CN107147472A

CN107147472A - Physical-layer network coding method and device

Info

Publication number: CN107147472A
Application number: CN201710221409.XA
Authority: CN
Inventors: 陈巍; 于志江; 郭欣
Original assignee: Tsinghua University
Current assignee: Tsinghua University
Priority date: 2017-04-06
Filing date: 2017-04-06
Publication date: 2017-09-08
Anticipated expiration: 2037-04-06
Also published as: CN107147472B

Abstract

The present invention provides a kind of physical-layer network coding method and device, including sets the first source node, the second source node and via node；In the aliasing planisphere that via node is received, Euclidean distance is mapped to the same constellation point of new planisphere less than the point of predetermined threshold value；Control the decoding reliability of the first source node, the second source node respectively using two Euclidean distance constrained parameters；Set up optimization relation；Optimization relation is solved, to obtain the approximate optimal solution of the new planisphere of bilateral relay network and network code mapping mode under physical-layer network coding mechanism.Constellation G- Design under line can be achieved, on line the phase that source node (the first source node and the second source node) sends out planisphere is corrected according to channel coefficients, the computing load of via node can be reduced, the requirement to via node operational capability is reduced, time delay is reduced.

Description

Physical-layer network coding method and device

Technical field

The present invention relates to communication technical field, more particularly to a kind of physical-layer network coding method and device.

Background technology

Using the bidirectional relay system of physical-layer network coding mechanism compared with traditional relay system, imitated with higher spectrum And effect, the rate of information throughput of bilateral relay network can be improved 100% by it, so either educational circles or work in recent years Industry has carried out numerous studies to it.Want to come into operation the system, one is his star the problem of solving substantially The design of seat G- Design and network code mapping mode.

The network code mapping mode and planisphere design method gone out given in existing literature is carried out independently of one another, first Planned network coding mapping mode, designs planisphere afterwards.And network code mapping mode has been selected in source node planisphere In the case of carry out, planisphere used in its source node is QPSK, the common planisphere such as 16QAM, on this basis based on making in After planisphere points few principle as far as possible used in node, reflecting for network code is given by the way of nearest-neighbor first polymerize Mode is penetrated, and the network code mapping mode that only discuss using planisphere during for QPSK and 16QAM is designed.

Shape of the above method due to directly defining planisphere used in source node, equivalent to having added very strong hypothesis bar Part, so the network code mapping mode and planisphere designed by can not ensureing are to use double under physical-layer network coding mechanism To the optimal design mode of system.

The content of the invention

The present invention provides a kind of physical-layer network coding method and device, is compiled to solve the network designed by prior art The bilateral system of code mapping mode and planisphere in the case where using physical-layer network coding mechanism can not ensure as optimal design mode Defect.

One aspect of the present invention provides a kind of physical-layer network coding method, including：

Step 1, the first source node, the second source node and via node are set；

Step 2, in the aliasing planisphere via node received, the point that Euclidean distance is less than predetermined threshold value maps To the same constellation point of new planisphere, make satisfaction：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0

Wherein, the planisphere used in first source node, second source node and the via node is respectively A= {a₁,...,a_M, B={ b₁,...,b_N, S={ s_ij| i=1 ..., M, j=1 ..., N }, M and N represent described first respectively The exponent number of the planisphere of the exponent number of the planisphere of source node and second source node, h₁And h₂Represent channel coefficients, ε_RIt is default Threshold value, for adjusting the reliability that network code maps at via node；s_ij=C (a_i,b_j) represent to work as first source node Transmission signal a_i, the second source node transmission signal b_jWhen, the via node transmission signal s_ij, C represents that network code reflects Penetrate mode：

Step 3, two Euclidean distance constrained parameters ε are utilized_A,ε_BTo control first source node, second source respectively The decoding reliability of node, makes satisfaction：

|s_ij-s_ik|²≥ε_A,s_ij≠s_ik∈S

|s_ji-s_ki|²≥ε_B,s_ji≠s_ki∈S

Step 4, withFor object function, optimization relation is set up：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0

a_i,a_p∈A,b_j,b_q∈B,s_ij,s_pq∈S,i≠p,j≠q

Wherein, ()^HThe conjugate transposition of representing matrix；

Step 5, the optimization relation is solved, to obtain bilateral relay network under physical-layer network coding mechanism The approximate optimal solution of new planisphere and network code mapping mode.

Further, step 5 is specifically included：

Step 51, linear transformation and the first substitution of variable are carried out to the optimization relation, to obtain the first intermediate optima pass It is formula,

Wherein, n₁、n₂And n₃The quantity accordingly constrained, n are represented respectively₁、n₂And n₃It is exponent number M and N function,Represent corresponding coefficient matrix；z₁And z₂The up planisphere of design is respectively needed with Planetary figure；

First substitution of variable is specially：

Step 52, the first intermediate optima relational expression is converted to two suboptimums of quadratic constraints using the second substitution of variable Change problem, the double optimization problem expression formula of the quadratic constraints is：

z₃ ^TF_jz₃>=0 ,=1,2 ..., n₃

Wherein,c_jRepresent coefficient vector；

Second substitution of variable is：

Wherein, p_j,q_jFor intermediate variable；

Step 53, the double optimization problem is solved, to obtain bi-directional relaying under physical-layer network coding mechanism The new planisphere of network and the approximate optimal solution of network code mapping mode.

Further, step 53 is specifically included：

Step 531, the double optimization problem is solved using semidefinite decoding algorithm, to obtain optimal solution X^*；

Step 532, stochastic approximation structured approach is carried out using Gaussian vectors method, from the optimal solution X^*It is middle to extract described secondary The suboptimal solution of optimization problem, the suboptimal solution is approximate optimal solution.

