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CN111327558B - Method and system for GMM non-uniform quantization for filter multi-carrier modulation optical communication - Google Patents

Method and system for GMM non-uniform quantization for filter multi-carrier modulation optical communication Download PDF

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CN111327558B
CN111327558B CN202010129233.7A CN202010129233A CN111327558B CN 111327558 B CN111327558 B CN 111327558B CN 202010129233 A CN202010129233 A CN 202010129233A CN 111327558 B CN111327558 B CN 111327558B
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毕美华
林嘉芊
杨国伟
周雪芳
池灏
胡淼
李齐良
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Hangzhou Dianzi University
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Abstract

The invention discloses a GMM non-uniform quantization system for filter multi-carrier modulation optical communication, which comprises: the device comprises a preprocessing module, a calculating module and an output module; the preprocessing module is used for preprocessing data of the data sequence sent by the filter bank multi-carrier modulation transmitter to obtain a sample vector and taking the sample vector as an input vector of the GMM quantization module; the sample vectors comprise real signal sample vectors and imaginary signal sample vectors; the computing module is used for computing the GMM parameter of the input real part signal sample vector according to a maximum expectation algorithm, and then estimating the GMM parameter of the imaginary part signal sample vector according to the GMM parameter computed by the real part signal sample vector to respectively obtain a Gaussian mixture model with the maximum responsivity; and the output module is used for inputting the samples into the Gaussian mixture model with the maximum responsivity for clustering operation to obtain and output a quantization result.

Description

Method and system for GMM non-uniform quantization for filter multi-carrier modulation optical communication
Technical Field
The invention relates to the technical field of optical communication, in particular to a method and a system for GMM non-uniform quantization of filter multi-carrier modulation optical communication.
Background
In recent years, with the emergence of emerging technologies such as machine learning, social networking, cloud computing and the like, people have a rapidly increasing trend on the demand of flow throughput and bandwidth, and in order to meet the requirements of high capacity, asynchronous transmission and objective spectrum efficiency, an Intensity Modulation Direct Detection (IMDD) technology based on a multi-carrier modulation technology is very popular in short-distance optical fiber links due to the fact that the IMDD technology is simple to implement and low in complexity. Meanwhile, compared with the traditional multi-carrier modulation technology Orthogonal Frequency Division Multiplexing (OFDM), multi-carrier modulation signals based on filter banks including multi-carrier (FBMC) based on filter banks, multi-carrier (UFMC) based on general filters and the like are widely applied to optical fibers and wireless communication systems, particularly the UFMC balances the advantages and disadvantages of multi-carrier and orthogonal frequency division multiplexing of the filter banks, the block diagram is simpler to realize, and the spectrum efficiency is higher than that of generalized frequency division multiplexing. In a practical multicarrier modulated IMDD system, a high resolution DAC is required to convert a digital signal into an electronic analog signal. As the network part closest to the user, both the optical fiber access network and the wireless forward access network are very sensitive to the system cost requirement, the low-resolution digital-to-analog converter (DAC) cannot guarantee the system performance although the cost is low, and the high-resolution digital-to-analog converter (DAC) can meet the system requirement, but the cost and the power consumption of the system can be increased. Therefore, how to reduce the system cost on the premise of ensuring the system performance is one of the research focuses of the IMDD multi-carrier modulation system, and it is very necessary to research a method based on the non-uniform quantization DAC to improve the performance of the low-bit-number DAC to reduce the system cost.
The quantization modes mainly comprise a uniform quantization mode and a non-uniform quantization mode, and the non-uniform quantization method comprises the quantization modes of exponential quantization, power quantization, broken line quantization, signal distribution estimation quantization and the like. The quantization method based on signal distribution estimation is a method of calculating a quantization level at the time of a minimum quantization error by nonlinear programming. In a traditional OFDM system, for example, Jizong Peng published in 2017 in IEEE Photonics Journal, "SQNR improved Enabled by way of non-null before DAC Output Levels for IM-DD OFDM Systems", the scheme obtains an optimal quantization level with minimum quantization noise through nonlinear programming iteration according to the fact that OFDM signals accord with Gaussian distribution, so that the performance of the IMDD-OFDM system is improved in SQNR, BER and EVM. However, in the general filter multi-carrier system, the processing of the filter can make the waveform appear sharp and not be a complete gaussian distribution, and the quantization order optimization algorithm under the assumption of the gaussian distribution proposed by Jizong Peng is not suitable for the general filter-based multi-carrier modulation system. The quantization level can be determined by non-parametric estimation after the distribution estimation of the signal.
