyperplane, is searched in a GS-QAM signal constellation diagram received by an access network by utilizing a Support Vector Machine (SVM), a plurality of hyperplanes realize clustering of the constellation points, different types of constellation points correspond to different QAM modulation symbols, the higher the classification accuracy is, the higher the demodulation and decoding accuracy is, and the better the performance of a communication system is. Compared with the traditional constellation point judgment method based on Euclidean distance, the constellation point judgment method based on Euclidean distance can accurately judge and classify the constellation points under the condition of not correcting phase shift and constellation distortion, obviously reduces the influence of signal phase shift and distortion caused by the characteristics of an access network channel on the demodulation accuracy, simplifies the complexity of a demodulation scheme and simultaneously improves the demodulation performance.

Description

GS-QAM constellation-based decision decoding method in optical fiber access network

Technical Field

The invention belongs to the technical field of optical fiber communication, and particularly relates to a decision decoding method based on a Geometric Shaping (GS) Quadrature Amplitude Modulation (QAM) constellation, which is applied to an optical fiber access network.

Background

Newly emerging access network application scenes such as high-definition video streaming media service, virtual reality, cloud computing and the like are promoting the capacity upgrade of a next-generation passive optical access network (PON), and the advantages of low cost and flexibility are highly approved. Meanwhile, the communication industry is studying the standardization of 50Gb/s/λ passive optical networks. Low cost intensity modulation and direct detection (IM/DD) transmission schemes using optical transmission devices with bandwidths of 10Gbps have been widely validated. To implement high-speed PONs on bandwidth-limited optical elements, advanced modulation formats and efficient digital signal processing algorithms are central research topics. High-order modulation formats such as duobinary coding, Pulse Amplitude Modulation (PAM), carrierless amplitude phase modulation (CAP), QAM and the like are applied to become potential low-cost solutions of the middle-distance and long-distance PON system.

In fiber optic communication systems, higher order QAM modulation may result in higher spectral efficiency, but at the same time intersymbol interference increases, which requires a higher signal-to-noise ratio (SNR) to ensure reliable transmission of the system. However, for a large capacity PON system based on a conventional optical fiber, the signal-to-noise ratio is reduced due to a severe distortion of the signal caused by a bandwidth limitation and fiber dispersion. To overcome these drawbacks, commonly used Digital Signal Processing (DSP) algorithms include Feed Forward Equalization (FFE), Decision Feedback Equalization (DFE), Least Mean Square (LMS) equalization, and other digital equalization algorithms. These schemes introduce excessive computational complexity while achieving the distortion suppression effect, and are costly in actual deployment. In order to relieve the calculation pressure of the equalization algorithm on a demodulation system, the distribution of a high-order constellation can be designed by using a Geometric Shaping (GS) technology at a transmitting end, so that the constellation points meet the minimum Euclidean distance maximization, and the common distribution comprises circular distribution, triangular distribution and the like. The shaped QAM signal can resist the influence of signal distortion and signal-to-noise ratio reduction on demodulation after channel transmission.

The shaped constellation still has distortion due to the nonlinear characteristics of devices and channels, and the distortion is embodied as that constellation peripheral constellation points are compressed into the constellation, and the constellation points which are originally converged at a transmitting end are diverged. The method is distinguished from the method of restraining distortion by using a complex digital equalization algorithm, the LMS equalization is combined with the multi-classification SVM to delimit different regions in the constellation, the constellation point in the same region corresponds to the same emission constellation point, and the constellation point can be directly demodulated after classification. The fact proves that the invention can realize effective suppression of signal distortion under the condition of low calculation complexity, and greatly improves the demodulation performance.

Disclosure of Invention

The invention aims to provide a decision decoding method based on a Geometric Shaping (GS) Quadrature Amplitude Modulation (QAM) constellation in a low-complexity optical fiber access network, which can directly decide in a signal constellation by using less computing resources to obtain a better decoding effect.

The invention provides a decision decoding method based on a geometry shaping quadrature amplitude modulation (marked as GS-QAM) constellation in a fiber access network, which adopts a Least Mean Square (LMS) equalizer and a plurality of two-class Support Vector Machines (SVM) to carry out decision classification on GS-QAM signals; wherein:

the LMS equalizer performs adaptive filtering on the input signal by using a classical LMS algorithm;

each of said two classes of SVM, for one 2^NQAM signal of order (with constellation points divided into 2)^NClass), one class of constellation points and the other 2, respectively^NClass 1 constellation point distinction, each constellation point being decided by only one binary SVM as the value 1, and the other 2^NThe classification result of the-1 type constellation points is a numerical value-1.

