CN112367284B - Probability distribution identification method, device, equipment and medium under probability shaping constellation - Google Patents
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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 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
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 constellation has the advantages of higher spectral efficiency and lower optical signal to noise ratio, and is more and more a reliable technical scheme of the next generation optical network. 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. See in detail [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] cheh 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.A.El-Rahman, J.C.Cartledge, and S.A.Etemail, "Extending a non-linear sensor assay to include mapping identification for probabistically shaped 64-QAM signals," J.Light.Techniol., 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 document for details [4 ]]W, zhang, D.Zhu, N.Zhang, H.xu, X.Zhang, H.Zhang, and Y.Li, "identification basic mapping for models through 2D stocks plants with two-stage deep neural networks," IEEE ACCESS, vol.8, pp.6742-6750, jan.2020). However, the above algorithm based on the artificial neural network and the convolutional neural network requires a large number of samples to be trained offline, and a large number of received symbols are also required to be input into the neural network during online testing, which makes the practical implementation of the algorithm highly complex. 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.
“Blind decoding-metric estimation for probabilistic shaping via expectation maximization,”in PrEur.conf.opt.commun., 2018). 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 probability shaping constellation requires prior information to know the probability distribution (see the literature: [6 ]]Yan, L.Liu, and X.hong, "band carrier frequency offset estimation in coherent communication system with probabilistically mapped M-QAM," J.Lightw.Techninol., 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 finding of the probability distribution recognition 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 therefore, there is no need to perform frequency offset compensation and carrier phase recovery on an input signal, and training is not required, and therefore, the present invention has strong practicability.
The first purpose of the invention is to provide a probability distribution identification method under probability shaping constellations.
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 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:
wherein, P l-1 (a n ) Represents the candidate probability distribution after the update of the (l-1) th iteration, when l =1, P 0 ＝P j ＝{P j (a n ) | N =1,2, · N } denotes an initial value of the probability distribution;
to selected probability distributionP 0 Corresponding power normalization factor delta 0 ；P R|A (r k |a n ；Δ 0 ) Channel transition probability representing signal amplitude, a n An nth amplitude value representing an M-order quadrature amplitude modulation constellation;
updating the probability distribution based on the auxiliary distribution as follows:
wherein, P l (a n ) The probability distribution after the ith iteration update is represented, and K represents the total number of symbols for the desired maximum algorithm.
Further, the channel transition probability P of the signal amplitude R|A (r k |a n ；Δ 0 ) The calculation of (c) is as follows:
wherein, P 0 Representing an initial value of the probability distribution, P 0 ＝P j ＝{P j (a n )|n＝1,2,...,N}，P j Representing the jth candidate probability distribution, Δ 0 Represents a group of formulae and P 0 Corresponding power normalization factor, σ 2 Variance, I, representing the real and imaginary parts of additive white Gaussian noise 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:
wherein, P L (a n ) Representing each probability distribution, P, after L iterative updates j Representing the j-th candidate probability distribution, P j ＝{P j (a n )，n＝1，2…N}，a n Representing 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 expectation maximization 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:
wherein, delta t-1 Power normalization factor updated for the t-1 th iteration, Δ when t =1 0 A power normalization factor corresponding to the preliminary estimate representing the probability distribution;
calculating the auxiliary distribution as follows:
wherein, P t-1 (a n ) Updated probability distribution for the t-1 st iteration, when t =1, P 0 ＝{P 0 (a n ) | N =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:
wherein the content of the first and second substances,
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:
further, the adjustable parameter
The acquisition process is as follows:
assume that there are S candidate probability distributions to identify, denoted as P 1 ，P 2 ，…，P S (ii) a Under a certain signal-to-noise ratio, the probability distribution of the transmitted signal is P i The preliminary estimate of the probability distribution is output as P j Has a probability of f ij For 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:
normalizing the matrix F column by column to obtain the initial estimation output P of probability distribution j Probability distribution of transmission signal is P i Weighting coefficient of time
When the preliminary estimate of the probability distribution is output as P j The signal adopts a probability distribution P i The success rate of time-dependent recognition
The recognition success rate is compared with
Is a function of
Description is given;
using a weighting coefficient w ij Obtaining a weighted recognition success rate function as follows:
wherein, the first and the second end of the pipe are connected with each other,
the subscript j denotes the preliminary estimate output of the probability distribution as P j To select out
Maximum size
The output of the preliminary estimate as a probability distribution is P j The optimum parameter of (2).
