CN112367284A - Probability distribution identification method, device, equipment and medium under probability shaping constellation - Google Patents

Probability distribution identification method, device, equipment and medium under probability shaping constellation Download PDF

Info

Publication number
CN112367284A
CN112367284A CN202011201788.4A CN202011201788A CN112367284A CN 112367284 A CN112367284 A CN 112367284A CN 202011201788 A CN202011201788 A CN 202011201788A CN 112367284 A CN112367284 A CN 112367284A
Authority
CN
China
Prior art keywords
probability distribution
probability
candidate
normalization factor
relative entropy
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202011201788.4A
Other languages
Chinese (zh)
Other versions
CN112367284B (en
Inventor
洪学智
严启峰
张佩珊
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
South China Normal University
Original Assignee
South China Normal University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by South China Normal University filed Critical South China Normal University
Priority to CN202011201788.4A priority Critical patent/CN112367284B/en
Publication of CN112367284A publication Critical patent/CN112367284A/en
Application granted granted Critical
Publication of CN112367284B publication Critical patent/CN112367284B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03171—Arrangements involving maximum a posteriori probability [MAP] detection
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03178—Arrangements involving sequence estimation techniques
    • H04L25/03248—Arrangements for operating in conjunction with other apparatus
    • H04L25/03273—Arrangements for operating in conjunction with other apparatus with carrier recovery circuitry

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Power Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Complex Calculations (AREA)

Abstract

The invention discloses a probability distribution identification method, a device, equipment and a medium under a probability shaping constellation, wherein the method comprises the following steps: selecting each candidate probability distribution and a power normalization factor thereof in all candidate probability distributions of a constellation shaping system as a first initial condition; calculating the relative entropy between each probability distribution after L iterations and all candidate probability distributions, selecting the candidate probability distribution corresponding to the minimum relative entropy as the initial estimation of unknown probability distribution, and taking the initial estimation of probability distribution and the corresponding power normalization factor as a second initial condition; and calculating the relative entropy between the probability distribution after T iterations and all candidate probability distributions, wherein the candidate probability distribution corresponding to the minimum relative entropy is used as the final estimation of the unknown probability distribution. The invention can extract the constellation probability distribution information from the received signal without carrier phase recovery, and has important application value for constellation shaping probability distribution identification in the elastic optical network.