The two-class SVM has 2 in total^N2, all of^NThe two classification SVM are used for combining the classification results of the same constellation point to obtain a length of 2^NThe one-hot coding is as follows:

-1-1-1…-1 1-1

wherein, only one bit has a value of 1, and the rest are-1, such codes and classifications have a unique corresponding relation, and the unique category of the constellation point, that is, the QAM symbol corresponding to the constellation point, can be obtained; a multi-class QAM constellation decision device can be formed by a plurality of two-class SVM.

The GS-QAM signal is obtained by carrying out GS-QAM coding on the signal from a transmitting end, and the purpose of the signal coding is to enable the minimum Euclidean distance of constellation points in a signal constellation to be maximum. The common shapes include triangular distribution, square distribution, circular distribution, etc.

In the invention, before each classifier is classified, the classifier needs to be trained by using a small amount (such as 4-7%) of constellation of communication transceiving data; through training, an optimal interface is searched in a constellation of received data, and the basis of the boundary is accurate constellation distribution of the transmitted data. If x represents two-dimensional training data containing horizontal and vertical coordinates of a received constellation, y belongs to {1, -1} and is a corresponding label, wherein y is equal to 1 when the received constellation point is in the same type with the transmitting constellation point, and otherwise, y is equal to-1.

For linearly classifiable data, there is a decision function:

f(x)＝w^Tx+b

wherein w and b represent weights and offsets, such that when y ═ 1, f (x) < 0; when y is 1, (x) is > 0; f (x) 0 is the decision boundary between the two classes, i.e. the hyperplane; the constellation points on the plane f (x) ± 1 are called support vectors, the distance between the planes f (x) ± 1 is 2/| w | |, and when 2/| w | reaches the maximum, the optimal interface is found. The training process of the SVM can be expressed as the following optimization process:

constraint conditions are as follows: y is_i(w^Tx_i+ b) is not less than 1, where i ═ 1, 2

In the formula, y_iRepresents the ith training data x_iA corresponding label.

For some cases where the non-perfect linear split is possible, a relaxation variable ξ may be introduced_i>0, indicating that the classification result allows a certain abnormal point, the optimization process can be rewritten as:

constraint y_i(w^Tx_i+b)≥1-ξ_i

ξ_i≥0，i＝1，2，...，

In the formula, y_iRepresents the ith training data x_iCorresponding label, C>And 0 is a penalty coefficient for adjusting the influence of the relaxation variables on the optimization result.

When the constellation deformation is serious, for the data which is linear and inseparable, the training data x can be mapped into a high-dimensional space by using a nonlinear function phi, the SVM searches a linear separable hyperplane in the high-dimensional space, and maximizes 2/| w | |, then the optimization process can be rewritten as follows:

constraint y_i(w^Tφ(x_i)+b)≥1-ξ_i

ξ_i≥0，i＝1，2，...，n

In the formula, y_iRepresents the ith training data x_iCorresponding label, C>And 0 is a penalty coefficient for adjusting the influence of the relaxation variables on the optimization result. K (x) consisting of a function phi_i，x_j)＝φ(x_i)^Tφ(x_j) Called kernel functions, the four most basic kernel functions include:

1) linear function:

2) polynomial function:

3) radial basis function: k (x)_i，x_j)＝exp(-γ||x_i-x_j||²)，γ＞0

4) Logic function:

in which γ, r and d are all kernel functionsAnd (4) adjusting parameters. When the kernel function is chosen to be a linear function, phi (x)_i)＝x_iThe optimization process for linearly indivisible data degenerates to an optimization process for non-fully linearly indivisible data. In the invention, because the constellation at the receiving end of the communication system belongs to the data which can be divided by the non-complete linearity, the kernel function directly uses the linear function to obtain better classification effect in the subsequent concrete implementation, the input data does not need to be mapped to a high-dimensional space, and the complexity of calculation is controlled. However, in practical applications, when the constellation distortion is severe, the kernel function is replaced by other non-linear functions, without departing from the spirit and scope of the present invention.