Further, step 531 is specifically included：

According to the property of the mark of matrix product, following variable replacement is carried out to the double optimization problem：

x^HΔ x=tr (x^HΔ x)=tr (Δ xx^H)

Wherein, Δ represents Arbitrary Coefficient matrix, xx^TIt is equivalent for 1 positive semidefinite matrix X with order；

The double optimization problem is replaced by ternary, the second optimal relation, second optimization is converted to The expression formula of relational expression is：

s.t.tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

rank(Z₁)=1, rank (Z₂)=1

Wherein,Rank () is seeks rank of matrix, and tr () operates for the mark of matrix；

Rank (Z are fallen by relaxation₁)=1, rank (Z₂)=1, and willRelaxation isBy described second Optimal relation relaxation is the first Semidefinite Programming, wherein first Semidefinite Programming is：

s.t.tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

Using convex optimized algorithm, first Semidefinite Programming is solved, to obtain optimal solution X^*。

Further, step 53 is specifically included：

Step 533, using the 4th substitution of variable, the 5th substitution of variable and the 6th substitution of variable, the double optimization is asked Topic is converted to the 3rd optimal relation, wherein the 3rd optimal relation is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

rank(Z₁)=1, rank (Z₂)=1, rank (Z₃)=1

Wherein, F_i,G_j,H_i,D_k,f_i,g_j,h_i,d_kFor correspondingly coefficient matrix and coefficient vector；

4th substitution of variable is：

5th substitution of variable is：

6th substitution of variable is：

Step 534, the order constraint rank (Z in the 3rd optimal relation are fallen in relaxation₁)=1, rank (Z₂)=1, rank (Z₃The He of)=1To obtain relaxation problem, the relaxation problem expression formula is

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

Step 535, the solution of the relaxation problem is converted into the solution of the second Semidefinite Programming, second semidefinite Planning problem is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

Step 536, two suboptimum is extracted from the optimal solution of second Semidefinite Programming using Gaussian approximation The suboptimal solution of change problem, the suboptimal solution is approximate optimal solution.

Another aspect of the present invention provides a kind of physical-layer network coding device, including：

Setup module, for setting the first source node, the second source node and via node；

Mapping block, in the aliasing planisphere that receives the via node, Euclidean distance to be less than predetermined threshold value Point be mapped to the same constellation point of new planisphere, make satisfaction：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0

Control module, for utilizing two Euclidean distance constrained parameters ε_A,ε_BTo control first source node, institute respectively The decoding reliability of the second source node is stated, makes satisfaction：

|s_ij-s_ik|²≥ε_A,s_ij≠s_ik∈S

|s_ji-s_ki|²≥ε_B,s_ji≠s_ki∈S

Optimization relation sets up module, forFor object function, set up Following optimization relation：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0

a_i,a_p∈A,b_j,b_q∈B,s_ij,s_pq∈S,i≠p,j≠q

Wherein, ()^HThe conjugate transposition of representing matrix；

Solve module, for being solved to the optimization relation, with obtain under physical-layer network coding mechanism it is two-way in After the new planisphere and the approximate optimal solution of network code mapping mode of network.

Further, module is solved to specifically include：

First intermediate optima relational expression acquisition submodule, for carrying out linear transformation and the first variable to the optimization relation Replacement, to obtain the first intermediate optima relational expression,

First substitution of variable is specially：

Double optimization problem expression formula acquisition submodule, using the second substitution of variable by the first intermediate optima relational expression The double optimization problem of quadratic constraints is converted to, the double optimization problem expression formula of the quadratic constraints is：

z₃ ^TF_jz₃>=0 ,=1,2 ..., n₃

Wherein,c_jRepresent coefficient vector；

Second substitution of variable is：

Wherein, p_j,q_jFor intermediate variable；

Submodule is solved, for being solved to the double optimization problem, to obtain under physical-layer network coding mechanism The new planisphere of bilateral relay network and the approximate optimal solution of network code mapping mode.

Further, submodule is solved to specifically include：

Optimal solution acquisition submodule, for being solved using semidefinite decoding algorithm to the double optimization problem, to obtain Obtain optimal solution X^*；

First suboptimal solution acquisition submodule, for carrying out stochastic approximation structured approach using Gaussian vectors method, from described optimal Solve X^*The middle suboptimal solution for extracting the double optimization problem, the suboptimal solution is approximate optimal solution.

Further, optimal solution acquisition submodule specifically for：

x^HΔ x=tr (x^HΔ x)=tr (Δ xx^H)

s.t.tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

rank(Z₁)=1, rank (Z₂)=1

s.t.tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

Further, submodule is solved to specifically include：

3rd optimal relation acquisition submodule, for utilizing the 4th substitution of variable, the 5th substitution of variable and the 6th variable Replacement, is converted to the 3rd optimal relation, wherein the 3rd optimal relation is by the double optimization problem：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

rank(Z₁)=1, rank (Z₂)=1, rank (Z₃)=1

4th substitution of variable is：

5th substitution of variable is：

6th substitution of variable is：

Relaxation problem expression formula acquisition submodule, the order constraint rank in the 3rd optimal relation is fallen for relaxation (Z₁)=1, rank (Z₂)=1, rank (Z₃The He of)=1To obtain relaxation problem, the relaxation problem expression formula is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

Second Semidefinite Programming acquisition submodule, for the solution of the relaxation problem to be converted into the second Semidefinite Programming The solution of problem, second Semidefinite Programming is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

Second suboptimal solution acquisition submodule, for utilizing optimal solution of the Gaussian approximation from second Semidefinite Programming The middle suboptimal solution for extracting the double optimization problem, the suboptimal solution is approximate optimal solution.

