CN101741448A - Information transmission method based on minimum mean square error beamforming in bidirectional channel - Google Patents

Abstract

The invention discloses a minimum mean square error beam forming-based information transmission method in a two-way channel, belongs to the technical field of wireless communication, and mainly solves the problem of high technical complexity of the prior art. Particularly, the invention provides the information transmission method capable of improving channel capacity and error ratio performance, and reducing complexity at the same time by aiming at a wireless communication network of two source nodes and a relay node. The method comprises the following steps that: the two source nodes simultaneously send encoding information to the relay node; the relay node builds a beam forming matrix according to a minimum mean square error rule; the relay node carries out beam forming processing on the received source node mixed information, and then broadcasts the source node mixed information after the beam forming processing to the source nodes; and the source nodes are decoded to acquire information of other parts. The method reduces the complexity and ensures the correctness of transmission without great influence on system performance, and can be used for reliable information transmission in a two-way relay system.

Description

Information transmission method based on minimum mean square error beamforming in bidirectional channel

technical field

The invention belongs to the technical field of wireless communication, and relates to network coding and beam forming, in particular to a wireless communication network of two source nodes and a relay node, which can be used to improve channel capacity and bit error rate performance.

Background technique

Using relays to help mobile users forward data can obtain additional diversity gain and improve the bit error BER performance of the receiving end. It is one of the effective means to improve the call quality of mobile users at the edge of the cell. For the wireless two-way relay channel shown in Figure 1, when two source nodes exchange information through a relay node, four time slots are usually required, that is, two source nodes respectively occupy one time slot to communicate with the relay node. The relay node occupies two time slots and forwards data for the two source nodes respectively.

As a design scheme in modern communication networks, network coding allows network nodes to perform certain linear or non-linear coding on signals received by multiple links before forwarding, reducing the number of data packet transmissions, improving network throughput, and enhancing The fault tolerance and robustness of the network provide an effective method for improving the transmission efficiency of the two-way relay channel. Especially in wireless networks, due to its broadcast characteristics in wireless transmission, it can make better use of network coding, and more effectively solve the interference problem in wireless networks.

Usually, four time slots are required to exchange information. By using network coding at the relay node, we can complete an exchange within three time slots. The basic principle is that two source nodes occupy one time slot respectively to communicate with the relay node. , and then the relay node will decode and obtain the data information of the two source nodes, perform modulo 2 operation, and then re-encode and forward. It takes three time slots to exchange a data packet. Using TWRC based on analog network coding ANC can be used in two This process is completed within the time slot, the source node sends information to the relay at the same time, and then the relay performs amplification and forwarding operations, thus realizing the exchange of information between the two source nodes.

The beamforming method in the wireless communication network designs the beamforming matrix according to the state of the fading channel, and uses the beamforming matrix to preprocess the transmitted signal to eliminate inter-channel interference, improve the transmission performance in the multipath fading channel, and the capacity of the two-way relay channel is optimal The beamforming method is different from the design in the traditional network. The beamforming matrix is designed based on the capacity limit of the system. Although the existing optimal beamforming method can meet the system capacity and eliminate the interference at the same time, it is more complicated. However, although the sub-optimal beamforming method reduces the complexity, the bit error rate performance is poor, which brings more error bits to the transmission process and affects the correctness of the transmission.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art, and proposes an information transmission method based on minimum mean square error beamforming in a two-way channel, so as to reduce the complexity of the beamforming matrix under the condition of limited relay power, Improve the bit error rate performance of the system, avoid erroneous bits during transmission, and ensure the correctness of transmission.

