CN102510324B

CN102510324B - Signal transmission method based on network coding in multi-input and multi-output Y channel

Info

Publication number: CN102510324B
Application number: CN201210000363.6A
Authority: CN
Inventors: 苏玉萍; 李颖; 孙岳; 林昊; 常光辉
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2012-01-02
Filing date: 2012-01-02
Publication date: 2014-08-20
Anticipated expiration: 2032-01-02
Also published as: CN102510324A

Abstract

The invention discloses a signal transmission method based on network coding in a multi-input multi-output Y channel, which mainly solves the problems of low reachability and low rate in the prior art. The implementation steps include: the user node precodes the original signal, that is, the signal space alignment matrix, the user node additional precoding matrix, and the power allocation matrix multiplied by the original signal vector; the user node sends the precoded signal to the relay Node; the relay node separates the received signal, and multiplies the separated signal with the interference cancellation matrix, the additional precoding matrix of the relay node, and the power allocation matrix to obtain the transmission signal of the relay node; the relay node precodes to obtain The sent signal is broadcast to the user node; the user node restores the data according to the received signal and the signal sent by itself. Simulation results show that compared with the existing signal transmission method, the present invention has greatly improved reachability and speed.

Description

Signal transmission method based on network coding in multiple-input multiple-output Y channel

技术领域 technical field

本发明属于无线通信技术领域，涉及预编码和网络编码，具体地说是一种基于网络编码的信号传输方法，可用于多输入多输出Y信道中，以在保证最大自由度可达的基础上提高系统的可达和速率。The invention belongs to the technical field of wireless communication, and relates to precoding and network coding, in particular to a signal transmission method based on network coding, which can be used in a multi-input multi-output Y channel, so as to guarantee the maximum degree of freedom reachable Improve system reachability and speed.

背景技术 Background technique

传统的双向中继信道是一对用户或多对用户通过中继互发信息，这种模型下，每个用户只给其中一个用户发送信息，同时接收来自这个用户发送的信息。在实际应用中，每个用户经常需要给多个用户发送信息，同时接收来自不同用户的信息。在这种情形下，出现了多向中继信道模型，多输入多输出Y信道就是其中一种重要的通信模式。In the traditional two-way relay channel, a pair of users or multiple pairs of users send information to each other through the relay. In this model, each user only sends information to one of the users and receives information from this user at the same time. In practical applications, each user often needs to send information to multiple users and receive information from different users at the same time. In this case, a multi-directional relay channel model appears, and the MIMO Y channel is one of the important communication modes.

多输入多输出Y信道模型如图1所示。它包括三个用户节点和一个中继节点，其中每个用户节点装备M根天线，中继节点装备N根天线。不同的用户之间没有直接的链路，且每个用户节点通过中继节点给另外两个用户节点各发送一个单播信息，具体的通信过程如下：首先，三个用户节点同时发送数据给中继节点，这个阶段称为MAC阶段；然后，中继节点对接收到的信息进行处理后广播给三个用户节点，这个阶段称为BC阶段；最后，由三个用户节点分别根据自己的接收信号以及自己在MAC阶段所发送的信息译出另外两个用户节点发给自己的信息。The multi-input multi-output Y channel model is shown in Figure 1. It includes three user nodes and a relay node, wherein each user node is equipped with M antennas, and the relay node is equipped with N antennas. There is no direct link between different users, and each user node sends a unicast message to the other two user nodes through the relay node. The specific communication process is as follows: First, the three user nodes simultaneously send data to the middle The relay node, this stage is called the MAC stage; then, the relay node processes the received information and broadcasts it to the three user nodes, this stage is called the BC stage; finally, the three user nodes respectively according to their own received signal And the information sent by itself in the MAC stage is translated to the information sent to itself by the other two user nodes.

韩国学者Namyoon Lee等在文章″Degrees of Freedom of the MIMO Y Channel：Signal Space Alignment for Network coding，IEEE Trans.Inform.Theory″中对多输入多输出Y信道的自由度进行了分析，文章通过在MAC阶段采用信号空间对齐技术和在BC阶段采用基于网络编码的干扰消除波束成形技术，证明了当时，多输入多输出Y信道在译码转发模式下的最大自由度为3M，即每个用户可以发送M个独立的数据流，表示大于等于3M/2的最小整数。Korean scholar Namyoon Lee et al. analyzed the degrees of freedom of the MIMO Y channel in the article "Degrees of Freedom of the MIMO Y Channel: Signal Space Alignment for Network coding, IEEE Trans.Inform. Theory". The signal space alignment technology is adopted in the stage and the interference cancellation beamforming technology based on network coding is adopted in the BC stage, which proves that when , the maximum degree of freedom of the MIMO Y channel in the decoding and forwarding mode is 3M, that is, each user can send M independent data streams, Indicates the smallest integer greater than or equal to 3M/2.

虽然文章中给出了多输入多输出Y信道的最大自由度，但如何优化其预编码设计，从而在保证最大自由度可达的基础上提高系统的和速率仍是需要解决的一个问题。Although the maximum degree of freedom of the MIMO Y channel is given in the article, how to optimize its precoding design to improve the sum rate of the system on the basis of ensuring the maximum degree of freedom is still a problem that needs to be solved.

发明内容：Invention content:

本发明的目的在于针对上述已有技术的不足，根据放大转发模式下的多输入多输出Y信道模型，提出一种多输入多输出Y信道中基于网络编码的信号传输方法，以在保证最大自由度可达的基础上提高系统的和速率。The purpose of the present invention is to address the deficiencies of the above-mentioned prior art, according to the MIMO Y channel model under the amplification and forwarding mode, propose a signal transmission method based on network coding in the MIMO Y channel, to ensure maximum freedom Improve system performance and speed on the basis of degree reachability.

实现本发明的目的技术方案，包括如下步骤：Realize the technical scheme of the object of the present invention, comprise the steps:

(1)用户节点对原始信号进行预编码步骤(1) The user node precodes the original signal

每个用户节点将发给另外两个用户节点的信息进行预编码，得到发送用户节点的M×1维发送信号为： $x_{i} = Σ_{j = 1, j &NotEqual; i}^{3} V^{[j, i]} W_{π (j, i)} Σ^{[j, i]} s^{[j, i]},$ Each user node precodes the information sent to the other two user nodes, and the M×1-dimensional sending signal of the sending user node is obtained as: $x_{i} = Σ_{j = 1, j &NotEqual; i}^{3} V^{[j, i]} W_{π (j, i)} Σ^{[j, i]} {the s}^{[j, i]},$

式中i表示发送用户节点，j表示接收用户节点，且i，j∈{1，2，3}，i≠j，M表示发送用户节点处配制的天线个数，且M为偶数，s^[j，i]是发送用户节点i发给接收用户节点j的M/2×1个数据流构成的原始信号向量，该向量的每个元素是均值为零、方差为1的相互独立的随机变量，∑^[j，i]是M/2×M/2的发送节点功率分配对角矩阵，W_π(j，i)是M/2×M/2用户节点附加预编码矩阵，下标π(j，i)是一个索引函数，满足π(i，j)＝π(j，i)，且有π(1，2)＝1，π(1，3)＝2，π(2，3)＝3，因此有W_π(2，1)＝W_π(1，2)＝W₁，W_π(3，1)＝W_π(1，3)＝W₂，W_π(3，2)＝W_π(2，3)＝W₃，V^[j，i]是M×M/2的信号空间对齐矩阵，满足H^[r，i]V^[j，i]＝H^[r，j]V^[i，j]，H^[r，i]表示用户节点i到中继节点r的N×M的信道矩阵，N表示中继节点r处配置的天线个数，且有N＝3M/2，该信道矩阵的每个元素为服从均值为零、方差为1的相互独立的复高斯随机变量；In the formula, i represents the sending user node, j represents the receiving user node, and i, j∈{1, 2, 3}, i≠j, M represents the number of antennas configured at the sending user node, and M is an even number, s ^{[ j, i]} is the original signal vector composed of M/2×1 data streams sent from the sending user node i to the receiving user node j, and each element of this vector is a mutually independent random variable with a mean value of zero and a variance of 1 , Σ ^{[j, i]} is the M/2×M/2 transmitting node power allocation diagonal matrix, W _{π(j, i)} is the M/2×M/2 user node additional precoding matrix, subscript π( j, i) is an index function that satisfies π(i,j)=π(j,i), and π(1,2)=1, π(1,3)=2, π(2,3) =3, so W _π(2,1) =W _π(1,2) =W ₁ , W _π(3,1) =W _π(1,3) =W ₂ , W _π(3,2) =W _π(2,3) ＝W ₃ , V ^{[j, i]} is an M×M/2 signal space alignment matrix, satisfying H ^{[r, i]} V ^{[j, i]} = H ^{[r, j]} V ^{[i, j]} , H ^{[r, i]} represents the N×M channel matrix from user node i to relay node r, N represents the number of antennas configured at relay node r, and N=3M/2 , each element of the channel matrix is a mutually independent complex Gaussian random variable with a mean of zero and a variance of 1;

(2)用户节点向中继节点发送信号步骤(2) The user node sends a signal to the relay node

发送用户节点i将进行预编码得到的发送信号x_i发送给中继节点r，得到中继节点的N×1维接收信号为：The transmitting user node i sends the transmitted signal x _i obtained by precoding to the relay node r, and the N×1-dimensional received signal of the relay node is obtained as:

${y the y}_{r r} = = {Σ Σ}_{i i = = 11}^{33} {H h}^{[[r r,, i i]]} {x x}_{i i} + + {n no}_{r r}$

$= = {Σ Σ}_{i i = = 11}^{33} {H h}^{[[r r,, i i]]} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{33} {V V}^{[[j j,, i i]]} {W W}_{π π ((j j,, i i))} {Σ Σ}^{[[j j,, i i]]} {s the s}^{[[j j,, i i]]} + + {n no}_{r r}$

