CN110808780B - New boundary calculation method for capacity region of visible light communication multiple access channel - Google Patents

New boundary calculation method for capacity region of visible light communication multiple access channel Download PDF

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CN110808780B
CN110808780B CN201911133383.9A CN201911133383A CN110808780B CN 110808780 B CN110808780 B CN 110808780B CN 201911133383 A CN201911133383 A CN 201911133383A CN 110808780 B CN110808780 B CN 110808780B
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capacity
probability
visible light
transmitter
signal
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CN110808780A (en
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马帅
王婧
张凡
贺阳
李世银
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Zhongtian Communication Technology Co.,Ltd.
Zhongtian Broadband Technology Co Ltd
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China University of Mining and Technology CUMT
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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
    • H04B10/11—Arrangements specific to free-space transmission, i.e. transmission through air or vacuum
    • H04B10/114—Indoor or close-range type systems
    • H04B10/116—Visible light communication
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
    • H04B17/318—Received signal strength

Abstract

The invention provides a new boundary calculation method for a capacity region of a multiple access channel of visible light communication. Specifically, the proposed inner bound is established by implementing an input distribution for each user using a single user capacity. The proposed outer boundary is derived by determining the single-user capacity of each user and relaxing the input constraints to calculate the sum capacity ceiling. Numerical results indicate that the proposed new boundary is very tight and superior to the existing boundary over a wide range of SNRs.

Description

New boundary calculation method for capacity region of visible light communication multiple access channel
Technical Field
The invention relates to a new boundary calculation method for a capacity region of a visible light communication multiple access channel.
Background
Visible Light Communication (Visible Light Communication), one of the key technologies for 5G Communication, has attracted attention of scholars at home and abroad due to its abundant spectrum resources. The VLC technology can supplement the traditional radio frequency technology, and through the emitter light emitting diode, the VLC system can not only realize simultaneous illumination and communication, but also has the advantages of ultralow electromagnetic radiation, high transmission safety, high energy efficiency and the like. A multi-user scenario in a wireless communication network can be modeled as a Multiple Access Channel (MAC), and therefore, the channel capacity of the MAC can characterize the achievable rate of a user with a limitation condition, and thus, the channel capacity of the MAC can also serve as a theoretical basis for other VLC network designs.
VLC uses the intensity modulation direct detection (IM \ DD) method, and information is characterized by the intensity of the signal. Meanwhile, peak and average light power are constraints that VLC must satisfy for eye safety and illumination considerations. Based on these constraints, the scholars have made much effort to study the inner and outer boundaries of the achievable rate of VLC MAC and to obtain an approximation of the channel capacity at high and low signal-to-noise ratios. However, to date, the exact VLC MAC capacity domain and optimal input distribution remain unknown.
Disclosure of Invention
The purpose of the invention is as follows: the technical problem to be solved by the present invention is to provide a new boundary calculation method for a capacity region of a visible light communication multiple access channel, aiming at the defects of the prior art, comprising the following steps:
step 1, setting a typical visible light communication multiple access channel VLC MAC system;
and 2, calculating the channel capacity and the inner and outer boundaries of the channel capacity.
The step 1 comprises the following steps: typical light intensity MAC system settings were performed: the system comprises two transmitters and a receiver, wherein the two transmitters are respectively a first transmitter and a second transmitter, each transmitter is provided with an LED, the receiver is provided with a single photon detector, and X is arranged1And X2Representing the transmitted signals of the first transmitter and the second transmitter, respectively.
In step 1, the peak optical power and the average optical power are limited as follows: x is not less than 01≤A1，
Figure GDA0002607935430000011
0≤X2≤A2，
Figure GDA0002607935430000012
Wherein A is1And A2Respectively, the transmission signals X of the first transmitter1And the amplitude range of the second transmitter and the transmission signal X of the second transmitter2Amplitude range of (D), mu1And mu2Respectively the mean value of the transmission signal of the first transmitter and the mean value of the transmission signal of the second transmitter,
Figure GDA0002607935430000021
to average.