Description

Probability distribution identification method, device, equipment and medium under probability shaping constellation
Technical Field
The invention relates to a probability distribution identification method, a probability distribution identification device, probability distribution identification equipment and a probability distribution identification medium under a probability shaping constellation, and belongs to the technical field of optical communication.
Background
With the rapid development of cloud computing, virtual reality, 5G, and the like, the annual global data traffic presents an exponential explosion, which poses a huge challenge to existing optical communication systems. Coherent transceivers with single wavelengths of 100G, 400G, and even 800G are increasingly attractive to researchers and the industry. Probability shaping constellations have the advantages of higher spectral efficiency and lower optical signal-to-noise ratio requirements, and are becoming a reliable technical scheme of next-generation optical networks. In addition, due to the characteristic that the entropy of the probability shaping constellation is continuously adjustable, the rate adjustable receiver based on the probability shaping constellation has more advantages than a mixed modulation format and a bit loading constant rate adjustable scheme. Details are disclosed in [1] J.Cho, and P.J.Winzer, "basic containment mapping for optical fiber communications," J.Lightw.Technol., vol.37, No.6, pp.1590-1607, Mar.2019; [2] che and W.Shieh, "applicable the capacity of color-sn optical channels by multicarrier entry loading," J.Lightw.Technol., vol.36, No.1, pp.68-78, Jan.2018.
Since the forward error correction decoding and signal recovery processes such as the distributed inverse matcher at the receiving end need to predict the probability distribution of the constellation to work normally, it is very important to be able to extract the probability distribution in the digital signal processing at the receiving end. Researchers use the relationship between nonlinear parameters and shaping distribution and use artificial neural network to realize probability distribution identification (see the document: 3)]A.s.kashi, a.i.a.el-Rahman, j.c.cartledge, and s.a.email, "Extending a non-linear sensor to include mapping identification for probabilistically mapped 64-QAM signals," j.light w.technol., vol.37, No.13, pp.3252-3260, jul.2019). In addition, researchers utilize the characteristic that signals with different probability distributions have different two-dimensional images in a Stokes space, and realize the identification of the probability distributions by cascading two convolutional neural network networks (see the detailed document: [4 ]]W, Zhang, D.Zhu, N.Zhang, H.xu, X.Zhang, H.Zhang, and Y.Li, "identification basic mapping for models through 2D stocks pages with two-stage deep neural networks," IEEE ACCESS, vol.8, pp.6742-6750, Jan.2020). However, the aboveBecause the algorithm based on the artificial neural network and the convolutional neural network needs a large number of samples to be trained offline, and a large number of received symbols are input into the neural network during online testing, the practical implementation of the algorithm has high complexity. In addition, researchers have proposed a shaping distribution recognition algorithm based on expectation maximization, which can realize the shaping distribution recognition content without any training sample (see the literature: 5 in detail)]F.Steiner,P.Schulte,and G.
Figure BDA0002755484950000011
"blistering-polymerization for basic shaping vision amplification," in proc. However, the implementation of the algorithm requires frequency offset compensation and carrier phase recovery. Recent studies have shown that the frequency offset compensation algorithm under the probability shaped constellation requires prior information of the known probability distribution (see document: [6 ]]Yan, l.liu, and x.hong, "band carrier frequency offset estimation in coherent communication system with probabilistically mapped M-QAM," j.light w.technol., vol.37, No.23, pp.5856-5866, dec.2019); the performance of a common carrier phase recovery algorithm, such as a blind phase search algorithm, is also affected by the shaping strength, and the performance of the carrier phase recovery algorithm can be effectively improved by using the prior information of probability distribution (see document [7 ]]Barbosa, s.m.rossi, and d.a.a.mello, "Phase and frequency recovery algorithms for basic mapping transmission," j.light w.technol., vol.38, No.7, pp.1827-1835, apr.2020). Therefore, the search for a probability distribution identification algorithm which is insensitive to the carrier phase and does not need training has important practical value for improving the performance of the constellation probability shaping system.
Disclosure of Invention
In view of this, the present invention provides a method, an apparatus, a device, and a medium for identifying probability distribution in a probability shaping constellation, which can overcome the disadvantages and shortcomings of the existing expectation maximization algorithm, and the identified probability distribution information of a signal can be used in subsequent signal recovery processes such as frequency offset estimation and carrier phase recovery, and there is no need to perform frequency offset compensation and carrier phase recovery on an input signal, and training is not required, so that the practicability is strong.
The first purpose of the invention is to provide a probability distribution identification method under probability shaping constellation.
A second object of the present invention is to provide a probability distribution identification apparatus under a probability shaped constellation.
It is a third object of the invention to provide a computer apparatus.
It is a fourth object of the present invention to provide a storage medium.
The first purpose of the invention can be achieved by adopting the following technical scheme:
a method of probability distribution identification under a probability shaped constellation, the method comprising:
selecting each candidate probability distribution and a power normalization factor thereof in all candidate probability distributions of a constellation shaping system as a first initial condition;
under a first initial condition, according to the amplitude of a received signal, carrying out iterative updating on probability distribution based on an expected maximum criterion, and calculating the relative entropy between each probability distribution after L iterations and all candidate probability distributions to serve as a first relative entropy;
selecting the candidate probability distribution corresponding to the first minimum relative entropy as the initial estimation of the unknown probability distribution, and taking the initial estimation of the probability distribution and the corresponding power normalization factor as a second initial condition;
under a second initial condition, according to the amplitude of the received signal, based on an expected maximum criterion, carrying out iterative updating on the probability distribution and the power normalization factor at the same time, and calculating the relative entropy between the probability distribution after T iterations and all candidate probability distributions to serve as a second relative entropy;
and selecting the candidate probability distribution corresponding to the second minimum relative entropy as the final estimation of the unknown probability distribution.
Further, in the iterative updating of the probability distribution based on the expected maximum criterion according to the amplitude of the received signal, the ith iteration includes:
updating the computational assistance profile as follows:
Figure BDA0002755484950000031
wherein, Pl-1(an) Represents the candidate probability distribution after the update of the l-1 th iteration, and when l is equal to 1, P0＝Pj＝{Pj(an) 1, 2., N } represents an initial value of the probability distribution;
Figure BDA0002755484950000032
for a selected probability distribution P0Corresponding power normalization factor delta0；PR|A(rk|an；Δ0) Channel transition probability representing signal amplitude, anAn nth amplitude value representing an M-th order quadrature amplitude modulation constellation;
updating the probability distribution based on the auxiliary distribution as follows:
Figure BDA0002755484950000033
wherein, Pl(an) Representing the probability distribution after the ith iteration update, and K representing the total number of symbols for the desired maximum algorithm.