Further, the relative entropy between the probability distribution after T iterations and all candidate probability distributions is calculated as follows:
wherein, P T (a n ) Representing each probability distribution, P, updated over T iterations j Representing the j-th candidate probability distribution, P j ＝{P j (a n )，n＝1，2…N}，a n Representing the nth possible amplitude value in an 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 based on 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 corresponding constellation probability distribution from signals after channel equalization, the whole identification algorithm is divided into two stages, the first stage utilizes data to be identified to obtain initial estimation of probability distribution, the second stage utilizes the estimation result of the previous stage and the data to be identified to obtain updated probability distribution estimation, specifically, after the amplitude of received signals is obtained, the algorithm first stage respectively takes each candidate probability distribution and corresponding power normalization factor as first initial conditions, carries out iterative update on the probability distribution based on an expected maximum criterion, respectively calculates relative entropy between the candidate probability distribution and the probability distribution 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 distribution 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 expectation maximization 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 received signals 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 in embodiment 1 of the present invention.
Fig. 2 is a flowchart of a probability distribution identification method under a probability shaped constellation in embodiment 2 of the present invention.
FIG. 3 shows that the SNR of example 2 of the present invention is 13dB
And weighted correspondingly
Graph of (a).
FIG. 4 shows the arbitrary SNR of the SNR interval in example 2 of the present invention
Graph is shown.
Fig. 5 is a performance diagram of the recognition success rate and the signal-to-noise ratio according to 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
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, it is obvious that the described embodiments are some, but not all, embodiments of the present invention, 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, \8230;, S) candidate probability distribution can be described as: p j ＝{P j (a n )，n＝1，2…N}，a n Representing 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 distribution j So that
Where N is the total number of turns of the M-QAM constellation,selecting the jth candidate probability distribution P j And its power normalization factor delta j As 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 P 0 ＝P j ＝{P j (a n ) When | N =1,2,. So, N }, it is assumed that the kth received symbol is y k Amplitude r of k ＝|y k First, the channel transition probability of the signal amplitude is calculated as follows:
wherein, delta 0 Is represented by the formula P 0 Corresponding power normalization factor, σ 2 Variance, I, representing the real and imaginary parts of additive white Gaussian noise 0 () 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:
wherein, P l-1 (a n ) Represents the candidate probability distribution after the update of the (l-1) th iteration, when l =1, P 0 ＝P j ＝{P j (a n ) I N =1,2,. -, N } represents an initial value of the probability distribution.
S1022, updating the probability distribution based on the auxiliary distribution, as follows:
wherein, P l (a n ) 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:
wherein, P L (a n ) Each probability distribution after 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 =1,2,3, \ 8230, 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 obtained 2 The 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.
Using 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 update on the probability distribution and the power normalization factor simultaneously through an expected maximum criterion, wherein the t iteration step comprises the following steps:
s1041, calculating a channel transfer probability of the signal amplitude as follows:
wherein, delta t-1 Power normalization factor updated for the t-1 th iteration, Δ when t =1 0 A power normalization factor corresponding to the preliminary estimate representing the probability distribution.
S1042, calculating the auxiliary distribution as follows:
wherein, P t-1 (a n ) Updated probability distribution for the t-1 st iteration, when t =1, P 0 ＝{P 0 (a n ) I N =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:
wherein the content of the first and second substances,
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:
in the above step of one iteration, the embodiment needs to perform T iterations, substitute the updated power normalization factor and probability distribution into the formulas of step S1041 and step S1042 in the subsequent iterations, and then execute step S1043 to perform a new update.
Calculating relative entropy between the probability distribution after T iterations and all candidate probability distributions, as follows:
wherein, P T (a n ) Each probability distribution after T iterations is represented, and because there are S probability distributions to be identified, there are S relative entropies in the above equation, i.e., j =1,2,3, \8230;, S. These S relative entropies serve as second relative entropies.
