CN112910562A - Communication method based on probability shaping - Google Patents

Communication method based on probability shaping Download PDF

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CN112910562A
CN112910562A CN202110055098.0A CN202110055098A CN112910562A CN 112910562 A CN112910562 A CN 112910562A CN 202110055098 A CN202110055098 A CN 202110055098A CN 112910562 A CN112910562 A CN 112910562A
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probability
pam
sequence
amplitude
symbol
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CN112910562B (en
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董宇涵
阳帆
耿祖航
李志德
权进国
金爽
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Shenzhen International Graduate School of Tsinghua University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/50—Transmitters
    • H04B10/516—Details of coding or modulation
    • H04B10/524—Pulse modulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/50—Transmitters
    • H04B10/516—Details of coding or modulation
    • H04B10/5161—Combination of different modulation schemes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/50—Transmitters
    • H04B10/516—Details of coding or modulation
    • H04B10/54—Intensity modulation
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Abstract

The invention discloses a communication method based on probability shaping, which comprises the following steps: s1, initializing the amplitude and probability of the PAM constellation points; s2, generating a corresponding PAM symbol sequence by utilizing distribution matching based on the initialized amplitude and probability, and converting the PAM symbol sequence into a final transmitting signal; wherein, a part of the PAM symbol sequence is used as a training sequence; s3, estimating the transmission function and the noise power of the channel by using the training sequence; s4, carrying out judgment decoding on a receiving end by using the estimated transmission function and the noise power to obtain a decoding signal; and S5, calculating mutual information between the emission signal and the decoding signal, and solving the position of the PAM constellation point with the maximum mutual information and the corresponding probability by using an iterative mode. The invention can effectively relieve the distortion caused by the nonlinearity of the light source device.

Description

Communication method based on probability shaping
Technical Field
The invention relates to the field of wireless optical communication, in particular to a communication method based on probability shaping.
Background
Wireless Optical Communication (OWC) is a technology for Communication using Wireless Optical waves, and has the advantages of high speed and high security. However, OWCs may suffer from non-linearity in practical applications, wherein the non-linearity of Light source devices such as Light Emitting Diodes (LEDs) is one of the main sources. The nonlinearity of the LED is manifested by a bilateral shear of the transmitted signal with too large or too small amplitude, causing signal distortion. Therefore, in order to ensure communication quality, it is essential to mitigate such nonlinear distortion.
The common nonlinear mitigation methods can be mainly divided into two types: compensation and desensitization. The former mainly compensates the nonlinear distortion of the LED by using a pre-distortion or post-distortion mode; the latter is mainly to reduce the influence of nonlinearity by processing the transmitted signal to reduce its sensitivity to nonlinear distortion. For compensation, it is generally required to know a relatively accurate nonlinear model of the LED, and the calculation complexity is high by constructing an inverse function of the nonlinear model to perform the cancellation. And the desensitization does not need to know a nonlinear model, the amplitude of a transmitting signal is generally limited to avoid entering a nonlinear region, and the required computational complexity is low. For example, in an Orthogonal Frequency Division Multiplexing (OFDM) system, reducing nonlinear distortion indirectly by reducing a Peak to Average Power Ratio (PAPR) is a typical desensitization technique.
On the other hand, among various signal processing techniques for optimizing communication performance, the probability shaping technique is widely used in the field of optical communication with high flexibility and low complexity, and its core idea is to obtain a shaping gain by adjusting the probability of a constellation point. For example, Buchali F, Steiner F, Bocherer G et al, in the "Rate adaptation and access encryption by basic Modulation shaped 64-QAM, An Experimental demodulation", propose Quadrature Amplitude Modulation (QAM) technology based on probability shaping in optical fiber communication, for single carrier coherent optical transmission system of adaptive Rate; ma J, Chen M, Wu K and the like provide an OFDM technology based on probability shaping in Performance enhancement of behavioral shaped OFDM enabled by precoding technique in IM-DD system, which is used for an optical access network system and provides experimental verification. In free space optical communication, Elzanato A and Alouini M-S propose a Pulse Amplitude Modulation (PAM) technology based on probability shaping in Adaptive coding for IM/DD free-space optical beamforming, and improve communication capacity by an Adaptive coding mode. In the above prior art schemes, the probability shaping technique is usually only used to approximate shannon capacity limit, but the shaping gain embodied by the probability shaping technique makes it have a great potential to mitigate nonlinear distortion.