Further, the channel transition probability P of the signal amplitudeR|A(rk|an；Δ0) The calculation of (c) is as follows:
Figure BDA0002755484950000034
wherein, P0Representing an initial value of the probability distribution, P0＝Pj＝{Pj(an)|n＝1,2,...,N}，PjRepresenting the jth candidate probability distribution, Δ0Represents a group of formulae and P0Corresponding power normalization factor, σ2Representing the real and imaginary parts of additive white Gaussian noiseVariance of (I)0() Representing a zero order first-class modified bessel function.
Further, the relative entropy between each probability distribution after L iterations and all candidate probability distributions is calculated as follows:
Figure BDA0002755484950000035
wherein, PL(an) Representing each probability distribution, P, after L iterative updatesjRepresenting the j-th candidate probability distribution, Pj＝{Pj(an)，n＝1，2…N}，anRepresenting the nth possible amplitude value in the M-order quadrature amplitude modulation constellation.
Further, in the iterative updating of the probability distribution and the power normalization factor based on the expected maximum criterion according to the amplitude of the received signal, the t-th iteration includes:
calculating the channel transition probability of the signal amplitude as follows:
Figure BDA0002755484950000041
wherein, Deltat-1The power normalization factor updated for the t-1 th iteration, when t is 1, Δ0A power normalization factor corresponding to the preliminary estimate representing the probability distribution;
calculating the auxiliary distribution as follows:
Figure BDA0002755484950000042
wherein, Pt-1(an) Probability distribution updated for the t-1 st iteration, when t is 1, P0＝{P0(an) 1, 2.., N } represents a preliminary estimate of the probability distribution;
updating the probability distribution and the power normalization factor simultaneously based on the auxiliary distribution, wherein the power normalization factor is updated according to the following formula:
Figure BDA0002755484950000043
wherein the content of the first and second substances,
Figure BDA0002755484950000044
is an adjustable parameter.
Finding out the probability distribution corresponding to the power normalization factor by a table look-up method according to the relationship between the power normalization factor and the probability distribution shown in the following formula:
Figure BDA0002755484950000045
further, the adjustable parameter
Figure BDA0002755484950000046
The acquisition process is as follows:
assume that there are S candidate probability distributions to identify, denoted as P1，P2，…，PS(ii) a At a certain signal-to-noise ratio, the probability distribution of the transmitted signal is PiThe preliminary estimate of the probability distribution is output as PjHas a probability of fijFor S candidate probability distributions, the output of the preliminary estimate of the probability distribution is described by the following matrix F of S rows and S columns:
Figure BDA0002755484950000051
normalizing the matrix F column by column to obtain the initial estimation output P of probability distributionjProbability distribution of transmitted signal is PiWeighting coefficient of time
Figure BDA0002755484950000052
When the preliminary estimate of the probability distribution is output as PjThe signal adopts a probability distribution PiRecognition of timeSuccess rate depends on
Figure BDA0002755484950000053
The recognition success rate is compared with
Figure BDA0002755484950000054
Is a function of
Figure BDA0002755484950000055
Description is given;
using a weighting coefficient wijObtaining a weighted recognition success rate function as follows:
Figure BDA0002755484950000056
wherein the content of the first and second substances,
Figure BDA0002755484950000057
the subscript j denotes the preliminary estimate output of the probability distribution as PjSelect out
Figure BDA0002755484950000058
Largest size
Figure BDA0002755484950000059
The output of the preliminary estimate as a probability distribution is PjThe optimum parameter of (2).
Further, the relative entropy between the probability distribution after T iterations and all candidate probability distributions is calculated as follows:
Figure BDA00027554849500000510
wherein, PT(an) Representing each probability distribution, P, updated over T iterationsjRepresenting the j-th candidate probability distribution, Pj＝{Pj(an)，n＝1，2…N}，anRepresenting the nth possible amplitude value in the M-order quadrature amplitude modulation constellation.
The second purpose of the invention can be achieved by adopting the following technical scheme:
an apparatus for identifying a probability distribution under a probability shaped constellation, the apparatus comprising:
the first selection module is used for selecting each candidate probability distribution in all candidate probability distributions of the constellation shaping system and a power normalization factor thereof as a first initial condition;
the first calculation module is used for carrying out iterative updating on probability distribution based on an expected maximum criterion according to the amplitude of a received signal under a first initial condition, and calculating the relative entropy between each probability distribution after L iterations and all candidate probability distributions to serve as a first relative entropy;
the second selection module is used for selecting the candidate probability distribution corresponding to the minimum first relative entropy as the initial estimation of the unknown probability distribution and using the initial estimation of the probability distribution and the corresponding power normalization factor as a second initial condition;
the second calculation module is used for carrying out iterative updating on the probability distribution and the power normalization factor simultaneously on the basis of an expected maximum criterion according to the amplitude of the received signal under a second initial condition, and calculating the relative entropy between the probability distribution after T iterations and all candidate probability distributions to serve as a second relative entropy;
and the third selection module is used for selecting the candidate probability distribution corresponding to the second relative entropy as the final estimation of the unknown probability distribution.
The third purpose of the invention can be achieved by adopting the following technical scheme:
a computer device comprises a processor and a memory for storing a program executable by the processor, wherein the processor implements the probability distribution identification method under the probability shaping constellation when executing the program stored in the memory.
The fourth purpose of the invention can be achieved by adopting the following technical scheme:
a storage medium stores a program which, when executed by a processor, implements the above-described probability distribution identification method in a probability shaped constellation.
Compared with the prior art, the invention has the following beneficial effects:
the invention can extract the corresponding constellation probability distribution from the signal after the channel equalization, the whole identification algorithm is divided into two stages, the first stage obtains a preliminary estimation of the probability distribution by using the data to be identified, the second stage obtains an updated probability distribution estimation by using the estimation result of the previous stage and the data to be identified, particularly after the amplitude of the received signal is obtained, the first-stage algorithm respectively takes each candidate probability distribution and the corresponding power normalization factor as first initial conditions, iteratively updates the probability distributions based on an expected maximum criterion, respectively calculates the relative entropy between the candidate probability distributions and the probability distributions after L iterations, takes the probability distribution with the minimum relative entropy as the initial estimation of unknown probability distribution, and takes the initial estimation of the probability distributions and the corresponding power normalization factor as second initial conditions; the second stage of the algorithm takes the probability distribution preliminary estimation obtained by the first stage as a starting point, obtains an optimal value of an adjustable parameter according to the probability distribution preliminary estimation and the signal-to-noise ratio, then iteratively updates the probability distribution and the power normalization factor based on an expected maximum criterion at the same time, calculates the relative entropy between the probability distribution and all candidate probability distributions after T iterations, takes the minimum relative entropy as the final estimation of the probability distribution, does not need offline training or pilot frequency assistance, can extract constellation probability distribution information from a received signal on the premise of not carrying out carrier phase recovery, has strong practicability, and has important application value for constellation shaping probability distribution identification in an elastic optical network.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