In step 1, in the MAC system channel, the received signal Y is represented as:
Y＝X1+X2+Z (1)
where Z is the independent Gaussian noise with a mean of 0 and a variance of σ2。
In step 1, the capacity domain of the visible light communication multiple access channel VLC MAC is a convex hull
Figure GDA0002607935430000022
Wherein the achievable rate pair R (X)1,X2) Indicating, for a fixed product distribution satisfying a given input constraint
Figure GDA0002607935430000028
x1、x2Are respectively input signals X1、X2Discrete points taken, the set of rate pairs (R)1,R2) The following conditions are satisfied:
Figure GDA0002607935430000023
wherein R is1、R2Maximum achievable rates, I (X), for 1 st and 2 nd users, respectively1；Y|X2) For a known input signal X2Under the condition of (A) X1And mutual information of Y, I (X)2；Y|X1) For a known input signal X1Under the condition of (A) X2And mutual information of Y, I (X)1,X2(ii) a Y) is X1And X2Mutual information about Y is provided together.
The step 2 comprises the following steps: calculating channel capacity
Figure GDA00026079354300000210
And its inner and outer boundaries, where i is 1,2,
Figure GDA0002607935430000029
the method specifically comprises the following steps:
step 2-1, setting the outputIncoming signal XiGet KiA non-negative real value to obey a discrete distribution
Figure GDA0002607935430000024
As follows:
Figure GDA0002607935430000025
Figure GDA0002607935430000026
Figure GDA0002607935430000027
wherein xi,jIs XiJ (th) point of (p)i,jDenotes xi,jThe corresponding probability of the occurrence of the event,
Figure GDA0002607935430000031
represents K1Is defined as 1 to K1The set of (a) and (b),
Figure GDA0002607935430000032
pr { } is to solve the probability,
Figure GDA0002607935430000033
for averaging, ∑ (.) is the sum, so there are:
Figure GDA0002607935430000034
wherein the output signal
Figure GDA0002607935430000035
CiIs given by a probability P (X)i) Transmitting an input signal XiH (.) is the differential entropy, max (.) is the maximum, log2(. to) is to solve a logarithmic function with base 2, e, π are natural constants, σ2Is the variance;
Figure GDA00026079354300000312
to output a signal YiProbability density of yiTo output a signal YiThe obtained point, i ═ 1, 2;
since the noise Z follows a Gaussian distribution, the output signal YiProbability density of
Figure GDA0002607935430000036
Is written as:
Figure GDA0002607935430000037
the capacity of the visible light communication multiple access channel VLC MAC is finally obtained and expressed as a mathematical problem which is subject to optimization as shown in the following:
Figure GDA0002607935430000038
wherein
Figure GDA0002607935430000039
Representing an input signal
Figure GDA00026079354300000310
Has a probability of pk，
Figure GDA00026079354300000311
min (.) is the minimum value, and integral & (.) is the integral, log2(. 2) is a base-2 logarithmic function;
s.t.(3a),(3b),(3c)
step 2-2, calculate and Capacity I (X)1,X2(ii) a Y) inner boundary;
step 2-3, calculate and Capacity I (X)1,X2(ii) a Y) of the outer boundary.
Step 2-2 comprises:
definition of
Figure GDA0002607935430000041
Obtaining:
Figure GDA0002607935430000042
wherein max (.) is the maximum value;
Figure GDA0002607935430000043
for a fixed product distribution, the output signal Y is a probability density function fY(y) is:
Figure GDA0002607935430000044
where Y is the point at which the output signal Y is taken, p1,m,p2,nFor an input signal X1,m,X2,nGet x1,m,x2,nProbability of time, σ is the standard deviation;
the capacity domain of VLC MAC contains two variables
Figure GDA0002607935430000045
And
Figure GDA0002607935430000046
will be distributed
Figure GDA0002607935430000047
And
Figure GDA0002607935430000048
put to the far right of equation (7), the result obtained is the channel capacity C1，2The inner boundary of (a).