The physical-layer network coding method and device that the present invention is provided, can be achieved on constellation G- Design under line, line according to letter Road coefficient correction source node (the first source node and the second source node) sends out the phase of planisphere, can reduce the fortune of via node Load is calculated, the requirement to via node operational capability is reduced, time delay is reduced.In addition, in the case of designing planisphere under online Channel self-adapting can be realized, in power limited, selection meets the planisphere with maximum M and N of power limit.In constraint In the case of minimum European code distance, M and N are bigger, the rate of information throughput may be bigger.

Brief description of the drawings

The invention will be described in more detail below based on embodiments and refering to the accompanying drawings.Wherein：

Fig. 1 is the physical-layer network coding method flow schematic diagram that the embodiment of the present invention one is provided；

Fig. 2 is the nodal analysis method figure that the embodiment of the present invention one is provided；

Fig. 3 is the analog domain mapping rule schematic diagram that the embodiment of the present invention one is provided；

Fig. 4 is the physical-layer network coding method flow schematic diagram that the embodiment of the present invention two is provided；

Fig. 5 is that the embodiment of the present invention two provides planisphere and network code mapping mode schematic diagram；

Fig. 6 is the physical-layer network coding method flow schematic diagram that the embodiment of the present invention three is provided；

Fig. 7 is that the embodiment of the present invention three provides planisphere and network code mapping mode schematic diagram；

Fig. 8 is the physical-layer network coding apparatus structure schematic diagram that the embodiment of the present invention four is provided；

Fig. 9 is the physical-layer network coding apparatus structure schematic diagram that the embodiment of the present invention five is provided；

Figure 10 is the physical-layer network coding apparatus structure schematic diagram that the embodiment of the present invention six is provided.

In the accompanying drawings, identical part uses identical reference.Accompanying drawing is not drawn according to actual ratio.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.

Embodiment one

Fig. 1 is refer to, the present invention provides a kind of physical-layer network coding method, including：

Step 1, the first source node, the second source node and via node are set.

As shown in Fig. 2 the present embodiment uses physical-layer network coding mechanism, when completion primary information interaction needs two Gap, first the first source node S of time slot N₁(DN₁) and the second source node S N₂(DN₁) while sending signal to via node RN.This When, to via node RN send two paths of signals can at via node RN aliasing, the first source node S N₁(DN₁) and the second source section Point SN₂(DN₁) signal of the aliasing received is mapped on its planisphere.In second time slot, via node RN is simultaneously to two Individual destination node (the first source node S N₁With the second source node S N₂) broadcasted, destination node can according to existing prior information To be successfully decoded.

Step 2, in the aliasing planisphere via node received, the point that Euclidean distance is less than predetermined threshold value maps To same constellation point, make satisfaction：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0.

Wherein, the planisphere used in first source node, second source node and the via node is respectively A= {a₁,...,a_M, B={ b₁,...,b_N, S={ s_ij| i=1 ..., M, j=1 ..., N }, a_pFor the element in A, b_qFor in B Element, s_pqFor the element in S, M and N represent the exponent number and the planisphere of the second source node of the planisphere of the first source node respectively Exponent number, h₁And h₂Represent channel coefficients, ε_RFor predetermined threshold value, the reliability for adjusting network code mapping at via node； s_ij=C (a_i,b_j) represent to work as the first source node transmission signal a_i, the second source node transmission signal b_jWhen, the relaying Node transmission signal s_ij, C represents network code mapping mode：

a_kFor the element in A, b_kFor the element in B, k is subscript.

As shown in figure 3, Fig. 3 left figure represents the aliasing planisphere that via node (RN) is received, right figure is via node RN is used for the planisphere broadcasted, that is, the new planisphere being mapped to.According to analog domain mapping rule, received in via node RN Aliasing planisphere in, Euclidean distance be less than predetermined threshold value point will be mapped to that a constellation point.Above and below the criterion has been unified Capable constellation G- Design, and ensure that the reliability that network code maps at via node.

|s_ij-s_ik|²≥ε_A,s_ij≠s_ik∈S

|s_ji-s_ki|²≥ε_B,s_ji≠s_ki∈S。

Specifically, wanting in destination node (the first source node S N₁With the second source node S N₂) place successfully realizes decoding, one Necessary condition is that network code mapping mode C need to meet following rule (Exclusive Law)：

Planisphere S={ s i.e. used in via node RN_ij| i=1 ..., M, j=1 ..., N } it must is fulfilled for following condition：

By using two Euclidean distance constrained parameters ε_A,ε_BTo control the first source node S N respectively₁With the second source node SN₂Decoding reliability (error sign ratio), so above rule can be converted into following expression：

|s_ij-s_ik|²≥ε_A,s_ij≠s_ik∈S

|s_ji-s_ki|²≥ε_B,s_ji≠s_ki∈S

Step 4, withFor object function, following optimization relation is set up：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0

a_i,a_p∈A,b_j,b_q∈B,s_ij,s_pq∈S,i≠p,j≠q.

Wherein, ()^HThe conjugate transposition of representing matrix.

Specifically, for a communication system, in the case where error sign ratio and the rate of information throughput are certain, hair used Penetrate power lower, system is more excellent.So the average emitted power of the system of definition is：

And using it as object function, set up following optimization relation：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0

a_i,a_p∈A,b_j,b_q∈B,s_ij,s_pq∈S,i≠p,j≠q.

The optimal constellation figure of bilateral relay network under physical-layer network coding mechanism can be obtained by solving problem above With the layout strategy of network code mapping mode.

