CN115694569B - Capacity determining method for MIMO visible light communication system - Google Patents
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Abstract
The invention provides a capacity determining method of a MIMO visible light communication system. According to the method, firstly, a characteristic value decomposition SVD is adopted to decouple channels of the MIMO visible light communication system, the channels are decomposed into a plurality of independent SISO sub-channels, then, capacity and maximization models of the plurality of SISO sub-channels are established, the optimal modulation orders of the SISO sub-channels are determined through initialization, and then, the capacity and maximization models can be solved to obtain the capacity of the MIMO visible light communication system. The method of the invention can determine the capacity of any MIMO visible light communication system with smaller complexity.
Description
Technical Field
The invention belongs to the technical field of a visible light communication MIMO system, and particularly relates to a capacity determining method of the MIMO visible light communication system.
Background
At present, less capacity research is carried out on a MIMO visible light communication system, and the existing research has proved that a source suitable for MIMO-VLC channel transmission meets the discrete distribution, and a capacity problem solving method under the condition that the modulation orders of all sub-channels are the same is provided on the basis. In actual transmission, since the order for modulation is not the same due to the difference between the sub-channels, the current research on the capacity of the MIMO visible light communication system is not fully considered.
Disclosure of Invention
The invention aims to provide a capacity determining method of a MIMO visible light communication system, which aims to solve the technical problem that in actual transmission, the orders used for modulation are not the same due to the fact that the sub-channels are different.
In order to solve the technical problems, the specific technical scheme of the invention is as follows:
a capacity determining method of a MIMO visible light communication system comprises the following steps:
step A: decoupling the MIMO channel by adopting a eigenvalue decomposition SVD method, and decomposing the MIMO channel into K independent SISO sub-channels; the input-output relation expression of the MIMO channel is as follows:
Y＝HX+Z
wherein,output signal representing channel, Y= [ Y ] 1 ,…,Y i ,…,Y N ] T Y in (a) i Output signal representing the ith sub-channel in the channel, N representing the number of receivers, (-) T Representing a transpose of the matrix; />Represents a channel matrix, M represents the number of transmitters, and the element of the channel matrix is h nm ，h nm Being a positive constant, M represents the number of the transmitter, N represents the number of the receiver, and the channel matrix H is of full rank, the rank of the matrix being k=min (M, N); />Discrete power signal vector representing channel input, x= [ X ] 1 ,…,X j ,…,X M ] T Wherein X is j A discrete power signal representing the j-th sub-channel input; />Representing an additive Gaussian interference signal received in a communication process; the specific process of decoupling the MIMO channel is as follows:
step A-1: decomposing the matrix H into products of unitary and diagonal matrices:
H＝UDV T
wherein the matrixSum matrix->Are unitary matrices, UU T ＝I，VV T Matrix element of matrix U is represented by HH =i T Is composed of eigenvectors of matrix V, matrix elements of matrix V are composed of H T Characteristic vector composition of H; />As a diagonal matrix, HH T The non-zero eigenvalues of (a) are lambda in order from large to small 1 ,λ 2 ,…,λ K The method comprises the steps of carrying out a first treatment on the surface of the When m=n, d=diag(λ 1 ,λ 2 ,…,λ K ) The method comprises the steps of carrying out a first treatment on the surface of the When N > M, D has the formula:
wherein the method comprises the steps of0 (N-M)×M Representing an all 0 matrix of N-M rows, M columns; when N < M, D is represented by:
wherein the method comprises the steps of0 N×(M-N) Representing an all 0 matrix of N rows, M-N columns; diag () represents a diagonal matrix;
step A-2: the input and output relation expression of the MIMO channel is as follows:
Y＝UDV T X+Z
obtaining K decoupled SISO subchannels, and inputting and outputting a relational expression:
wherein the method comprises the steps of
And (B) step (B): establishing K sub-channel capacity and maximization models, wherein the capacity and maximization model A1 is as follows:
constraint C1:
C2:
C3:0<p ij ＜1,j＝1,2,…,N i