In 2018, the inventor adopts a non-parameter Estimation Histogram method to perform signal Estimation on an IMDD-OQAM-OFDM waveform in a Performance Optimization by Nonparametric Histogram Estimation for Low Resolution in IMDD-OQAM-OFDM System published by IEEE Photonics Journal, and then determines a quantization level by using a non-linear programming mode, so that a better effect is achieved in the aspect of improving the System Performance. However, the scheme also has the problems that the nonparametric estimation histogram method has a large demand on the number of samples, high calculation complexity and the like, so that an optimization space still exists for the non-uniform quantization algorithm of the general filter multi-carrier system.
Disclosure of Invention
The present invention addresses the deficiencies of the prior art by providing a method and system for GMM non-uniform quantization for filter multi-carrier modulated optical communications to improve the quantization performance of DACs.
In order to achieve the purpose, the invention adopts the following technical scheme:
a system for GMM non-uniform quantization for filter multi-carrier modulated optical communications, comprising: the device comprises a preprocessing module, a calculating module and an output module;
the preprocessing module is used for preprocessing data of a data sequence sent by the filter bank multi-carrier modulation transmitter to obtain a sample vector and taking the sample vector as an input vector of the GMM quantization module; the sample vectors comprise real signal sample vectors and imaginary signal sample vectors;
the computing module is used for computing the GMM parameter of the input real part signal sample vector according to a maximum expectation algorithm, and then estimating the GMM parameter of the imaginary part signal sample vector according to the GMM parameter computed by the real part signal sample vector to respectively obtain a Gaussian mixture model with the maximum responsivity;
and the output module is used for inputting the sample into the Gaussian mixture model with the maximum responsivity for clustering operation to obtain and output a quantization result.
Further, the preprocessing module is specifically data x to be transmitted1,x2,...,xnSplitting the real part signal and the imaginary part signal, respectively forming a one-dimensional sample vector sequence by the real part signal and the imaginary part signal, and taking the one-dimensional sample vector sequence as an input vector of a GMM quantization module; the one-dimensional sample vector sequence is used as an input vector of the GMM quantization module and is particularly real part signal data Re { x1}，Re{x2}，...，Re{xn} and imaginary signal data Im { x1},Im{x2},...,Im{xnAnd independently inputting the data according to the original data sequence.
Further, the calculation module comprises an initialization module, a responsiveness calculation module and a parameter calculation module;
the initialization module is used for initializing GMM parameters of a real part signal sample vector and an imaginary part signal sample vector; the parameter is (alpha)1,α2,...,αk；μ1μ2,...,μk,σ1,σ2,...,σk)；
The responsivity calculating module is used for calculating the responsivity of the GMM sample vectors of the real part signal and the imaginary part signal according to the GMM parameters of the real part signal sample vector and the imaginary part signal sample vector;
and the parameter calculation module is used for calculating the GMM parameter of the new round of sample vector according to the responsivity of the GMM sample vector of the obtained real part signal and the imaginary part signal, and converging the GMM parameter with the responsivity calculation module to obtain the Gaussian mixture model with the maximum responsivity.
Further, the formula of the GMM is:
Figure BDA0002395333120000031
wherein,
Figure BDA0002395333120000032
expressing probability density formulas of all mixed components in the Gaussian mixture model; mu.siAnd σiRespectively representing the mean and covariance, α, of the ith Gaussian distributioniRepresents a mixing coefficient satisfying
Figure BDA0002395333120000033
The parameters of the GMM of the real part signal sample vector in the initialization module are:
Figure BDA0002395333120000034
the GMM parameter of the imaginary signal sample vector is used as a GMM parameter initialization parameter of the imaginary signal sample vector through the GMM parameter of the real signal sample vector;
the responsivity calculation in the responsivity calculation module is specifically to calculate the posterior probability that the real part signal sample vector and the imaginary part signal sample vector are generated by the GMM mixed component of the real part signal sample vector and the imaginary part signal sample vector, and is expressed as:
Figure BDA0002395333120000041
the GMM model parameters of a new round of sample vectors in the parameter calculation module are represented as:
Figure BDA0002395333120000042
Figure BDA0002395333120000043
Figure BDA0002395333120000044
wherein, γjiRepresenting the generated posterior probability.