In the invention, after the optimal support vector is found in the optimization process, the hyperplane is determined. It should be noted that, for the GS-QAM constellation, each two-class SVM may include a plurality of hyperplanes, and for the decision function f (x) corresponding to each hyperplane, the constellation points belonging to this class should be f (x) <0, and the constellation points not belonging to this class should be f (x) >0, where the number of hyperplanes depends on the class number of other class constellation points adjacent to the constellation point of this class.

In the invention, the support vector and the hyperplane obtained by training each SVM classifier can be adjusted in different signal distortion degrees. As the channel response characteristics change, the constellation of the training data also has distortion and changes in the signal-to-noise ratio, which prompt the SVM to select a new support vector and the location of the hyperplane when finding the solution to the optimization problem. Compared with the traditional hard decision method based on Euclidean distance, the method for timely adjusting the decision boundary along with the change of the constellation shape has the function of identifying the deformation of the constellation points and can achieve better classification effect.

The method for judging and decoding utilizes a Support Vector Machine (SVM) to search an optimal interface, namely a hyperplane, in a GS-QAM signal constellation diagram received by an access network, clustering of constellation points is realized by a plurality of hyperplanes, different types of constellation points correspond to different QAM modulation symbols, the higher the classification accuracy is, the higher the demodulation and decoding accuracy is, and the better the performance of a communication system is. Compared with the traditional constellation point judgment method based on Euclidean distance, the constellation point judgment method based on Euclidean distance can accurately judge and classify the constellation points under the condition of not correcting phase shift and constellation distortion, obviously reduces the influence of signal phase shift and distortion caused by the characteristics of an access network channel on the demodulation accuracy, simplifies the complexity of a demodulation scheme and simultaneously improves the demodulation performance.

The geometric shaping constellation decision method provided by the invention has the following advantages by combining the classic machine learning method SVM and the LMS equalization algorithm:

(1) the invention is different from the equalization processing only carried out on the time domain signal, fully utilizes the characteristics of the geometric shaping technology, processes the signal distortion in the shaped constellation and reduces the complexity of the signal processing algorithm at the receiving end of the communication system.

(2) By selecting the support vector in the SVM and redistributing the hyperplane, the method can identify the change condition of signal distortion in time and make classification decision adjustment, and has better fault tolerance and accuracy compared with the traditional method based on Euclidean distance hard decision.

(3) Compared with the traditional equalization algorithm which needs to reserve bits with enough length in the transmitting signal for storing pilot frequency information, the method can train the SVM in the invention only by using few skilled data, thereby saving precious frequency spectrum resources and being beneficial to improving the communication capacity of a communication system.

Drawings

Fig. 1 is a schematic diagram of a GS-QAM constellation decision method proposed by the present invention.

FIG. 2 is a diagram of a GS-8QAM passive optical network communication system to which the decision method of the present invention is applied.

Fig. 3(a) is a diagram of the decision result of the decision method proposed by the present invention in three kinds of geometric shaping constellations.

Fig. 3(b) is a decision result diagram of the euclidean distance-based decision method in three geometric shaping constellations.

Fig. 4(a) is a diagram illustrating the improvement effect of the invention on demodulation error rate of a circularly distributed 8QAM constellation at different signal amplitudes.

Fig. 4(b) is a diagram showing the effect of improving demodulation error rate of square distribution 8QAM constellations under different signal amplitudes.

Fig. 4(c) is a diagram showing the improvement effect of the invention on the demodulation error rate of the triangular distribution 8QAM constellation under different signal amplitudes.

Fig. 5(a) is a diagram illustrating the improvement effect of the invention on demodulation error rate of circularly distributed 8QAM constellations under different channel bandwidths.

Fig. 5(b) is a diagram showing the effect of the invention on improving demodulation error rate of a square distribution 8QAM constellation under different channel bandwidths.

Fig. 5(c) is a diagram illustrating the improvement effect of the invention on the bit error rate of the triangularly distributed 8QAM constellation demodulation under different channel bandwidths.

Fig. 6(a) is a diagram illustrating the improvement effect of the invention on demodulation error rate of circularly distributed 8QAM constellations under different transmission powers.

Fig. 6(b) is a diagram showing the effect of improving demodulation error rate of square distribution 8QAM constellations under different transmission powers.

Fig. 6(c) is a diagram showing the improvement effect of the invention on the demodulation error rate of the triangular distribution 8QAM constellation under different transmission powers.