$= = {U u}_{11} {W W}_{11} {s the s}^{[[r r,, 11]]} + + {U u}_{22} {W W}_{22} {s the s}^{[[r r,, 22]]} + + {U u}_{33} {W W}_{33} {s the s}^{[[r r,, 33]]} + + {n no}_{r r},,$

式中，s^[r，1]＝∑^[2，1]s^[2，1]+∑^[1，2]s^[1，2]表示用户节点1与用户节点2的对齐信号，s^[r，2]＝∑^[3，1]s^[3，1]+∑^[1，3]s^[1，3]表示用户节点1与用户节点3的对齐信号，s^[r，3]＝∑^[3，2]s^[3，2]+∑^[2，3]s^[2，3]表示用户节点2与用户节点3的对齐信号，U₁＝H^[r，1]V^[2，1]＝H^[r，2]V^[1，2]表示信道矩阵H^[r，1]与信道矩阵H^[r，2]的列空间的交空间，U₂＝H^[r，1]V^[3，1]＝H^[r，3]V^[1，3]表示信道矩阵H^[r，1]与信道矩阵H^[r，3]的列空间的交空间，U₃＝H^[r，2]V^[3，2]＝H^[r，3]V^[2，3]表示信道矩阵H^[r，2]与信道矩阵H^[r，3]的列空间的交空间，n_r是N×1的噪声向量，该向量的每个元素是均值为零、方差为的相互独立的复高斯随机变量；In the formula, s ^{[r, 1]} = ∑ ^{[2, 1]} s ^{[2, 1]} + ∑ ^{[1, 2]} s ^{[1, 2]} represents the alignment signal between user node 1 and user node 2, s ^{[r , 2]} = ∑ ^{[3, 1]} s ^{[3, 1]} + ∑ ^{[1, 3]} s ^{[1, 3]} represents the alignment signal between user node 1 and user node 3, s ^{[r, 3]} = ∑ ^{[ 3, 2]} s ^{[3, 2]} + ∑ ^{[2, 3]} s ^{[2, 3]} represents the alignment signal between user node 2 and user node 3, U ₁ = H ^{[r, 1]} V ^{[2, 1]} =H ^{[r, 2]} V ^{[1, 2]} represents the intersection space of the channel matrix H ^{[r, 1]} and the column space of the channel matrix H ^{[r, 2]} , U ₂ =H ^{[r, 1]} V ^{[3 , 1]} = H ^{[r, 3]} V ^{[1, 3]} represents the intersection space of the channel matrix H ^{[r, 1]} and the column space of the channel matrix H ^{[r, 3]} , U ₃ = H ^{[r, 2]} V ^{[3, 2]} = H ^{[r, 3]} V ^{[2, 3]} represents the intersection space of the channel matrix H ^{[r, 2]} and the column space of the channel matrix H ^{[r, 3]} , n _r is N×1 A noise vector of , each element of which is zero mean and variance Independent complex Gaussian random variables of ;

(3)中继节点对接收信号进行预编码步骤(3) The relay node precodes the received signal

(3a)中继节点r对接收信号y_r中包含的对齐信号s^[r，1]，s^[r，2]和s^[r，3]进行分离，用s^[r，1]的M/2×N维分离矩阵H₁乘以y_r，满足H₁[U₂ U₃]＝0_M/2×M，得到第一个分离后的对齐信号y^[r，1]＝H₁y_r＝H₁U₁W₁s^[r，1]+H₁n_r，0_M/2×M表示M/2×M的全零矩阵，类似地，选择s^[r，2]，s^[r，3]的分离矩阵H₂，H₃，分别满足H₂[U₁ U₃]＝0_M/2×M，H₃[U₁ U₂]＝0_M/2×M，得到第二个分离后的对齐信号y^[r，2]＝H₂y_r＝H₂U₂W₂s^[r，2]+H₂n_r和第三个分离后的对齐信号，y^[r，3]＝H₃y_r＝H₃U₃W₃s^[r，3]+H₃n_r；(3a) The relay node r separates the alignment signals s ^{[r, 1]} , s ^{[r, 2]} and s ^{[r, 3]} ^contained in the received signal _yr , and uses the M/ The 2×N-dimensional separation matrix H ₁ is multiplied by y _r , satisfying H ₁ [U ₂ U ₃ ]=0 _M/2×M , and the first separated alignment signal y ^{[r, 1]} = H ₁ y _r =H ₁ U ₁ W ₁ s ^{[r, 1]} +H ₁ n _r , 0 _M/2×M means an all-zero matrix of M/2×M, similarly, select s ^{[r, 2]} , s ^{[r , 3]} the separation matrices H ₂ , H ₃ respectively satisfy H ₂ [U ₁ U ₃ ]=0 _M/2×M , H ₃ [U ₁ U ₂ ]=0 _M/2×M , get the second The separated alignment signal y ^[r,2] = H ₂ y _r = H ₂ U ₂ W ₂ s ^[r,2] + H ₂ n _r and the third separated alignment signal, y ^[r,3] = H ₃ y _r = H ₃ U ₃ W ₃ s ^{[r, 3]} + H ₃ n _r ;

(3b)对分离后的对齐信号y^[r，1]，y^[r，2]，y^[r，3]进行预编码，得到N×1的发送信号 $x_{r} = Σ_{i = 1}^{3} V^{[i, r]} Σ^{[i, r]} U^{[i, r]} y^{[r, i]},$ (3b) Precode the separated alignment signals y ^{[r, 1]} , y ^{[r, 2]} , y ^{[r, 3]} to obtain N×1 transmission signals $x_{r} = Σ_{i = 1}^{3} V^{[i, r]} Σ^{[i, r]} u^{[i, r]} {the y}^{[r, i]},$

式中，V^[i，r]为干扰消除矩阵，∑^[i，r]为中继节点的功率分配对角矩阵，其对角元素的值根据对齐信号s^[r，i]，i＝1，2，3中每个数据流采用平均功率分配来确定，U^[i，r]为中继节点附加预编码矩阵；In the formula, V ^{[i, r]} is the interference cancellation matrix, ∑ ^{[i, r]} is the power distribution diagonal matrix of the relay node, and the values of its diagonal elements are according to the alignment signal s ^{[r, i]} , i=1 , each data stream in 2, 3 is determined by the average power allocation, U ^{[i, r]} is the additional precoding matrix of the relay node;

(4)中继节点广播发送信号步骤(4) The relay node broadcasts and sends the signal steps

中继节点r将进行预编码得到的发送信号x_r广播给用户节点，得到用户节点i的M×1维接收信号为：y_i＝H^[i，r]x_r+n_i，i∈{1，2，3}，The relay node r broadcasts the transmitted signal x _r obtained by precoding to the user node, and the M×1-dimensional received signal of the user node i is obtained as: y _i =H ^{[i, r]} x _r +n _i , i∈{ 1, 2, 3},

式中n_i是M×1的噪声向量，该向量的每个元素是均值为零、方差为的相互独立的复高斯随机变量，H^[i，r]是中继节点到用户节点i的M×N的信道矩阵，该矩阵的每个元素是服从均值为零、方差为1的相互独立的复高斯随机变量；In the formula, n _i is a noise vector of M×1, and each element of this vector has a mean value of zero and a variance of The mutually independent complex Gaussian random variables, H ^{[i, r]} is the M×N channel matrix from the relay node to the user node i, and each element of this matrix is mutually independent complex Gaussian random variable;

(5)用户节点恢复数据步骤(5) User node recovery data steps

用户节点i根据接收信号y_i及自己的发送信号x_i来去掉自身的干扰，即从接收信号y_i中将x_i通过信道后形成的那部分信号减掉；然后采用迫零检测恢复用户j给用户i发送的原始信号s^[i，j]，j∈{1，2，3}，j≠i。User node i removes its own interference according to the received signal y _i and its own transmitted signal _xi , that is, subtracts the part of the signal formed after x _i passes through the channel from the received signal y _i ; then uses zero-forcing detection to restore user j The original signal s ^{[i, j]} sent to user i, j ∈ {1, 2, 3}, j≠i.

本发明与现有技术相比具有如下优点：Compared with the prior art, the present invention has the following advantages:

现有的多输入多输出Y信道中的信号传输方法是从自由度的角度设计的，用户节点和中继节点的附加预编码矩阵为单位阵，可达和速率较小，本发明在保证自由度可达的基础上，将用户节点和中继节点的附加预编码矩阵设计成了酉矩阵，与现有的附加预编码矩阵相比，增加了附加预编码矩阵元素选择的多样性，因此提高了系统的可达和速率。The signal transmission method in the existing multi-input multi-output Y channel is designed from the angle of freedom, the additional precoding matrix of the user node and the relay node is a unit matrix, and the reachability and rate are small. The present invention guarantees freedom On the basis of attainable degree, the additional precoding matrix of the user node and the relay node is designed as a unitary matrix. Compared with the existing additional precoding matrix, the diversity of element selection of the additional precoding matrix is increased, thus improving system reachability and speed.

附图说明 Description of drawings

图1是现有的多输入多输出Y信道模型；Fig. 1 is existing multi-input multi-output Y channel model;

图2是本发明的流程图；Fig. 2 is a flow chart of the present invention;

图3是本发明在固定中继节点信噪比条件下的性能仿真图；Fig. 3 is the performance simulation figure of the present invention under the condition of fixed relay node signal-to-noise ratio;

图4是本发明在固定用户节点信噪比条件下的性能仿真图。Fig. 4 is a performance simulation diagram of the present invention under the condition of fixed user node signal-to-noise ratio.