The step 2-3 comprises the following steps: defining input signals for determining outer boundaries
Figure GDA0002607935430000049
Then
Figure GDA00026079354300000410
Figure GDA00026079354300000411
Wherein the amplitude range of the input signal
Figure GDA00026079354300000412
Expectation of
Figure GDA00026079354300000413
Figure GDA00026079354300000414
Calculating an average value; setting input signal
Figure GDA00026079354300000415
Subject to a discrete distribution, take
Figure GDA00026079354300000416
A non-negative real value
Figure GDA00026079354300000417
This gives:
Figure GDA0002607935430000051
Figure GDA0002607935430000052
Figure GDA0002607935430000053
wherein
Figure GDA0002607935430000054
Pr { } is the probability, thus obtaining the channel capacity C1,2The outer boundary of (A) is as follows:
Figure GDA0002607935430000055
wherein
Figure GDA0002607935430000056
For input signals
Figure GDA0002607935430000057
Taking the probability when the probability P is sent, max (.) as a maximum value;
thus, the channel capacity C1,2The outer boundary of (a) is written as:
Figure GDA0002607935430000058
s.t.(9a),(9b),(9c)；
solving the problem (10) by an inaccurate gradient descent method and obtaining the channel capacity C of the outer boundary1，2。
Advantageous effects
The invention makes the calculation of the VLC MAC capacity domain of the visible light communication multiple access channel more accurate, and simultaneously realizes the resource allocation of the VLC system very simply and conveniently. The main value of the method is that the mathematical problem in the solving process is solved by a gradient descent method, so that the new inner and outer boundaries are the tightest under the existing calculation method. Meanwhile, the new boundary of the channel capacity provided by the invention is better than the existing boundary in the wide area of SNR. The closed expression obtained by the invention has simple form and complete calculation method, and the practical calculation method can be used as the basis of later research and can be directly applied to the performance optimization of VLC and other communication systems.
Drawings
The foregoing and other advantages of the invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
Fig. 1a is the optimal input position for the VLC MAC for the visible light communication channel at different signal-to-noise ratios SNR.
Fig. 1b is an optimal input distribution of a visible light communication channel VLC MAC at different signal-to-noise ratios SNR.
Fig. 2a is a boundary of different calculation methods of VLC MAC capacity domain of visible light communication channel at low signal-to-noise ratio.
Fig. 2b is the boundary of the visible light communication channel VLC MAC capacity domain under different calculation methods at high signal-to-noise ratio.
Fig. 3a is a boundary of different calculation methods of the capacity domain of the visible light communication channel under the condition of low signal-to-noise ratio under special conditions.
Fig. 3b is the boundary of the capacity domain of the visible light communication channel under different calculation methods under the condition of high signal-to-noise ratio under special conditions.
Fig. 4 is a graph of the capacity analysis simulation experiment and the rate-signal-to-noise ratio variation curve of the visible light communication channel.
Detailed Description
Consider a typical visible light communications multiple access channel VLC MAC system, where the system includes two transmitters and one receiver. Each transmitter is equipped with an LED and the receiver is equipped with a single Photon Detector (PD). Let X1And X2Representing the transmitted signals of the first transmitter and the second transmitter, respectively. Since the information is embedded in the intensity of the optical signal, X1And X2Should be real, non-negative. In addition, the peak and average optical power should be limited according to eye safety standards and actual lighting requirements, so 0 ≦ X1≤A1，
Figure GDA0002607935430000061
0≤X2≤A2，
Figure GDA0002607935430000062
Wherein A is1And A2For the amplitude range of the input signal, mu1And mu2Is taken as the mean value of the average value,
Figure GDA0002607935430000063
to average. In the MAC channel, the received signal Y is represented as:
Y＝X1+X2+Z (1)
where Z is the independent Gaussian noise with a mean of 0 and a variance of σ2；
Introduction 1: the capacity domain of VLC MAC of visible light communication multiple access channel is convex hull
Figure GDA0002607935430000064
Wherein the achievable rate field R (X)1,X2) Indicating, for a fixed product distribution satisfying a given input constraint
Figure GDA0002607935430000065
x1、x2Are respectively input signals X1X2Discrete points taken, the set of rate pairs (R)1,R2) The following conditions are satisfied:
Figure GDA0002607935430000066
wherein R is1、R2Maximum achievable rates, I (X), for 1 st and 2 nd users, respectively1；Y|X2) For a known input signal X2Under the condition of (A) X1And mutual information of Y, I (X)2；Y|X1) For a known input signal X1Under the condition of (A) X2And mutual information of Y, I (X)1,X2(ii) a Y) is X1And X2Mutual information about Y is provided together.