Specifically, as carried out using Enhanced-SDR algorithms and Fast-relaxation algorithms to the optimization relation Solve, Enhanced-SDR algorithms and the planisphere and network code mapping mode designed by Fast-relaxation algorithms, with BPSK, QPSK, 8QAM is respectively adopted and compares using one-to-one mapping and three nodes in the prior art, there is larger erratum number Rate performance gain.

The physical-layer network coding method that the present embodiment is provided, can be achieved on constellation G- Design under line, line according to channel system Number correction source node (the first source node S N₁With the second source node S N₂) phase of planisphere is sent out, via node can be reduced Computing load, reduces the requirement to via node operational capability, reduces time delay.In addition, designing the situation of planisphere under online Under can realize channel self-adapting, in power limited, selection meets the planisphere with maximum M and N of power limit.About In the case of the minimum European code distance of beam, M and N are bigger, the rate of information throughput may be bigger.

Embodiment two

As shown in figure 4, the present embodiment provides a kind of physical-layer network coding method, wherein, step 5 is specifically included：

First substitution of variable is specially：

z₃ ^TF_jz₃>=0 ,=1,2 ..., n₃.

Wherein,

Second substitution of variable is：

Wherein, p_j,q_jFor intermediate variable；

Further, the solution procedure of step 53 is carried out specifically using Enhanced-SDR algorithms in the present embodiment Bright, step 53 is specifically included：

Step 531, the double optimization problem is solved using semidefinite decoding algorithm, to obtain optimal solution X^*。

Specifically, step 531 is specifically included：

x^HΔ x=tr (x^HΔ x)=tr (Δ xx^H).

xx^TIt is equivalent for 1 positive semidefinite matrix X with order；

s.t.tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

rank(Z₁)=1, rank (Z₂)=1

s.t.tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

Using convex optimized algorithm, first Semidefinite Programming (SDP) is solved, to obtain optimal solution X^*.Using convex excellent Change related algorithm, such as Newton method, interior point method can solve this SDP problem in polynomial complexity.

The flow of stochastic approximation structured approach is as follows：

The first step：Generation

Second step：Construction(Interior element is descending constellation point)

3rd step：On the premise of without prejudice to Exclusive Law, merge as much as possibleIn point (points it is fewer, European code distance is bigger under same transmission power；Other 2 points of fusions, which at least have a kind of mode, can reduce target function value, i.e., Average emitted power).Exclusive Law are the necessary conditions for ensureing to be successfully decoded, and content is as follows：

Wherein C (a_j,b_i) etc. be the constellation point to be mapped to, i.e.,In point.

4th step：Generation

5th step：ConstructionAll H are included in wherein M_1iWith withCorresponding Part D_i,Mean not merge.

6th step：According to circumstances repeat the first to the 5th step N_randIt is secondary, ask for：

ChooseIt is used as output result.

In the case of constellation order M=2, N=4, N_rand=10⁷When its designed by planisphere and network code reflect Penetrate mode as shown in Figure 5.

Embodiment three

When computing resource is limited, algorithm for design needs have lower complexity, in order to realize communication performance With the compromise of computing resource, Fast-relaxation algorithms can be used, this algorithm can be with compared with Enhanced-SDR algorithms Further greatly reduce computation complexity.

The basic thought of Fast-relaxation algorithms is still first loose, then stochastic approximation.Calculated with Enhanced-SDR Unlike method, this algorithm does not introduce new variable, and takes full advantage of the relation in constraint between each coefficient, by institute Some redundant constaints obtained in relaxation problem are simplified, so as to greatly reduce the solving complexity of relaxation problem.

The present embodiment is carried out specific using Fast-relaxation algorithms to the solution procedure of the step 53 in embodiment two Illustrate, as shown in fig. 6, the present embodiment provides a kind of physical-layer network coding method, wherein, step 53 is specifically included：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

rank(Z₁)=1, rank (Z₂)=1, rank (Z₃)=1

4th substitution of variable is：

5th substitution of variable is：

6th substitution of variable is：

Step 534, the order constraint rank (Z in the 3rd optimal relation are fallen in relaxation₁)=1, rank (Z₂)=1, rank (Z₃The He of)=1To obtain relaxation problem, the relaxation problem expression formula is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

Specifically, because the presence of a large amount of non-convex quadratic constraints, gained problem is still non-convex.But by each Relation between constraint function coefficient is understood, works as Z₄When=0, it is possible to use the 4th group of constraint, i.e., the 4th group are released in first three groups constraint Constraint is redundancy.It follows that the solution of above relaxation problem, can be converted into asking for the 2nd SDP (Semidefinite Programming) problems Solution.

Specifically, similar to Enhanced-SDR algorithms, proposing a kind of Gauss for Fast-relaxation algorithms near Like method with the solution of the former problem of extraction from the optimal solution of relaxation problem, i.e., new planisphere.With Enhanced-SDR Algorithm for Solving mistakes Unlike journey, the constellation point for going to merge descending planisphere as much as possible is not selected, so as to ensure that gained solution is realized The possibility of global optimum.

Gaussian approximation flow is as follows：

The first step：Generation

Second step：Construction(Interior element is descending constellation point)；

3rd step：, will on the premise of without prejudice to Exclusive LawThe close point fusion of middle-range.(do not have herein There is selection to go fusion as much as possible, remain the possibility for asking for global optimum；2 points of fusions at least have a kind of mode can To reduce target function value, i.e. average emitted power).

4th step：GenerationWherein,

5th step：ConstructionAll coefficient matrix F are included in wherein M_i,G_jDimension mend 0 expand Exhibition, Yi JiyuCorresponding part Mean corresponding constellation Point is not merged.

ChooseIt is used as output result.