具体实施方式 Detailed ways

本发明所提出的信号传输方法适用于图1所述的多输入多输出Y信道模型，该信道模型包括三个用户节点和一个中继节点，其中每个用户节点装备M根天线，中继节点装备N根天线，每个用户节点通过中继节点给另外两个用户节点各发送一个单播信息；具体的通信过程如下：首先，三个用户节点同时发送信息给中继节点；然后，中继节点对接收到的信息进行处理后广播给三个用户节点；最后，由三个用户节点分别根据自己接收的信息以及自己所发送的信息恢复出另外两个用户节点发给自己的信息。The signal transmission method proposed by the present invention is applicable to the MIMO Y channel model described in Fig. 1, the channel model includes three user nodes and a relay node, wherein each user node is equipped with M antennas, and the relay node Equipped with N antennas, each user node sends a unicast message to the other two user nodes through the relay node; the specific communication process is as follows: first, the three user nodes send information to the relay node at the same time; then, the relay node The node processes the received information and broadcasts it to the three user nodes; finally, the three user nodes restore the information sent by the other two user nodes according to the information they receive and the information they send.

参照图2，本发明利用图1中的信道模型进行信号传输的步骤如下：With reference to Fig. 2, the present invention utilizes the channel model in Fig. 1 to carry out the steps of signal transmission as follows:

步骤1，用户节点对原始信号进行预编码。Step 1, the user node precodes the original signal.

(1.1)每个用户节点将发给另外两个用户节点的信息进行预编码，即将信号空间对齐矩阵，用户节点附加预编码矩阵，以及用户节点功率分配矩阵与原始信号向量相乘，得到发送用户节点的M×1维发送信号为： (1.1) Each user node precodes the information sent to the other two user nodes, that is, the signal space alignment matrix, the user node additional precoding matrix, and the user node power allocation matrix are multiplied by the original signal vector to obtain the sending user The M×1 dimension sending signal of the node is:

(1.2)根据信道矩阵H^[r，i]和H^[r，j]，确定信号空间对齐矩阵V^[j，i]：(1.2) Determine the signal space alignment matrix V ^{[j, i] according to the channel matrix H [r, i]} and H ^[r, ^j] :

方式一，对于用户1发给用户2的原始信号s^[2，1]所需的信号空间对齐矩阵V^[2，1]，以及用户2发给用户1的原始信号s^[1，2]所需的信号空间对齐矩阵V^[1，2]，选择方式如下：Method 1, for the signal space alignment matrix V ^{[2, 1] required by the original signal s [2} ^{, 1]} sent by user 1 to user 2, and the original signal s ^{[1, 2]} sent by user 2 to user 1 The required signal space alignment matrix V ^{[1, 2]} is selected as follows:

设V^[2，1]，V^[1，2]及U₁的第k列分别为u_k，1，k∈{1，2，…，M/2}，根据信号空间对齐矩阵V^[2，1]和V^[1，2]需要满足的条件：H^[r，1]V^[2，1]＝H^[r，2]V^[1，2]＝U₁，将这三个列向量的求解等价于求解下面的方程：Let V ^{[2, 1]} , V ^{[1, 2]} and the k-th column of U ₁ be u _{k, 1} , k ∈ {1, 2, ..., M/2}, according to the signal space alignment matrix V ^{[2, 1]} and V ^{[1, 2]} need to meet the conditions: H ^{[r, 1]} V ^{[ 2, 1]} = H ^{[r, 2]} V ^{[1, 2]} = U ₁ , the solution of these three column vectors is equivalent to solving the following equation:

$[\begin{matrix} {I I}_{N N} & {- - H h}^{[[r r,, 11]]} & 00_{N N \times \times M m} \\ {I I}_{N N} & 00_{N N \times \times M m} & {- - H h}^{[[r r,, 22]]} \end{matrix}] (\begin{matrix} {u u}_{k k,, 11} \\ {v v}_{k k}^{[[2,1 2,1]]} \\ {v v}_{k k}^{[[1,2 1,2]]} \end{matrix}) = = 00_{22 N N \times \times 11},, - - - - - - ((11))$

求解上述方程(1)得到M/2个解，将这M/2个解化为两两正交的单位向量作为U₁，V^[2，1]，V^[1，2]的M/2个列，式中，I_N表示N×N的单位阵，0_N×M表示N×M的全零矩阵，H^[r，1]和H^[r，2]分别表示用户节点1和用户节点2到中继节点的信道矩阵；Solve the above equation (1) to get M/2 solutions, and turn these M/2 solutions into pairwise orthogonal unit vectors as M/2 of U ₁ , V ^{[2, 1]} , V ^{[1, 2]} In the formula, _IN represents N×N unit matrix, 0 _N×M represents N×M all-zero matrix, H ^{[r, 1]} and H ^{[r, 2]} represent user node 1 and user node 2 to the channel matrix of the relay node;

方式二，对于用户1发给用户3的原始信号s^[3，1]所需的信号空间对齐矩阵V^[3，1]，以及用户3发给用户1的原始信号s^[1，3]所需的信号空间对齐矩阵V^[1，3]，选择方式如下：Method 2, for the signal space alignment matrix V ^{[3, 1] required by the original signal s [3} ^{, 1]} sent by user 1 to user 3, and the original signal s ^{[1, 3]} sent by user 3 to user 1 The required signal space alignment matrix V ^{[1, 3]} is selected as follows:

设V^[3，1]，V^[1，3]及U₂的第k列分别为u_k，2，k∈{1，2，…，M/2}，根据信号空间对齐矩阵V^[3，1]和V^[1，3]需要满足的条件：H^[r，1]V^[3，1]＝H^[r，3]V^[1，3]＝U₂，将这三个列向量的求解等价于求解下面的方程：Let V ^{[3, 1]} , V ^{[1, 3]} and the k-th column of U ₂ be u _{k, 2} , k ∈ {1, 2, ..., M/2}, according to the signal space alignment matrix V ^{[3, 1]} and V ^{[1, 3]} need to meet the conditions: H ^{[r, 1]} V ^{[ 3, 1]} = H ^{[r, 3]} V ^{[1, 3]} = U ₂ , the solution of these three column vectors is equivalent to solving the following equation:

$[\begin{matrix} {I I}_{N N} & {- - H h}^{[[r r,, 11]]} & 00_{N N \times \times M m} \\ {I I}_{N N} & 00_{N N \times \times M m} & {- - H h}^{[[r r,, 33]]} \end{matrix}] (\begin{matrix} {u u}_{k k,, 22} \\ {v v}_{k k}^{[[3,1 3,1]]} \\ {v v}_{k k}^{[[11,, 33]]} \end{matrix}) = = 00_{22 N N \times \times 11},, - - - - - - ((22))$

求解上述方程(2)得到M/2个解，将这M/2个解化为两两正交的单位向量作为U₂，V^[3，1]，V^[1，3]的M/2个列，式中，H^[r，1]和H^[r，3]分别表示用户节点1和用户节点3到中继节点的信道矩阵；Solve the above equation (2) to get M/2 solutions, and turn these M/2 solutions into pairwise orthogonal unit vectors as M/2 of U ₂ , V ^{[3, 1]} , V ^{[1, 3]} In the formula, H ^{[r, 1]} and H ^{[r, 3]} respectively represent the channel matrix from user node 1 and user node 3 to the relay node;

方式三，对于用户2发给用户3的原始信号s^[3，2]所需的信号空间对齐矩阵V^[3，2]，以及用户3发给用户2的原始信号s^[2，3]所需的信号空间对齐矩阵V^[2，3]，选择方式如下：Mode 3, for the signal space alignment matrix V ^{[3, 2] required by the original signal s [3,} ^2] sent by user 2 to user 3, and the original signal s ^{[2, 3]} sent by user 3 to user 2 The required signal space alignment matrix V ^{[2, 3]} , the selection method is as follows:

设V^[3，2]，V^[2，3]及U₃的第k列分别为u_k，3，k∈{1，2，…，M/2}，根据信号空间对齐矩阵V^[3，2]和V^[2，3]需要满足的条件：H^[r，2]V^[3，2]＝H^[r，3]V^[2，3]＝U₃，将这三个列向量的求解等价于求解下面的方程：Let V ^{[3, 2]} , V ^{[2, 3]} and the k-th column of U ₃ be u _{k, 3} , k ∈ {1, 2, ..., M/2}, according to the signal space alignment matrix V ^{[3, 2]} and V ^{[2, 3]} need to meet the conditions: H ^{[r, 2]} V ^{[ 3, 2]} = H ^{[r, 3]} V ^{[2, 3]} = U ₃ , the solution of these three column vectors is equivalent to solving the following equation:

$[\begin{matrix} {I I}_{N N} & {- - H h}^{[[r r,, 22]]} & 00_{N N \times \times M m} \\ {I I}_{N N} & 00_{N N \times \times M m} & {- - H h}^{[[r r,, 33]]} \end{matrix}] (\begin{matrix} {u u}_{k k,, 33} \\ {v v}_{k k}^{[[33,, 22]]} \\ {v v}_{k k}^{[[22,, 33]]} \end{matrix}) = = 00_{22 N N \times \times 11},, - - - - - - ((33))$

求解上述方程(3)得到M/2个解，将这M/2个解化为两两正交的单位向量作为U₃，V^[3，2]，V^[2，3]的M/2个列，式中，H^[r，2]和H^[r，3]分别表示用户节点2和用户节点3到中继节点的信道矩阵；Solve the above equation (3) to get M/2 solutions, and convert these M/2 solutions into pairwise orthogonal unit vectors as M/2 of U ₃ , V ^{[3, 2]} , V ^{[2, 3]} In the formula, H ^{[r, 2]} and H ^{[r, 3]} respectively represent the channel matrix from user node 2 and user node 3 to the relay node;

(1.3)确定用户节点附加预编码矩阵W_i：(1.3) Determine the additional precoding matrix W _i of the user node:

首先，根据以下三个条件：H₁[U₂ U₃]＝0_M/2×M，H₂[U₁ U₃]＝0_M/2×M，H₃[U₁ U₂]＝0_M/2×M，分别得到第一个分离矩阵H₁，第二个分离矩阵H₂，以及第三个分离矩阵H₃，式中，0_M/2×M表示M/2×M的全零矩阵，U₁＝H^[r，1]V^[2，1]＝H^[r，2]V^[1，2]表示信道矩阵H^[r，1]与信道矩阵H^[r，2]的列空间的交空间，U₂＝H^[r，1]V^[3，1]＝H^[r，3]V^[1，3]表示信道矩阵H^[r，1]与信道矩阵H^[r，3]的列空间的交空间，U₃＝H^[r，2]V^[3，2]＝H^[r，3]V^[2，3]表示信道矩阵H^[r，2]与信道矩阵H^[r，3]的列空间的交空间；First, according to the following three conditions: H ₁ [U ₂ U ₃ ]=0 _M/2×M , H ₂ [U ₁ U ₃ ]=0 _M/2×M , H ₃ [U ₁ U ₂ ]=0 _M/2×M , to get the first separation matrix H ₁ , the second separation matrix H ₂ , and the third separation matrix H ₃ , where 0 _M/2×M means the total of M/2×M Zero matrix, U ₁ = H ^{[r, 1]} V ^{[2, 1]} = H ^{[r, 2]} V ^{[1, 2]} represents the channel matrix H ^{[r, 1]} and the channel matrix H ^{[r, 2]} The intersection space of the column space, U ₂ =H ^{[r, 1]} V ^{[3, 1]} = H ^{[r, 3]} V ^{[1, 3]} represents the channel matrix H ^{[r, 1]} and the channel matrix H ^{[r, 3]} in the intersection space of the column space, U ₃ =H ^{[r, 2]} V ^{[3, 2]} = H ^{[r, 3]} V ^{[2, 3]} represents the channel matrix H ^{[r, 2]} and the channel matrix H The intersection space of the column space of ^{[r, 3]} ;

然后，将矩阵H_iU_i，i∈{1，2，3}进行奇异值分解，得到式中，上标H表示共轭转置，U_[i]和V_[i]是M/2×M/2的酉矩阵，∑_[i]是M/2×M/2的对角阵；Then, the matrix H _i U _i , i∈{1, 2, 3} is subjected to singular value decomposition to obtain In the formula, the superscript H represents the conjugate transpose, U _[i] and V _[i] are unitary matrices of M/2×M/2, and ∑ _[i] is a diagonal matrix of M/2×M/2;

最后，根据上述奇异值分解得到的酉矩阵V_[i]，选择用户节点附加预编码矩阵为：W_i＝V_[i]，i∈{1，2，3}；Finally, according to the unitary matrix V _[i] obtained by the above-mentioned singular value decomposition, select the additional precoding matrix of the user node as: W _i =V _[i] , i∈{1, 2, 3};

(1.4)确定发送节点功率分配对角矩阵∑^[j，i]的对角元素：(1.4) Determine the diagonal elements of the sending node power distribution diagonal matrix Σ ^{[j, i]} :

设发送用户节点功率分配矩阵∑^[j，i]的第k个对角元素为设定用户节点i的发送信号x_i满足功率约束条件为 $E {tr (x_{i} x_{i}^{H})} P_{i}, i &Element; {1,2,3},$ 即Let the kth diagonal element of the sending user node power allocation matrix Σ ^{[j, i]} be It is assumed that the transmitted signal x _i of user node i satisfies the power constraint condition as $E. {tr (x_{i} x_{i}^{h})} P_{i}, i &Element; {1,2,3},$ Right now

$tr tr {{{Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{33} {V V}^{[[j j,, i i]]} {V V}_{[[π π ((j j,, i i))]]} {Σ Σ}^{[[j j,, i i]]} {(({V V}^{[[j j,, i i]]} {V V}_{[[π π ((j j,, i i))]]} {Σ Σ}^{[[j j,, i i]]}))}^{H h}}}$

$= = {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{33} {Σ Σ}_{k k = = 11}^{M m / / 22} {w w}_{k k}^{[[j j,, i i]]} | | | | {\overset{~ ~}{v v}}_{k k}^{[[j j,, i i]]} | | | | \leq \leq {P P}_{i i}$

式中，符号E表示求期望，tr表示求矩阵的迹，V^[j，i]表示信号空间对齐矩阵，V_[π(j，i)]表示原始信号向量s^[j，i]的附加预编码矩阵，表示矩阵V^[j，i]V_[π(j，i)]的第k列，||·||表示求向量的欧几里德范数，是原始信号向量s^[j，i]的第k个数据流的功率；In the formula, the symbol E represents the expectation, tr represents the trace of the matrix, V ^{[j, i]} represents the signal space alignment matrix, and V _{[π(j, i)]} represents the additional prediction of the original signal vector s ^{[j, i].} encoding matrix, Indicates the k-th column of the matrix V ^{[j, i]} V _{[π(j, i)]} , ||·|| indicates the Euclidean norm of the vector, is the power of the kth data stream of the original signal vector s ^[j,i] ;

根据原始信号向量s^[j，i]，j∈{1，2，3}，j≠i中每个数据流采用平均功率分配的条件：得到发送节点功率分配矩阵∑^[j，i]的第k个对角元素为： $w_{k}^{[j, i]} = \sqrt{P_{i} / (M {| | {\tilde{v}}_{k}^{[j, i]} | |}^{2})},$ k∈{1，2，…，M/2}。According to the original signal vector s ^{[j, i]} , j ∈ {1, 2, 3}, each data stream in j≠i adopts the condition of average power distribution: The kth diagonal element of the sending node power allocation matrix Σ ^{[j, i]} is obtained as: $w_{k}^{[j, i]} = \sqrt{P_{i} / (m {| | {\tilde{v}}_{k}^{[j, i]} | |}^{2})},$ k ∈ {1, 2, ..., M/2}.

步骤2，用户节点向中继节点发送信号。Step 2, the user node sends a signal to the relay node.

式中，s^[r，1]＝∑^[2，1]s^[2，1]+∑^[1，2]s^[1，2]表示用户节点1与用户节点2的对齐信号，s^[r，2]＝∑^[3，1]s^[3，1]+∑^[1，3]s^[1，3]表示用户节点1与用户节点3的对齐信号，s^[r，3]＝∑^[3，2]s^[3，2]+∑^[2，3]s^[2，3]表示用户节点2与用户节点3的对齐信号，U₁＝H^[r，1]V^[2，1]＝H^[r，2]V^[1，2]表示信道矩阵H^[r，1]与信道矩阵H^[r，2]的列空间的交空间，U₂＝H^[r，1]V^[3，1]＝H^[r，3]V^[1，3]表示信道矩阵H^[r，1]与信道矩阵H^[r，3]的列空间的交空间，U₃＝H^[r，2]V^[3，2]＝H^[r，3]V^[2，3]表示信道矩阵H^[r，2]与信道矩阵H^[r，3]的列空间的交空间，n_r是N×1的噪声向量，该向量的每个元素是均值为零、方差为的相互独立的复高斯随机变量。In the formula, s ^{[r, 1]} = ∑ ^{[2, 1]} s ^{[2, 1]} + ∑ ^{[1, 2]} s ^{[1, 2]} represents the alignment signal between user node 1 and user node 2, s ^{[r , 2]} = ∑ ^{[3, 1]} s ^{[3, 1]} + ∑ ^{[1, 3]} s ^{[1, 3]} represents the alignment signal between user node 1 and user node 3, s ^{[r, 3]} = ∑ ^{[ 3, 2]} s ^{[3, 2]} + ∑ ^{[2, 3]} s ^{[2, 3]} represents the alignment signal between user node 2 and user node 3, U ₁ = H ^{[r, 1]} V ^{[2, 1]} =H ^{[r, 2]} V ^{[1, 2]} represents the intersection space of the channel matrix H ^{[r, 1]} and the column space of the channel matrix H ^{[r, 2]} , U ₂ =H ^{[r, 1]} V ^{[3 , 1]} = H ^{[r, 3]} V ^{[1, 3]} represents the intersection space of the channel matrix H ^{[r, 1]} and the column space of the channel matrix H ^{[r, 3]} , U ₃ = H ^{[r, 2]} V ^{[3, 2]} = H ^{[r, 3]} V ^{[2, 3]} represents the intersection space of the channel matrix H ^{[r, 2]} and the column space of the channel matrix H ^{[r, 3]} , n _r is N×1 A noise vector of , each element of which is zero mean and variance Independent complex Gaussian random variables of .

步骤3，中继节点对接收信号进行预编码。Step 3, the relay node precodes the received signal.