Disclosure of Invention
Based on the above, the present invention provides a communication method based on probability shaping, which alleviates the nonlinear distortion of wireless optical communication through a PAM technique based on probability shaping, and the core idea is to maximize the mutual information between the transmitted and received signals by solving the position and the corresponding probability of the PAM optimal constellation point.
A communication method based on probability shaping, comprising the steps of: s1, initializing the amplitude and probability of the PAM constellation points; s2, generating a corresponding PAM symbol sequence by utilizing distribution matching based on the initialized amplitude and probability, and converting the PAM symbol sequence into a final transmitting signal; wherein, a part of the PAM symbol sequence is used as a training sequence; s3, estimating the transmission function and the noise power of the channel by using the training sequence; s4, carrying out judgment decoding on a receiving end by using the estimated transmission function and the noise power to obtain a decoding signal; and S5, calculating mutual information between the emission signal and the decoding signal, and solving the position of the PAM constellation point with the maximum mutual information and the corresponding probability by using an iterative mode.
The invention has the beneficial effects that: the invention utilizes the nonlinear region to communicate by probability shaping, relieves the influence of the nonlinear region by adjusting the probability of the constellation point, and effectively reduces the distortion effect caused by the nonlinear region especially when the modulation order is increased.
Drawings
FIG. 1 is a flow chart of PAM probability shaping according to an embodiment of the present invention;
FIG. 2 is a graph of the nonlinear transmission characteristics of an LED according to an embodiment of the present invention;
FIG. 3 shows mutual information before and after optimization according to an embodiment of the present invention
Figure BDA0002900655480000021
And (3) a change relation diagram of the modulation order M.
Detailed Description
The invention is further described with reference to the following figures and detailed description of embodiments.
Embodiments of the present invention take into account nonlinear distortion in a wireless optical communication system. First, the position and probability of the PAM constellation point are initialized, and a corresponding symbol sequence is generated using Distribution Matching, for example, fixed combination Distribution Matching (CCDM) proposed by Schulte P and Bocherer G in the article "Constant Composition Distribution Matching", wherein a part of the symbol sequence is used as a training sequence. The training sequence is used to estimate the transmission characteristics and simultaneously the noise power. The received signal is then decision decoded in combination with the estimated transmission characteristics and noise power. And finally, calculating mutual information between the transmitting signal and the decoding signal, and solving the position of the constellation point with the maximum mutual information and the corresponding probability by using an iterative mode, thereby improving the communication performance of the system.
Fig. 1 is a PAM probability shaping flowchart according to an embodiment of the present invention, and referring to fig. 1, shows a bit sequence of U transmission to be used for generating a PAM symbol sequence;
Figure BDA0002900655480000032
representing the finally decoded bit sequence. Practice of the inventionThe communication method based on probability shaping comprises the following steps of S1-S5: s1, initializing the amplitude and probability of the PAM constellation points; s2, generating a corresponding PAM symbol sequence by utilizing distribution matching based on the initialized amplitude and probability, and converting the PAM symbol sequence into a final transmitting signal; wherein, a part of the PAM symbol sequence is used as a training sequence; s3, estimating the transmission function and the noise power of the channel by using the training sequence; s4, carrying out judgment decoding on a receiving end by using the estimated transmission function and the noise power to obtain a decoding signal; and S5, calculating mutual information between the emission signal and the decoding signal, and solving the position of the PAM constellation point with the maximum mutual information and the corresponding probability by using an iterative mode.
In some embodiments, step S1 specifically includes: let the modulation order of PAM be M, and for a single M-order PAM symbol X, the amplitude of the position of the constellation point where PAM is desirable is denoted as a ═ a1,a2,...,aMCorresponding to a probability of { p }1,p2,...,pMIn which a isiAnd piRepresenting the amplitude and probability of the ith constellation point, i is 1,2, M, a represents the value space of the amplitude; to ensure maximum utilization of the dynamic range of the LED, i.e., the linear region of Φ (·), let X be related to the midpoint of the linear region of the light source device
Figure BDA0002900655480000031
The constellation points are symmetrically distributed and initialized to be distributed in the linear region at equal probability and equal intervals; where Φ (·) represents a nonlinear transfer function of the light source device, a transfer characteristic curve thereof is shown in fig. 2.