Finally, the performance to Fast-relaxation algorithms carries out theory analysis, and obtained this algorithm in detail Approximation ratio：

Wherein,Represent the average emitted power of designed planisphere, v_optThe transmission power of representation theory optimal constellation figure, m₁,m₂,m₃It is the number accordingly constrained in optimization problem, it is planisphere order of modulation M, N function.

According to Fast-relaxation algorithms, in M=2, N=4, N_rand=10⁷In the case of designed planisphere and Network code mapping mode is as shown in Figure 7.

Example IV

As shown in figure 8, the present embodiment provides a kind of physical-layer network coding device, including setup module 201, mapping block 202nd, control module 203, optimization relation set up module 204 and solve module 205.

Wherein, setup module 201, for setting the first source node, the second source node and via node；

Mapping block 202, in the aliasing planisphere that receives the via node, Euclidean distance to be less than default threshold The point of value is mapped to the same constellation point of new planisphere, makes satisfaction：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0.

Wherein, the planisphere used in first source node, second source node and the via node is respectively A= {a₁,...,a_M, B={ b₁,...,b_N, S={ s_ij| i=1 ..., M, j=1 ..., N }, M and N represent that the first source is saved respectively The exponent number of the exponent number of the planisphere of point and the planisphere of the second source node, h₁And h₂Represent channel coefficients, ε_RFor predetermined threshold value, use The reliability of network code mapping at adjustment via node；s_ij=C (a_i,b_j) represent to work as the first source node transmission signal a_i, the second source node transmission signal b_jWhen, the via node transmission signal s_ij, C represents network code mapping mode：

Control module 203, for utilizing two Euclidean distance constrained parameters ε_A,ε_BCome control respectively first source node, The decoding reliability of second source node, makes satisfaction：

|s_ij-s_ik|²≥ε_A,s_ij≠s_ik∈S

|s_ji-s_ki|²≥ε_B,s_ji≠s_ki∈S

Optimization relation sets up module 204, forFor object function, Set up following optimization relation：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0

a_i,a_p∈A,b_j,b_q∈B,s_ij,s_pq∈S,i≠p,j≠q.

Module 205 is solved, it is two-way under physical-layer network coding mechanism to obtain for being solved to the optimization relation The new planisphere of junction network and the approximate optimal solution of network code mapping mode.

Example IV be with the corresponding device embodiment of embodiment one, for details, reference can be made to the record in embodiment one, herein Repeat no more.

Embodiment five

As shown in figure 9, the present embodiment provides a kind of physical-layer network coding device, wherein, solve module 205 and specifically wrap Include：

First intermediate optima relational expression acquisition submodule 2051, for carrying out linear transformation and first to the optimization relation Substitution of variable, to obtain the first intermediate optima relational expression,

Wherein, n₁、n₂And n₃The quantity accordingly constrained is represented respectively, is exponent number M and N function,Represent corresponding coefficient matrix；z₁And z₂The up planisphere of design is respectively needed with Planetary figure；

First substitution of variable is specially：

Double optimization problem expression formula acquisition submodule 2052, is closed first intermediate optima using the second substitution of variable It is the double optimization problem that formula is converted to quadratic constraints, the double optimization problem expression formula of the quadratic constraints is：

z₃ ^TF_jz₃>=0 ,=1,2 ..., n₃.

Wherein,

Second substitution of variable is：

Wherein, p_j,q_jFor intermediate variable；

Submodule 2053 is solved, for being solved to the double optimization problem, to obtain physical-layer network coding machine The new planisphere and the approximate optimal solution of network code mapping mode of the lower bilateral relay network of system.

Further, submodule 2053 is solved to specifically include：

Optimal solution acquisition submodule 2053a, for being solved using semidefinite decoding algorithm to the double optimization problem, To obtain optimal solution X^*。

Further, optimal solution acquisition submodule 2053a specifically for：

x^HΔ x=tr (x^HΔ x)=tr (Δ xx^H).

xx^TIt is equivalent for 1 positive semidefinite matrix X with order；

s.t.tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

rank(Z₁)=1, rank (Z₂)=1

s.t.tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

First suboptimal solution acquisition submodule 2053b, for carrying out stochastic approximation structured approach using Gaussian vectors method, from described Optimal solution X^*The middle suboptimal solution for extracting the double optimization problem, the suboptimal solution is approximate optimal solution.

Embodiment five be with the corresponding device embodiment of embodiment two, for details, reference can be made to the record in embodiment two, herein Repeat no more.

Embodiment six

As shown in Figure 10, the present embodiment provides a kind of physical-layer network coding device, wherein, solve submodule 2053 specific Including：

3rd optimal relation acquisition submodule 2054a, for utilizing the 4th substitution of variable, the 5th substitution of variable and the 6th Substitution of variable, the 3rd optimal relation is converted to by the double optimization problem, wherein the 3rd optimal relation is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

rank(Z₁)=1, rank (Z₂)=1, rank (Z₃)=1

4th substitution of variable is：

5th substitution of variable is：

6th substitution of variable is：

Relaxation problem expression formula acquisition submodule 2054b, the order constraint in the 3rd optimal relation is fallen for relaxation rank(Z₁)=1, rank (Z₂)=1, rank (Z₃The He of)=1To obtain relaxation problem, the relaxation problem expression Formula is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

Second Semidefinite Programming acquisition submodule 2054c, for the solution of the relaxation problem to be converted into the second half Determine the solution of planning problem, second Semidefinite Programming is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t.tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

Second suboptimal solution acquisition submodule 2054d, for utilizing Gaussian approximation from second Semidefinite Programming The suboptimal solution of the double optimization problem is extracted in optimal solution, the suboptimal solution is approximate optimal solution.