The present invention is achieved like this:

(1) Use Turbo code to encode the data information d ₁ and d ₂ of the two source nodes respectively to obtain the coded sequence x ₁ , x ₂ , modulate the coded sequence, and convert the modulated signal s ₁ (n) and s ₂ (n) are simultaneously sent to the relay node with power p ₁ and p ₂ ;

(2) The relay node constructs the beamforming matrix based on the minimum mean square error criterion:

(2a) Let H _UL = [h ₁ , h ₂ ], H _DL = [h ₂ , h ₁ ] ^T , h ₁ and h ₂ are the channels from the source node to the relay node respectively, and perform singular value decomposition on H _UL H _UL ＝U∑V ^H , U∈C ^M×2 , express the relay minimum mean square error beamforming matrix as A=U ^* BU ^H , B∈C ^2×2 ;

(2b) Construct the relay beamforming matrix using the minimum mean square error criterion:

The relay minimum mean square error beamforming matrix is constructed according to the receiver and transmitter expressions of the minimum mean square error criterion:

${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="MMSE"\; filenames="H2009102193421E0000031.png"\; state="\{\{state\}\}">MMSE</figure-callout></span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}\end{array}\right]{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}$

是最小均方误差接收机表达式，

是最小均方误差发射机表达式；where σ _n ² and σ _a ² are noise power and signal power respectively, a _MMSE and b _MMSE are two complex variables that need to be solved to construct the beamforming matrix, I is the complex identity matrix,

is the minimum mean square error receiver expression,

is the minimum mean square error transmitter expression;

和

分别对H_DL ^H和H_UL ^H进行分解，得到中继波束成型矩阵为：Using the singular value decomposition formula

and

The H _DL ^H and H _UL ^H are decomposed separately, and the relay beamforming matrix is obtained as:

${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{<span\; class="notranslate">\; *</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;V</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; V\&Sigma;U</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}$

make $B_{\mathrm{MMSE}}={\mathrm{\&Sigma;V}}^T{(h_{\mathrm{DL}}{h_{\mathrm{DL}}}^h+\frac{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout>}}^2}{{\mathrm{\&sigma;}}_a^2}I)}^{+}\left[\begin{array}{cc}0& a_{\mathrm{MMSE}}\\ b_{\mathrm{MMSE}}& 0\end{array}\right]{(h_{\mathrm{UL}}^h{h}_{\mathrm{UL}}+\frac{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout>}}^2}{{\mathrm{\&sigma;}}_a^2}I)}^{+}\mathrm{V\&Sigma;},$

Let A _MMSE = U ^* B _MMSE U ^H ;

In the formula, the B _MMSE matrix is obtained by solving the reachable rate of the source nodes S ₁ and S ₂ , U ^* is the conjugate matrix of U, and U ^H is the conjugate transpose matrix of U;

(3) Use the obtained minimum mean square error beamforming matrix to perform minimum mean square error beamforming on the mixed signal received by the relay node, expressed as x _R (n) = A _MMSE y _R (n), n = 1 ,..., N, where y _R (n) is the mixed information of the two source nodes received by the relay node;

(4) The relay node broadcasts the beamforming information x _R (n) to two source nodes in the second time slot, and the two source nodes subtract the self-interference from the received information respectively, and then solve the Call to obtain the information of the other source node, so as to realize the exchange of information between the source nodes within two time slots.

Compared with the prior art, the present invention has the following advantages:

1. Since the present invention uses reachable rate optimization to construct the minimum mean square error beamforming matrix at the relay node, it greatly reduces the complexity compared with the optimal beamforming method without causing a great impact on system performance, and at the same time The correctness of transmission is guaranteed.

2. Since the present invention adopts the minimum mean square error beamforming on the relay node, the relay node does not need to decode the transmission information of the two source nodes and directly amplifies and forwards, and can complete the two source nodes in two time slots The information interaction makes the throughput reach 1/2 symbol/user/symbol period, which improves the system throughput;

Description of drawings

Fig. 1 is the schematic diagram of existing wireless two-way relay communication network model;

Fig. 2 is the flow chart of information transmission of the present invention;

Fig. 3 is the flow chart of attainable rate optimization solution matrix B _MMSE of the present invention;

FIG. 4 is a comparison diagram of capacity domain performance in the present invention;

Fig. 5 is a comparison chart of bit error rate performance of the present invention.