Fig. 1 is a flowchart of a probability distribution identification method under a probability shaped constellation according to embodiment 1 of the present invention.
Fig. 2 is a flowchart of a probability distribution identification method under a probability shaped constellation according to embodiment 2 of the present invention.
FIG. 3 shows that the SNR of example 2 of the present invention is 13dB
Figure BDA0002755484950000071
And weighted correspondingly
Figure BDA0002755484950000072
A graph of (a).
FIG. 4 shows the arbitrary SNR of the SNR interval in example 2 of the present invention
Figure BDA0002755484950000073
Graph is shown.
Fig. 5 is a performance diagram of the recognition success rate and the signal-to-noise ratio in embodiment 2 of the present invention.
Fig. 6 is a block diagram of a structure of a probability distribution identification apparatus under a probability shaping constellation according to embodiment 3 of the present invention.
Fig. 7 is a block diagram of a computer device according to embodiment 4 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer and more complete, the technical solutions in the embodiments of the present invention will be described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments, and all other embodiments obtained by a person of ordinary skill in the art without creative efforts based on the embodiments of the present invention belong to the protection scope of the present invention.
Example 1:
as shown in fig. 1, the present embodiment provides a method for identifying probability distribution under a probability shaped constellation, where the method includes the following steps:
s101, selecting each candidate probability distribution and a power normalization factor thereof in all candidate probability distributions of the constellation shaping system as first initial conditions.
Assuming that the constellation shaping system has S candidate probability distributions in common, the jth (j ═ 1,2, …, S) candidate probability distribution can be described as: pj＝{Pj(an)，n＝1，2…N}，anRepresenting the nth possible amplitude value in an M-order quadrature amplitude modulation (M-QAM) constellation, and the constellation power normalization factor delta corresponding to the candidate probability distributionjSo that
Figure BDA0002755484950000074
Wherein N is the total number of turns of the M-QAM constellation, and selecting the jth candidate probability distribution PjAnd its power normalization factor deltajAs an initial condition.
S102, under a first initial condition, according to the amplitude of a received signal, carrying out iterative updating on probability distribution based on an expected maximum criterion, and calculating the relative entropy between each probability distribution after L iterations and all candidate probability distributions to serve as a first relative entropy.
When the initial value of the probability distribution is P0＝Pj＝{Pj(an) When | N ═ 1, 2.. times, N }, it is assumed that the kth received symbol is ykAmplitude r ofk＝|ykFirst, the channel transition probability of the signal amplitude is calculated as follows:
Figure BDA0002755484950000081
wherein, Delta0Represents a group of formulae and P0Corresponding power normalization factor, σ2Variance, I, representing the real and imaginary parts of additive white Gaussian noise0() Representing a zero order first-class modified bessel function.
The probability distribution is then iteratively updated by the desired maximum criterion, wherein the l-th iteration comprises the steps of:
s1021, updating the calculation auxiliary distribution as follows:
Figure BDA0002755484950000082
wherein, Pl-1(an) Represents the candidate probability distribution after the update of the l-1 th iteration, and when l is equal to 1, P0＝Pj＝{Pj(an) I N1, 2.., N represents an initial value of the probability distribution.
S1022, updating the probability distribution based on the auxiliary distribution, as follows:
Figure BDA0002755484950000083
wherein, Pl(an) Representing the probability distribution after the ith iteration update, and K representing the total number of symbols for the desired maximum algorithm.
After L iterations, the relative entropy between each probability distribution and all candidate probability distributions is calculated as follows:
Figure BDA0002755484950000084
wherein, PL(an) Each probability distribution after being updated by L iterations is represented, and since there are S probability distributions to be identified, there are a total of S relative entropies in the above equation, i.e., j is 1,2, 3, …, S.
In order to calculate one of the candidate probability distributions, the same calculation is performed for the remaining S-1 candidate probability distributions, so that S can be obtained2The relative entropy is taken as the first relative entropy.
S103, selecting the candidate probability distribution corresponding to the first minimum relative entropy as the initial estimation of the unknown probability distribution, and taking the initial estimation of the probability distribution and the power normalization factor corresponding to the initial estimation as a second initial condition.
And S104, under a second initial condition, according to the amplitude of the received signal, carrying out iterative updating on the probability distribution and the power normalization factor based on an expected maximum criterion, and calculating the relative entropy between the probability distribution after T iterations and all candidate probability distributions to serve as a second relative entropy.
Taking the initial estimation of the probability distribution and the corresponding power normalization factor as initial values, using the amplitude of the received signal, and carrying out iterative updating on the probability distribution and the power normalization factor through an expected maximum criterion, wherein the t-th iteration step comprises the following steps:
s1041, calculating a channel transfer probability of the signal amplitude as follows:
Figure BDA0002755484950000091
wherein, Deltat-1The power normalization factor updated for the t-1 th iteration, when t is 1, Δ0A power normalization factor corresponding to the preliminary estimate representing the probability distribution.
S1042, calculating the auxiliary distribution as follows:
Figure BDA0002755484950000092
wherein, Pt-1(an) Probability distribution updated for the t-1 st iteration, when t is 1, P0＝{P0(an) 1, 2.. N } represents a preliminary estimate of the probability distribution.
S1043, updating the probability distribution and the power normalization factor simultaneously based on the auxiliary distribution, wherein the power normalization factor is updated according to the following formula:
Figure BDA0002755484950000093
wherein the content of the first and second substances,
Figure BDA0002755484950000094
is an adjustable parameter.
Finding out the probability distribution corresponding to the power normalization factor by a table look-up method according to the relationship between the power normalization factor and the probability distribution shown in the following formula:
Figure BDA0002755484950000095
in the above-mentioned step of one iteration, in this embodiment, after T iterations are required, the updated power normalization factor and probability distribution are substituted into the formulas of step S1041 and step S1042 in subsequent iterations, and then step S1043 is executed to perform a new update.
Calculating the relative entropy between the probability distribution after T iterations and all candidate probability distributions, as follows:
Figure BDA0002755484950000101
wherein, PT(an) Each probability distribution after updating through T iterations is represented, and since there are S probability distributions to be identified, there are a total of S relative entropies in the above equation, i.e., j is 1,2, 3, …, S. These S relative entropies serve as second relative entropies.
Adjustable parameter
Figure BDA0002755484950000102