Embodiment six be with the corresponding device embodiment of embodiment three, for details, reference can be made to the record in embodiment three, herein Repeat no more.

Although by reference to preferred embodiment, invention has been described, is not departing from the situation of the scope of the present invention Under, various improvement can be carried out to it and part therein can be replaced with equivalent.Especially, as long as in the absence of structure punching Prominent, the every technical characteristic being previously mentioned in each embodiment can combine in any way.The invention is not limited in text Disclosed in specific embodiment, but all technical schemes including falling within the scope of the appended claims.

Claims

1. a kind of physical-layer network coding method, it is characterised in that including：

Step 1, the first source node, the second source node and via node are set；

Step 2, in the aliasing planisphere via node received, the point that Euclidean distance is less than predetermined threshold value is mapped to newly The same constellation point of planisphere, makes satisfaction：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0

<mrow> <mi>C</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>&NotEqual;</mo> <mi>C</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>&ForAll;</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>&NotEqual;</mo> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>&Element;</mo> <mi>B</mi> <mo>,</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>&Element;</mo> <mi>A</mi> </mrow>

<mrow> <mi>C</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>j</mi> </msub> <mo>,</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&NotEqual;</mo> <mi>C</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>&ForAll;</mo> <msub> <mi>a</mi> <mi>j</mi> </msub> <mo>&NotEqual;</mo> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>&Element;</mo> <mi>A</mi> <mo>,</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>&Element;</mo> <mi>B</mi> </mrow>

Step 3, two Euclidean distance constrained parameters ε are utilized_A,ε_BTo control first source node, second source node respectively Decoding reliability, make satisfaction：

|s_ij-s_ik|²≥ε_A,s_ij≠s_ik∈S

|s_ji-s_ki|²≥ε_B,s_ji≠s_ki∈S

Step 4, withFor object function, optimization relation is set up：

<mrow> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>S</mi> </mrow> </munder> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> <msup> <mi>A</mi> <mi>H</mi> </msup> <mi>A</mi> <mo>+</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msup> <mi>B</mi> <mi>H</mi> </msup> <mi>B</mi> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mi>M</mi> <mi>N</mi> </mrow> </mfrac> <munder> <mo>&Sigma;</mo> <mi>i</mi> </munder> <munder> <mo>&Sigma;</mo> <mi>j</mi> </munder> <msup> <mrow> <mo>|</mo> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow>

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <msup> <mrow> <mo>|</mo> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mi>k</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>&GreaterEqual;</mo> <msub> <mi>&epsiv;</mi> <mi>A</mi> </msub> <mo>,</mo> <mo>&ForAll;</mo> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mi>k</mi> </mrow> </msub> <mo>&Element;</mo> <mi>S</mi> </mrow> </mtd> </mtr> </mtable> </mfenced>

<mrow> <msup> <mrow> <mo>|</mo> <mrow> <msub> <mi>s</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mi>i</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>&GreaterEqual;</mo> <msub> <mi>&epsiv;</mi> <mi>B</mi> </msub> <mo>,</mo> <mo>&ForAll;</mo> <msub> <mi>s</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mi>i</mi> </mrow> </msub> <mo>&Element;</mo> <mi>S</mi> </mrow>

<mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>&GreaterEqual;</mo> <msub> <mi>&epsiv;</mi> <mi>R</mi> </msub> <mo>,</mo> <mo>&ForAll;</mo> <msub> <mi>a</mi> <mi>j</mi> </msub> <mo>,</mo> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>&Element;</mo> <mi>A</mi> </mrow>

<mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>&GreaterEqual;</mo> <msub> <mi>&epsiv;</mi> <mi>R</mi> </msub> <mo>,</mo> <mo>&ForAll;</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>,</mo> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>&Element;</mo> <mi>B</mi> </mrow>

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0

a_i,a_p∈A,b_j,b_q∈B,s_ij,s_pq∈S,i≠p,j≠q

Wherein, ()^HThe conjugate transposition of representing matrix；

Step 5, the optimization relation is solved, to obtain the nova of bilateral relay network under physical-layer network coding mechanism The approximate optimal solution of seat figure and network code mapping mode.

2. physical-layer network coding method according to claim 1, it is characterised in that step 5 is specifically included：

Step 51, linear transformation and the first substitution of variable are carried out to the optimization relation, to obtain the first intermediate optima relational expression,

<mrow> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>z</mi> <mn>1</mn> <mi>H</mi> </msubsup> <msub> <mi>H</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>&GreaterEqual;</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> </mrow>

<mrow> <msubsup> <mi>z</mi> <mn>2</mn> <mi>H</mi> </msubsup> <msub> <mi>H</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>&GreaterEqual;</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> </mrow> 1

<mrow> <mo>(</mo> <msubsup> <mi>z</mi> <mn>1</mn> <mi>H</mi> </msubsup> <msub> <mi>D</mi> <mi>i</mi> </msub> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mo>(</mo> <msubsup> <mi>z</mi> <mn>2</mn> <mi>H</mi> </msubsup> <msub> <mi>E</mi> <mi>i</mi> </msub> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>)</mo> <mo>&GreaterEqual;</mo> <mn>0</mn> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>n</mi> <mn>3</mn> </msub> </mrow>

First substitution of variable is specially：

<mrow> <msubsup> <mi>z</mi> <mn>1</mn> <mi>T</mi> </msubsup> <mo>=</mo> <mo>&lsqb;</mo> <mfrac> <mn>1</mn> <msqrt> <mi>M</mi> </msqrt> </mfrac> <msup> <mi>A</mi> <mi>T</mi> </msup> <mfrac> <mn>1</mn> <msqrt> <mi>N</mi> </msqrt> </mfrac> <msup> <mi>B</mi> <mi>T</mi> </msup> <mo>&rsqb;</mo> <mo>&Element;</mo> <msup> <mi>C</mi> <mrow> <mi>M</mi> <mo>+</mo> <mi>N</mi> </mrow> </msup> <mo>;</mo> </mrow>