Detailed ways

Referring to Figure 2, the information transmission method based on minimum mean square error beamforming in a two-way channel includes the following steps:

Step 1, two source nodes send information at the same time

Referring to Fig. 1, the data information d ₁ and d ₂ of the two source nodes are respectively coded by using Turbo codes to obtain coded sequences x ₁ , x ₂ , and the coded sequences are modulated, and the modulated signal s ₁ (n ) and s ₂ (n) are simultaneously sent to the relay node with power p ₁ and p ₂ .

Step 2, the relay node constructs the beamforming matrix

The relay node constructs the beamforming matrix according to the minimum mean square error criterion:

(2.1) Let the uplink channel H _UL = [h ₁ , h ₂ ], the downlink channel H _DL = [h ₂ , h ₁ ] ^T , h ₁ and h ₂ are the channels from the source node to the relay node respectively , perform singular value decomposition on the uplink channel H _UL H _UL = U∑V ^H , U∈C ^M×2 , express the relay minimum mean square error beamforming matrix as A _MMSE = U ^* B _MMSE U ^H , B _MMSE ∈ ^{C 2×2} ;

(2.2) Construct the relay minimum mean square error beamforming matrix according to the receiver and transmitter expressions of the minimum mean square error criterion:

${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="MMSE"\; filenames="H2009102193421E0000031.png"\; state="\{\{state\}\}">MMSE</figure-callout></span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}\end{array}\right]{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}$

where σ _n ² and σ _a ² are noise power and signal power respectively, a _MMSE and b _MMSE are two complex variables that need to be solved to construct the beamforming matrix, I is the complex identity matrix,

为已知基于最小均方误差的接收机表达式为，

It is known that the receiver expression based on the minimum mean square error is,

为已知基于最小均方误差的发射机表达式为，

The expression for the known transmitter based on the minimum mean square error is,

和对H_DL ^H和H_UL ^H分别进行分解，代入上述最小均方误差波束成型矩阵，将其转化为：(2.3) Using the singular value decomposition formula

and Decompose H _DL ^H and H _UL ^H respectively, substitute into the above minimum mean square error beamforming matrix, and transform it into:

${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{<span\; class="notranslate">\; *</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;V</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; V\&Sigma;U</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}$

make $B_{\mathrm{MMSE}}={\mathrm{\&Sigma;V}}^T{(h_{\mathrm{DL}}{h_{\mathrm{DL}}}^h+\frac{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout>}}^2}{{\mathrm{\&sigma;}}_a^2}I)}^{+}\left[\begin{array}{cc}0& a_{\mathrm{MMSE}}\\ b_{\mathrm{MMSE}}& 0\end{array}\right]{(h_{\mathrm{UL}}^h{h}_{\mathrm{UL}}+\frac{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="no"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">no</figure-callout>}}^2}{{\mathrm{\&sigma;}}_a^2}I)}^{+}\mathrm{V\&Sigma;},$

Let A _MMSE = U ^* B _MMSE U ^H ;

In the formula, U ^* is the conjugate matrix of U, U ^H is the conjugate transpose matrix of U, and the B _MMSE matrix is obtained by solving the attainable rates of source nodes S ₁ and S ₂ ;

(2.4) With reference to Fig. 3, optimize the B _MMSE matrix by using the reachable rate of the source node:

R_snm＝r₂₁+r₁₂，r₁₂为源节点S₁通过中继节点向源节点S₂传输的可达速率，r₂₁为源节点S₂通过中继节点向源节点S₁传输的可达速率，对于确定的向量α，源节点可达速率优化表达式为：First, introduce the vector α=[α ₂₁ , α ₁₂ ] ^T ,

R _snm =r ₂₁ +r ₁₂ , r ₁₂ is the achievable transmission rate from source node S ₁ to source node S ₂ via relay node, and r ₂₁ is the achievable transmission rate from source node S ₂ to source node S ₁ via relay node reachable rate, for a certain vector α, the optimal expression of source node reachable rate is:

$\underset{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; sum</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; B</span>}}}{\mathrm{<span\; class="notranslate">\; Maximize</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; sum</span>}}$

$\mathrm{<span\; class="notranslate">\; Subject\; to</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">B</figure-callout></span><figure-callout\; id="2"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{}_{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="p"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="MMSE\; h\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">MMSE</figure-callout></span><figure-callout\; id="1"\; label="MMSE\; h\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{}_{}^{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; sum</span>}}$

$\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">B</figure-callout></span><figure-callout\; id="1"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{}_{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="p"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="MMSE\; h\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">MMSE</figure-callout></span><figure-callout\; id="2"\; label="MMSE\; h\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{}_{}^{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; sum</span>}}<span\; class="notranslate">\; ,</span>$

${<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">B</figure-callout></span><figure-callout\; id="1"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{}_{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="p"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">B</figure-callout></span><figure-callout\; id="2"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{}_{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="p"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; tr</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}$

Where g ₁ ＝U ^H h ₁ and g ₂ ＝U ^H h ₂ are the equivalent channels from the two source nodes to the relay node respectively, and R _sum is the reachable rate of the source node;

Secondly, the expression for transforming the above achievable rate optimization into relay transmit power optimization solution is:

${\underset{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; Minimize</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">B</figure-callout></span><figure-callout\; id="1"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{}_{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="p"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">B</figure-callout></span><figure-callout\; id="2"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{}_{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="p"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; tr</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; subject\; to</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">B</figure-callout></span><figure-callout\; id="2"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{}_{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="p"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="MMSE\; h\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">MMSE</figure-callout></span><figure-callout\; id="1"\; label="MMSE\; h\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{}_{}^{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; ,</span>$

$\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">B</figure-callout></span><figure-callout\; id="1"\; label="B\; MMSE\; g"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{}_{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="p"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="MMSE\; h\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">MMSE</figure-callout></span><figure-callout\; id="2"\; label="MMSE\; h\; g"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">\; </figure-callout>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{}_{}^{}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}\mathrm{<span\; class="notranslate">\; r</span>}$

Where r is a constant in the solution process;

Finally, to solve the above relay transmission power optimization expression, the steps are as follows:

及中继发射功率上限P_R均为已知，令

r_min＝0，

(a) Set the upper limit of vector α, source node speed and

and relay transmission power upper limit P _R are known, so that

_rmin = 0,

令r_min＝r，否则令r_max＝r；(b) Solve the relay transmission power optimization expression according to the set parameters, and obtain the optimal solution p _R ^* and the matrix B _MMSE at this time, if

Let r _min = r, otherwise let r _max = r;

更新r的值后，返回步骤(b)执行循环，继续求解中继发射功率优化表达式，直到r_max-r_min≤δ_r，循环结束，最终得到矩阵B_MMSE。(c) Let δ _r be a given constant, if r _max -r _min ≥ δ _r , use

After updating the value of r, return to step (b) to execute the loop, and continue to solve the relay transmission power optimization expression until r _max -r _min ≤δ _r , the loop ends, and the matrix B _MMSE is finally obtained.

Step 3, relay node beamforming

z_R(n)表示加性高斯白噪声，中继节点波束成型表示为x_R(n)＝A_MMSEy_R(n)，n＝1，...，N，其中A_MMSE∈C^M×M为中继节点最小均方误差波束成型矩阵。Using the obtained minimum mean square error beamforming matrix, the minimum mean square error beamforming is performed on the mixed signal received by the relay node, and the mixed signal received by the relay node represents

z _R (n) represents additive white Gaussian noise, and relay node beamforming is expressed as x _R (n) = A _MMSE y _R (n), n = 1,..., N, where A _MMSE ∈ ^{C M× M} is the minimum mean square error beamforming matrix of the relay node.