Reference numbers in the figures: 1-electroabsorption modulator, 2-twenty kilometer length standard single mode fiber, 3-avalanche photodiode, 4-transgroup amplifier.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, it will be appreciated by those of ordinary skill in the art that numerous technical details are set forth in order to provide a better understanding of the present application in various embodiments of the present invention. However, the technical solutions claimed in the claims of the present application can be implemented without these technical details and with various changes and modifications based on the following embodiments.

The invention aims to provide a low-complexity decision decoding method based on a geometric shaping constellation, which is applied to an optical access network, can directly decide in a signal constellation by using less computing resources and obtains better decoding effect.

The geometric wholeAnd the shape constellation is obtained by carrying out GS-QAM coding on the signal from the transmitting end, the shape of the coded signal constellation is the minimum Euclidean distance between constellation points, and the shape of the coded signal constellation is triangular distribution, square distribution, circular distribution and the like. The decision method of the invention is composed of a plurality of two-class SVM, and for one 2^NQAM signal of order whose constellation points are divided into 2^NAnd (4) class. Each two-class SVM classifies one class of constellation points into a value 1 and the other class of constellation points into a value 2^NThe classification result of the class-1 constellation points is a value-1, and each constellation point is and is only decided as a value 1 by one binary SVM. Thus, the two classes of SVM have a total of 2^N2, all of^NThe classification results of the same constellation point are combined by the two classification SVM to obtain a length of 2^NThe one-hot coding is as follows:

-1-1-1…-1 1-1

wherein, only one bit has a value of 1, the rest are-1, the code and the classification have a unique corresponding relation, the unique class of the constellation point can be obtained, namely the QAM symbol corresponding to the constellation point, and a multi-classification QAM constellation decision device can be formed by a plurality of two-classification SVM.

Each two-classification SVM classifier needs to use a small amount of constellation of communication transceiving data for training before classification is implemented, an optimal interface is searched in the constellation of the received data in the training process, and the boundary is the accurate constellation distribution of the transmitted data. If x represents two-dimensional training data containing horizontal and vertical coordinates of a received constellation, y belongs to {1, -1} and is a corresponding label, wherein y is equal to 1 when the received constellation point is in the same type with the transmitting constellation point, and otherwise, y is equal to-1. For classifiable data, there is at least one such decision function:

f(x)＝w^Tx+b

wherein w and b represent weights and offsets, such that when y is-1, f (x)<0; when y is 1, f (x)>0. And f (x) 0 is the decision boundary between the two classes, i.e. the hyperplane. The constellation points on the plane f (x) ± 1 are called support vectors, the distance between the planes f (x) ± 1 is 2/| w | |, and when 2/| w | | reaches the maximum, the optimal interface is found. Introducing a relaxation variable xi_i>0, so that the classification boundaryIf a range of outliers are allowed in the vicinity, the training process of the SVM can be expressed as the following optimization process:

constraint conditions are as follows: y is_i(w^Tx_i+b)≥1-ξ_i

ξ_i≥0，i＝1，2，...，n

constraint y_i(w^Tφ(x_i)+b)≥1-ξ_i

ξ_i≥0，i＝1，2，...，n

In the formula, y_iRepresents the ith training data x_iCorresponding label, C>And 0 is a penalty coefficient for adjusting the influence of the relaxation variables on the optimization result. When the kernel function is chosen to be a linear function, phi (x)_i)＝x_iThe two optimization processes are equivalent. In the invention, because the constellation at the receiving end of the communication system belongs to the data which can be divided by the non-complete linearity, the kernel function directly uses the linear function to obtain better classification effect in the subsequent concrete implementation, the input data does not need to be mapped to a high-dimensional space, and the complexity of calculation is controlled. However, in practical applications, when the constellation distortion is severe, the kernel function is replaced by other non-linear functions, without departing from the spirit and scope of the present invention.

After the optimal support vector is found in the optimization process, the hyperplane is determined. It should be noted that, for the GS-QAM constellation, each two-class SVM may include a plurality of hyperplanes, the number of hyperplanes depends on the number of classes of other constellation points adjacent to the constellation point of this class, and the decision function f (x) corresponding to each hyperplane has a limited domain where the constellation points belonging to this class should have f (x) <0, and the constellation points not belonging to this class should have f (x) > 0.