<mrow> <msubsup> <mi>z</mi> <mn>2</mn> <mi>T</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mrow> <mi>M</mi> <mi>N</mi> </mrow> </msqrt> </mfrac> <mo>&lsqb;</mo> <msub> <mi>s</mi> <mn>11</mn> </msub> <msub> <mi>s</mi> <mn>12</mn> </msub> <mo>...</mo> <msub> <mi>s</mi> <mrow> <mi>M</mi> <mi>N</mi> </mrow> </msub> <mo>&rsqb;</mo> <mo>&Element;</mo> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>&times;</mo> <mi>M</mi> <mi>N</mi> </mrow> </msup> <mo>;</mo> </mrow>

Step 52, the double optimization that the first intermediate optima relational expression is converted to quadratic constraints is asked using the second substitution of variable Inscribe, the double optimization problem expression formula of the quadratic constraints is：

<mrow> <msubsup> <mi>z</mi> <mn>2</mn> <mi>H</mi> </msubsup> <msub> <mi>H</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>&GreaterEqual;</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> </mrow>

<mrow> <msup> <msub> <mi>z</mi> <mn>3</mn> </msub> <mi>T</mi> </msup> <msub> <mi>F</mi> <mi>j</mi> </msub> <msub> <mi>z</mi> <mn>3</mn> </msub> <mo>&GreaterEqual;</mo> <mn>0</mn> <mo>,</mo> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>n</mi> <mn>3</mn> </msub> </mrow>

Wherein,c_jRepresent coefficient vector；

Second substitution of variable is：

Wherein, p_j,q_jFor intermediate variable；

Step 53, the double optimization problem is solved, to obtain bilateral relay network under physical-layer network coding mechanism New planisphere and network code mapping mode approximate optimal solution.

3. physical-layer network coding method according to claim 2, it is characterised in that step 53 is specifically included：

Step 532, stochastic approximation structured approach is carried out using Gaussian vectors method, from the optimal solution X^*It is middle to extract the double optimization The suboptimal solution of problem, the suboptimal solution is approximate optimal solution.

4. physical-layer network coding method according to claim 3, it is characterised in that step 531 is specifically included：

x^HΔ x=tr (x^HΔ x)=tr (Δ xx^H)

The double optimization problem is replaced by ternary, the second optimal relation, the second optimization relation is converted to The expression formula of formula is：

s.t. tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

rank(Z₁)=1, rank (Z₂)=1

Rank (Z are fallen by relaxation₁)=1, rank (Z₂)=1, and willRelaxation isDescribed second is optimized Relational expression relaxation is the first Semidefinite Programming, wherein first Semidefinite Programming is：

s.t. tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <msubsup> <mi>z</mi> <mn>3</mn> <mi>H</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mn>3</mn> </msub> </mtd> <mtd> <msub> <mi>Z</mi> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>&PlusMinus;</mo> <mn>0</mn> </mrow>

5. physical-layer network coding method according to claim 3, it is characterised in that step 53 is specifically included：

Step 533, using the 4th substitution of variable, the 5th substitution of variable and the 6th substitution of variable, the double optimization problem is turned The 3rd optimal relation is changed to, wherein the 3rd optimal relation is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t. tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

<mrow> <mo>&lsqb;</mo> <mi>t</mi> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mi>i</mi> </msub> <msub> <mi>Z</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&PlusMinus;</mo> <mn>2</mn> <mi>t</mi> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <msubsup> <mi>g</mi> <mi>j</mi> <mi>H</mi> </msubsup> <msub> <mi>Z</mi> <mn>4</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mi>j</mi> </msub> <msub> <mi>Z</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mn>1</mn> <mo>&rsqb;</mo> <mi>t</mi> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>D</mi> <mi>k</mi> </msub> <msub> <mi>Z</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mo>&GreaterEqual;</mo> <mn>0</mn> </mrow>

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

rank(Z₁)=1, rank (Z₂)=1, rank (Z₃)=1

4th substitution of variable is：

<mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mi>M</mi> </msqrt> </mfrac> <mi>A</mi> <mo>&Element;</mo> <msup> <mi>C</mi> <mi>M</mi> </msup> <mo>;</mo> </mrow>

<mrow> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mi>N</mi> </msqrt> </mfrac> <mi>B</mi> <mo>&Element;</mo> <msup> <mi>C</mi> <mi>N</mi> </msup> <mo>;</mo> </mrow> 3

<mrow> <msubsup> <mi>z</mi> <mn>3</mn> <mi>T</mi> </msubsup> <mo>=</mo> <mo>&lsqb;</mo> <mfrac> <mn>1</mn> <msqrt> <mrow> <mi>M</mi> <mi>N</mi> </mrow> </msqrt> </mfrac> <mo>&lsqb;</mo> <msub> <mi>s</mi> <mn>11</mn> </msub> <msub> <mi>s</mi> <mn>12</mn> </msub> <mo>...</mo> <msub> <mi>s</mi> <mrow> <mi>M</mi> <mi>N</mi> </mrow> </msub> <mo>&rsqb;</mo> <mo>&Element;</mo> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>&times;</mo> <mi>M</mi> <mi>N</mi> </mrow> </msup> <mo>;</mo> </mrow>

5th substitution of variable is：

6th substitution of variable is：

Step 534, the order constraint rank (Z in the 3rd optimal relation are fallen in relaxation₁)=1, rank (Z₂)=1, rank (Z₃) =1 HeTo obtain relaxation problem, the relaxation problem expression formula is

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t. tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

Step 535, the solution of the relaxation problem is converted into the solution of the second Semidefinite Programming, second Semidefinite Programming Problem is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t. tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

Step 536, the double optimization is extracted from the optimal solution of second Semidefinite Programming using Gaussian approximation to ask The suboptimal solution of topic, the suboptimal solution is approximate optimal solution.