Symbol sequence X obeying a particular amplitude and probability distributionnCan be composed of a bit sequence Uk∈{0,1}kGenerated by the CCDM. Therefore, step S2 specifically includes S21 to S23:
s21, constructing a codebook
Figure BDA0002900655480000041
Containing a PAM symbol sequence XnIs expressed as:
Figure BDA0002900655480000042
wherein v ∈ AnRepresenting that each element of the sequence v of length n belongs to the amplitude space a,
Figure BDA0002900655480000043
representing the amplitude a in the sequence viThe number of symbols of (a);
s22, converting the binary bit sequence U with the length of kk∈{0,1}kOne-to-one mapping to codebooks
Figure BDA0002900655480000044
In (2), PAM symbol sequence X with length n is generatedn(ii) a Wherein the content of the first and second substances,
Figure BDA0002900655480000045
Figure BDA0002900655480000047
a size of the codebook is represented and,
Figure BDA0002900655480000046
represents rounding down;
s23, PAM mapping: for the generated PAM symbol sequence XnAnd performing digital-to-analog conversion (D/A) to generate a final transmission signal. Due to the bit sequence UkThe PAM symbol sequence is in one-to-one correspondence relationship with the PAM symbol sequence, so that the CCDM is reversible, and the distribution de-matching at the receiving end is the inverse mapping process.
In some embodiments, step S3 specifically includes steps S31-S34:
s31, for the transmitted single M-order PAM symbol X, after transmission through the wireless optical channel, the symbol Y received by the receiving end is represented as:
Y＝GΦ(X)+W＝Ψ(X)+W (2)
wherein the content of the first and second substances,
Figure BDA0002900655480000048
indicating turbulence from the atmosphereOr the channel gain due to other factors,
Figure BDA0002900655480000049
representing the real number domain, Ψ (-) to Φ (-) representing the total transfer function, W represents the variance σ2Zero mean gaussian white noise;
s32, a transfer function may be estimated based on the transmitted symbols and corresponding received symbols in the training sequence. The commonly used estimation methods mainly include polynomial regression, linear regression, and the like. The polynomial regression can obtain a more accurate result, but the required computational complexity is higher, and the method is not suitable for a high-speed communication scene similar to wireless optical communication. The embodiment of the invention adopts a linear regression mode with lower computational complexity to estimate the transmission function:
Figure BDA00029006554800000410
wherein the content of the first and second substances,
Figure BDA00029006554800000411
an estimation function representing an estimated transfer function, i.e., the total transfer function Ψ (x);
Figure BDA00029006554800000412
the average signal gain after the direct current part is removed is shown as the only parameter to be estimated in the formula (3);
s33, defining a training sequence X with length Nts＝[X1,X2,...,XN]The corresponding received symbol is Yts＝[Y1,Y2,...,YN]And estimating a parameter eta by using a least square method:
Figure BDA0002900655480000051
when the training sequence is long enough, the relative frequency of the received symbols is equal to the target probability and the noise is negligible, so equation (4) can be rewritten as:
Figure BDA0002900655480000052
wherein E {. denotes a mathematical expectation; the equation (5) is derived about η, and let the derivative be 0, and the parameter η is obtained as:
Figure BDA0002900655480000053
substituting the estimated value formula (6) of eta into formula (3) to obtain the estimated function of the total transfer function psi (x)
Figure BDA0002900655480000057
S34, the noise power can be estimated from the estimated transfer function, and the transfer function estimated in step S33 is used
Figure BDA0002900655480000058
To estimate the noise power of the channel, the estimated value of the noise power being expressed as:
Figure BDA0002900655480000054
likewise, when the training sequence is long enough, equation (7) is rewritten as:
Figure BDA0002900655480000055
thereby obtaining an estimate of the noise power.
