阅读说明：本技术 一种可见光通信多址接入信道容量区域的新边界计算方法 (New boundary calculation method for capacity region of visible light communication multiple access channel ) 是由 马帅 王婧 张凡 贺阳 李世银 于 2019-11-19 设计创作，主要内容包括：本发明提供了一种可见光通信多址接入信道容量区域的新边界计算方法,本发明提出了,在峰值和平均光功率约束下,可见光通信网络中多址信道容量域的新的内边界和外边界。具体地说,所提出的内界是通过使用单用户容量为每个用户实现输入分布来建立的。所提出的外部边界是通过确定每个用户的单用户容量,并放宽输入约束来计算总和容量上限推导出的。数值结果表明,所提出的新边界是非常紧的,并且在SNR的广域上优于现有边界。(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.)

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;

and 2, calculating the channel capacity and the inner and outer boundaries of the channel capacity.

2. The method of claim 1, wherein step 1 comprises: 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 X₂Representing the transmitted signals of the first transmitter and the second transmitter, respectively.

3. The method of claim 2, wherein in step 1, the peak optical power P is measured_pAnd an average optical power P_oThe following restrictions apply: x is not less than 0₁≤A₁，

4. The method of claim 3, wherein in step 1, in the visible light communication multiple access channel MAC system, 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。

5. The method of claim 4, wherein in step 1, the capacity region of the visible light communication multiple access channel is a convex hull

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.

6. The method of claim 5, wherein step 2 comprises: calculating channel capacity

step 2-1, setting input signal X_iGet K_iA non-negative real value to obey a discrete distribution

wherein x_i，jIs X_iJ (th) point of (p)_i，jDenotes x_i，jThe corresponding probability of the occurrence of the event,

wherein the output signalC_iIs given by a probability P (X)_i) Transmitting an input signal X_iH (.) 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;

since the noise Z follows a Gaussian distribution, the output signal Y_iProbability density of

the capacity of the visible light communication multiple access channel is finally obtained to be expressed as a mathematical problem which follows optimization:

s.t.(3a)，(3b)，(3c)

wherein{p_k}，

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.

7. The method of claim 6, wherein step 2-2 comprises:

definition ofObtaining:

wherein max (.) is the maximum value;

where Y is the point at which the output signal Y is taken, p_1，m，p_2，nFor an input signal X_1，m，X_2，nGet x_1，m，x_2，nProbability of time, σ is the standard deviation;

the capacity domain of the visible light communication multiple access channel comprises two variables

8. The method of claim 7, wherein steps 2-3 comprise: defining input signals for determining outer boundaries

wherein

wherein

thus, the channel capacity C_1，2The outer boundary of (a) is written as:

s.t.(9a)，(9b)，(9c)

solving the problem (10) by an inaccurate gradient descent method and obtaining the channel capacity C of the outer boundary_1，2。

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 sum of the peak optical powers is calculatedThe average optical power is limited as follows: x is not less than 0₁≤A₁，

0≤X₂≤A₂，

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,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 hullWherein the achievable rate pair R (X)₁,X₂) Indicating, for a fixed product distribution satisfying a given input constraintx₁、x₂Are respectively input signals X₁、X₂Discrete points taken, the set of rate pairs (R)₁,R₂) The following conditions are satisfied:

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 I (X)_i；Y|X_i) And its inner and outer boundaries, where i is 1,2,the method specifically comprises the following steps:

step 2-1, setting input signal X_iGet K_iA non-negative real value to obey a discrete distributionAs follows:

wherein x_i,jIs X_iJ (th) point of (p)_i,jDenotes x_i,jThe corresponding probability of the occurrence of the event,

represents K₁Is defined as 1 to K₁The set of (a) and (b),

pr { } is to solve the probability,

for averaging, Σ () is a sum, therefore, there are：

Wherein the output signal

i＝1,2；C_iIs given by a probability P (X)_i) Transmitting an input signal X_iH (.) 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;

to output a signal Y_iProbability density of y_iTo output a signal Y_iThe obtained point, i ═ 1, 2;

since the noise Z follows a Gaussian distribution, the output signal Y_iProbability density of

Is written as:

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:

wherein

Representing an input signal

Has a probability of p_k，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

Obtaining:

wherein max (.) is the maximum value;

for a fixed product distribution, the output signal Y is a probability density function f_Y(y) is:

where Y is the point at which the output signal Y is taken, p_1,m,p_2,nFor an input signal X_1,m,X_2,nGet x_1,m,x_2,nProbability of time, σ is the standard deviation;

the capacity domain of VLC MAC contains two variablesAnd

will be distributed

And

put to the far right of equation (7), the result obtained is the channel capacity C_1，2The inner boundary of (a).