Further, the output module clusters the sample data according to the responsivity, and the clustering is represented as:
Figure BDA0002395333120000045
accordingly, there is provided a method for GMM non-uniform quantization for filter multi-carrier modulated optical communications, comprising the steps of:
s1, performing data preprocessing on a data sequence sent by a filter bank multi-carrier modulation transmitter to obtain a sample vector, and taking the sample vector as an input vector of a GMM quantization module; the sample vectors comprise real signal sample vectors and imaginary signal sample vectors;
s2, calculating GMM parameters of input real part signal sample vectors according to a maximum expectation algorithm, and estimating the GMM parameters of imaginary part signal sample vectors according to the GMM parameters calculated by the real part signal sample vectors to respectively obtain Gaussian mixture models with the maximum responsivity;
and S3, inputting the sample into a Gaussian mixture model with the maximum responsiveness for clustering operation, and obtaining and outputting a quantization result.
Further, the step S1 is to transmit data x specifically1,x2,...,xnSplitting the real part signal and the imaginary part signal, respectively forming a one-dimensional sample vector sequence by the real part signal and the imaginary part signal, and taking the one-dimensional sample vector sequence as an input vector of a GMM quantization module; the one-dimensional sample vector sequence is used as an input vector of the GMM quantization module and is particularly real part signal data Re { x1}，Re{x2}，...，Re{xn} and imaginary signal data Im { x1},Im{x2},...,Im{xnAnd independently inputting the data according to the original data sequence.
Further, the step S2 includes:
s21, initializing GMM parameters of a real part signal sample vector and an imaginary part signal sample vector; the parameter is (alpha)1,α2,...,αk；μ1μ2,...,μk,σ1,σ2,...,σk)；
S22, calculating the responsivity of the GMM sample vectors of the real part signal and the imaginary part signal according to the GMM parameters of the real part signal sample vector and the imaginary part signal sample vector;
and S23, calculating the GMM parameter of the new round of sample vector according to the responsivity of the GMM sample vector of the obtained real part signal and imaginary part signal, and iteratively converging with the step S22 to obtain the Gaussian mixture model with the maximum responsivity.
Further, the formula of the GMM is:
Figure BDA0002395333120000051
wherein,
Figure BDA0002395333120000052
expressing probability density formulas of all mixed components in the Gaussian mixture model; mu.siAnd σiRespectively representing the mean and covariance, alpha, of the ith Gaussian distributioniRepresents a mixing coefficient satisfying
Figure BDA0002395333120000053
The parameters of the GMM of the real part signal sample vector in step S21 are:
Figure BDA0002395333120000054
the GMM parameter of the imaginary signal sample vector is used as a GMM parameter initialization parameter of the imaginary signal sample vector through the GMM parameter of the real signal sample vector;
the responsivity calculation in step S22 is specifically to calculate a posterior probability that the real signal sample vector and the imaginary signal sample vector are generated by GMM mixed components of the real signal sample vector and the imaginary signal sample vector, and is expressed as:
Figure BDA0002395333120000061
the GMM model parameters of the sample vector of the new round in step S23 are represented as:
Figure BDA0002395333120000062
Figure BDA0002395333120000063
Figure BDA0002395333120000064
wherein, γjiRepresenting the generated posterior probability.
Further, the step S3 includes clustering the sample data according to the responsiveness, which is represented as:
Figure BDA0002395333120000065
compared with the prior art, the invention has the following beneficial effects:
1. compared with the traditional uniform quantization method, the algorithm performance of the invention can obtain better quantization performance, thereby improving the performance of the general filter multi-carrier modulation optical communication system.
2. Compared with a nonlinear programming quantization method based on signal estimation, the algorithm performance of the invention can obtain better signal estimation effect and quantization effect, and the algorithm is simpler and has lower complexity.
3. Compared with other clustering learning algorithms such as neural networks and the like, the algorithm provided by the invention is simpler, more intuitive and easy to realize.
Drawings
Fig. 1 is a system block diagram of GMM non-uniform quantization for filter multi-carrier modulation optical communications according to an embodiment;
fig. 2 is a block diagram of a filter bank multi-carrier modulation optical communication system based on GMM parameter estimation according to an embodiment;
fig. 3 is a diagram illustrating SQNR performance comparison of digital signals in a high-speed optical filter bank multi-carrier system according to an embodiment.