The acquisition process is as follows:
s1044, assuming that S candidate probability distributions need to be identified and marked as P1，P2，…，PS(ii) a At a certain signal-to-noise ratio, the probability distribution of the transmitted signal is PiThen, the output of step S103 (preliminary estimation of probability distribution) is PjHas a probability of fijFor S candidate probability distributions, the output result of step S103 is described by the following matrix F of S rows and S columns:
Figure BDA0002755484950000103
normalizing the matrix F column by column to obtain the initial estimation output P of probability distributionjProbability distribution of transmitted signal is PiWeighting factor (i.e. weighting factor) of time
Figure BDA0002755484950000104
S1045, when the output of the step S103 is PjThe signal adopts a probability distribution PiThe success rate of time-dependent recognition
Figure BDA0002755484950000105
The identification success rate and the identification success rate are obtained in a numerical simulation or experiment mode
Figure BDA0002755484950000106
Provided that this relationship can be expressed as a function
Figure BDA0002755484950000107
A description is given.
S1046, using weighting coefficient wijObtaining a weighted recognition success rate function as follows:
Figure BDA0002755484950000108
wherein the content of the first and second substances,
Figure BDA0002755484950000109
the subscript j denotes the preliminary estimate output of the probability distribution as PjSelect out
Figure BDA00027554849500001010
Largest size
Figure BDA00027554849500001011
The output of the preliminary estimate as a probability distribution is PjThe optimum parameter of (2).
S1047, obtaining S optimal parameters corresponding to a certain signal-to-noise ratio for all possible S probability distribution initial values through steps S1044-S1046
Figure BDA00027554849500001012
And S105, selecting the candidate probability distribution corresponding to the second relative entropy minimum as the final estimation of the unknown probability distribution.
Example 2:
the present embodiment is a specific application of the probability distribution identification method under the probability shaped constellation, and in the present embodiment, the following are set: a total of 7 probability distributions need to be identified, and the shaping distributions are obtained by adjusting a shaping parameter λ in Maxwell-boltzmann (MB) distribution under a 64-QAM template, wherein the MB distribution formula is as follows:
Figure BDA0002755484950000111
in 64QAM, M is 64; λ of these 7 probability distributionsiAnd the constellation entropy is as shown in table 1 below, and the power normalization factors corresponding to the 7 shaping distributions are obtained to satisfy:
Figure BDA0002755484950000112
a 64QAM constellation has 9 circles with different amplitudes, so that N is 9, and the 7 power normalization factors are: delta1，Δ2，…，Δ70.3258, 0.3028, 0.2814, 0.2612, 0.2421, 0.2237, and 0.2054; at the receiving end, the local oscillator frequency difference is assumed to be 1GHz (the system baud rate is 28GBaud), and the line width of the combined laser is 200kHz to simulate the carrier phase fluctuation. The number of symbols used for probability distribution recognition is 2048, i.e., K2048. The number of iterations in the initialization process and the subsequent iteration process in the expectation maximization algorithm is 3 and 30(L is 3 and T is 30), respectively.
TABLE 1 probability distribution used in this example
Probability distribution P1 P2 P3 P4 P5 P6 P7
λ 0.106 0.091 0.078 0.066 0.055 0.045 0.034
Entropy of constellation 4.33 4.54 4.75 4.96 5.17 5.38 5.59
As shown in fig. 2, the probability distribution identification method of the present embodiment includes the following steps:
s201, assuming that the signal-to-noise ratio is 13dB, the number of symbols used in initialization isThe number is also 2048, and the initialization result obtained according to step S1044 of embodiment 1 is shown in table 2, in which the data indicates when the transmitted shaping distribution is PiWhen the initial value of the probability distribution is PjIs the percentage probability of f mentioned in step S1044 of example 1 aboveijThen, according to the formula
Figure BDA0002755484950000113
The weighting coefficients were calculated and the results are shown in table 3 below.
TABLE 2 initialization results
Figure BDA0002755484950000114
TABLE 3 weighting coefficients
wij i＝1 i＝2 i＝3 i＝4 i＝5 i＝6 i＝7
j＝1 80.35 16.59 2.66 0.16 0.24 0 0
j＝2 0.2 78.14 20.08 1.48 0 0.1 0
j＝3 0 0.43 80.11 19.03 0.43 0 0
j＝4 0 0 2.33 77.22 20.45 0 0
j＝5 0 0 0 5.09 84.48 10.43 0
j＝6 0 0 0 0.1 7.84 88.14 3.92
j＝7 0 0 0 0 0 3.42 96.58
According to step S1045 of embodiment 1, when the probability distribution of step S103 of embodiment 1 is initialized to PjTime, different probability distribution PiSuccess rate of recognition and
Figure BDA0002755484950000121
in relation to (2)
Figure BDA0002755484950000122
Using the weighting coefficients w of (2-5)ijAnd (3) weighting:
Figure BDA0002755484950000123
wherein the content of the first and second substances,
Figure BDA0002755484950000124
the subscript j indicates that the probability distribution in step S103 of embodiment 1 is initialized to Pj. FIG. 3 shows a signal-to-noise ratio of 13dB
Figure BDA0002755484950000125
And weighted correspondingly
Figure BDA0002755484950000126
Curve (c) of (d). When noteworthy, due to the weighting factor w14,w24,w64,w74Are all 0, so FIG. 3 is not drawn
Figure BDA0002755484950000127
S202, finding out
Figure BDA0002755484950000128
Corresponding to when maximum is reached
Figure BDA0002755484950000129
At this time
Figure BDA00027554849500001210
Is 0.988, i.e., when the probability distribution in step S103 of the above-described embodiment 1 is initialized to P4Optimum of time
Figure BDA00027554849500001211
Was 0.988. For initial values of other probability distributions and other signal-to-noise ratios
Figure BDA00027554849500001212
Are obtained by the same procedure. Since it is impractical to traverse any signal-to-noise ratio in actual operation, it is possible to traverse the signal-to-noise ratio interval of interest (e.g., 9dB-19dB) at certain signal-to-noise ratio intervals (e.g., 1dB), and then obtain any signal-to-noise ratio in this interval by polynomial fitting
Figure BDA00027554849500001213
The results are shown in FIG. 4.
S203, obtaining sigma according to the signal-to-noise ratio2Then, the initialization process of steps S101 to S103 of embodiment 1 described above is performed, and a preliminary estimate of the probability distribution is obtained.
S204, finding out the optimal parameter according to the signal-to-noise ratio and the probability distribution preliminary estimation in the S203
Figure BDA00027554849500001214
S205, according to the selected optimal
Figure BDA00027554849500001215
The iterative process of step S104 of embodiment 1 described above is performed to obtain the final estimate of the probability distribution. The performance graph of the recognition success rate and the signal-to-noise ratio of the probability distribution recognition algorithm is shown in fig. 4, and it can be seen from the result that the algorithm can accurately extract the information of the probability distribution hidden in the signal.
Those skilled in the art will appreciate that all or part of the steps in the method for implementing the above embodiments may be implemented by a program to instruct associated hardware, and the corresponding program may be stored in a computer-readable storage medium.
It should be noted that although the method operations of the above-described embodiments are depicted in the drawings in a particular order, this does not require or imply that these operations must be performed in this particular order, or that all of the illustrated operations must be performed, to achieve desirable results. Rather, the depicted steps may change the order of execution. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step execution, and/or one step broken down into multiple step executions.
Example 3:
as shown in fig. 6, the present embodiment provides a probability distribution identification apparatus under a probability shaped constellation, the apparatus includes a first selecting module 601, a first calculating module 602, a second selecting module 603, a second calculating module 604, and a third selecting module 605, and specific functions of each module are as follows:
the first selecting module 601 is configured to select each candidate probability distribution of all candidate probability distributions of the constellation shaping system and a power normalization factor thereof as a first initial condition.