In the implementation process of the present invention, after LMS equalization and training of the multi-class SVM, the signal decision process applied to the GS-QAM constellation in the optical fiber access network is shown in fig. 1. After the constellation to be classified is input into SVM, normalization processing is carried out through a linear kernel function, the normalization result is input into a group of decision functions defined by support vectors, the positive and negative are judged through a sign function sign (DEG), and finally the output length is 2^NThe unique hot code of (2) uniquely corresponds to the QAM symbol corresponding to the constellation point.

On the right of fig. 1, it is shown that under different nonlinear distortion degrees, peripheral star points of three GS-8QAM constellations are compressed to different degrees, resulting in distortion of the whole constellation. The partially distorted constellation points are used as training data of the SVM, each two-classification SVM is prompted to solve the optimization problem again, a new hyperplane is obtained, and the change of the position and the direction of the hyperplane directly reflects the countermeasure of constellation distortion, so that the influence of distortion on the constellation point classification effect can be inhibited, and the characteristic is absent in the decision method based on the Euclidean distance.

In order to prove the effect of the present invention in the communication system, the verification steps and the verification results of the LMS equalization combined multi-class SVM geometric shaping constellation decision method in the PON access network are introduced next. The system structure of the PON access network is shown in FIG. 2, and the whole PON system is in a professional simulation software VPItransnission maker^TMThe method is built and simulated, bandwidth limitation, chromatic dispersion and nonlinearity of the optical fiber link are fully considered in the simulation, and the specific working steps are as follows:

first, at the transmitter, to simulate a bandwidth limited system, the electrical signal generated from the transmitter DSP is passed through a low-pass fourth-order bessel filter with a cutoff frequency less than 25GHz before being input to an electro-absorption modulator (EAM). On the other branch, a continuous emitting laser generates 228.33THz continuous waves and inputs them into the EAM, whose transmission characteristics are determined by a transmission curve with strong nonlinearity. Then, the modulated optical signal is sent to a band-pass optical filter to generate a single sideband signal. This operation can reduce power attenuation caused by dispersion. For flexible control of the transmission power, the output signal of the filter is passed through an optical amplifier. The signal is then transmitted through a 20 km long Standard Single Mode Fiber (SSMF) attenuated 0.32e-3dB/m to two 1 x 8 splitters in series for simulating a multi-user optical distribution network. One of the outputs of the optical distribution network passes the optical signal through a variable attenuator to an Avalanche Photodiode (APD). The APD converts the optical signal into a current signal and is further converted into a voltage signal by a transimpedance amplifier (TIA). And then, the voltage signal is analyzed by an off-line receiving end DSP.

In the transmit side DSP, GS-8QAM symbols are generated and then oversampled for each symbol, 4 samples per symbol. An orthogonal root-mean-square raised cosine shaping filter pair containing an I/Q channel is applied, and the filter has a variable roll-off coefficient to obtain a carrier-free amplitude phase modulation signal (CAP). The receiving end DSP consists of a synchronization module, a matched filter pair for extracting in-band signals, a down sampler for generating a symbol every 4 samples, a simple LMS equalizer, a multi-class SVM classifier and a QAM decoder for converting SVM output symbols into bit streams, and the bit streams output by the receiving end DSP are used for calculating the bit error rate of recovered signals to serve as an evaluation standard of system performance.

The multi-classification SVM classifier uses 5% of the sending and receiving data as a training data set; the transmitted data and the received data are normalized and then take values between-1 and 1; the kernel function being a linear function, i.e.

φ(x_i)＝x_i(ii) a The penalty coefficient C is taken to be 2^-5To 2¹⁰And searching and finally determining that C is 5. The optimization process implemented this time is set as follows:

constraint y_i(w^Tx_i+b)≥1-ξ_i

ξ_i≥0，i＝1，2，...，n

The value of n is determined by the number of abnormal constellation points near the interface, and the variation range of n in the implementation process is 0-2⁸In the meantime. The optimization problem is solved by using a Sequence Minimum Optimization (SMO) algorithm to obtain a support vector in each two-classification SVM, and values of w, b and xi are further determined. The trained 8 binary SVM classifiers are used for classifying the constellation points of the test data, the classification results form the single hot codes with the length of 8, the coding results directly correspond to the symbols of 8QAM, an 8QAM decoder is used for decoding the symbols, and the decoding results can be used for calculating the error code condition of the receiving system.