The step S4 of deciding decoding specifically includes: the probability is estimated by calculating the relative frequency of the symbols in the training sequence at the receiving end, when the probability estimation is accurate enough, the maximum posterior probability decoding is the optimal decoding, and the decoding rule is as follows:
Figure BDA0002900655480000056
wherein the content of the first and second substances,
Figure BDA0002900655480000066
representing symbols decoded by the receiving end, fY|X(Y|X)、pX(X) and pX|Y(X | Y) represents a conditional probability density function of X with respect to Y, a probability mass function of X, and a conditional probability mass function with respect to Y, respectively; for Gaussian noise, fY|XThe expression of (Y | X) is:
Figure BDA0002900655480000061
substituting psi (X) and noise power with corresponding estimated values according to the estimation result of step S3 to obtain fY|XThe estimated value of (Y | X) is:
Figure BDA0002900655480000062
since the probability mass function of X is pX(ai)＝piThus, the decision domain of the decoding can be obtained
Figure BDA0002900655480000067
Is composed of
Figure BDA0002900655480000063
Wherein Z isiIndicating that the received symbol Y is decoded into
Figure BDA0002900655480000068
Set of symbols of (1), pjThe amplitude of the PAM symbol is ajThe probability of (d); namely: if Y is equal to ZiThen Y is decoded into
Figure BDA0002900655480000069
Mutual information between the transmission signal and the decoded signal in step S5
Figure BDA00029006554800000610
Can be expressed as:
Figure BDA0002900655480000064
wherein p isijDenotes the symbol X ═ a transmitted fromiTo the decoded symbol
Figure BDA00029006554800000611
Is 1,2, M, then pijCan be calculated from the following formula:
Figure BDA0002900655480000065
wherein the content of the first and second substances,
Figure BDA00029006554800000612
to represent
Figure BDA00029006554800000613
Conditional probability mass function for X, ZjIndicating that the received symbol Y is decoded as ajA set of symbols of (1).
In order to obtain better communication performance, the probability shaping scheme of the embodiment of the invention has the optimization aim of maximizing mutual information
Figure BDA00029006554800000614
The optimization variables are the positions and probabilities of the constellation points:
Figure BDA00029006554800000615
and
Figure BDA00029006554800000616
in view of the fact that the calculation complexity required for directly optimizing the mutual information is too high and is not suitable for a high-speed communication scene, the embodiment of the invention can be correspondingly simplified. In particular, optimal constellation point trends are taken into accountThe following two requirements are met: 1) the constellation points are sufficiently dispersed to be better resistant to noise; 2) the constellation points in the linear region have higher probability so as to reduce the distortion effect brought by the non-linear region. Thus, mutual information can be paired
Figure BDA0002900655480000072
The optimization problem of (2) is simplified as follows:
simplifying the distance between one and M constellation points to be constant, denoted by Δ, i.e.
ai+1-ai＝Δ,i＝1,2,...,M-1 (15)
Simplifying the second step,
Figure BDA0002900655480000073
The values of the constellation points are subjected to Maxwell-Boltzmann distribution so as to ensure that the constellation points are about the middle point of a linear area
Figure BDA0002900655480000074
Is distributed in a symmetrical way and is provided with a plurality of symmetrical grooves,
Figure BDA0002900655480000075
can be written as
Figure BDA0002900655480000071
Wherein λ represents a rate parameter of a Maxwell-Boltzmann distribution;
after the above simplification, the number of optimization variables is reduced from 2M to 2, i.e. from
Figure BDA0002900655480000076
And
Figure BDA0002900655480000077
reducing to delta and lambda; thus, for maximizing mutual information
Figure BDA0002900655480000078
The optimization problem of (2) can be solved by the following iterative algorithm:
(1) Initializing delta and lambda, and calculating
Figure BDA0002900655480000079
(2) Fixing lambda, and finding out the optimal delta in a one-dimensional search mode;
(3) fixing delta, and finding out the optimal lambda in a one-dimensional search mode;
(4) repeating (2) and (3) until the algorithm converges;
due to each iteration, will cause
Figure BDA00029006554800000710
Is improved, and
Figure BDA00029006554800000711
with an upper bound, i.e. maximum source entropy
Figure BDA00029006554800000712
The iterative algorithm must be convergent. Wherein p represents the outline of X
The rate density function, H (X), is the source entropy.
The performance of the present invention is verified below.
Assuming that the noise power is σ2＝10-4And G is 1 after the channel gain is normalized. For the nonlinear transfer characteristic of the LED, the following nonlinear function is used:
Figure BDA0002900655480000081
FIG. 3 compares the mutual information after and before optimization of PAM constellation points using probability shaping
Figure BDA0002900655480000082
The variation relation with respect to the modulation order M. The modulation method adopted before optimization is that constellation points are distributed in a linear region at equal intervals with equal probability, that is, (M-1) Δ ═ 0.5 and λ ═ 0. It can be seen that the probability shaping scheme proposed by the present invention can effectively improve mutual information, especially when the modulation order M increasesAnd when it is large. The mutual information gain is about 2.4% when M is 16 and about 9.5% when M is 48. The gain is not significant when the modulation order is small because the constellation point spacing is large enough to combat noise in this case. At the moment, mutual information is closer to the entropy of the information source, and the range for optimization is smaller.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several equivalent substitutions or obvious modifications can be made without departing from the spirit of the invention, and all the properties or uses are considered to be within the scope of the invention.