C4:
C5:N i ≥2
wherein N is i Representing the modulation order of the ith sub-channel;for the power of the respective output channel, < > for>The power of the j point representing the input discrete distribution signal of the i sub-channel is required to satisfy the condition of the visible light communication system for the power constraint, p ij Representing the probability of the jth point of the input discrete distribution signal of the ith SISO subchannel; sigma represents the standard deviation of the noise of each sub-channel; w represents the maximum power of the channel input signal; />Nth representing input discrete spread signal of ith sub-channel i Modulating power of each point;
step C: solving the model A1 to obtain the optimal modulation order N of the SISO sub-channel i The specific solving steps are as follows:
step C-1: initializing the modulation order of each SISO sub-channel to be 2;
step C-2: let the modulation order N of the ith SISO subchannel i T, t is an intermediate variable, initializing t=3, and solving the optimal solution of the model A1;
step C-3: judging p in the optimal solution of the model A1 ij If p ij < ε, the i-th SISO subchannel optimal modulation order N i =t-1, where ε is a given threshold; otherwise, let t add 1, let N i =t, and solve the optimal solution of model A1;
step C-4: repeating the step C-3; obtaining optimal modulation orders of all K SISO sub-channels;
step D: solving the sum of the capacities of all SISO sub-channels; and bringing the optimal modulation orders of the K SISO subchannels into a model A1 for solving, so as to determine the capacity of the MIMO visible light communication system.
Further, in step C-3, the threshold ε has a value of 10 -4 。
The capacity determining method of the MIMO visible light communication system has the following advantages:
the invention firstly adopts eigenvalue decomposition SVD to decouple the channel of the MIMO visible light communication system, decomposes the channel into a plurality of independent SISO sub-channels, and then establishes a capacity and maximization model of the plurality of independent SISO sub-channels. For the SISO subchannel capacities and the maximization model, the variables meet the symmetry, so that half of optimized variables can be saved in the solving process. The method of the invention can determine the capacity of any MIMO visible light communication system with smaller complexity.
Detailed Description
In order to better understand the purpose, structure and function of the present invention, a capacity determining method of the MIMO visible light communication system of the present invention is described in further detail.
The invention provides a capacity determining method of a MIMO visible light communication system. According to the method, firstly, a characteristic value decomposition SVD is adopted to decouple channels of the MIMO visible light communication system, the channels are decomposed into a plurality of independent SISO sub-channels, and then a maximum model of the sum of the capacities of the plurality of independent SISO sub-channels is established. In the solving process of the capacity and maximization model, firstly, the modulation order of each SISO sub-channel is initialized, then the optimal modulation order of each sub-channel is obtained by utilizing the continuity of the information entropy, so that the solution of the capacity and maximization model is obtained, and finally the capacity of the MIMO visible light communication system is obtained.
For a better illustration of the process according to the invention, reference is made to the following more detailed examples:
the first step: the input-output relation expression of the channel in the MIMO visible light communication system is as follows:
Y＝HX+Z
wherein,output signal representing channel, Y= [ Y ] 1 ,…,Y i ,…,Y N ] T Y in (a) i Output signal representing the ith sub-channel in the channel, N representing the number of receivers, (-) T Representing a transpose of the matrix; />Represents a channel matrix, M represents the number of transmitters, and the element of the channel matrix is h nm ，h nm Being a positive constant, M represents the number of the transmitter, N represents the number of the receiver, and the channel matrix H is of full rank, the rank of the matrix being k=min (M, N); />Discrete power signal vector representing channel input, x= [ X ] 1 ,…,X j ,…,X M ] T Wherein X is j A discrete power signal representing the j-th sub-channel input;representing an additive Gaussian interference signal received in a communication process;
and a second step of: and performing eigenvalue decomposition (SVD) on the MIMO channel, and decoupling the MIMO channel into K independent SISO subchannels.