(3.1)中继节点r对接收信号y_r中包含的对齐信号s^[r，1]、s^[r，2]和s^[r，3]进行分离，用s^[r，1]的M/2×N维分离矩阵H₁乘以y_r，满足H₁[U₂ U₃]＝0_M/2×M，得到第一个分离后的对齐信号y^[r，1]＝H₁y_r＝H₁U₁W₁s^[r，1]+H₁n_r，0_M/2×M表示M/2×M的全零矩阵，类似地，选择s^[r，2]，s^[r，3]的分离矩阵H₂，H₃，分别满足H₂[U₁ U₃]＝0_M/2×M，H₃[U₁ U₂]＝0_M/2×M，得到第二个和第三个分离后的对齐信号：(3.1) The relay node r separates the alignment signals s ^{[r, 1]} , s ^{[r, 2]} and s ^{[r, 3]} ^contained in the received signal _yr , and uses the M/ The 2×N-dimensional separation matrix H ₁ is multiplied by y _r , satisfying H ₁ [U ₂ U ₃ ]=0 _M/2×M , and the first separated alignment signal y ^{[r, 1]} = H ₁ y _r =H ₁ U ₁ W ₁ s ^{[r, 1]} +H ₁ n _r , 0 _M/2×M means an all-zero matrix of M/2×M, similarly, select s ^{[r, 2]} , s ^{[r , 3]} the separation matrices H ₂ , H ₃ respectively satisfy H ₂ [U ₁ U ₃ ]=0 _M/2×M , H ₃ [U ₁ U ₂ ]=0 _M/2×M , get the second and the third detached alignment signal:

y^[r，2]＝H₂y_r＝H₂U₂W₂s^[r，2]+H₂n_r，y^[r，3]＝H₃y_r＝H₃U₃W₃s^[r，3]+H₃n_r；y ^{[r, 2]} = H ₂ y _r = H ₂ U ₂ W ₂ s ^{[r, 2]} + H ₂ n _r , y ^{[r, 3]} = H ₃ y _r = H ₃ U ₃ W ₃ s ^{[ r, 3]} +H ₃ n _r ;

(3.2)对分离后得到的对齐信号y^[r，i]，i∈{1，2，3}进行预编码：(3.2) Pre-encode the alignment signal y ^{[r, i]} obtained after separation, i ∈ {1, 2, 3}:

(3.2a)设分离后的对齐信号y^[r，i]，i∈{1，2，3}的附加预编码矩阵为U^[i，r]，该矩阵按如下方式得到：(3.2a) Let the separated aligned signal y ^{[r, i]} , the additional precoding matrix for i ∈ {1, 2, 3} be U ^{[i, r]} , which is obtained as follows:

将矩阵H_iU_i，i∈{1，2，3}进行奇异值分解，得到式中，H_i表示对齐信号s^[r，i]的分离矩阵，U_i表示对应的用户节点到中继节点的一对信道矩阵的列空间的交空间，上标H表示共轭转置，U_[i]和V_[i]是M/2×M/2的酉矩阵，∑_[i]是M/2×M/2的对角阵；Singular value decomposition is performed on the matrix H _i U _i , i∈{1, 2, 3} to obtain In the formula, H _i represents the separation matrix of the alignment signal s ^{[r, i]} , U _i represents the intersection space of the column space of a pair of channel matrices from the corresponding user node to the relay node, and the superscript H represents the conjugate transpose, U _[i] and V _[i] are unitary matrices of M/2×M/2, and ∑ _[i] is a diagonal matrix of M/2×M/2;

根据上述奇异值分解得到的酉矩阵U_[i]，选择中继节点附加预编码矩阵为： $U^{[i, r]} = U_{[i]}^{H}, i &Element; {1,2,3} .$ According to the unitary matrix U _[i] obtained by the above singular value decomposition, the additional precoding matrix of the selected relay node is: $u^{[i, r]} = u_{[i]}^{h}, i &Element; {1,2,3} .$

(3.2b)设分离后的对齐信号y^[r，i]，i∈{1，2，3}的干扰消除矩阵为V^[i，r]，该矩阵根据信道矩阵H^[j，r]按如下方式之一确定：(3.2b) Let the separated alignment signal y ^{[r, i]} , the interference cancellation matrix of i ∈ {1, 2, 3} be V ^{[i, r]} , the matrix is according to the channel matrix H ^{[j, r]} according to Determined in one of the following ways:

方式1，设干扰消除矩阵V^[1，r]的第k列为k∈{1，2，…，M/2}，根据干扰消除矩阵V^[1，r]需要满足的条件：将V^[1，r]的M/2个列向量的求解等价于求解下面的方程：Mode 1, set the k-th column of the interference cancellation matrix V ^{[1, r]} as k ∈ {1, 2, ..., M/2}, according to the conditions that the interference cancellation matrix V ^{[1, r]} needs to satisfy: Solving the M/2 column vectors of V ^[1,r] is equivalent to solving the following equation:

${H h}^{[[33,, r r]]} {v v}_{k k}^{[[11,, r r]]} = = 00_{M m \times \times 11},, - - - - - - 11))$

求解上述方程1)得到M/2个解，将这M/2个解化为两两正交的单位向量作为V^[1，r]的M/2个列，式中，0_M×1表示M×1的全零向量；Solve the above equation 1) to get M/2 solutions, and turn these M/2 solutions into pairwise orthogonal unit vectors as M/2 columns of V ^{[1, r]} . In the formula, 0 _M×1 means M×1 all-zero vector;

方式2，设干扰消除矩阵V^[2，r]的第k列为k∈{1，2，…，M/2}，根据干扰消除矩阵V^[2，r]需要满足的条件：将对V^[2，r]的M/2个列向量的求解等价于求解下面的方程：Mode 2, set the kth column of the interference cancellation matrix V ^{[2, r]} as k ∈ {1, 2, ..., M/2}, according to the conditions that the interference cancellation matrix V ^{[2, r]} needs to satisfy: Solving the M/2 column vectors of V ^[2,r] is equivalent to solving the following equation:

${H h}^{[[22,, r r]]} {v v}_{k k}^{[[22,, r r]]} = = 00_{M m \times \times 11},, - - - - - - 22))$

求解上述方程2)得到M/2个解，将这M/2个解化为两两正交的单位向量作为V^[2，r]的M/2个列；Solve the above equation 2) to obtain M/2 solutions, and convert these M/2 solutions into pairwise orthogonal unit vectors as M/2 columns of V ^{[2, r]} ;

方式3，设干扰消除矩阵V^[3，r]的第k列为k∈{1，2，…，M/2}，根据干扰消除矩阵V^[3，r]需要满足的条件：将V^[3，r]的M/2个列向量的求解等价于求解下面的方程：Mode 3, set the kth column of the interference cancellation matrix V ^{[3, r]} as k ∈ {1, 2, ..., M/2}, according to the conditions that the interference cancellation matrix V ^{[3, r]} needs to satisfy: Solving the M/2 column vectors of V ^[3,r] is equivalent to solving the following equation:

${H h}^{[[11,, r r]]} {v v}_{k k}^{[[33,, r r]]} = = 00_{M m \times \times 11},, - - - - - - 33))$

求解上述方程3)得到M/2个解，将这M/2个解化为两两正交的单位向量作为V^[3，r]的M/2个列。Solve the above equation 3) to obtain M/2 solutions, and convert these M/2 solutions into pairwise orthogonal unit vectors as M/2 columns of V ^{[3, r]} .

(3.2c)设分离后的对齐信号y^[r，i]，i∈{1，2，3}的功率分配对角矩阵为∑^[i，r]，该矩阵按如下方式得到：(3.2c) Let the separated alignment signal y ^{[r, i]} , i ∈ {1, 2, 3} power distribution diagonal matrix be ∑ ^{[i, r]} , the matrix can be obtained as follows:

首先，设中继节点的功率分配对角矩阵∑^[i，r]的第k个对角元素为i∈{1，2，3}，k∈{1，2，…M/2}，根据中继节点的发送信号为：First, let the kth diagonal element of the relay node’s power allocation diagonal matrix ∑ ^[i,r] be i∈{1, 2, 3}, k∈{1, 2,...M/2}, according to the signal sent by the relay node:

${x x}_{r r} = = {Σ Σ}_{i i = = 11}^{33} {V V}^{[[i i,, r r]]} {Σ Σ}^{[[i i,, r r]]} {Σ Σ}_{[[i i]]} {s the s}^{[[r r,, i i]]} + + {Σ Σ}_{i i = = 11}^{33} {V V}^{[[i i,, r r]]} {Σ Σ}^{[[i i,, r r]]} {U u}_{[[i i]]}^{H h} {H h}_{i i} {n no}_{r r}$

记表示中继节点发送信号x_r中的有用信号；remember Indicates the useful signal in the signal x _r sent by the relay node;

其次，设有用信号的功率为表示为：Second, there is a signal The power is Expressed as:

${P P}_{{x x}_{r r}^{s the s}} = = E E. {{tr tr (({x x}_{r r}^{s the s} {(({x x}_{r r}^{s the s}))}^{H h}))}}$

$= = {Σ Σ}_{i i = = 11}^{33} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{33} {Σ Σ}_{k k = = 11}^{M m / / 22} {(({α α}_{k k}^{[[π π ((j j,, i i)),, r r]]} {β β}_{[[k k,, π π ((j j,, i i))]]}))}^{22} {{{(({w w}_{k k}^{[[j j,, i i]]}))}^{22} + + {(({w w}_{k k}^{[[i i,, j j]]}))}^{22}}}$

式中，上标H表示共轭转置，符号tr表示求矩阵的迹，β_{[k，π(j，i)}，π(j，i)∈{1，2，3}，j≠i，k∈{1，2，…，M/2}表示矩阵∑_[π(j，i)]的第k个对角元素，j，i∈{1，2，3}，j≠i，k∈{1，2，…，M/2}表示用户节点功率分配矩阵∑^[j，i]的第k个对角元素；In the formula, the superscript H represents the conjugate transpose, the symbol tr represents the trace of the matrix, β _{[k, π(j, i)} , π(j, i) ∈ {1, 2, 3}, j≠i, k ∈ {1, 2, ..., M/2} represents the kth diagonal element of the matrix Σ _{[π(j, i)]} , j, i ∈ {1, 2, 3}, j ≠ i, k ∈ {1, 2, ..., M/2} represents the kth diagonal element of the user node power allocation matrix ∑ ^{[j, i]} ;

最后，设有用信号包含的3M/2个数据流的功率均为λ²，根据中继节点发送信号x_r满足的功率约束条件：求得λ的值；根据关系式：Finally, there is a signal The power of the included 3M/2 data streams is λ ² , according to the power constraint condition that the relay node sends the signal x _r to meet: Obtain the value of λ; according to the relational expression:

${(({α α}_{k k}^{[[π π ((j j,, i i)),, r r]]} {β β}_{[[k k,, π π ((j j,, i i))]]}))}^{22} {{{(({w w}_{k k}^{[[1,2 1,2]]}))}^{22} + + {(({w w}_{k k}^{[[2,1 2,1]]}))}^{22}}} = = {λ λ}^{22}$