Adjustable parameter
The acquisition process of (1) is as follows:
s1044, assuming that S candidate probability distributions need to be identified, and marking as P 1 ，P 2 ，…，P S (ii) a Under a certain signal-to-noise ratio, the probability distribution of the transmitted signal is P i Then, the output of step S103 (preliminary estimation of probability distribution) is P j Has a probability of f ij For S candidate probability distributions, the output result of step S103 is described by the following matrix F of S rows and S columns:
normalizing the matrix F column by column to obtain the initial estimation output P of probability distribution j Probability distribution of transmitted signal is P i Weighting factor (i.e. weighting factor) of time
S1045, when the output of the step S103 is P j The signal adopts a probability distribution P i The success rate of time-dependent recognition
The success rate and the result of the identification at the moment are obtained by numerical simulation or experiment
Provided that this relationship can be expressed as a function
A description is given.
S1046, using weighting coefficient w ij Obtaining a weighted recognition success rate function as follows:
wherein the content of the first and second substances,
the subscript j denotes the preliminary estimate output of the probability distribution as P j To select out
Maximum size
The output of the preliminary estimate as a probability distribution is P j The 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
And S105, selecting the candidate probability distribution corresponding to the minimum second relative entropy 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 a Maxwell-Boltzmann (MB) distribution under a 64-QAM template, wherein the MB distribution formula is as follows:
in 64QAM, M =64; λ of these 7 probability distributions i And 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:
a 64QAM constellation has 9 circles of different amplitudes, so N =9,7 power normalization factors are: delta 1 ，Δ 2 ，…，Δ 7 =0.3258,0.3028,0.2814,0.2612,0.2421,0.2237, and 0.2054; at the receiving end, the local oscillator frequency difference is assumed to be 1GHz (the system baud rate is 28 GBaud), and the line width of the combined laser is 200kHz to simulate the carrier phase fluctuation. The number of symbols used for probability distribution identification is 2048, i.e., K =2048. The number of iterations in the initialization process and the iteration process in the following expectation maximization algorithm is 3 and 30 (L =3, t = 30), respectively.
TABLE 1 probability distribution used in this example
| Probability distribution | P 1 | P 2 | P 3 | P 4 | P 5 | P 6 | P 7 |
| 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 snr is 13dB, the number of symbols used in the initialization is also 2048, and the initialization result obtained according to step S1044 of the above embodiment 1 is shown in table 2, where the data in the table indicates that when the transmitted shaping distribution is P i When the initial value of the probability distribution is P j Is the percentage probability of f mentioned in step S1044 of example 1 above ij Then, according to the formula
The weighting coefficients were calculated and the results are shown in table 3 below.
TABLE 2 initialization results
TABLE 3 weighting coefficients
| w ij | 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 P j Time, different probability distribution P i Success rate of recognition and
in relation to (2)
And using the weighting coefficient w of (2-5) ij And (3) weighting:
wherein the content of the first and second substances,
the subscript j indicates that the probability distribution in step S103 of embodiment 1 is initialized to P j . FIG. 3 shows a signal-to-noise ratio of 13dB
And weighted correspondingly
Curve (c) of (d). When noteworthy, due to the weighting factor w 14 ,w 24 ,w 64 ,w 74 Are all 0, so FIG. 3 is not drawn
S202, finding out
Corresponding to when maximum is reached
At this time
Is 0.988, i.e., when the probability distribution in step S103 of the above-described embodiment 1 is initialized to P 4 Time of flight optimization
Was 0.988. For initial values of other probability distributions and other signal-to-noise ratios
Are obtained by the same procedure. Since it is impractical to traverse any signal-to-noise ratio in actual practice, it is possible to traverse the signal-to-noise ratio interval of interest (e.g., 9dB-19 dB) at certain signal-to-noise ratio intervals (e.g., 1 dB), and then obtain any signal-to-noise ratio within this interval by polynomial fitting
The results are shown in FIG. 4.
S203, obtaining sigma according to the signal-to-noise ratio 2 Then, the initialization process of steps S101 to S103 of embodiment 1 described above is performed, and a preliminary estimation 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
S205, according to the selected optimal
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 iteratively update the probability distribution and the power normalization factor based on an expected maximum criterion according to the amplitude of the received signal under a second initial condition, and calculate a relative entropy between the probability distribution after T iterations and all candidate probability distributions, 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.