It is known that a channel matrix H of full rank can be decomposed into products of unitary and diagonal matrices:
H＝UDV T
wherein the matrixSum matrix->Are unitary matrices, UU T ＝I，VV T Matrix element of matrix U is represented by HH =i T Is composed of eigenvectors of matrix V, matrix elements of matrix V are composed of H T Characteristic vector composition of H; />As a diagonal matrix, HH T The non-zero eigenvalues of (a) are lambda in order from large to small 1 ,λ 2 ,…,λ K The method comprises the steps of carrying out a first treatment on the surface of the When m=n, d=diag (λ 1 ,λ 2 ,…,λ K ) The method comprises the steps of carrying out a first treatment on the surface of the When N > M, D has the formula:
wherein the method comprises the steps of0 (N-M)×M Representing an all 0 matrix of N-M rows, M columns; when N < M, D is represented by:
wherein the method comprises the steps of0 N×(M-N) Representing an all 0 matrix of N rows, M-N columns; diag () represents a diagonal matrix; the MIMO channel input and output relationship can therefore continue to be expressed as:
Y＝UDV T X+Z
two-side co-riding U T Obtaining U T Y＝DV T X+U T Z, orderObtaining K decoupled SISO subchannels, and inputting and outputting a relational expression:
and a third step of: and establishing K sub-channel capacity and a maximization model.
The source suitable for SISO visible light communication system channel transmission is known as discrete source, so that the input source of the i-th sub-channel after decouplingThe probability density function of (2) should have the expression:
wherein N is i Representing the modulation order of the ith sub-channel;the power of the j point of the input discrete distribution signal representing the i sub-channel needs to meet the power constraint of the actual situation. Lambda (lambda) i Is HH T Is the ith non-zero eigenvalue, p ij The probability of the j-th point of the input discrete distribution signal representing the i-th SISO subchannel is satisfied with the constraint that the sum of the probabilities in each SISO subchannel is 1.
In addition, the input source of the i-th sub-channel after decouplingThe probability density function of (2) also satisfies distribution symmetry, namely, the position vector is symmetrical about the position center, and the probability vector is even symmetrical about the position center, so that half of optimization variables can be saved in the actual solving process.
In the independent SISO sub-channels after decoupling, the noise meets the Gaussian distribution of zero mean value, and the variance is sigma 2 Thus, in the ith sub-channel, noiseSound productionThe probability density function of (2) is:
since in the ith sub-channel the input signalAnd noise random signal->Independent of each other, available according to the basic knowledge of probability theory, output signal +.>The probability density function of (2) is:
the channel capacity is characterized as the maximum value of the average mutual information quantity of input and output, so that a capacity and maximization model of K independent SISO sub-channels can be established, wherein the capacity and maximization model is A1:
constraint C1:
C2:
C3:0<p ij ＜1,j＝1,2,…,N i
C4:
C5:N i ≥2
wherein,sigma represents the standard deviation of each sub-channel noise for the power of each output channel; w represents the maximum power of the channel input signal; />Nth representing input discrete spread signal of ith sub-channel i Modulated power at each point.
Fourth step: solving the decoupled K independent SISO sub-channel capacity and the maximization model, wherein the method comprises the following specific steps of:
step 4-1: initializing the modulation order of each SISO sub-channel to be 2;
step 4-2: let the modulation order N of the ith SISO subchannel i T, t is an intermediate variable, t=3, solving the optimal solution of model A1;
step 4-3: judging p in the optimal solution of the model A1 ij If p ij < ε, the i-th SISO subchannel optimal modulation order N i =t-1, where ε is a given threshold; otherwise, let t add 1, let N i =t, and solve the optimal solution of model A1;
step 4-4: repeating the step C-3; obtaining optimal modulation orders of all K SISO sub-channels;
step 4-5: solving the sum of the capacities of all SISO sub-channels; and bringing the optimal modulation orders of the K SISO subchannels into a model A1 for solving, so as to determine the capacity of the MIMO visible light communication system.
It will be understood that the invention has been described in terms of several embodiments, and that various changes and equivalents may be made to these features and embodiments by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.