Due to the limited amplitude (peak optical power constraint), the optimal input profile of equation (2) should be a limited set of discrete points-unfortunately, there is no efficient method for (2) to estimate the channel capacity under a discrete profile, except for an exhaustive method search. Then, the discrete input distribution is estimated to obtain the accurate channel capacity
Figure GDA0002607935430000071
And its inner and outer boundaries, where i is 1,2,
Figure GDA0002607935430000072
accurate single user channel capacity
Figure GDA00026079354300000712
To find the optimum distribution, signal X is setiGet KiA non-negative real value to obey a discrete distribution
Figure GDA0002607935430000073
As follows:
Figure GDA0002607935430000074
Figure GDA0002607935430000075
Figure GDA0002607935430000076
wherein xi,jIs XiJ (th) point of (p)i,jIndicating the probability with which it corresponds to,
Figure GDA0002607935430000077
Figure GDA0002607935430000078
pr { } is to solve the probability,
Figure GDA0002607935430000079
for averaging, ∑ (.) is the sum;
thus, there are:
Figure GDA00026079354300000710
wherein the output signal
Figure GDA00026079354300000711
CiIs given by a probability P (X)i) Transmitting an input signal XiH (.) is the differential entropy, max (.) is the maximum, log2(. to) is to solve a logarithmic function with base 2, e, π are natural constants, σ2Is the variance;
Figure GDA0002607935430000081
to output a signal YiProbability density of yiTo output a signal YiThe obtained point, i ═ 1, 2;
since the noise Z follows a Gaussian distribution, the output signal YiProbability density of
Figure GDA0002607935430000082
Is written as:
Figure GDA0002607935430000083
wherein y isiTo output a signal YiThe obtained point, i ═ 1, 2; σ is the standard deviation;
therefore, obtaining the capacity of the VLC MAC of the visible light communication channel represents a mathematical problem subject to optimization as follows:
Figure GDA0002607935430000084
s.t.(3a),(3b),(3c)
wherein min (.) is the minimum value;
Figure GDA0002607935430000085
to output a signal YiProbability density of yiTo output a signal YiThe obtained point, i ═ 1, 2;
due to the variable Ki，{pi,jAnd { x }i,jProblem (6) is a discrete non-convex problem. In addition, the objective function (6) has no closed-form expression and no analytical expression.
Therefore, the problem (6) is difficult to solve. To overcome this difficulty, the present invention applies an imprecise descent gradient method and obtains an optimal input profile
Figure GDA0002607935430000086
Namely, it is
Figure GDA0002607935430000087
Sum channel capacity Ci。
And capacity I (X)1,X2(ii) a Y) inner boundary: definition of
Figure GDA0002607935430000088
Obtaining:
Figure GDA0002607935430000089
wherein max (.) is the maximum value;
Figure GDA00026079354300000810
is a fixed product distribution; wherein the probability density function f of the output signal YY(y) is:
Figure GDA0002607935430000091
where Y is the point at which the output signal Y is taken, ∑ (. -) is the sum, p is1,m,p2,nFor an input signal X1,m,X2,nGet x1,m,x2,nThe probability of time, pi is a natural constant, and sigma is a standard deviation;
unlike problem (6), the capacity domain of VLC MAC contains two variables
Figure GDA0002607935430000092
And
Figure GDA0002607935430000093
this makes the optimization problem difficult to solve. Therefore, a sub-optimal solution needs to be found. In particular, will distribute
Figure GDA0002607935430000094
And
Figure GDA0002607935430000095
put to the rightmost side of formula (7), the result obtained is the inner boundary C1，2。
And capacity I (X)1,X2(ii) a Y) outer boundary: defining input signals for determining outer boundaries
Figure GDA0002607935430000096
Then
Figure GDA0002607935430000097
Mean value
Figure GDA0002607935430000098
Wherein the amplitude range of the input signal
Figure GDA0002607935430000099
Expectation of
Figure GDA00026079354300000910
Figure GDA00026079354300000911
Setting input signal
Figure GDA00026079354300000912
Subject to a discrete distribution, take
Figure GDA00026079354300000913
A non-negative real value
Figure GDA00026079354300000914
This gives:
Figure GDA00026079354300000915
Figure GDA00026079354300000916
Figure GDA00026079354300000917
wherein
Figure GDA00026079354300000918
Pr{. is the probability, thus obtaining C1,2The outer boundary of (A) is as follows:
Figure GDA00026079354300000919
wherein
Figure GDA00026079354300000920
For input signals
Figure GDA00026079354300000921
The probability when the probability P is transmitted, max (lambda), is taken as the maximum value, sigma2Is the variance;
thus, the outer boundary C1,2Write as:
Figure GDA00026079354300000922
s.t.(9a),(9b),(9c)；
this is a discrete non-convex problem.