A first calculating module 602, configured to iteratively update the probability distributions based on an expected maximum criterion according to the amplitude of the received signal under a first initial condition, and calculate a relative entropy between each probability distribution after L iterations and all candidate probability distributions as a first relative entropy.
A second selecting module 603, configured to select a candidate probability distribution corresponding to the smallest first relative entropy as a preliminary estimate of an unknown probability distribution, and use the preliminary estimate of the probability distribution and a power normalization factor corresponding to the preliminary estimate as a second initial condition.
A second calculating module 604, configured to, under a second initial condition, perform iterative update on the probability distribution and the power normalization factor based on an expected maximum criterion according to the amplitude of the received signal, and calculate a relative entropy between the probability distribution after T iterations and all candidate probability distributions, which is used as a second relative entropy.
A third selecting module 605, configured to select the candidate probability distribution corresponding to the second relative entropy minimum as a final estimate of the unknown probability distribution.
The specific implementation of each module in this embodiment may refer to embodiment 1, which is not described herein any more; it should be noted that, the apparatus provided in this embodiment is only illustrated by dividing the functional modules, and in practical applications, the functions may be distributed by different functional modules according to needs, that is, the internal structure is divided into different functional modules to complete all or part of the functions described above.
Example 4:
as shown in fig. 7, the present embodiment provides a computer device, which includes a processor 702, a memory and a network interface 703 connected by a system bus 701, where the processor is used to provide computing and control capabilities, the memory includes a nonvolatile storage medium 704 and an internal memory 705, the nonvolatile storage medium 704 stores an operating system, a computer program and a database, the internal memory 705 provides an environment for the operating system and the computer program in the nonvolatile storage medium to run, and when the processor 702 executes the computer program stored in the memory, the probability distribution identifying method of the above embodiment 1 is implemented, as follows:
selecting each candidate probability distribution and a power normalization factor thereof in all candidate probability distributions of a constellation shaping system as a first initial condition;
under a first initial condition, according to the amplitude of a received signal, carrying out iterative updating on probability distribution based on an expected maximum criterion, and calculating the relative entropy between each probability distribution after L iterations and all candidate probability distributions to serve as a first relative entropy;
selecting the candidate probability distribution corresponding to the first minimum relative entropy as the initial estimation of the unknown probability distribution, and taking the initial estimation of the probability distribution and the corresponding power normalization factor as a second initial condition;
under a second initial condition, according to the amplitude of the received signal, based on an expected maximum criterion, carrying out iterative updating on the probability distribution and the power normalization factor at the same time, and calculating the relative entropy between the probability distribution after T iterations and all candidate probability distributions to serve as a second relative entropy;
and selecting the candidate probability distribution corresponding to the second minimum relative entropy as the final estimation of the unknown probability distribution.
Example 5:
the present embodiment provides a storage medium, which is a computer-readable storage medium, and stores a computer program, and when the computer program is executed by a processor, the computer program implements the probability distribution identification method of embodiment 1, as follows:
selecting each candidate probability distribution and a power normalization factor thereof in all candidate probability distributions of a constellation shaping system as a first initial condition;
under a first initial condition, according to the amplitude of a received signal, carrying out iterative updating on probability distribution based on an expected maximum criterion, and calculating the relative entropy between each probability distribution after L iterations and all candidate probability distributions to serve as a first relative entropy;
selecting the candidate probability distribution corresponding to the first minimum relative entropy as the initial estimation of the unknown probability distribution, and taking the initial estimation of the probability distribution and the corresponding power normalization factor as a second initial condition;
under a second initial condition, according to the amplitude of the received signal, based on an expected maximum criterion, carrying out iterative updating on the probability distribution and the power normalization factor at the same time, and calculating the relative entropy between the probability distribution after T iterations and all candidate probability distributions to serve as a second relative entropy;
and selecting the candidate probability distribution corresponding to the second minimum relative entropy as the final estimation of the unknown probability distribution.
It should be noted that the computer readable storage medium of the present embodiment may be a computer readable signal medium or a computer readable storage medium or any combination of the two. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples of the computer readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
In summary, the present invention can extract the corresponding constellation probability distribution from the signal after channel equalization, the whole recognition algorithm is divided into two stages, the first stage obtains a preliminary estimation of probability distribution by using the data to be recognized, the second stage obtains an updated probability distribution estimation by using the estimation result of the previous stage and the data to be recognized, specifically after obtaining the amplitude of the received signal, in the first stage of the algorithm, each candidate probability distribution and the corresponding power normalization factor are respectively used as first initial conditions, the probability distributions are subjected to iterative updating based on an expected maximum criterion, the relative entropies between the candidate probability distributions and all the candidate probability distributions are respectively calculated, the probability distribution with the minimum relative entropy is taken as the initial estimation of unknown probability distribution, and the initial estimation of the probability distributions and the corresponding power normalization factor are used as second initial conditions; the second stage of the algorithm takes the probability distribution preliminary estimation obtained by the first stage as a starting point, obtains an optimal value of an adjustable parameter according to the probability distribution preliminary estimation and the signal-to-noise ratio, then iteratively updates the probability distribution and the power normalization factor based on an expected maximum criterion at the same time, calculates the relative entropy between the probability distribution after T iterations and all candidate probability distributions, takes the minimum relative entropy as the final estimation of the probability distribution, does not need offline training or pilot frequency assistance, can extract constellation probability distribution information from a received signal on the premise of not carrying out carrier phase recovery, has strong practicability, and has important application value for constellation shaping probability distribution identification in an elastic optical network.
The above description is only for the preferred embodiments of the present invention, but the protection scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution and the inventive concept of the present invention within the scope of the present invention.