Claims (2)
1. A capacity determining method of a MIMO visible light communication system, comprising the steps of:
step A: decoupling the MIMO channel by adopting a eigenvalue decomposition SVD method, and decomposing the MIMO channel into K independent SISO sub-channels; the input-output relation expression of the MIMO channel is as follows:
Y＝HX+Z
wherein,output signal representing channel, Y= [ Y ] 1 ,…,Y i ,…,Y N ] T Y in (a) i Output signal representing the ith sub-channel in the channel, N representing the number of receivers, (-) T Representing a transpose of the matrix; />Represents a channel matrix, M represents the number of transmitters, and the element of the channel matrix is h nm ，h nm Being a positive constant, M represents the number of the transmitter, N represents the number of the receiver, and the channel matrix H is of full rank, the rank of the matrix being k=min (M, N); />Discrete power signal vector representing channel input, x= [ X ] 1 ,…,X j ,…,X M ] T Wherein X is j A discrete power signal representing the j-th sub-channel input; />Indicating the additions experienced during a communicationA linear gaussian interference signal; the specific process of decoupling the MIMO channel is as follows:
step A-1: decomposing the matrix H into products of unitary and diagonal matrices:
H＝UDV T
wherein the matrixSum matrix->Are unitary matrices, UU T ＝I，VV T Matrix element of matrix U is represented by HH =i T Is composed of eigenvectors of matrix V, matrix elements of matrix V are composed of H T Characteristic vector composition of H; />As a diagonal matrix, HH T The non-zero eigenvalues of (a) are lambda in order from large to small 1 ,λ 2 ,…,λ K The method comprises the steps of carrying out a first treatment on the surface of the When m=n, d=diag (λ 1 ,λ 2 ,…,λ K ) The method comprises the steps of carrying out a first treatment on the surface of the When N > M, D has the formula:
wherein the method comprises the steps of0 (N-M)×M Representing an all 0 matrix of N-M rows, M columns; when N < M, D is represented by:
wherein the method comprises the steps of0 N×(M-N) The number of N rows is indicated,all 0 matrices for M-N columns; diag () represents a diagonal matrix;
step A-2: the input and output relation expression of the MIMO channel is as follows:
Y＝UDV T X+Z
obtaining K decoupled SISO subchannels, and inputting and outputting a relational expression:
wherein the method comprises the steps of
And (B) step (B): establishing K sub-channel capacity and maximization models, wherein the capacity and maximization model A1 is as follows:
constraint conditions
C3:0<p ij ＜1,j＝1,2,…,N i
C5:N i ≥2
Wherein N is i Representing the modulation order of the ith sub-channel;work for each output channelRate of->The power of the j point representing the input discrete distribution signal of the i sub-channel is required to satisfy the condition of the visible light communication system for the power constraint, p ij Representing the probability of the jth point of the input discrete distribution signal of the ith SISO subchannel; sigma represents the standard deviation of the noise of each sub-channel; w represents the maximum power of the channel input signal; />Nth representing input discrete spread signal of ith sub-channel i Modulating power of each point;
step C: solving the model A1 to obtain the optimal modulation order N of the SISO sub-channel i The specific solving steps are as follows:
step C-1: initializing the modulation order of each SISO sub-channel to be 2;
step C-2: let the modulation order N of the ith SISO subchannel i T, t is an intermediate variable, initializing t=3, and solving the optimal solution of the model A1;
step C-3: judging p in the optimal solution of the model A1 ij If p ij < ε, the i-th SISO subchannel optimal modulation order N i =t-1, where ε is a given threshold; otherwise, let t add 1, let N i =t, and solve the optimal solution of model A1;
step C-4: repeating the step C-3; obtaining optimal modulation orders of all K SISO sub-channels;
step D: solving the sum of the capacities of all SISO sub-channels; and bringing the optimal modulation orders of the K SISO subchannels into a model A1 for solving, so as to determine the capacity of the MIMO visible light communication system.
2. The capacity determining method of a MIMO visible light communication system as claimed in claim 1, wherein in step C-3, the threshold value epsilon has a value of 10 -4 。
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| CN113489536A (en) * | 2021-07-01 | 2021-10-08 | 中国矿业大学 | Method for reaching channel capacity of visible light communication multi-input multi-output system |
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| CN113162689A (en) * | 2021-04-26 | 2021-07-23 | 东南大学 | Power distribution method for multi-input multi-output visible light communication characteristic channel |
| CN113489536A (en) * | 2021-07-01 | 2021-10-08 | 中国矿业大学 | Method for reaching channel capacity of visible light communication multi-input multi-output system |
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