Detailed Description
The following embodiments of the present invention are provided by way of specific examples, and other advantages and effects of the present invention will be readily apparent to those skilled in the art from the disclosure herein. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
It is an object of the present invention to address the deficiencies of the prior art by providing a system for GMM non-uniform quantization for filter multi-carrier modulated optical communications.
The input data sequence is preprocessed and composed into n sample vectors. And the GMM quantization module respectively performs iterative computation through an EM algorithm to obtain k Gaussian distributions of the signals, the signals are clustered into a cluster with the maximum responsivity, the mean value of the cluster is used as the quantization center of the quantization interval, and the mean value of the cluster is output according to the input sequence of the sample vector to be the quantization result.
Example one
The present embodiment provides a system for GMM non-uniform quantization for filter multi-carrier modulation optical communication, as shown in fig. 1, including: the device comprises a preprocessing module 11, a calculating module 12 and an output module 13;
the preprocessing module 11 is configured to perform data preprocessing on a data sequence sent by a filter bank multi-carrier modulation transmitter to obtain a sample vector, and use the sample vector as an input vector of the GMM quantization module; the sample vectors comprise real signal sample vectors and imaginary signal sample vectors;
the calculation module 12 is configured to calculate a GMM parameter of an input real signal sample vector according to a maximum expectation algorithm, and then estimate a GMM parameter of an imaginary signal sample vector according to the GMM parameter calculated by the real signal sample vector, so as to obtain a gaussian mixture model with the maximum responsivity, respectively;
and the output module 13 is used for inputting the samples into the Gaussian mixture model with the maximum responsivity for clustering operation, and obtaining and outputting a quantization result.
The GMM is a Gaussian mixture model and is a machine learning algorithm based on a statistical learning theory. The GMM can be used for non-parametric estimation, and input sample data is fitted according to a plurality of Gaussian distribution functions, and the mean value of a plurality of Gaussian distributions is obtained and is the quantization center. Meanwhile, GMM is also an unsupervised clustering analysis algorithm, and the quantization order of the waveform can be determined by performing non-parametric estimation on the multi-carrier transmission signal data of the general filter to obtain K Gaussian model functions of the waveform without the need of early training.
In a preprocessing module 11, data preprocessing is performed on a data sequence sent by a filter bank multi-carrier modulation transmitter to obtain a sample vector, and the sample vector is used as an input vector of a GMM quantization module; the sample vectors comprise a real signal sample vector and an imaginary signal sample vector.
Specifically, a data sequence sent by the filter bank multi-carrier modulation transmitter is input to a data preprocessing module, and a generated sample vector is used as the input of a GMM quantization module.
Data x to be transmitted1,x2,...,xnThe real part signal and the imaginary part signal are split, the real part signal and the imaginary part signal are respectively formed into a one-dimensional sample vector sequence, and the one-dimensional sample vector sequence is used as GMM quantizationAn input vector of a module; the one-dimensional sample vector sequence is used as an input vector of the GMM quantization module and is particularly real part signal data Re { x1}，Re{x2}，...，Re{xn} and imaginary signal data Im { x1},Im{x2},...,Im{xnAnd independently inputting the data according to the original data sequence.
In the calculation module 12, the GMM parameter of the input real signal sample vector is calculated according to the maximum expectation algorithm, and then the GMM parameter of the imaginary signal sample vector is estimated according to the GMM parameter calculated by the real signal sample vector, so as to respectively obtain the gaussian mixture models with the maximum responsivity.
Specifically, parameters of the Gaussian mixture model conforming to the input real signal sample vector are calculated according to a maximum expectation algorithm (EM algorithm), and then the parameters of the Gaussian mixture model of the imaginary signal sample vector are estimated according to a model result calculated by the real signal.
Among them, the Expectation-Maximization (EM) algorithm or the Dempster-Laird-Rubin algorithm is a kind of optimization algorithm for Maximum Likelihood Estimation (MLE) by iteration, and is usually used as a substitute for Newton-Raphson method for parameter Estimation of probability model containing hidden variables (latent variables) or missing data (incomplete-data).