Claims (10)

1. A method for identifying probability distribution under a probability shaped constellation, the method comprising:
selecting each candidate probability distribution and a power normalization factor thereof in all candidate probability distributions of a constellation shaping system as a first initial condition;
under a first initial condition, according to the amplitude of a received signal, carrying out iterative updating on probability distribution based on an expected maximum criterion, and calculating the relative entropy between each probability distribution after L iterations and all candidate probability distributions to serve as a first relative entropy;
selecting the candidate probability distribution corresponding to the first minimum relative entropy as the initial estimation of the unknown probability distribution, and taking the initial estimation of the probability distribution and the corresponding power normalization factor as a second initial condition;
under a second initial condition, according to the amplitude of the received signal, based on an expected maximum criterion, carrying out iterative updating on the probability distribution and the power normalization factor at the same time, and calculating the relative entropy between the probability distribution after T iterations and all candidate probability distributions to serve as a second relative entropy;
and selecting the candidate probability distribution corresponding to the second minimum relative entropy as the final estimation of the unknown probability distribution.
2. The method of claim 1, wherein the iterative updating of the probability distribution based on the expected maximum criterion according to the amplitude of the received signal comprises:
updating the computational assistance profile as follows:
Figure FDA0002755484940000011
wherein, Pl-1(an) Represents the candidate probability distribution after the update of the l-1 th iteration, and when l is equal to 1, P0＝Pj＝{Pj(an) 1, 2., N } represents an initial value of the probability distribution;
Figure FDA0002755484940000012
for a selected probability distribution P0Corresponding power normalization factor delta0；PR|A(rk|an；Δ0) Channel transition probability representing signal amplitude, anAn nth amplitude value representing an M-th order quadrature amplitude modulation constellation;
updating the probability distribution based on the auxiliary distribution as follows:
Figure FDA0002755484940000013
wherein, Pl(an) To representThe probability distribution after the ith iteration update, K represents the total number of symbols for the desired maximum algorithm.
3. The probability distribution identification method of claim 2, wherein the channel transition probability P of the signal amplitudeR|A(rk|an；Δ0) The calculation of (c) is as follows:
Figure FDA0002755484940000021
wherein, P0Representing an initial value of the probability distribution, P0＝Pj＝{Pj(an)|n＝1,2,...,N}，PjRepresenting the jth candidate probability distribution, Δ0Represents a group of formulae and P0Corresponding power normalization factor, σ2Variance, I, representing the real and imaginary parts of additive white Gaussian noise0() Representing a zero order first-class modified bessel function.
4. The method of identifying probability distributions of claim 1, wherein the relative entropy between each probability distribution and all candidate probability distributions after L iterations is calculated as follows:
Figure FDA0002755484940000022
wherein, PL(an) Representing each probability distribution, P, after L iterative updatesjRepresenting the j-th candidate probability distribution, Pj＝{Pj(an)，n＝1，2…N}，anRepresenting the nth possible amplitude value in the M-order quadrature amplitude modulation constellation.
5. The method of claim 1, wherein in the iterative updating of the probability distribution and the power normalization factor based on the desired maximum criterion based on the amplitude of the received signal, the t-th iteration comprises:
calculating the channel transition probability of the signal amplitude as follows:
Figure FDA0002755484940000023
wherein, Deltat-1The power normalization factor updated for the t-1 th iteration, when t is 1, Δ0A power normalization factor corresponding to the preliminary estimate representing the probability distribution;
calculating the auxiliary distribution as follows:
Figure FDA0002755484940000024
wherein, Pt-1(an) Probability distribution updated for the t-1 st iteration, when t is 1, P0＝{P0(an) 1, 2.., N } represents a preliminary estimate of the probability distribution;
updating the probability distribution and the power normalization factor simultaneously based on the auxiliary distribution, wherein the power normalization factor is updated according to the following formula:
Figure FDA0002755484940000031
wherein the content of the first and second substances,
Figure FDA0002755484940000032
is an adjustable parameter.
Finding out the probability distribution corresponding to the power normalization factor by a table look-up method according to the relationship between the power normalization factor and the probability distribution shown in the following formula:
Figure FDA0002755484940000033
。
6. the probability distribution identification method of claim 5, wherein the adjustable parameter is
Figure FDA0002755484940000034
The acquisition process is as follows:
assume that there are S candidate probability distributions to identify, denoted as P1，P2，…，PS(ii) a At a certain signal-to-noise ratio, the probability distribution of the transmitted signal is PiThe preliminary estimate of the probability distribution is output as PjHas a probability of fijFor S candidate probability distributions, the output of the preliminary estimate of the probability distribution is described by the following matrix F of S rows and S columns:
Figure FDA0002755484940000035
normalizing the matrix F column by column to obtain the initial estimation output P of probability distributionjProbability distribution of transmitted signal is PiWeighting coefficient of time
Figure FDA0002755484940000036
When the preliminary estimate of the probability distribution is output as PjThe signal adopts a probability distribution PiThe success rate of time-dependent recognition
Figure FDA0002755484940000037
The recognition success rate is compared with
Figure FDA0002755484940000038
Is a function of
Figure FDA0002755484940000039
Description is given;
using a weighting coefficient wijObtaining a weighted recognition success rate function as follows:
Figure FDA00027554849400000310
wherein the content of the first and second substances,
Figure FDA00027554849400000311
the subscript j denotes the preliminary estimate output of the probability distribution as PjSelect out
Figure FDA00027554849400000312
Largest size
Figure FDA00027554849400000313
The output of the preliminary estimate as a probability distribution is PjThe optimum parameter of (2).
7. The method of identifying probability distributions of claim 1, wherein the relative entropy between the probability distribution after T iterations and all candidate probability distributions is calculated as follows:
Figure FDA0002755484940000041
wherein, PT(an) Representing each probability distribution, P, updated over T iterationsjRepresenting the j-th candidate probability distribution, Pj＝{Pj(an)，n＝1，2…N}，anRepresenting the nth possible amplitude value in the M-order quadrature amplitude modulation constellation.
8. An apparatus for identifying a probability distribution under a probability shaped constellation, the apparatus comprising:
the first selection module is used for selecting each candidate probability distribution in all candidate probability distributions of the constellation shaping system and a power normalization factor thereof as a first initial condition;
the first calculation module is used for carrying out iterative updating on probability distribution based on an expected maximum criterion according to the amplitude of a received signal under a first initial condition, and calculating the relative entropy between each probability distribution after L iterations and all candidate probability distributions to serve as a first relative entropy;
the second selection module is used for selecting the candidate probability distribution corresponding to the minimum first relative entropy as the initial estimation of the unknown probability distribution and using the initial estimation of the probability distribution and the corresponding power normalization factor as a second initial condition;
the second calculation module is used for carrying out iterative updating on the probability distribution and the power normalization factor simultaneously on the basis of an expected maximum criterion according to the amplitude of the received signal under a second initial condition, and calculating the relative entropy between the probability distribution after T iterations and all candidate probability distributions to serve as a second relative entropy;
and the third selection module is used for selecting the candidate probability distribution corresponding to the second relative entropy as the final estimation of the unknown probability distribution.
9. A computer device comprising a processor and a memory for storing a program executable by the processor, wherein the processor, when executing the program stored in the memory, implements the probability distribution identifying method of any one of claims 1-7.
10. A storage medium storing a program, wherein the program, when executed by a processor, implements the probability distribution identifying method according to any one of claims 1 to 7.
CN202011201788.4A 2020-11-02 2020-11-02 Probability distribution identification method, device, equipment and medium under probability shaping constellation Active CN112367284B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011201788.4A CN112367284B (en) 2020-11-02 2020-11-02 Probability distribution identification method, device, equipment and medium under probability shaping constellation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011201788.4A CN112367284B (en) 2020-11-02 2020-11-02 Probability distribution identification method, device, equipment and medium under probability shaping constellation