Claims (8)

1. A communication method based on probability shaping, comprising the steps of:
s1, initializing the amplitude and probability of the PAM constellation points;
s2, generating a corresponding PAM symbol sequence by utilizing distribution matching based on the initialized amplitude and probability, and converting the PAM symbol sequence into a final transmitting signal; wherein, a part of the PAM symbol sequence is used as a training sequence;
s3, estimating the transmission function and the noise power of the channel by using the training sequence;
s4, carrying out judgment decoding on a receiving end by using the estimated transmission function and the noise power to obtain a decoding signal;
and S5, calculating mutual information between the emission signal and the decoding signal, and solving the position of the PAM constellation point with the maximum mutual information and the corresponding probability by using an iterative mode.
2. The probability shaping-based communication method as claimed in claim 1, wherein the step S1 includes:
let the modulation order of PAM be M, and for a single M-order PAM symbol X, the amplitude of the position of the constellation point where PAM is desirable is denoted as a ═ a1,a2,...,aM}, corresponding summaryA ratio of { p1,p2,...,pMIn which a isiAnd piThe amplitude and the probability of the ith constellation point are represented, i is 1,2, …, M, A represents the value space of the amplitude;
let X be related to the middle point of linear region of light source device
Figure FDA0002900655470000011
The constellation points are symmetrically distributed and initialized to be distributed in the linear region at equal probability and equal intervals; where Φ (·) represents a nonlinear transfer function of the light source device.
3. The probability shaping-based communication method as claimed in claim 2, wherein the PAM symbol sequence is generated by mapping a bit sequence into a codebook using fixed combining distribution matching in step S2.
4. The probability shaping-based communication method as claimed in claim 3, wherein the step S2 includes:
s21, constructing a codebook
Figure FDA0002900655470000012
All value spaces containing the PAM symbol sequence are expressed as:
Figure FDA0002900655470000013
wherein v ∈ AnRepresenting that each element of the sequence v of length n belongs to the amplitude space a,
Figure FDA0002900655470000014
representing the amplitude a in the sequence viThe number of symbols of (a);
s22, converting the binary bit sequence U with the length of kk∈{0,1}kOne-to-one mapping to codebooks
Figure FDA0002900655470000021
In (2), PAM symbol sequence X with length n is generatedn(ii) a Wherein the content of the first and second substances,
Figure FDA0002900655470000022
Figure FDA0002900655470000023
a size of the codebook is represented and,
Figure FDA0002900655470000024
represents rounding down;
s23, for the PAM symbol sequence XnAnd D/A conversion is carried out to generate a final transmitting signal.
5. The probability shaping-based communication method as claimed in claim 2, wherein the step S3 includes:
s31, for the transmitted single M-order PAM symbol X, after being transmitted through the wireless optical channel, the symbol Y received by the receiving end is represented as:
Y＝GΦ(X)+W＝Ψ(X)+W (2)
wherein the content of the first and second substances,
Figure FDA0002900655470000025
which represents the gain of the channel and is,
Figure FDA0002900655470000026
representing the real number domain, Ψ (-) to Φ (-) representing the total transfer function, W represents the variance σ2Zero mean gaussian white noise;
s32, based on the transmitting symbols and the corresponding receiving symbols in the training sequence, estimating the transmission function by adopting a linear regression mode:
Figure FDA0002900655470000027
wherein the content of the first and second substances,
Figure FDA0002900655470000028
an estimation function representing an estimated transfer function, i.e., the total transfer function Ψ (x);
Figure FDA0002900655470000029
the average signal gain after the direct current part is removed is shown as a parameter to be estimated;
s33, defining a training sequence X with length Nts＝[X1,X2,...,XN]The corresponding received symbol is Yts＝[Y1,Y2,...,YN]And estimating a parameter eta by using a least square method:
Figure FDA00029006554700000210
when the training sequence is long enough, the relative frequency of the received symbols is equal to the target probability and the noise is negligible, so equation (4) is transformed as:
Figure FDA00029006554700000211
wherein E {. denotes a mathematical expectation; the equation (5) is derived about η, and let the derivative be 0, and the parameter η is obtained as:
Figure FDA0002900655470000031
substituting the estimated value formula (6) of eta into formula (3) to obtain the estimated function of the total transfer function psi (x)
Figure FDA0002900655470000032