Fig. 3(a) shows the decision result of the present invention after LMS equalization and SVM classification are performed on the received signal constellation in the DSP at the receiving end of the emulated PON system, where the thick dotted line in the figure is the interface obtained after SVM training. Comparing the decision boundary (i.e. the thick solid line in the figure) obtained by the decision method based on euclidean distance in fig. 3(b), it can be found that the decision boundary generated by the present invention reallocates the decision boundary along with the generation of constellation distortion, and the decision method based on euclidean distance fixes the decision boundary according to the distortion-free distribution of the transmitted constellation. In order to verify the performance improvement brought by the invention, the bias current of the laser is firstly fixed, and then the amplitude of the modulation signal is adjusted, so that the change curve of the demodulation error rate of the three GS-8QAM signals along with the amplitude of the transmission signal is obtained as shown in FIGS. 4(a), (b) and (c). With the increase of the amplitude, the change curves of the demodulation bit error rate of the three GS-8QAM signals all have a turning point at the bottom, which is because the larger signal amplitude brings higher signal-to-noise ratio and shows more serious nonlinear distortion due to the nonlinear modulation characteristic of the EAM, and the increase of the nonlinear distortion is not favorable for accurately judging the constellation point. Fig. 4(a), (b) and (c) show that the method using LMS equalization in combination with SVM classification can better suppress the influence of nonlinear distortion on constellation point decision. In fig. 4(a), the enhancement of the circular constellation is most obvious compared with the euclidean distance decision method. This is because the ratio of the distance from the outer ring constellation point to the center of the circular geometry shaping constellation to the distance from the inner ring constellation point to the center is larger than that of the other two shaping constellations, which means that the circular GS-8QAM constellation is more seriously damaged by nonlinearity after EAM modulation, and the situation that the constellation is compressed on the periphery is more obvious. The deformation of the constellation point deviates from the boundary of Euclidean distance judgment seriously, and the judgment method of the invention can update the judgment boundary according to the deformation of the constellation, thereby bringing greater performance improvement.

Fig. 5(a), (b) and (c) show the variation curve of the demodulation error rate of three GS-8QAM signals with the channel bandwidth of the access network. With the increase of the channel bandwidth, the three GS-8QAM signals show better performance, and the demodulation results of the three geometric shaping constellations using the judging method of the invention are all improved to a certain extent, which means that the required modulation bandwidth is lower under the condition of the same error code. In fig. 5(a), the improvement of the circular constellation is still more obvious compared with the euclidean distance decision method. Similarly, the circular GS-8QAM constellation is more seriously damaged by nonlinearity after being modulated by EAM, the situation that the periphery of the constellation is compressed is more obvious, and the SVM can adjust the position and the direction of the hyperplane by a better distortion degree, so that more performance is improved.

Fig. 6(a), (b) and (c) show the variation curve of the demodulation error rate of three GS-8QAM signals with the transmission signal power of the access network.

With the increase of transmission power, the error rate is obviously reduced. When the transmission power reaches 12.5mW, the demodulation error rate is reduced to 3.8 multiplied by 10 by the auxiliary demodulation system^-3Below this hard decision forward error correction threshold (HD-FEC), this means that the system can achieve error-free transmission using very little Forward Error Correction (FEC) redundancy coding. Without using the decision method of the inventionIn the demodulation process, only the geometric shaping constellation with triangular distribution reduces the error rate to be lower than the HD-FEC threshold when the LMS equalization and Euclidean distance judgment method is used. The invention realizes the lowest bit error rate in all test results in the geometric shaping constellation with circular distribution, which further verifies the superiority of the judgment method of the invention under the condition of strong nonlinear distortion.

In summary, through simulation comparison of multiple dimensions, the present embodiment shows that compared to the existing decision scheme based on euclidean distance, the proposed decision method for geometry shaping constellation based on LMS equalization and SVM classification needs to use less modulation bandwidth, less redundant coding and lower power budget under the same error performance. The performance of the PON access network based on the geometric shaping scheme with limited bandwidth is greatly improved due to the constellation decision method provided by the invention.

The division of each step in this embodiment is only for clarity of description, and implementation may be combined into one step or split some steps into multiple steps, and all that is included in the same logical relationship is within the scope of the present patent.

It will be understood by those of ordinary skill in the art that the foregoing embodiments are specific examples for carrying out the invention, and that various changes in form and details may be made therein without departing from the spirit and scope of the invention in practice.