Wherein, the formula of GMM is:
Figure BDA0002395333120000081
wherein,
Figure BDA0002395333120000082
expressing probability density formulas of all mixed components in the Gaussian mixture model; mu.siAnd σiRespectively representing the mean and covariance, alpha, of the ith Gaussian distributioniRepresents a mixing coefficient satisfying
Figure BDA0002395333120000091
In this embodiment, the calculation module 12 includes an initialization module, a responsiveness calculation module, and a parameter calculation module;
the initialization module is used for initializing GMM parameters of a real part signal sample vector and an imaginary part signal sample vector; the parameter is (alpha)1,α2,...,αk；μ1μ2,...,μk,σ1,σ2,...,σk)；
The parameters of the GMM of the real signal sample vector are:
Figure BDA0002395333120000092
the GMM parameter of the imaginary signal sample vector is a GMM parameter initialization parameter passing the GMM parameter of the real signal sample vector as the imaginary signal sample vector.
The responsivity calculation module is used for calculating the responsivity of the GMM sample vectors of the real part signal and the imaginary part signal according to the GMM parameters of the real part signal sample vector and the imaginary part signal sample vector; calculating each model pair sample vector x according to model parametersiThe responsivity of (2).
The responsivity calculation is specifically to calculate the posterior probability that the real signal sample vector and the imaginary signal sample vector are generated by the GMM mixed component of the real signal sample vector and the imaginary signal sample vector, and is expressed as:
Figure BDA0002395333120000093
and the parameter calculation module is used for calculating the GMM parameter of the new round of sample vector according to the responsivity of the GMM sample vector of the obtained real part signal and the imaginary part signal, and converging the GMM parameter and the responsivity calculation module to obtain the Gaussian mixture model with the maximum responsivity.
Specifically, calculating a new round of model parameters through the obtained responsivity; and iterating the first calculation module and the second calculation module until convergence.
The GMM model parameters for the sample vector of the new round are represented as:
Figure BDA0002395333120000094
Figure BDA0002395333120000101
Figure BDA0002395333120000102
in the present embodiment, γ is used as the posterior probability of generationjiAnd (4) showing.
The iteration convergence condition is as follows: the number of iterations reaching the maximum number of iterations, or likelihood function
Figure BDA0002395333120000103
Hardly growing any more. The GMM estimation algorithm of the imaginary signal sample vector is similar to the real signal.
In the output module 13, the samples are input into the gaussian mixture model with the maximum responsivity for clustering operation, and a quantization result is obtained and output.
Clustering the sample data according to the responsivity, and expressing as follows:
Figure BDA0002395333120000104
that is, the sample vectors are divided into corresponding clusters according to the maximum posterior probability principle, and the vectors in the clusters are all model parameters mu obtained by iteration of a GMM quantization modulejInstead of implementing quantization, the quantization results are output in the order of input.
The quantization algorithm of the embodiment fully considers the characteristics of a high-speed general filter multi-carrier system, finds a quantization mode suitable for the waveform aiming at the characteristics of the filter multi-carrier waveform, and further greatly improves the performance of DAC quantization.
The present embodiment further discloses a filter bank multi-carrier modulation optical communication system based on GMM parameter estimation, as shown in fig. 2, including: the optical fiber module comprises an optical transmitting module, an optical receiving module and an optical fiber channel. Specifically, a digital signal containing data information is input into a quantization module based on GMM parameter estimation by an optical transmission module to obtain an analog signal, the analog signal is converted into a high-speed optical signal by an optical modulator and is sent to an optical fiber channel, the optical signal is converted into a corresponding electric signal by an optical receiving module, and information data is obtained by demodulation.
In this embodiment, the light emitting module includes: the device comprises a digital signal module, a baseband modulation module, a GMM-based non-uniform quantization module and an optical modulator;
the digital signal module is used for coding and mapping the input data sequence and generating a high-speed digital electric signal to be transmitted;
the baseband modulation module is connected with the digital signal module and outputs a digital signal to the GMM-based non-uniform quantization module;
a non-uniform quantization module based on GMM connected with the baseband modulation module for dividing the real part and imaginary part of the digital signal into sample vectors, performing GMM parameter estimation on the sample vectors, performing clustering operation on the sample vectors according to the principle of maximum responsiveness, and outputting the centers of the clusters (i.e. model parameters mu) according to the input sequence of the sample vectorsj) As a quantized output;
and the optical modulator is connected with the non-uniform quantization module based on the GMM and used for completing electro-optical conversion of the signal serving as the quantization output through the optical modulator.
In this embodiment, the light receiving module includes: the device comprises a photoelectric detector, a real-time oscilloscope, a baseband demodulation module and a data output unit; after the photoelectric detector samples the received electric signal through the real-time oscilloscope, the output signal of the real-time oscilloscope is processed and output through the baseband demodulation module, and the receiving of user data is achieved.