得到中继节点处功率分配矩阵∑^{[π(j，i)，r]}，π(j，i)∈{1，2，3}的对角元素值k∈{1，2，…M/2}为：Get the diagonal element values of the power allocation matrix ∑ ^{[π(j, i), r]} at the relay node, π(j, i) ∈ {1, 2, 3} k ∈ {1, 2, ... M/2} is:

${α α}_{k k}^{[[π π ((j j,, i i)),, r r]]} = = \frac{λ λ}{{β β}_{[[k k,, π π ((j j,, i i))]]} \sqrt{{{{(({w w}_{k k}^{[[j j,, i i]]}))}^{22} + + {(({w w}_{k k}^{[[j j,, i i]]}))}^{22}}}}} - - - - - - ((a a))$

根据上述公式(a)，可分别得到功率分配对角矩阵∑^[1，r]的第k个对角元素为：According to the above formula (a), the kth diagonal element of the power distribution diagonal matrix ∑ ^{[1, r]} can be obtained as:

${α α}_{k k}^{[[11,, r r]]} = = \frac{λ λ}{{β β}_{[[k k,, 11]]} \sqrt{{{{(({w w}_{k k}^{[[2,1 2,1]]}))}^{22} + + {(({w w}_{k k}^{[[1,2 1,2]]}))}^{22}}}}},, k k &Element; &Element; {{1,2 1,2,, . . . . . . M m / / 22}},,$

功率分配对角矩阵∑^[2，r]的第k个对角元素为：The kth diagonal element of the power distribution diagonal matrix Σ ^[2,r] is:

${α α}_{k k}^{[[22,, r r]]} = = \frac{λ λ}{{β β}_{[[k k,, 22]]} \sqrt{{{{(({w w}_{k k}^{[[3,1 3,1]]}))}^{22} + + {(({w w}_{k k}^{[[1,3 1,3]]}))}^{22}}}}},, k k &Element; &Element; {{1,2 1,2,, . . . . . . M m / / 22}},,$

功率分配对角矩阵∑^[3，r]的第k个对角元素为：The kth diagonal element of the power distribution diagonal matrix Σ ^[3,r] is:

${α α}_{k k}^{[[33,, r r]]} = = \frac{λ λ}{{β β}_{[[k k,, 33]]} \sqrt{{{{(({w w}_{k k}^{[[33,, 22]]}))}^{22} + + {(({w w}_{k k}^{[[22,, 33]]}))}^{22}}}}},, k k &Element; &Element; {{1,2 1,2,, . . . . . . M m / / 22}} . .$

(3.2d)将步骤(3.2a)-(3.2c)中得到的中继节点附加预编码矩阵U^[i，r]，干扰消除矩阵V^[i，r]，以及中继节点功率分配对角矩阵∑^[i，r]，i∈{1，2，3}与分离后的对齐信号y^[r，i]，i∈{1，2，3}相乘，得到中继节点r的N×1的发送信号： (3.2d) Additional precoding matrix U ^{[i, r]} , interference cancellation matrix V ^{[i, r]} , and relay node power allocation diagonal obtained in steps (3.2a)-(3.2c) The matrix ∑ ^{[i, r]} , i ∈ {1, 2, 3} is multiplied with the separated alignment signal y ^{[r, i]} , i ∈ {1, 2, 3} to obtain the N× 1's send signal:

步骤4，中继节点广播发送信号。Step 4, the relay node broadcasts and sends the signal.

式中n_i是M×1的噪声向量，该向量的每个元素是均值为零、方差为的相互独立的复高斯随机变量，H^[i，r]是中继节点到用户节点i的M×N的信道矩阵，该矩阵的每个元素是服从均值为零、方差为1的相互独立的复高斯随机变量。In the formula, n _i is a noise vector of M×1, and each element of this vector has a mean value of zero and a variance of The mutually independent complex Gaussian random variables, H ^{[i, r]} is the M×N channel matrix from the relay node to the user node i, and each element of this matrix is mutually independent Complex Gaussian random variable.

步骤5，用户节点恢复数据。Step 5, the user node restores data.

本发明的效果可以通过以下仿真进一步说明：Effect of the present invention can be further illustrated by following simulation:

1.仿真条件：1. Simulation conditions:

设定多输入多输出Y信道的每个用户节点和中继节点配置的天线数分别为：M＝6，N＝9，设每个用户节点和中继节点处的噪声方差均为σ²，即定义用户节点i，i∈{1，2，3}和中继节点r的信噪比分别为： $SNR (i) = \frac{P_{i}}{σ^{2}}, SNR (r) = \frac{P_{r}}{σ^{2}} .$ The number of antennas configured by each user node and relay node of the MIMO Y channel is set to be: M=6, N=9, and the noise variance at each user node and relay node is σ ² , Right now Define the SNR of user node i, i∈{1, 2, 3} and relay node r as: $SNR (i) = \frac{P_{i}}{σ^{2}}, SNR (r) = \frac{P_{r}}{σ^{2}} .$

2.仿真内容2. Simulation content

(a)在固定中继处的信噪比SNR(r)＝15dB的条件下，比较等功率条件下本发明所提出的信号传输方法和现有信号传输方法的可达和速率，仿真结果如图3所示，图3中的横坐标表示用户节点的信噪比，纵坐标表示多输入多输出Y信道的可达和速率，和速率的单位为bits/trans，即每传输一次所能发送的比特数。(a) Under the condition of the signal-to-noise ratio SNR (r)=15dB at the fixed relay place, compare the signal transmission method proposed by the present invention and the reachability and rate of the existing signal transmission method under equal power conditions, the simulation results are as follows As shown in Figure 3, the abscissa in Figure 3 represents the signal-to-noise ratio of the user node, and the ordinate represents the reachable sum rate of the multi-input multi-output Y channel, and the unit of the sum rate is bits/trans, that is, each transmission can send the number of bits.

图3中两条曲线表示的意义如下：The meanings of the two curves in Figure 3 are as follows:

“现有方法”表示等功率条件下的现有信号传输方法，“本发明”表示本发明所提出的信号传输方法。"Existing method" means the existing signal transmission method under equal power conditions, and "the present invention" means the signal transmission method proposed by the present invention.

由图3可以看出，在固定中继处的信噪比的条件下，本发明所提出的信号传输方法比现有的信号传输方法的可达和速率有明显的提高，且随着用户节点处信噪比的增加，改善更加明显，在信噪比为20dB时，本发明的和速率比现有信号传输方法大约增加4比特。It can be seen from Figure 3 that under the condition of a fixed SNR at the relay, the signal transmission method proposed by the present invention has significantly improved reachability and rate compared with the existing signal transmission method, and as the user node The increase of the signal-to-noise ratio is more obvious, and when the signal-to-noise ratio is 20dB, the sum rate of the present invention increases by about 4 bits compared with the existing signal transmission method.

(b)在固定每个用户节点的信噪比SNR(i)＝15dB，i∈{1，2，3}的条件下，比较等功率条件下本发明所提出的信号传输方法和现有信号传输方法的可达和速率，仿真结果如图4所示，图4中的横坐标表示中继节点的信噪比，纵坐标表示多输入多输出Y信道的可达和速率。(b) Under the condition of fixing the signal-to-noise ratio SNR(i)=15dB of each user node, i∈{1, 2, 3}, compare the signal transmission method proposed by the present invention and the existing signal under equal power conditions The reachability and rate of the transmission method, the simulation results are shown in Figure 4, the abscissa in Figure 4 represents the signal-to-noise ratio of the relay node, and the ordinate represents the reachability and rate of the MIMO Y channel.

图4中两条曲线表示的意义如下：The meanings of the two curves in Figure 4 are as follows:

由图4可以看出，在固定每个用户节点处的信噪比的条件下，本发明所提出的信号传输方法比现有的信号传输方法的可达和速率也有明显的增益，当和速率为10bits/trans时，本发明与现有信号传输方法相比，有4dB的增益。As can be seen from Fig. 4, under the condition of fixing the signal-to-noise ratio at each user node, the signal transmission method proposed by the present invention also has obvious gain compared with the reachable sum rate of the existing signal transmission method, when the sum rate When it is 10bits/trans, compared with the existing signal transmission method, the present invention has a gain of 4dB.

由图3、图4的仿真结果可以看出，在分别固定中继节点信噪比和固定用户节点信噪比的情况下，本发明所提出的信号传输方法的可达和速率均比现有信号传输方法的可达和速率有明显提高，这是因为本发明所提出的信号传输方法是在现有方法的基础上进行了附加预编，从而增加了预编码矩阵元素选择的多样性，因此可以得到更高的和速率。As can be seen from the simulation results of Fig. 3 and Fig. 4, in the case of fixing the SNR of the relay node and the SNR of the user node respectively, the reachability and rate of the signal transmission method proposed by the present invention are higher than that of the existing The reachability and rate of the signal transmission method are significantly improved, because the signal transmission method proposed by the present invention is additionally pre-programmed on the basis of the existing method, thereby increasing the diversity of precoding matrix element selection, so Higher sum rates can be obtained.