6. a kind of physical-layer network coding device, it is characterised in that including：

Mapping block, in the aliasing planisphere that receives the via node, Euclidean distance to be less than the point of predetermined threshold value The same constellation point of new planisphere is mapped to, makes satisfaction：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0

Control module, for utilizing two Euclidean distance constrained parameters ε_A,ε_BTo control first source node, described respectively The decoding reliability of two source nodes, makes satisfaction：

|s_ij-s_ik|²≥ε_A,s_ij≠s_ik∈S

|s_ji-s_ki|²≥ε_B,s_ji≠s_ki∈S

Optimization relation sets up module, forFor object function, set up as follows Optimization relation：

[|(h₁a_i+h₂b_j)-(h₁a_p+h₂b_q)|²-ε_R]|s_ij-s_pq|²≥0

a_i,a_p∈A,b_j,b_q∈B,s_ij,s_pq∈S,i≠p,j≠q

Wherein, ()^HThe conjugate transposition of representing matrix；

Module is solved, for being solved to the optimization relation, to obtain bi-directional relaying net under physical-layer network coding mechanism The new planisphere of network and the approximate optimal solution of network code mapping mode.

7. physical-layer network coding device according to claim 6, it is characterised in that solve module and specifically include：

First intermediate optima relational expression acquisition submodule, for carrying out linear transformation and the first variable generation to the optimization relation Change, to obtain the first intermediate optima relational expression,

First substitution of variable is specially：

Double optimization problem expression formula acquisition submodule, is changed the first intermediate optima relational expression using the second substitution of variable For the double optimization problem of quadratic constraints, the double optimization problem expression formula of the quadratic constraints is：

z₃ ^TF_jz₃>=0 ,=1,2 ..., n₃

Wherein,c_jRepresent coefficient vector；

Second substitution of variable is：

Wherein, p_j,q_jFor intermediate variable；

Submodule is solved, it is two-way under physical-layer network coding mechanism to obtain for being solved to the double optimization problem The new planisphere of junction network and the approximate optimal solution of network code mapping mode.

8. physical-layer network coding device according to claim 7, it is characterised in that solve submodule and specifically include：

Optimal solution acquisition submodule, for being solved using semidefinite decoding algorithm to the double optimization problem, to obtain most Excellent solution X^*；

First suboptimal solution acquisition submodule, for carrying out stochastic approximation structured approach using Gaussian vectors method, from the optimal solution X^*In The suboptimal solution of the double optimization problem is extracted, the suboptimal solution is approximate optimal solution.

9. physical-layer network coding device according to claim 8, it is characterised in that optimal solution acquisition submodule is specifically used In：

x^HΔ x=tr (x^HΔ x)=tr (Δ xx^H)

s.t. tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

rank(Z₁)=1, rank (Z₂)=1

s.t. tr(H_1iZ₁) >=1, i=1,2 ..., n₁

tr(H_2iZ₂) >=1, i=1,2 ..., n₂

tr(D_jZ₁)-c_jz₃=1, tr (E_jZ₂)-d_jz₃=0

tr(F_jZ₃) >=0, j=1,2 ..., n₃

10. physical-layer network coding device according to claim 8, it is characterised in that solve submodule and specifically include：

3rd optimal relation acquisition submodule, for utilizing the 4th substitution of variable, the 5th substitution of variable and the 6th substitution of variable, The double optimization problem is converted into the 3rd optimal relation, wherein the 3rd optimal relation is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t. tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

rank(Z₁)=1, rank (Z₂)=1, rank (Z₃)=1

4th substitution of variable is：

<mrow> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mi>N</mi> </msqrt> </mfrac> <mi>B</mi> <mo>&Element;</mo> <msup> <mi>C</mi> <mi>N</mi> </msup> <mo>;</mo> </mrow>

5th substitution of variable is：

<msubsup> <mrow> <mo>{</mo> <msub> <mi>F</mi> <mi>i</mi> </msub> <mo>:</mo> <mo>=</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <msubsup> <mi>f</mi> <mi>i</mi> <mi>H</mi> </msubsup> <mo>}</mo> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>m</mi> <mn>1</mn> </msub> </msubsup> 7

6th substitution of variable is：

Relaxation problem expression formula acquisition submodule, the order constraint rank (Z in the 3rd optimal relation are fallen for relaxation₁)= 1,rank(Z₂)=1, rank (Z₃The He of)=1To obtain relaxation problem, the relaxation problem expression formula is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t. tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

I=1,2 ..., m₁, j=1,2 ..., m₂, k=1,2 ..., 2m₁m₂

Second Semidefinite Programming acquisition submodule, for the solution of the relaxation problem to be converted into the second Semidefinite Programming Solution, second Semidefinite Programming is：

min tr(Z₁)+tr(Z₂)+tr(Z₃)

s.t. tr(F_iZ₁) >=1, i=1,2 ..., m₁

tr(G_jZ₂) >=1, j=1,2 ..., m₂

tr(H_iZ₃) >=1, i=1,2 ..., m₃

Second suboptimal solution acquisition submodule, for being carried using Gaussian approximation from the optimal solution of second Semidefinite Programming The suboptimal solution of the double optimization problem is taken, the suboptimal solution is approximate optimal solution.