Step 4, the relay node broadcasts information

The relay node broadcasts the beamformed information x _R (n) to two source nodes in the second time slot. The channels from the relay node to the source node are h ₁ ^T and h ₂ ^T respectively, and the source node S ₁ and the signal received by _S2 is expressed as:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="p"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="p"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="p"\; filenames="H2009102193421E0000011.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="p"\; filenames="H2009102193421E0000031.png,H2009102193421E0000032.png"\; state="\{\{state\}\}">p</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

和

后，通过解调得到对方源节点的信息，从而在两个时隙内实现源节点之间信息的交换。where z ₁ (n) and z ₂ (n) are the additive white Gaussian noise from the relay node to the source nodes S ₁ and S ₂ respectively, and the source nodes subtract the self-phase interference from the received information respectively

and

Finally, the information of the other source node is obtained through demodulation, so as to realize the exchange of information between the source nodes in two time slots.

The beneficial results of the present invention are illustrated by the following further simulations:

In the simulation, a system model of two source nodes and one relay node is used. Each source node is configured with one antenna, and the relay node is configured with four antennas. The source node information is processed by turbo coding and BPSK modulation. The system capacity and error code rate simulation.

Fig. 4 shows the capacity performance comparison between the present invention and the existing optimal beamforming method and two suboptimal beamforming methods. As can be seen from Fig. 4, the present invention will not affect the system capacity performance while reducing the complexity of the beamforming matrix to have a greater impact.

Fig. 5 has provided the bit error rate performance comparison of the present invention and existing optimal beamforming method and two kinds of suboptimal beamforming methods, as can be seen from Fig. 5, the present invention has improved system bit error rate performance preferably, has reduced Transmission of error bits ensures the correctness of transmission.

Claims (2)

1. an information transmission method based on minimum mean square error beamforming in a two-way channel, comprising the steps: (1) Use Turbo code to encode the data information d ₁ and d ₂ of the two source nodes respectively to obtain the coded sequence x ₁ , x ₂ , modulate the coded sequence, and convert the modulated signal s ₁ (n) and s ₂ (n) are simultaneously sent to the relay node with power p ₁ and p ₂ ; (2) The relay node constructs the beamforming matrix based on the minimum mean square error criterion: 2a) Let H _UL =[h ₁ , h ₂ ], H _DL =[h ₂ , h ₁ ]T, h ₁ and h ₂ are the channels from the source node to the relay node respectively, perform singular value decomposition on H _{UL UL} ＝U∑V ^H , U∈C ^M×2 , express the relay minimum mean square error beamforming matrix as A _MMSE ＝U ^* B _MMSE U ^H , B _MMSE ∈C ^2×2 ; 2b) Construct the relay beamforming matrix using the minimum mean square error criterion: The relay minimum mean square error beamforming matrix is constructed according to the receiver and transmitter expressions of the minimum mean square error criterion: ${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}\end{array}\right]{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}$ where σ _n ² and σ _a ² are noise power and signal power respectively, a _MMSE and b _MMSE are two complex variables that need to be solved to construct the beamforming matrix, I is the complex identity matrix,

is the minimum mean square error receiver expression, is the minimum mean square error transmitter expression; Using the singular value decomposition formula