Claims

1. A signal transmission method based on network coding in a multi-input multi-output Y channel, comprising:

(1) The user node precodes the original signal

Each user node precodes the information sent to the other two user nodes, and the M×1-dimensional sending signal of the sending user node is obtained as:

x_{i} = Σ_{j = 1, j &NotEqual; i}^{3} V^{[j, i]} W_{π (j, i)} Σ^{[j, i]} {the s}^{[j, i]},

In the formula, i represents the sending user node, j represents the receiving user node, and i, j∈{1,2,3}, i≠j, M represents the number of antennas configured at the sending user node, and M is an even number, s ^{[ j,i]} is the original signal vector composed of M/2×1 data streams sent from the sending user node i to the receiving user node j, and each element of this vector is a mutually independent random variable with a mean value of zero and a variance of 1 , Σ ^[j,i] is the M/2×M/2 diagonal matrix for power allocation of transmitting nodes, W _π(j,i) is the additional precoding matrix of M/2×M/2 user nodes, subscript π( j,i) is an index function that satisfies π(i,j)=π(j,i), and π(1,2)=1, π(1,3)=2,π(2,3) = 3, so W _π(2,1) = W _π(1,2) = W ₁ , W _π(3,1) = W _π(1,3) = W ₂ , W _π(3,2) =W _π(2,3) ＝W ₃ , V ^[j,i] is M×M/2 signal space alignment matrix, satisfying H ^[r,i] V ^[j,i] ＝H ^[r,j] V ^[i,j] , H ^[r,i] represents the N×M channel matrix from user node i to relay node r, N represents the number of antennas configured at relay node r, and N=3M/2 , each element of the channel matrix is a mutually independent complex Gaussian random variable with a mean of zero and a variance of 1;

(2) The user node sends a signal to the relay node

The transmitting user node i sends the transmitted signal x _i obtained by precoding to the relay node r, and the N×1-dimensional received signal of the relay node is obtained as:

\begin{matrix} {y the y}_{r r} = = {Σ Σ}_{i i = = 11}^{33} {H h}^{[[r r,, i i]]} {x x}_{i i} + + {n no}_{r r} \\ = = {Σ Σ}_{i i = = 11}^{33} {H h}^{[[r r,, i i]]} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{33} {V V}^{[[j j,, i i]]} {W W}_{π π ((j j,, i i))} {Σ Σ}^{[[j j,, i i]]} {s the s}^{[[j j,, i i]]} + + {n no}_{r r} \\ = = {U u}_{11} {W W}_{11} {s the s}^{[[r r,, 11]]} + + {U u}_{22} {W W}_{22} {s the s}^{[[r r,, 22]]} + + {U u}_{33} {W W}_{33} {s the s}^{[[r r,, 33]]} + + {n no}_{r r} \end{matrix},,

In the formula, s ^[r,1] = Σ ^[2,1] s ^[2,1] + Σ ^[1,2] s ^[1,2] represents the alignment signal between user node 1 and user node 2,

s ^[r,2] = Σ ^[3,1] s ^[3,1] + Σ ^[1,3] s ^[1,3] represents the alignment signal between user node 1 and user node 3,

s ^[r,3 ]=Σ ^[3,2] s ^[3,2] +Σ ^[2,3] s ^[2,3] represents the alignment signal between user node 2 and user node 3,

U ₁ ＝H ^[r,1] V ^[2,1] ＝H ^[r,2] V ^[1,2] represents the relationship between the channel matrix H ^[r,1] and the column space of the channel matrix H ^[r,2] Intersecting space, U ₂ ＝H ^[r,1] V ^[3,1] ＝H ^[r,3] V ^[1,3] means the channel matrix H ^[r,1] and the channel matrix H ^[r,3] The intersection space of the column space, U ₃ ＝H ^[r,2 ]V ^[3,2] ＝H ^[r,3] V ^[2,3] represents the channel matrix H ^[r,2] and the channel matrix H ^{[r, 3]} in the intersection space of the column space, n _r is a noise vector of N×1, and each element of this vector has a mean value of zero and a variance of Independent complex Gaussian random variables of ;

(3) The relay node precodes the received signal

(3a) The relay node r separates the alignment signals s ^[r,1] , s ^[r,2] and s ^[r,3] ^contained in the received signal _yr , and uses the M/ The 2×N-dimensional separation matrix H ₁ is multiplied by y _r , satisfying H ₁ [U ₂ U ₃ ]=0 _M/2×M , and the first separated alignment signal y ^[r,1] = H ₁ y _r ＝H ₁ U ₁ W ₁ s ^[r,1] +H ₁ n _r , 0 _M/2×M means the all-zero matrix of M/2×M, similarly, choose s ^[r,2] , s ^{[r ,3]} separation matrices H ₂ , H ₃ , respectively satisfy H ₂ [U ₁ U ₃ ]=0 _M/2×M , H ₃ [U ₁ U ₂ ]=0 _M/2×M , get the second The separated alignment signal y ^[r,2] = H ₂ y _r = H ₂ U ₂ W ₂ s ^[r,2 ] + H ₂ n _r and the third separated alignment signal, y ^[r,3] =H ₃ y _r =H ₃ U ₃ W ₃ s ^[r,3] +H ₃ n _r ;

(3b) Precode the separated alignment signals y ^[r,1] , y ^[r,2] , y ^[r,3] to obtain N×1 transmission signals

x_{r} = Σ_{i = 1}^{3} V^{[i, r]} Σ^{[i, r]} u^{[i, r]} {the y}^{[r, i]},

In the formula, V ^{[i, r]} is the interference cancellation matrix, Σ ^{[i, r]} is the power distribution diagonal matrix of the relay node, and the values of its diagonal elements are according to the alignment signal s ^{[r, i]} , i=1 , Each data stream in 2 and 3 is determined by average power allocation, and U ^{[i, r]} is an additional precoding matrix for the relay node;

(4) The relay node broadcasts and sends the signal steps

The relay node r broadcasts the precoded transmission signal x _r to the user node, and the M×1-dimensional received signal of the user node i is obtained as: y _i =H ^[i,r] x _r +n _i ,i∈{ 1,2,3},

In the formula, n _i is a noise vector of M×1, and each element of this vector has a mean value of zero and a variance of The mutually independent complex Gaussian random variables, H ^[i,r] is the M×N channel matrix from the relay node to the user node i, and each element of this matrix is mutually independent complex Gaussian random variable;

(5) User node recovery data steps

User node i removes its own interference according to the received signal y _i and its own transmitted signal _xi , that is, subtracts the part of the signal formed after x _i passes through the channel from the received signal y _i ; then uses zero-forcing detection to restore user j The original signal s ^[i,j] sent to user i, j∈{1,2,3},j≠i;

The signal space alignment matrix V ^{[j, i]} in the step (1) is determined in one of the following ways according to the channel matrix H ^{[r, i]} and H ^{[r, j]} :

Method 1, assuming V ^[2,1] , V ^[1,2] and the k-th column of U ₁ are respectively u _k,1 ,k∈{1,2,…,M/2}, according to the signal space alignment matrix V ^[2,1] and V ^[1,2] need to meet the conditions: H ^[r,1] V ^{[ 2,1]} ＝H ^[r,2] V ^[1,2] ＝U ₁ , the solution of these three column vectors is equivalent to solving the following equation:

[\begin{matrix} {I I}_{N N} & - - {H h}^{[[r r,, 11]]} & 00_{N N \times \times M m} \\ {I I}_{N N} & 00_{N N \times \times M m} & - - {H h}^{[[r r,, 22]]} \end{matrix}] (\begin{matrix} {u u}_{k k,, 11} \\ {v v}_{k k}^{[[2,1 2,1]]} \\ {v v}_{k k}^{[[1,2 1,2]]} \end{matrix}) = = 00_{22 N N \times \times 11},, - - - - - - < < 11 > >

Solve the above equation <1> to get M/2 solutions, and turn these M/2 solutions into pairwise orthogonal unit vectors as U ₁ , V ^[2,1] , M/2 of V ^[1,2] In the formula, _IN represents N×N unit matrix, 0 _N×M represents N×M all-zero matrix, H ^[r,1] and H ^[r,2] represent user node 1 and user node 2 to the channel matrix of the relay node;

Method 2. Let V ^[3,1] , V ^[1,3] and the k-th column of U ₂ be u _k,2 ,k∈{1,2,…,M/2}, according to the signal space alignment matrix V ^[3,1] and V ^[1,3] need to meet the conditions: H ^[r,1] V ^{[ 3,1]} = H ^[r,3] V ^[1,3] = U ₂ , the solution of these three column vectors is equivalent to solving the following equation:

[\begin{matrix} {I I}_{N N} & - - {H h}^{[[r r,, 11]]} & 00_{N N \times \times M m} \\ {I I}_{N N} & 00_{N N \times \times M m} & - - {H h}^{[[r r,, 33]]} \end{matrix}] (\begin{matrix} {u u}_{k k,, 22} \\ {v v}_{k k}^{[[3,1 3,1]]} \\ {v v}_{k k}^{[[1,3 1,3]]} \end{matrix}) = = 00_{22 N N \times \times 11},, - - - - - - < < 22 > >

Solve the above equation <2> to get M/2 solutions, and turn these M/2 solutions into pairwise orthogonal unit vectors as U ₂ , V ^[3,1] , M/2 of V ^[1,3] In the formula, H ^[r,1] and H ^[r,3] respectively represent the channel matrix from user node 1 and user node 3 to the relay node;

Method 3, set the k-th column of V ^[3,2] , V ^[2,3] and U ₃ as u _k,3 ,k∈{1,2,…,M/2}, according to the signal space alignment matrix V ^[3,2] and V ^[2,3] need to meet the conditions:

H ^[r,2] V ^[3,2] = H ^[r,3] V ^[2,3] = U ₃

Solving these three column vectors is equivalent to solving the following equation:

[\begin{matrix} {I I}_{N N} & - - {H h}^{[[r r,, 22]]} & 00_{N N \times \times M m} \\ {I I}_{N N} & 00_{N N \times \times M m} & - - {H h}^{[[r r,, 33]]} \end{matrix}] (\begin{matrix} {u u}_{k k,, 33} \\ {v v}_{k k}^{[[3,2 3,2]]} \\ {v v}_{k k}^{[[2,3 2,3]]} \end{matrix}) = = 00_{22 N N \times \times 11},, - - - - - - < < 33 > >