S34, utilizing the estimated transfer function of the step S33
Figure FDA0002900655470000033
To estimate the noise power of the channel, the estimated value of the noise power being expressed as:
Figure FDA0002900655470000034
likewise, when the training sequence is long enough, equation (7) is rewritten as:
Figure FDA0002900655470000035
6. the probability shaping-based communication method as claimed in claim 5, wherein the step S4 includes:
the probability is estimated by calculating the relative frequency of the symbols in the training sequence at the receiving end, when the probability estimation is accurate enough, the maximum posterior probability decoding is the optimal decoding, and the decoding rule is as follows:
Figure FDA0002900655470000036
wherein the content of the first and second substances,
Figure FDA0002900655470000037
representing symbols decoded by the receiving end, fY|X(Y|X)、pX(X) and pX|Y(X | Y) represents a conditional probability density function of X with respect to Y, a probability mass function of X, and a conditional probability mass function with respect to Y, respectively; for Gaussian noise, fY|XThe expression of (Y | X) is:
Figure FDA0002900655470000038
substituting psi (X) and noise power with corresponding estimated values according to the estimation result of step S3 to obtain fY|XThe estimated value of (Y | X) is:
Figure FDA0002900655470000041
since the probability mass function of X is pX(ai)＝piThus, the decision domain of the decoding can be obtained
Figure FDA0002900655470000042
Is composed of
Figure FDA0002900655470000043
Wherein Z isiIndicating that the received symbol Y is decoded into
Figure FDA0002900655470000044
Set of symbols of (1), pjThe amplitude of the PAM symbol is ajThe probability of (d); namely: if Y is equal to ZiThen Y is decoded into
Figure FDA0002900655470000045
7. The probability shaping-based communication method as claimed in claim 6, wherein mutual information between the transmission signal and the decoded signal is obtained in step S5
Figure FDA0002900655470000046
Comprises the following steps:
Figure FDA0002900655470000047
wherein p isijDenotes the symbol X ═ a transmitted fromiTo the decoded symbol
Figure FDA0002900655470000048
Is transferred toProbability, i, j ═ 1,2ijCan be calculated from the following formula:
Figure FDA0002900655470000049
wherein the content of the first and second substances,
Figure FDA00029006554700000410
to represent
Figure FDA00029006554700000411
Conditional probability mass function for X, ZjIndicating that the received symbol Y is decoded as ajA set of symbols of (1).
8. The method according to claim 7, wherein the step S5 of solving the position of the PAM constellation point and the corresponding probability that maximize the mutual information in an iterative manner includes:
make mutual information
Figure FDA00029006554700000412
The largest optimization variables are the position and probability of the constellation point, namely:
Figure FDA00029006554700000413
and
Figure FDA00029006554700000414
the optimal constellation point based approach tends to satisfy the following two requirements: 1) the constellation points are sufficiently dispersed; 2) the constellation points in the linear region have higher probability and can carry out mutual information
Figure FDA00029006554700000415
The optimization problem of (2) is simplified as follows:
simplifying the distance between one and M constellation points to be constant, denoted by Δ, i.e.
ai+1-ai＝Δ,i＝1,2,...,M-1 (15)
Simplifying the second step,
Figure FDA0002900655470000051
The values of the constellation points are subjected to Maxwell-Boltzmann distribution so as to ensure that the constellation points are about the middle point of a linear area
Figure FDA0002900655470000052
Is distributed in a symmetrical way and is provided with a plurality of symmetrical grooves,
Figure FDA0002900655470000053
can be written as
Figure FDA0002900655470000054
Wherein λ represents a rate parameter of a Maxwell-Boltzmann distribution;
after simplification, the number of optimization variables is reduced from 2M to 2, i.e. from
Figure FDA0002900655470000055
And
Figure FDA0002900655470000056
reducing to delta and lambda; thus, mutual information is maximized
Figure FDA0002900655470000057
The optimization problem of (2) can be solved by the following iterative algorithm:
(1) initializing delta and lambda, and calculating
Figure FDA0002900655470000058
(2) Fixing lambda, and finding out the optimal delta in a one-dimensional search mode;
(3) fixing delta, and finding out the optimal lambda in a one-dimensional search mode;
(4) repeating (2) and (3) until the algorithm converges;
due to each iteration, will cause
Figure FDA0002900655470000059
Is improved, and
Figure FDA00029006554700000510
with an upper bound, i.e. maximum source entropy
Figure FDA00029006554700000511
The iterative algorithm must be convergent.
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