Claims

1. A decision decoding method based on GS-QAM constellation in the optical fiber access network is characterized in that a Least Mean Square (LMS) equalizer and a plurality of Support Vector Machines (SVM) of two classes are adopted to carry out decision classification on GS-QAM signals; wherein:

each of the two classes of SVM is classified into 2 for one constellation point^NClass 2^NOrder QAM signal, which respectively combines one kind of constellation point with the other 2^NClass 1 constellation points, each constellation point being separated by only one binary classThe SVM decides on the value 1 and on the other 2^N-the classification result of the class 1 constellation points is a value of-1;

the two-class SVM has 2 in total^N2, all of^NThe two classification SVM are used for combining the classification results of the same constellation point to obtain a length of 2^NIs in the shape of: -unique heat encoding of 1-1-1 … -11-1; namely, only one bit has a value of 1, and the rest are-1, and the unique corresponding relation exists between the codes and the classification, so that the unique class of the constellation point is obtained, namely, the QAM symbol corresponding to the constellation point is obtained; a multi-class QAM constellation decision device is formed by a plurality of two-class SVM;

the GS-QAM signal is obtained by carrying out GS-QAM coding on the signal from a transmitting end, and the purpose of the signal coding is to enable the minimum Euclidean distance of constellation points in a signal constellation to be maximum.

2. The decision decoding method according to claim 1 wherein the constellation shape is a triangular distribution, a square distribution and/or a circular distribution.

3. The method according to claim 1, wherein each classifier needs to be trained by using a small number of constellations for communication transceiving data before performing classification; through training, searching an optimal interface in a constellation of received data, wherein the basis of the boundary is accurate constellation distribution of transmitted data; setting x as two-dimensional training data containing horizontal and vertical coordinates of a receiving constellation, wherein y belongs to {1, -1} as a corresponding label, and if the receiving constellation point and a transmitting constellation point are similar, y is 1, otherwise, y is-1;

for linearly classifiable data, there is a decision function:

f(x)＝w^Tx+b

wherein w and b represent weights and offsets, such that when y ═ 1, f (x) < 0; when y is 1, (x) is > 0; f (x) 0 is the decision boundary between the two classes, i.e. the hyperplane; the constellation points on the plane f (x) ± 1 are called support vectors, the distance between the planes f (x) ± 1 is 2/| w | |, and when the 2/| w | | reaches the maximum, the optimal interface is found; the training process of the SVM is represented as the following optimization process:

In the formula, y_iRepresents the ith training data x_iA corresponding label.

4. Decision decoding method according to claim 3, characterized in that for a non-fully linear separable case a relaxation variable ξ is introduced_iIf >0, the classification result allows a certain abnormal point, the optimization process is as follows:

constraint y_i(w^Tx_i+b)≥1-ξ_i

ξ_i≥0，i＝1，2，...，n

In the formula, y_iRepresents the ith training data x_iAnd C & gt 0 is a penalty coefficient for adjusting the influence of the relaxation variable on the optimization result.

5. The decision decoding method according to claim 4, wherein for the linearly indivisible data, the training data x is mapped into a high-dimensional space by using a non-linear function phi, the SVM finds a linearly separable hyperplane in the high-dimensional space, and maximizes 2/| w | |, then the above optimization process is rewritten as:

constraint y_i(w^Tφ(x_i)+b)≥1-ξ_i

ξ_i≥0，i＝1，2，...，n

In the formula, y_iRepresents the ith training data x_iC is greater than 0 and is a punishment coefficient for adjusting the influence of the relaxation variable on the optimization result; the function phi is a function for realizing non-linear mapping, and K (x) is composed of the function phi_i，x_j)＝φ(x_i)^Tφ(x_j) Referred to as the kernel function of the SVM.

6. The decision decoding method according to claim 5, wherein the kernel function is one of four:

(1) linear function:

(2) polynomial function:

(3) radial basis function: k (x)_i，x_j)＝exp(-γ||x_i-x_j||²)，γ＞0；

(4) Logic function:

where γ, r and d are all adjustable parameters of the kernel function.

7. The decision decoding method according to claim 5, wherein the support vector and the hyperplane obtained by training of each SVM classifier are not always fixed, and with the change of link characteristics, the constellation of training data has deformation and the change of signal-to-noise ratio, and these changes promote SVM to obtain the new positions of the support vector and the hyperplane when solving the optimization problem, thereby achieving better classification effect.