The step 2-3 comprises the following steps: defining input signals for determining outer boundaries

Then

Wherein the amplitude range of the input signalExpectation of

Calculating an average value; setting input signal

Subject to a discrete distribution, take

A non-negative real valueThis gives:

whereinPr { } is the probability, thus obtaining the channel capacity C_1,2The outer boundary of (A) is as follows:

wherein

For input signals

Taking the probability when the probability P is sent, max (.) as a maximum value;

thus, the channel capacity C_1,2The outer boundary of (a) is written as:

s.t.(9a),(9b),(9c)；

solving the problem (10) by an inaccurate gradient descent method and obtaining the channel capacity C of the outer boundary_1，2。

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≤A₁，0≤X₂≤A₂，

Wherein A is₁And A₂For amplitude ranges of the input signalRound, mu₁And mu₂Is taken as the mean value of the average value,

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

Wherein the achievable rate field R (X)₁,X₂) Indicating, for a fixed product distribution satisfying a given input constraint

x₁、x₂Are respectively input signals X₁X₂Discrete points taken, the set of rate pairs (R)₁,R₂) The following conditions are satisfied:

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, under the condition of discrete input distribution estimation, the accurate channel capacity I (X) is obtained_i；Y|X_i) And itWherein i is 1,2,

accurate single user channel capacity I (X)_i；Y|X_i): to find the optimum distribution, signal X is set_iGet K_iA non-negative real value to obey a discrete distribution

As follows:

wherein x_i,jIs X_iJ (th) point of (p)_i,jIndicating the probability with which it corresponds to,

pr { } is to solve the probability,

to average, Σ () is the sum;

thus, there are:

wherein the output signal

i＝1,2；C_iIs given by a probability P (X)_i) Transmitting an input signal X_iH (.) 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;

to output a signal Y_iProbability density of y_iTo output a signal Y_iThe obtained point, i ═ 1, 2;

since the noise Z follows a Gaussian distribution, the output signal Y_iProbability density of

Is written as:

wherein y is_iTo output a signal Y_iThe 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:

s.t.(3a),(3b),(3c)

wherein min (.) is the minimum value;

to output a signal Y_iProbability density of y_iTo output a signal Y_iThe obtained point, i ═ 1, 2;

due to the variable K_i，{p_i,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, an imprecise gradient descent method was applied and obtainedOptimum input distribution

Namely, it is

Sum channel capacity C_i。

And capacity I (X)₁,X₂(ii) a Y) inner boundary: definition of

Obtaining:

wherein max (.) is the maximum value;

is a fixed product distribution; wherein the probability density function f of the output signal Y_Y(y) is:

where Y is the point taken by the output signal Y, Σ () is the sum, p_1,m,p_2,nFor an input signal X_1,m,X_2,nGet x_1,m,x_2,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

Andthis makes the optimization problem difficult to solve. Therefore, a sub-optimal solution needs to be found. In particular, will distribute

And

put to the rightmost side of formula (7), the result obtained is the inner boundary C_1，2。

And capacity I (X)₁,X₂(ii) a Y) outer boundary: defining input signals for determining outer boundaries

Then

Mean value

Wherein the amplitude range of the input signalExpectation of

Setting input signalSubject to a discrete distribution, takeA non-negative real value

This gives:

wherein

P_r{. is the probability, thus obtaining C_1,2The outer boundary of (A) is as follows:

wherein

For input signals

The probability when the probability P is transmitted, max (lambda), is taken as the maximum value, sigma²Is the variance;

thus, the outer boundary C_1,2Write as:

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 boundary_1，2. 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

Outside world

Outside world

Outside world

Inner boundary

And the maximum discrete entropy bound in (a), wherein for all i,

note, external worldAnd inner bound

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

And discrete distributed optimal input

Wherein

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 respectively, at low SNR, i.e.

And

and at high SNR, i.e.

And

inner and outer boundaries of VLC MAC capacity domain, wherein

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

And

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, whereFig. 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

The other existing inner boundaries on the high SNR side are all high, i.e. in FIG. 3b

Sum rate R₁+R₂。

Fig. 4 shows the proposed inner and outer boundaries, maximizing the discrete entropy inner boundary,and

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

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

The inner boundary is high. At the time of a high SNR, it is,

highest (only peak optical power constraint). Furthermore, the proposed outer boundary is higher than the existing outer boundaryAnd

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 in 2017, scholars such as A. Chaaban, O.M.S. -AI-Ebraheemy, etc. in Capacity bounds for the gaussian IM-DDAs mentioned in the optical multiple access channel, the channel capacity analysis is one of the important bases of information processing and coding, energy efficiency optimization and resource optimization, so that the practical calculation method can be directly used for the performance optimization of the visible light communication system.

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.