Similarly, an inaccurate gradient descent method can solve the problem (10) and obtain the channel capacity C of the outer boundary1，2. The method for analyzing the channel capacity of the two users can be directly expanded to N users (N is more than or equal to 3) multiple access channels.
Numerical evaluation and discussion:
in order to evaluate the signal capacity obtained by the present invention, the present example lists the external world
Figure GDA0002607935430000101
Outside world
Figure GDA0002607935430000102
Outside world
Figure GDA0002607935430000103
Outside world
Figure GDA0002607935430000104
Inner boundary
Figure GDA0002607935430000105
And the maximum discrete entropy bound in (a), wherein for all i,
Figure GDA0002607935430000106
note, external world
Figure GDA0002607935430000107
And inner bound
Figure GDA0002607935430000108
The method is only suitable for a specific situation, namely, the method is firstly applied to the visible light communication channel VLC MAC field under the peak light power constraint and the maximum discrete entropy inner limit.
First, consider the general case of the visible light communication channel VLC MAC capacity domain, i.e., under peak and average optical power constraints. FIGS. 1a and 1b illustrate respective optimum input positions of VLC MAC at different SNRs
Figure GDA0002607935430000109
And discrete distributed optimal input
Figure GDA00026079354300001010
Wherein
Figure GDA00026079354300001011
For SNR ≦ 10dB, the optimal input location has two discrete points {0, A }, i.e., {0.8,0.2} for different probabilities. Therefore, the OOK modulation system can obtain the capacity of the VLC MAC of the visible light communication channel even under low SNR. At SNR>At 10dB, there are more than two discrete points at the optimal input position, which indicates that the PAM modulation system can obtain the capacity of VLC MAC of the visible light communication channel.
FIGS. 2a and 2b illustrate, respectively, that at low SNR, i.e., low
Figure GDA00026079354300001012
And
Figure GDA00026079354300001013
and at high SNR, i.e.
Figure GDA00026079354300001014
And
Figure GDA00026079354300001015
inner and outer boundaries of VLC MAC capacity domain, wherein
Figure GDA00026079354300001016
As can be seen from fig. 2a, the proposed outer boundary is lower than the existing outer boundary, i.e. it is lower than the existing outer boundary
Figure GDA00026079354300001017
And
Figure GDA00026079354300001018
and the proposed inner boundary is larger than the maximum discrete entropy inner boundary.
Fig. 3a and 3b illustrate the special case, i.e. only under peak optical power constraints, where
Figure GDA00026079354300001019
Fig. 2a, 2b and 3a, 3b all show that the proposed outer boundary is lower than the existing outer boundary, whereas the proposed inner boundary is lower than the outer boundary except for
Figure GDA0002607935430000111
The other existing inner boundaries on the high SNR side are all high, i.e. in FIG. 3b
Figure GDA0002607935430000112
Sum rate R1+R2。
Fig. 4 shows the proposed inner and outer boundaries, maximizing the discrete entropy inner boundary,
Figure GDA0002607935430000113
and
Figure GDA0002607935430000114
rate and R of dual users at a particular SNR (dB)1+R2(bits/s/Hz), i.e. when only the peak optical power is constrained, wherein
Figure GDA0002607935430000115
It can be seen that at low SNR the proposed inner boundary is very close to the maximum discrete entropy inner boundary, whereas at high SNR the proposed inner boundary is higher than the maximum discrete entropy inner boundary. The reason is that maximizing the discrete entropy inner boundary is to input the discrete entropy H (X)1)+H(X2) Maximized, this is only the difference entropy h (X)1+X2+ Z) is an approximation. At low and medium SNR, the proposed inner boundary ratio
Figure GDA0002607935430000116
The inner boundary is high. At the time of a high SNR, it is,
Figure GDA0002607935430000117
highest (only peak optical power constraint). Furthermore, the proposed outer boundary is higher than the existing outer boundary
Figure GDA0002607935430000118
And
Figure GDA0002607935430000119
in the present invention, the capacity I (X) is calculated1；Y|X2) And I (X)2；Y|X1) And I (X)1,X2(ii) a Y), the invention obtains the visible light communication multiple access channel VLC MAC capacity domain. The present example further numerically verifies that the boundaries proposed by the present invention are the tightest and simple in form among the existing benchmarks. As mentioned in 2017, scholars such as a. chaaban, o.m.s. -AI-eibraheemy, etc., in Capacity bound for the gaussian IM-DD optical multiple access channel, channel Capacity analysis is one of the important bases for information processing and coding, energy efficiency optimization, and resource optimization, so that this practical calculation method can be directly used for performance optimization of visible light communication systems.