For specific implementation of each module in this embodiment, reference may be made to embodiment 1 above, which is not described in detail herein; 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 minimum first 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;
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 relative entropy minimum 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 corresponding constellation probability distributions from signals after channel equalization, the whole recognition algorithm is divided into two stages, the first stage obtains a preliminary estimation of a probability distribution by using 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 received signals, the first stage of the algorithm respectively uses each candidate probability distribution and the corresponding power normalization factor as the first initial condition, iteratively updates the probability distributions based on the expectation maximization criterion, respectively calculates the relative entropies between them and all candidate probability distributions, takes the probability distribution with the minimum relative entropy as the preliminary estimation of unknown probability distributions, and uses the preliminary estimation of the probability distributions and the corresponding power normalization factor as the second initial condition; 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 a 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;
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:
wherein, P l-1 (a n ) Represents the candidate probability distribution after the update of the (l-1) th iteration, when l =1, P 0 ＝P j ＝{P j (a n ) I N =1,2, ·, N } denotes a probability distribution initial value;
for a selected probability distribution P 0 Corresponding power normalization factor delta 0 ；r k Signal amplitude for the kth received symbol; p is R|A (r k |a n ；Δ 0 ) Channel transition probability representing signal amplitude, a n An nth amplitude value representing an M-th order quadrature amplitude modulation constellation;
the probability distribution is updated based on the auxiliary distribution as follows:
wherein, P l (a n ) Representing the probability distribution after the ith iteration update, and K representing 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 amplitude R|A (r k |a n ；Δ 0 ) The calculation of (c) is as follows:
wherein, P 0 Representing an initial value of the probability distribution, P 0 ＝P j ＝{P j (a n )|n＝1,2,...,N}，P j Representing the jth candidate probability distribution, Δ 0 Represents a group of formulae and P 0 Corresponding power normalization factor, σ 2 Variance, I, representing the real and imaginary parts of additive white Gaussian noise 0 () 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:
wherein, P L (a n ) Representing each probability distribution, P, after L iterative updates j Representing the j-th candidate probability distribution, P j ＝{P j (a n )，n＝1，2…N}，a n Representing 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:
wherein r is k Signal amplitude, Δ, for the k-th received symbol t-1 Power normalization factor updated for the t-1 th iteration, Δ when t =1 0 Representation outlinePower normalization factors corresponding to the preliminary estimation of the rate distribution;
calculating the auxiliary distribution as follows:
wherein, P t-1 (a n ) Probability distribution updated for the t-1 st iteration, when t =1, P 0 ＝{P 0 (a n ) | N =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:
wherein the content of the first and second substances,
is an adjustable parameter;
according to the relation between the power normalization factor and the probability distribution shown in the following formula, finding out the probability distribution corresponding to the power normalization factor by a table look-up method:
6. the probability distribution identification method of claim 5, wherein the adjustable parameter is
The acquisition process is as follows:
assume that there are S candidate probability distributions to identify, denoted as P 1 ，P 2 ，…，P S (ii) a Probability distribution of transmitted signals at a certain signal-to-noise ratioIs P i The preliminary estimate of the probability distribution is output as P j Has a probability of f ij For S candidate probability distributions, the output of the preliminary estimation of the probability distribution is described by the following matrix F of S rows and S columns:
normalizing the matrix F column by column to obtain the initial estimation output P of probability distribution j Probability distribution of transmission signal is P i Weighting factor of time
When the preliminary estimate of the probability distribution is output as P j The signal adopts a probability distribution P i The success rate of recognition depends on
The recognition success rate is compared with
Is a function of
Description;
using a weighting coefficient w ij Obtaining a weighted recognition success rate function as follows:
wherein the content of the first and second substances,
the subscript j denotes the preliminary estimate output of the probability distribution as P j Select out
Maximum size
The output of the preliminary estimation as a probability distribution is P j The 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:
wherein, P T (a n ) Representing each probability distribution, P, updated over T iterations j Representing the j-th candidate probability distribution, P j ＝{P j (a n )，n＝1，2…N}，a n Representing 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 of the candidate probability distribution as a first initial condition;
a first calculating module, 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;
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 based on 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 minimum 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 implements the probability distribution identifying method of any one of claims 1-7 when executing the program stored in the memory.
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.
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