The example verifies that the parameters of the GMM non-uniform quantization method are as follows: the signal is modulated by UFMC, and the length of input digital signal sequence is 524288 bit. The uniform quantization method inputs a digital signal sequence of length 524288 bit.
Fig. 3 is a diagram showing SQNR performance comparison of digital signals respectively subjected to 3-5 bit uniform quantization, NPHE non-uniform quantization and GMM non-uniform quantization in a high-speed optical filter bank multi-carrier system, where: the horizontal axis represents the clipping value, and the vertical axis represents the magnitude of the quantum noise ratio in dB. It can be seen that the algorithm of the present embodiment obtains better quantization performance than the conventional uniform quantization method under the condition of the same quantization bit number, and unlike the NPHE scheme, the scheme based on GMM parameter estimation does not have the condition that the SQNR decreases with the increase of the shear rate, so that the non-uniform quantization scheme based on GMM does not need to shear signals, and the system complexity is reduced.
In summary, the GMM-based non-uniform quantization algorithm of the present embodiment can better consider the influence factors of the small amplitude signal in signal quantization. Compared with uniform quantization DAC, the method has the advantages of lower cost and better quantization effect. Meanwhile, the GMM principle is simple and easy to realize. Therefore, the algorithm of the embodiment can be well applied to the requirements of the general filter multi-carrier optical communication system.
Compared with the prior art, the embodiment has the following beneficial effects:
1. compared with the traditional uniform quantization method, the algorithm performance of the invention can obtain better quantization performance, thereby improving the performance of the general filter multi-carrier modulation optical communication system.
2. Compared with a signal estimation-based nonlinear programming quantization method, the algorithm performance of the invention can obtain better signal estimation effect and quantization effect, and the algorithm is simpler and has lower complexity.
3. Compared with other clustering learning algorithms such as neural networks and the like, the algorithm provided by the invention is simpler, more intuitive and easy to realize.
Example two
The embodiment provides a method for GMM non-uniform quantization of filter multi-carrier modulation optical communication, which comprises the following steps:
s11, data preprocessing is carried out on a data sequence sent by a filter bank multi-carrier modulation transmitter to obtain a sample vector, and the sample vector is used as an input vector of a GMM quantization module; the sample vectors comprise a real signal sample vector and an imaginary signal sample vector;
s12, calculating GMM parameters of input real part signal sample vectors according to a maximum expectation algorithm, and estimating the GMM parameters of imaginary part signal sample vectors according to the GMM parameters calculated by the real part signal sample vectors to respectively obtain Gaussian mixture models with the maximum responsivity;
and S13, inputting the sample into a Gaussian mixture model with the maximum responsivity for clustering operation, and obtaining and outputting a quantization result.
Further, step S11 is specifically to send data x1,x2,...,xnThe real part signal and the imaginary part signal are split, the real part signal and the imaginary part signal form a one-dimensional sample vector sequence respectively, and the one-dimensional sample vector sequence is used as an input vector of a GMM quantization module; the one-dimensional sample vector sequence is used as an input vector of the GMM quantization module and is particularly real part signal data Re { x1}，Re{x2}，...，Re{xn} and imaginary signal data Im { x1},Im{x2},...,Im{xnAnd independently inputting the data according to the original data sequence.
Further, the step S12 includes:
s121, initializing GMM parameters of a real part signal sample vector and an imaginary part signal sample vector; the parameter is (alpha)1,α2,...,αk；μ1μ2,...,μk,σ1,σ2,...,σk)；
S122, calculating the responsivity of the GMM sample vectors of the real part signal and the imaginary part signal according to the GMM parameters of the real part signal sample vector and the imaginary part signal sample vector;
and S123, calculating the GMM parameter of the sample vector in the new round according to the responsivity of the GMM sample vector of the obtained real part signal and the imaginary part signal, and iteratively converging the GMM parameter and the step S122 to obtain a Gaussian mixture model with the maximum responsivity.