The present invention provides a new boundary calculation method for a capacity region of a multiple access channel for visible light communication, and a plurality of methods and approaches for implementing the technical solution are provided, and the above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, a plurality of improvements and modifications may be made without departing from the principle of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (3)

1. A new boundary calculation method for a capacity region of a visible light communication multiple access channel is characterized by comprising the following steps:
step 1, setting a typical visible light communication multiple access channel system;
step 2, calculating the channel capacity and the inner and outer boundaries thereof;
the step 1 comprises the following steps: typical visible light communication multiple access channel system setting is carried out: the system comprises two transmitters and a receiver, wherein the two transmitters are respectively a first transmitter and a second transmitter, each transmitter is provided with a light source LED, the receiver is provided with a single photon detector PD and X1And X2Respectively representing the transmission signals of a first transmitter and a second transmitter;
in step 1, the peak light power P is adjustedpAnd an average optical power PoThe following restrictions apply: x is not less than 01≤A1，
Figure FDA0002629228990000011
0≤X2≤A2，
Figure FDA0002629228990000012
Wherein A is1And A2Respectively, the transmission signals X of the first transmitter1And the amplitude range of the second transmitter and the transmission signal X of the second transmitter2Amplitude range of (D), mu1And mu2Respectively the mean value of the transmission signal of the first transmitter and the mean value of the transmission signal of the second transmitter,
Figure FDA0002629228990000013
calculating an average value;
in step 1, in a visible light communication multiple access channel MAC system, a received signal Y is represented as:
Y＝X1+X2+Z (1)
where Z is the independent Gaussian noise with a mean of 0 and a variance of σ2；
In step 1, the capacity domain of the visible light communication multiple access channel is convex hull
Figure FDA0002629228990000014
Wherein the set of rate pairs (R)1,R2) The following conditions are satisfied:
Figure FDA0002629228990000015
wherein R is1、R2Maximum achievable rates, I (X), for 1 st and 2 nd users, respectively1；Y|X2) For a known input signal X2Under the condition of (A) X1And mutual information of Y, I (X)2；Y|X1) For a known input signal X1Under the condition of (A) X2And mutual information of Y, I (X)1,X2(ii) a Y) is X1And X2Mutual information about Y provided together;
the step 2 comprises the following steps: calculating channel capacity
Figure FDA0002629228990000016
And its inner and outer boundaries, where i is 1,2,
Figure FDA0002629228990000017
the method specifically comprises the following steps:
step 2-1, setting input signal XiGet KiA non-negative real value
Figure FDA0002629228990000021
And obey a discrete distribution, as follows:
Figure FDA0002629228990000022
Figure FDA0002629228990000023
Figure FDA0002629228990000024
wherein xi,jIs XiJ-th discrete point of (1), pi,jDenotes xi,jThe corresponding probability of the occurrence of the event,
Figure FDA0002629228990000025
Figure FDA0002629228990000026
pr { } is to solve the probability,
Figure FDA0002629228990000027
for averaging ∑ (. eta.) is the sum, and thus, there are:
Figure FDA0002629228990000028
wherein the output signal
Figure FDA0002629228990000029
i＝1,2；CiIs given by a probability P (X)i) Transmitting an input signal XiH (.) is the differential entropy, max (.) is the maximum, log2(. to) is to solve a logarithmic function with base 2, e, π are natural constants, σ2Is the variance;
Figure FDA00026292289900000210
to output a signal YiProbability density of yiTo output a signal YiThe point of the obtained point,i＝1,2；
since the noise Z follows a Gaussian distribution, the output signal YiProbability density of
Figure FDA00026292289900000211
Is written as:
Figure FDA00026292289900000212
the capacity of the visible light communication multiple access channel is finally obtained to be expressed as a mathematical problem which follows optimization:
Figure FDA0002629228990000031
s.t.(3a),(3b),(3c)
wherein, Ki,{pi,j},{xi,jDenotes the probability as pi,jK of }iA non-negative real number { xi,j}, variables in the above mathematical problem; min (.) is to find the minimum value, log2(. 2) is a base-2 logarithmic function;
solving the problem (6) by an imprecise gradient descent method, resulting in a solution to the problem
Figure FDA0002629228990000032
I.e. the optimal input distribution
Figure FDA0002629228990000033
And channel capacity Ci；
Step 2-2, calculating and channel capacity I (X)1,X2(ii) a Y) inner boundary;
step 2-3, calculating and channel capacity I (X)1,X2(ii) a Y) of the outer boundary.