Solve the above equation <3> to get M/2 solutions, and turn these M/2 solutions into pairwise orthogonal unit vectors as U ₃ , V ^[3,2] , M/2 of V ^[2,3] In the formula, H ^{[r, 2]} and H ^{[r, 3]} respectively represent the channel matrix from user node 2 and user node 3 to the relay node;

The interference cancellation matrix V ^{[i, r]} in the step (3b) is determined according to the channel matrix H ^{[j, r]} in one of the following ways:

Mode 1, set the k-th column of the interference cancellation matrix V ^{[1, r]} as k∈{1,2,…,M/2}, according to the conditions to be satisfied by the interference cancellation matrix V ^[1,r] :

span (v_{1}^{[1, r]}, . . ., v_{m / 2}^{[1, r]}) &Subset; null (h^{[3, r]}),

Solving the M/2 column vectors of V ^[1,r] is equivalent to solving the following equation:

{H h}^{[[33,, r r]]} {v v}_{k k}^{[[11,, r r]]} = = 00_{M m \times \times 11},, - - - - - - 11))

Solve the above equation 1) to get M/2 solutions, and convert these M/2 solutions into pairwise orthogonal unit vectors as M/2 columns of V ^{[1, r]} , where 0 _M×1 means M×1 all-zero vector;

Mode 2, set the k-th column of the interference cancellation matrix V ^{[2, r]} as k∈{1,2,…,M/2}, according to the conditions to be satisfied by the interference cancellation matrix V ^[2,r] :

span (v_{1}^{[2, r]}, . . ., v_{m / 2}^{[2, r]}) &Subset; null (h^{[2, r]}),

Solving the M/2 column vectors of V ^[2,r] is equivalent to solving the following equation:

{H h}^{[[22,, r r]]} {v v}_{k k}^{[[22,, r r]]} = = 00_{M m \times \times 11},, - - - - - - 22))

Solve the above equation 2) to obtain M/2 solutions, and convert these M/2 solutions into pairwise orthogonal unit vectors as M/2 columns of V ^{[2, r]} ;

Mode 3, set the k-th column of the interference cancellation matrix V ^{[3, r} ] as k∈{1,2,…,M/2}, according to the conditions to be satisfied by the interference cancellation matrix V ^[3,r] :

span (v_{1}^{[3, r]}, . . ., v_{m / 2}^{[3, r]}) &Subset; null (h^{[1, r]}),

Solving the M/2 column vectors of V ^[3,r] is equivalent to solving the following equation:

{H h}^{[[11,, r r]]} {v v}_{k k}^{[[33,, r r]]} = = 00_{M m \times \times 11},, - - - - - - 33))

Solve the above equation 3) to obtain M/2 solutions, and transform these M/2 solutions into pairwise orthogonal unit vectors as M/2 columns of V ^[3,r] .

2. the signal transmission method based on network coding in the MIMO Y channel according to claim 1, wherein the additional precoding matrix _Wi of the user node in the step (1) is determined in the following manner:

Decompose the matrix H _i U _i ,i∈{1,2,3} into singular value, and get In the formula, H _i represents the separation matrix of the alignment signal s ^{[r, i]} , U _i represents the intersection space of the column space of a pair of channel matrices from the corresponding user node to the relay node, and the superscript H represents the conjugate transpose, U _[i] and V _[i] are unitary matrices of M/2×M/2, Σ _[i] is a diagonal matrix of M/2×M/2,

According to the unitary matrix V _[i] obtained by the above singular value decomposition, the additional precoding matrix of the selected user node is: W _i =V _[i] , i∈{1,2,3}.

3. the signal transmission method based on network coding in the MIMO Y channel according to claim 1, wherein the diagonal element of the sending node power allocation matrix Σ ^{[j, i]} in the step (1) is Determined as follows:

Let the kth diagonal element of the sending user node power allocation matrix Σ ^[j,i] be k∈{1,2,…,M/2}, set the transmission signal x _i of user node i to satisfy the power constraint condition as

E. {tr (x_{i} x_{i}^{h})} \leq P_{i}, i &Element; {1,2,3},

Right now

\begin{matrix} tr tr {{{Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{33} {V V}^{[[j j,, i i]]} {V V}_{[[π π ((j j,, i i))]]} {Σ Σ}^{[[j j,, i i]]} {(({V V}^{[[j j,, i i]]} {V V}_{[[π π ((j j,, i i))]]} {Σ Σ}^{[[j j . . i i]]}))}^{H h}}} \\ = = {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{33} {Σ Σ}_{k k = = 11}^{M m / / 22} {(({w w}_{k k}^{[[j j,, i i]]}))}^{22} {| | | | {\overset{~ ~}{v v}}_{k k}^{[[j j,, i i]]} | | | |}^{22} \leq \leq {P P}_{i i} \end{matrix}

In the formula, the symbol E represents the expectation, tr represents the trace of the matrix, V ^{[j, i]} represents the signal space alignment matrix, and V _{[π(j, i)]} represents the additional prediction of the original signal vector s ^{[j, i].} encoding matrix, Indicates the k-th column of the matrix V ^[j,i] V _[π(j,i)] , ||·|| indicates the Euclidean norm of the vector, is the power of the kth data stream of the original signal vector s ^[j,i] ;

According to the original signal vector s ^[j,i] ,j∈{1,2,3}, each data stream in j≠i adopts the condition of average power distribution: The kth diagonal element of the sending user node power allocation matrix Σ ^{[j, i]} is obtained as

w_{k}^{[j, i]} = \sqrt{P_{i} / (m {| | {\tilde{v}}_{k}^{[j, i]} | |}^{2})}, k &Element; {1,2, . . ., m / 2} .

4. The signal transmission method based on network coding in the MIMO Y channel according to claim 1, wherein the relay node in the step (3b) adds a precoding matrix U ^{[i, r]} as follows Sure:

Decompose the matrix H _i U _i ,i∈{1,2,3} into singular value, and get In the formula, H _i represents the separation matrix of the alignment signal s ^{[r, i]} , U _i represents the intersection space of the column space of a pair of channel matrices from the corresponding user node to the relay node, and the superscript H represents the conjugate transpose, U _[i] and V _[i] are unitary matrices of M/2×M/2, and Σ _[i] is a diagonal matrix of M/2×M/2;

According to the unitary matrix U _[i] obtained by the above singular value decomposition, the additional precoding matrix of the selected relay node is:

u^{[i, r]} = u_{[i]}^{h}, i &Element; {1,2,3} .

5. the signal transmission method based on network coding in the MIMO Y channel according to claim 1, wherein the value of the diagonal element described in the step (3b) is according to the alignment signal s ^{[r, i]} , i= Each data stream in 1, 2, and 3 is determined by the average power allocation, as follows:

First, let the power allocation matrix Σ ^[i,r] of the relay node, the kth diagonal element of i∈{1,2,3} be i∈{1,2,3}, k∈{1,2,...M/2}, according to the signal sent by the relay node:

{x x}_{r r} = = {Σ Σ}_{i i = = 11}^{33} {V V}^{[[i i,, r r]]} {Σ Σ}^{[[i i,, r r]]} {Σ Σ}_{[[i i]]} {s the s}^{[[r r,, i i]]} + + {Σ Σ}_{i i = = 11}^{33} {V V}^{[[i i,, r r]]} {Σ Σ}^{[[i i,, r r]]} {U u}_{[[i i]]}^{H h} {H h}_{i i} {n no}_{r r}

remember

x_{r}^{the s} = Σ_{i = 1}^{3} V^{[i, r]} Σ^{[i, r]} Σ_{[i]} {the s}^{[r, i]},

Indicates the useful signal in the signal x _r sent by the relay node;

Second, there is a signal The power is Expressed as:

\begin{matrix} {P P}_{{x x}_{r r}^{s the s}} = = E E. {{tr tr (({x x}_{r r}^{s the s} {(({x x}_{r r}^{s the s}))}^{H h}))}} \\ = = {Σ Σ}_{i i = = 11}^{33} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{33} {Σ Σ}_{k k = = 11}^{M m / / 22} {(({α α}_{k k}^{[[π π ((j j,, i i)),, r r]]} {β β}_{[[k k,, π π ((j j,, i i))]]}))}^{22} {{{(({w w}_{k k}^{[[j j,, i i]]}))}^{22} + + {(({w w}_{k k}^{[[j j,, i i]]}))}^{22}}} \end{matrix}

In the formula, the superscript H represents the conjugate transpose, the symbol tr represents the trace of the matrix, β _[k,π(j,i)] , π(j,i)∈{1,2,3},j≠i , k∈{1,2,...,M/2} represents the kth diagonal element of the matrix Σ _[π(j,i)] , j,i∈{1,2,3},j≠i,k∈{1,2,...,M/2} represents the kth diagonal element of the user node power distribution diagonal matrix Σ ^[j,i] ;

Finally, there is a signal The power of the included 3M/2 data streams is λ ² , according to the power constraint condition that the relay node sends the signal x _r to meet: Obtain the value of λ; according to the relation

{(({α α}_{k k}^{[[π π ((j j,, i i)),, r r]]} {β β}_{[[k k,, π π ((j j,, i i))]]}))}^{22} {{{(({w w}_{k k}^{[[1,2 1,2]]}))}^{22} + + {(({w w}_{k k}^{[[2,1 2,1]]}))}^{22}}} = = {λ λ}^{22}

Get the diagonal element values of the power allocation matrix Σ ^[π(j,i),r] at the relay node, π(j,i)∈{1,2,3} for:

{α α}_{k k}^{[[π π ((j j,, i i)),, r r]]} = = \frac{λ λ}{{β β}_{[[k k,, π π ((j j,, i i))]]} \sqrt{{{{(({w w}_{k k}^{[[j j,, i i]]}))}^{22} + + {(({w w}_{k k}^{[[j j,, i i]]}))}^{22}}}}},, k k &Element; &Element; {{1,2 1,2,, . . . . . .,, M m / / 22}} . .