Further, the formula of the GMM is:
Figure BDA0002395333120000131
wherein,
Figure BDA0002395333120000132
expressing probability density formulas of all mixed components in the Gaussian mixture model; mu.siAnd σiRespectively representing the mean and covariance, alpha, of the ith Gaussian distributioniRepresents a mixing coefficient satisfying
Figure BDA0002395333120000133
The parameters of the GMM of the real part signal sample vector in step S121 are:
Figure BDA0002395333120000134
the GMM parameter of the imaginary signal sample vector is used as a GMM parameter initialization parameter of the imaginary signal sample vector through the GMM parameter of the real signal sample vector;
the responsivity calculation in step S122 is specifically to calculate a posterior probability that the real signal sample vector and the imaginary signal sample vector are generated by GMM mixed components of the real signal sample vector and the imaginary signal sample vector, and is expressed as:
Figure BDA0002395333120000135
the GMM model parameters of the sample vector of the new round in step S123 are represented as:
Figure BDA0002395333120000136
Figure BDA0002395333120000141
Figure BDA0002395333120000142
wherein, γjiRepresenting the generated posterior probability.
Further, the step S13 includes clustering the sample data according to the responsiveness, which is represented as:
Figure BDA0002395333120000143
it should be noted that, a method for GMM non-uniform quantization for filter multi-carrier modulation optical communication provided in this embodiment is similar to the embodiment, and is not described herein again.
Compared with the prior art, the embodiment has the following beneficial effects:
1. compared with the traditional uniform quantization method, the algorithm performance of the invention can obtain better quantization performance, thereby improving the performance of the general filter multi-carrier modulation optical communication system.
2. Compared with a signal estimation-based nonlinear programming quantization method, the algorithm performance of the invention can obtain better signal estimation effect and quantization effect, and the algorithm is simpler and has lower complexity.
3. Compared with other clustering learning algorithms such as neural networks and the like, the algorithm provided by the invention is simpler, more intuitive and easy to realize.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (10)

1. A system for GMM non-uniform quantization for filter multi-carrier modulated optical communications, comprising: the device comprises a preprocessing module, a calculating module and an output module;
the preprocessing module is used for preprocessing data of the data sequence sent by the filter bank multi-carrier modulation transmitter to obtain a sample vector and taking the sample vector as an input vector of the GMM quantization module; the sample vectors comprise real signal sample vectors and imaginary signal sample vectors;
the computing module is used for computing the GMM parameter of the input real part signal sample vector according to a maximum expectation algorithm, and then estimating the GMM parameter of the imaginary part signal sample vector according to the GMM parameter computed by the real part signal sample vector to respectively obtain a Gaussian mixture model with the maximum responsivity;
and the output module is used for inputting the samples into the Gaussian mixture model with the maximum responsivity for clustering operation to obtain and output a quantization result.
2. The system according to claim 1, wherein the pre-processing module is specifically configured to transmit data x1,x2,...,xnSplitting the real part signal and the imaginary part signal, respectively forming a one-dimensional sample vector sequence by the real part signal and the imaginary part signal, and taking the one-dimensional sample vector sequence as an input vector of a GMM quantization module; the one-dimensional sample vector sequence is used as an input vector of the GMM quantization module and is particularly real part signal data Re { x1}，Re{x2}，...，Re{xn} and imaginary signal data Im { x1},Im{x2},...,Im{xnAnd independently inputting the data according to the original data sequence.
3. The system according to claim 1, wherein said calculation module comprises an initialization module, a responsivity calculation module, a parameter calculation module;
the initialization module is used for initializing the real part signal sample vector and the imaginary part signal sampleGMM parameters of the vector; the parameter is (alpha)1,α2,...,αk；μ1μ2,...,μk,σ1,σ2,...,σk)；
The responsivity calculating module is used for calculating the responsivity of the GMM sample vectors of the real part signal and the imaginary part signal according to the GMM parameters of the real part signal sample vector and the imaginary part signal sample vector;
and the parameter calculation module is used for calculating the GMM parameter of the new round of sample vector according to the responsivity of the GMM sample vector of the obtained real part signal and the imaginary part signal, and converging the GMM parameter with the responsivity calculation module to obtain the Gaussian mixture model with the maximum responsivity.