2. The method of claim 1, wherein step 2-2 comprises:
definition and channel capacity
Figure FDA0002629228990000034
Obtaining:
Figure FDA0002629228990000035
wherein max (.) is the maximum value, and the probability density function f of the output signal Y isY(y) is:
Figure FDA0002629228990000036
where Y is the point at which the output signal Y is taken, p1,m,p2,nFor an input signal X1,m,X2,nGet x1,m,x2,nProbability of time, σ is the standard deviation;
two variables contained in capacity domain of visible light communication multiple access channel
Figure FDA0002629228990000037
And
Figure FDA0002629228990000038
making the optimization problem difficult to solve, therefore, the optimal distribution obtained in step 2-1 is adopted
Figure FDA0002629228990000039
Optimal distribution when i is 1,2
Figure FDA00026292289900000310
And
Figure FDA00026292289900000311
put to the far right of equation (7), the resulting sum channel capacity C1，2The inner boundary of (a).
3. The method of claim 2, wherein steps 2-3 comprise: defining input signals for determining outer boundaries
Figure FDA0002629228990000041
Then
Figure FDA0002629228990000042
Figure FDA0002629228990000043
Wherein the amplitude range of the input signal
Figure FDA0002629228990000044
Expectation of
Figure FDA0002629228990000045
Figure FDA0002629228990000046
Calculating an average value; setting input signal
Figure FDA0002629228990000047
Subject to a discrete distribution, take
Figure FDA0002629228990000048
A non-negative real value
Figure FDA0002629228990000049
This gives:
Figure FDA00026292289900000410
Figure FDA00026292289900000411
Figure FDA00026292289900000412
wherein
Figure FDA00026292289900000413
Is that
Figure FDA00026292289900000414
The k-th discrete point of (1), pkTo represent
Figure FDA00026292289900000415
The corresponding probability of the occurrence of the event,
Figure FDA00026292289900000416
pr { } is the probability, from which the sum channel capacity C is obtained1,2The outer boundary of (A) is as follows:
Figure FDA00026292289900000417
wherein
Figure FDA00026292289900000418
For input signals
Figure FDA00026292289900000419
Taking the probability when the probability P is sent, max (.) as a maximum value;
thus, and the channel capacity C1,2The outer boundary of (a) is written as:
Figure FDA00026292289900000420
s.t.(9a),(9b),(9c)
wherein the content of the first and second substances,
Figure FDA00026292289900000421
representing a probability of pkOf
Figure FDA00026292289900000422
A non-negative real number
Figure FDA00026292289900000423
In question (10) is a variable; solving the problem (10) by an inaccurate gradient descent method and obtaining the sum channel capacity C of the outer boundary1，2。
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107046441A (en) * 2017-04-06 2017-08-15 中国矿业大学 The capacity analysis of visible light communication interference channel and computational methods
CN108242955A (en) * 2017-03-14 2018-07-03 中国矿业大学 A kind of point-to-point visible light communication system and its energy efficiency analysis method for air
CN108270485A (en) * 2016-12-30 2018-07-10 徐州坤泰电子科技有限公司 Visible ray is point-to-point and broadcast communication system signal generates and capacity calculation methods

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103595454B (en) * 2013-11-22 2018-06-12 东南大学 Utilize the MIMO multiple access wireless communication methods of statistical channel status information
US11212008B2 (en) * 2018-05-09 2021-12-28 University Of Virginia Patent Foundation Power allocation for visible light communication

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108270485A (en) * 2016-12-30 2018-07-10 徐州坤泰电子科技有限公司 Visible ray is point-to-point and broadcast communication system signal generates and capacity calculation methods
CN108242955A (en) * 2017-03-14 2018-07-03 中国矿业大学 A kind of point-to-point visible light communication system and its energy efficiency analysis method for air
CN107046441A (en) * 2017-04-06 2017-08-15 中国矿业大学 The capacity analysis of visible light communication interference channel and computational methods

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
Capacity Bounds and Interference Management for Interference Channel in Visible Light Communication Networks;Shuai Ma等;《IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS》;20181106;第182-193页 *

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