and

The H _DL ^H and H _UL ^H are decomposed separately, and the relay beamforming matrix is obtained as: ${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{<span\; class="notranslate">\; *</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;V</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; DL</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; UL</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; V\&Sigma;U</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}$ make $B_{\mathrm{MMSE}}={\mathrm{\&Sigma;V}}^T{(h_{\mathrm{DL}}{h_{\mathrm{DL}}}^h+\frac{{\mathrm{\&sigma;}}_{\mathrm{no}}^2}{{\mathrm{\&sigma;}}_a^2}I)}^{+}\left[\begin{array}{cc}0& a_{\mathrm{MMSE}}\\ b_{\mathrm{MMSE}}& 0\end{array}\right]{(h_{\mathrm{UL}}^h{h}_{\mathrm{UL}}+\frac{{\mathrm{\&sigma;}}_{\mathrm{no}}^2}{{\mathrm{\&sigma;}}_a^2}I)}^{+}\mathrm{V\&Sigma;},$ Let A _MMSE = U ^* B _MMSE U ^H ; In the formula, the B _MMSE matrix is obtained by solving the reachable rate of the source nodes S ₁ and S ₂ , U ^* is the conjugate matrix of U, and U ^H is the conjugate transpose matrix of U; (3) Use the obtained minimum mean square error beamforming matrix to perform minimum mean square error beamforming on the mixed signal received by the relay node, expressed as x _R (n) = A _MMSE y _R (n), n = 1 ,..., N, where y _R (n) is the mixed information of the two source nodes received by the relay node; (4) The relay node broadcasts the beamforming information x _R (n) to two source nodes in the second time slot, and the two source nodes subtract the self-interference from the received information respectively, and then solve the Call to obtain the information of the other source node, so as to realize the exchange of information between the source nodes within two time slots. 2. the information transmission method based on minimum mean square error beamforming in the two-way channel according to claim 1, wherein step 2b) described matrix B _MMSE solves by the attainable rate of source node, carries out according to the following steps: The first step is to introduce the vector α=[α ₂₁ , α ₁₂ ] ^T , where

R _sum =r ₂₁ +r ₁₂ , r ₁₂ is the achievable transmission rate from source node S ₁ to source node S ₂ through relay node, and r ₂₁ is the achievable transmission rate from source node S ₂ to source node S ₁ through relay node reach rate, For a certain vector α, the source node reachable rate optimization is expressed as: $\begin{array}{cc}\underset{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; sum</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; B</span>}}}{\mathrm{<span\; class="notranslate">\; Maximize</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; sum</span>}}\end{array}$ $\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; subject</span>}& \mathrm{<span\; class="notranslate">\; to</span>}& \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; sum</span>}}\end{array}<span\; class="notranslate">\; ,</span>$ $\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; sum</span>}}$ ${<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; tr</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; MMSE</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}$ Where g ₁ = U ^H h ₁ , g ₂ = U ^H h ₂ , R _sum is the reachable rate of the source node; In the second step, the above achievable rate optimization is transformed into the expression of relay transmission power optimization solution: p _R ＝||B _MMSE g ₁ || ² p ₁ +||B _MMSE g ₂ || ² p ₂ +tr(B _MMSE B _MMSE ^H ) subject to $\frac{1}{2}{\log }_2(1+\frac{{\left|g_1^T{B}_{\mathrm{MMSE}}{g}_2\right|}^2{p}_2}{{\left|\right|{B_{\mathrm{MMSE}}}^h{g}_1^{*}\left|\right|}^2+1})\&Greater\; Equal;{\mathrm{\&alpha;}}_{\mathrm{twenty\; one}}r,$ $\frac{1}{2}{\log }_2(1+\frac{{\left|g_2^T{B}_{\mathrm{MMSE}}{g}_1\right|}^2{p}_1}{{\left|\right|{B_{\mathrm{MMSE}}}^h{g}_2^{*}\left|\right|}^2+1})\&Greater\; Equal;{\mathrm{\&alpha;}}_{12}r$ r is a constant during the solution process: The third step is to solve the relay transmission power optimization solution expression in the second step: (a) Set the upper limit of vector α, source node speed and

and relay transmission power upper limit P _R are known, so that _rmin = 0, (b) Solve the relay transmission power optimization expression according to the set parameters, and obtain the optimal solution p _R ^* and the matrix B _MMSE at this time, if Let r _min = r, otherwise let r _max = r; (c) Let δ _r be a given constant, if r _max -r _min ≥ δ _r , use

After updating the value of r, return to step (b) to execute the loop, and continue to solve the relay transmission power optimization expression until r _max -r _min ≤δ _r , the loop ends, and the matrix B _MMSE is finally obtained.

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