4. The system for GMM non-uniform quantization for filter multi-carrier modulated optical communication of claim 3, wherein the formula of the GMM is:
Figure FDA0002395333110000021
wherein,
Figure 1
expressing probability density formulas of all mixed components in the Gaussian mixture model; mu.siAnd σiRespectively representing the mean and covariance, alpha, of the ith Gaussian distributioniRepresents a mixing coefficient satisfying
Figure FDA0002395333110000023
The parameters of the GMM of the real part signal sample vector in the initialization module are:
Figure FDA0002395333110000024
the GMM parameter of the imaginary signal sample vector is used as a GMM parameter initialization parameter of the imaginary signal sample vector through the GMM parameter of the real signal sample vector;
the responsivity calculation in the responsivity calculation module is specifically to calculate the posterior probability that the real part signal sample vector and the imaginary part signal sample vector are generated by the GMM mixed component of the real part signal sample vector and the imaginary part signal sample vector, and is expressed as:
Figure FDA0002395333110000025
the GMM model parameters of a new round of sample vectors in the parameter calculation module are represented as:
Figure FDA0002395333110000026
Figure FDA0002395333110000027
Figure FDA0002395333110000028
wherein, γjiRepresenting the generated posterior probability.
5. The system according to claim 4, wherein said output module clusters sample data according to responsivity, represented as:
Figure FDA0002395333110000031
6. a method for GMM non-uniform quantization for filter multi-carrier modulated optical communications, comprising the steps of:
s1, performing data preprocessing on a data sequence sent by a filter bank multi-carrier modulation transmitter to obtain a sample vector, and taking the sample vector as an input vector of a GMM quantization module; the sample vectors comprise real signal sample vectors and imaginary signal sample vectors;
s2, calculating GMM parameters of input real part signal sample vectors according to a maximum expectation algorithm, and estimating the GMM parameters of imaginary part signal sample vectors according to the GMM parameters calculated by the real part signal sample vectors to respectively obtain Gaussian mixture models with the maximum responsivity;
and S3, inputting the sample into the Gaussian mixture model with the maximum responsivity for clustering operation, and obtaining and outputting a quantization result.
7. The method of GMM non-uniform quantization for filter multi-carrier modulated optical communication according to claim 6, wherein said step S1 is specifically data x to be transmitted1,x2,...,xnSplitting the real part signal and the imaginary part signal, respectively forming a one-dimensional sample vector sequence by the real part signal and the imaginary part signal, and taking the one-dimensional sample vector sequence as an input vector of a GMM quantization module; the one-dimensional sample vector sequence is used as an input vector of the GMM quantization module and is particularly real part signal data Re { x1}，Re{x2}，...，Re{xn} and imaginary signal data Im { x1},Im{x2},...,Im{xnAnd independently inputting the data according to the original data sequence.
8. The method GMM non-uniform quantization for filter multi-carrier modulated optical communication according to claim 6, characterized in that said step S2 comprises:
s21, initializing GMM parameters of a real part signal sample vector and an imaginary part signal sample vector; the parameter is (alpha)1,α2,...,αk；μ1μ2,...,μk,σ1,σ2,...,σk)；
S22, calculating the responsivity of the GMM sample vectors of the real part signal and the imaginary part signal according to the GMM parameters of the real part signal sample vector and the imaginary part signal sample vector;
and S23, calculating the GMM parameter of the sample vector in the new round according to the responsivity of the GMM sample vector of the obtained real part signal and the imaginary part signal, and iteratively converging the GMM parameter and the step S22 to obtain the Gaussian mixture model with the maximum responsivity.
9. The method of claim 8, wherein the GMM is formulated as:
Figure FDA0002395333110000041
wherein,
Figure FDA0002395333110000042
expressing probability density formulas of all mixed components in the Gaussian mixture model; mu.siAnd σiRespectively representing the mean and covariance, alpha, of the ith Gaussian distributioniRepresents a mixing coefficient satisfying
Figure FDA0002395333110000043
The parameters of the GMM of the real part signal sample vector in step S21 are:
Figure FDA0002395333110000044
the GMM parameter of the imaginary signal sample vector is a GMM parameter initialization parameter which takes the GMM parameter of the real signal sample vector as the imaginary signal sample vector;
the responsivity calculation of step S22 is specifically to calculate the posterior probability that the real signal sample vector and the imaginary signal sample vector are generated by the GMM mixed component of the real signal sample vector and the imaginary signal sample vector, and is expressed as:
Figure FDA0002395333110000045
the GMM model parameters of the sample vector of the new round in step S23 are represented as:
Figure FDA0002395333110000046
Figure FDA0002395333110000047
Figure FDA0002395333110000051
wherein, γjiRepresenting the generated posterior probability.
10. The method of claim 9, wherein the step S3 further comprises clustering the sample data according to responsivity, expressed as:
Figure FDA0002395333110000052
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