Publications (2)

Publication Number Publication Date
CN112367284A true CN112367284A (en) 2021-02-12
CN112367284B CN112367284B (en) 2023-01-03

Family

ID=74513221

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011201788.4A Active CN112367284B (en) 2020-11-02 2020-11-02 Probability distribution identification method, device, equipment and medium under probability shaping constellation

Country Status (1)

Country Link
CN (1) CN112367284B (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113285762A (en) * 2021-02-25 2021-08-20 广西师范大学 Modulation format identification method based on relative entropy calculation
CN114338316A (en) * 2021-12-29 2022-04-12 北京邮电大学 Method for identifying standard modulation format and probability shaping modulation format
CN114401049A (en) * 2022-01-26 2022-04-26 西南交通大学 Probability shaping signal shaping distribution identification method based on amplitude distribution characteristics
CN114598581A (en) * 2022-01-24 2022-06-07 北京邮电大学 Training method, recognition method and device for two-stage detection model of probability shaping signal

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111064516A (en) * 2019-12-18 2020-04-24 南京信息工程大学 Radio over fiber communication method based on hexagonal constellation forming iteration
WO2020108771A1 (en) * 2018-11-30 2020-06-04 Huawei Technologies Co., Ltd. Device and method for probabilitic constellation shaping
US10700807B1 (en) * 2019-07-01 2020-06-30 Fujitsu Limited Fiber input power selection for probabilistically shaped signals in optical networks
CN111555819A (en) * 2020-04-22 2020-08-18 华南理工大学 Carrier phase estimation and compensation method and system

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2020108771A1 (en) * 2018-11-30 2020-06-04 Huawei Technologies Co., Ltd. Device and method for probabilitic constellation shaping
US10700807B1 (en) * 2019-07-01 2020-06-30 Fujitsu Limited Fiber input power selection for probabilistically shaped signals in optical networks
CN111064516A (en) * 2019-12-18 2020-04-24 南京信息工程大学 Radio over fiber communication method based on hexagonal constellation forming iteration
CN111555819A (en) * 2020-04-22 2020-08-18 华南理工大学 Carrier phase estimation and compensation method and system

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
YAN, QIFENG等: "Blind Carrier Frequency Offset Estimation in Coherent Optical Communication Systems With Probabilistically Shaped M-QAM", 《JOURNAL OF LIGHTWAVE TECHNOLOGY》 *
彭家昕等: "基于算数编码的概率星座整形技术的研究", 《网络新媒体技术》 *

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113285762A (en) * 2021-02-25 2021-08-20 广西师范大学 Modulation format identification method based on relative entropy calculation
CN113285762B (en) * 2021-02-25 2022-08-05 广西师范大学 Modulation format identification method based on relative entropy calculation
CN114338316A (en) * 2021-12-29 2022-04-12 北京邮电大学 Method for identifying standard modulation format and probability shaping modulation format
CN114338316B (en) * 2021-12-29 2024-01-05 北京邮电大学 Identification method for standard modulation format and probability shaping modulation format
CN114598581A (en) * 2022-01-24 2022-06-07 北京邮电大学 Training method, recognition method and device for two-stage detection model of probability shaping signal
CN114598581B (en) * 2022-01-24 2023-08-04 北京邮电大学 Training method, recognition method and device for double-stage detection model of probability shaping signal
CN114401049A (en) * 2022-01-26 2022-04-26 西南交通大学 Probability shaping signal shaping distribution identification method based on amplitude distribution characteristics

Also Published As

Publication number Publication date
CN112367284B (en) 2023-01-03

Similar Documents

Publication Publication Date Title
CN112367284B (en) Probability distribution identification method, device, equipment and medium under probability shaping constellation
CN110648292B (en) High-noise image denoising method based on deep convolutional network
CN112735460B (en) Beam forming method and system based on time-frequency masking value estimation
US20140269887A1 (en) Equalizer and detector arrangement employing joint entropy-based calibration
TWI381674B (en) Candidate List Amplification Apparatus for Channel Decoding System and Method
CN114726692B (en) SERESESESENet-LSTM-based radiation source modulation mode identification method
CN108737022B (en) Low-complexity SCMA decoding method and device based on quantum computation
CN112787964A (en) BPSK and QPSK signal modulation identification method based on range median domain features
Bakulin et al. Bayesian estimation with successive rejection and utilization of a priori knowledge
CN109547374B (en) Depth residual error network and system for underwater communication modulation recognition
CN114925720A (en) Small sample modulation signal identification method based on space-time mixed feature extraction network
CN113343801A (en) Automatic wireless signal modulation and identification method based on lightweight convolutional neural network
JP6507320B2 (en) Method of recovering original signal in DS-CDMA system based on complexity reduction
CN114938232B (en) LSTM-based simultaneous co-frequency full-duplex digital domain self-interference suppression method
Wallayt et al. Automatic modulation classification for low SNR digital signal in frequency-selective fading environments
CN114172770A (en) Modulation signal identification method of quantum root tree mechanism evolution extreme learning machine
CN113630160A (en) Large-scale MIMO detection method, device, equipment and storage medium
Yu et al. Distributed blind system identification in sensor networks
CN110443194B (en) Time-varying signal component extraction method based on SPI sparse constraint
Zhang et al. Complex-Valued Neural Network with Multi-Step Training for Single-Snapshot DOA Estimation
CN116318470B (en) Method and device for estimating communication interference signal power under non-Gaussian noise
Chang et al. Sparsity update subspace pursuit algorithm for compressed spectrum sensing
Omondi et al. DNN-Based MIMO Signal Detection Using Variational Autoencoder
CN118118301A (en) Nonlinear MIMO channel estimation method based on Inception-ResNet network and dense residual error network
CN117560256A (en) Self-interference suppression method for simultaneous same-frequency full duplex communication system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant