CN106027206B - A kind of two-way cooperating relay channel calculation forwarding code coefficient vector search method and communication means - Google Patents

Abstract

The invention discloses a kind of two-way cooperating relay channel calculation forwarding code coefficient vector search method and communication means, the code coefficient Vector Optimization Problems of relay node are modeled as the integer quadratic programming model with quadratic constraints by this method is for forwarding coding work mode is calculated in two-way cooperating relay channel the characteristics of；The characteristics of for the optimization problem, by promotion, convex relaxation, generate cutting plane and etc. convert former optimization problem to the new loose planning problem for being easier to solve, by the solution to relaxation planning problem effectively to obtain the optimal solution of former problem.The selection of code coefficient vector has an important influence network reachability energy index, and method proposed by the present invention can effectively obtain the combination of the optimal coefficient vector under current channel condition, provides good optimization basis to calculate the application of forwarding coding.

Description

A bidirectional cooperative relay channel calculation and forwarding coding coefficient vector search method and communication method letter method

technical field

The invention belongs to the technical field of wireless communication, relates to the cooperative communication technology under physical layer network coding, and proposes a method for searching forward coding coefficient vectors for calculation of a bidirectional cooperative relay channel.

Background technique

In wireless communication systems, transmitted signals are transmitted at the physical layer through electromagnetic waves. In the wireless multi-source communication network, the broadcast characteristics of the transmitting node make the receiving node may receive the transmitted information from multiple different source nodes in the same time slot, which will cause mutual interference between different transmission signals, thus affecting the whole network performance. Therefore, how to effectively deal with the mutual interference between multiple received signals at the receiving end is a major challenge in the research of wireless communication technology.

In recent years, linear network coding technology has achieved remarkable research results in wired network applications. Network coding has strong compatibility and information extraction capabilities, which makes it possible to solve the above-mentioned interference problem between multi-user signals. Most of the traditional network coding schemes run at the MAC layer. In order to reduce the corresponding modification of the existing wireless communication system software and hardware equipment and protocols, MAC layer resources and user scheduling algorithms are generally used to minimize interference. But traditional network coding methods are still inefficient when sending multi-source data. In a wireless network, how to effectively utilize the broadcast characteristics of the transmitting node to improve the wireless channel capacity is more important.

The computational forwarding network coding scheme based on nested Lattice can not only solve the decoding problem at the relay node under high-order modulation, but also approach the capacity of the AWGN bidirectional relay channel. The structural characteristics of Lattice coding make the superimposed signal vector still a codeword, and the relay node only needs to decode the linear combination of each codeword. The destination node can effectively decode the information sent by the source node by obtaining the linear combination information forwarded by each relay node.

SUMMARY OF THE INVENTION

Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a two-way cooperative relay channel calculation forwarding coding coefficient vector search method and communication method, the present invention can effectively obtain the optimal coefficient vector combination under the current channel state, It provides a good optimization basis for the application of computational forwarding coding.

Technical scheme: In order to realize the above-mentioned purpose, the technical scheme adopted in the present invention is:

A method for searching forwarding coding coefficient vector for bidirectional cooperative relay channel calculation. In the bidirectional cooperative relaying channel calculation and forwarding coding scheme, the optimization problem of calculating forwarding coding coefficient vector of relay nodes is modeled as an integer with quadratic constraints. Quadratic programming model. An auxiliary variable is introduced according to the forwarding coding coefficient vector of the relay node to promote the quadratic term in the integer quadratic programming model to a new high-dimensional space. Through the convexization and relaxation process, the integer quadratic programming model upgraded to a new high-dimensional space is transformed into a new relaxation problem, and the relaxation problem is solved. If the obtained optimal solution satisfies the integer requirements, it is the optimal solution of the original problem. optimal solution. Otherwise, define a cutting plane constraint according to the introduction of auxiliary variables and the convexity and relaxation constraints of the previous step, and add it to the constraint set of the relaxation problem to cut off part of the feasible solutions that do not meet the requirements, reduce the feasible region, and then solve the new slack planning problem. Repeat the above process until the integer optimal solution is obtained.

Specifically include the following steps:

Step 1: In the calculation and forwarding coding strategy of the bidirectional cooperative relay channel, the optimization objective function of the coefficient vector a of the relay node is obtained.

Step 2: According to the coefficient vector a of the relay node, the auxiliary variable A _ij is introduced to upgrade the quadratic term of the optimization objective function of the coefficient vector a of the relay node to a new high-dimensional space, and the coefficient vector a of the new relay node is obtained. optimization objective function.

Step 3: Use the PSD relaxation method to perform convex relaxation of the non-convex constraints in the original problem in step 2, and rewrite the optimization objective function of the coefficient vector a of the new relay node obtained in step 2 as a relaxation problem.

Step 4: Solve the relaxation problem in Step 3. If the obtained optimal solution satisfies the integer requirement, it is the optimal solution of the original problem, and skip to Step 6. Otherwise skip to step 4.

Step 5: In the constraint set of the relaxation problem obtained in Step 3, add the cutting plane constraints according to the introduction of auxiliary variables and the convexity and relaxation constraints of the previous step to cut off a part of the feasible solutions that do not meet the requirements, reduce the feasible region, and then , to solve a new relaxed programming problem.

Step 6: Return and output the optimal solution.

The optimization objective function of the coefficient vector a of the relay node obtained in the step 1 is as follows:

a=argmin(a ^T Ga)

st‖a‖ ² ≤1+P‖h‖ ²

a ₁ ≠0,a ₂ ≠0

Among them, a represents the coefficient vector of the relay node, that is, the integer coefficient of the linear combination of network coding, a ₁ represents the integer coefficients of the network coding of the node S ₁ , a ₂ represents the integer coefficients of the network coding of the node S ₂ , represents the matrix transpose, P represents the constraint power, h=[h ₁ , h ₂ ] ^T , is the real-valued channel gain between nodes S ₁ , S ₂ and the relay, and I represents the identity matrix.

The optimization objective function of the coefficient vector a of the new relay node in the step 2 is:

a=argmin<G,A>

and

Among them, I is a 2×2 identity matrix, S ² is a 2×2 symmetric matrix set, and b=1+P‖h‖ ² . The symmetric matrix A can be expressed as A=aa ^T . <A,B> represents the Frobenius inner product of symmetric matrices A and B, ie tr(A ^T B). Then the quadratic term a ^T Ga in the original problem can be expressed as <G, aa ^T >.

The relaxation problem obtained in step 3 is:

in, Indicates that A is a symmetric positive semi-definite matrix.

v represents an arbitrary real vector.

The cutting plane constraint obtained in the step 5 is expressed as:

Among them, v _k respectively represent The eigenvalues of the corresponding eigenvectors, express Any point in the variable space of , k=1,2.

A bidirectional cooperative relay channel communication method, comprising the following steps:

In step (1), in the bidirectional cooperative relay channel calculation forwarding coding scheme, the source nodes map their respective information from a finite field to a nested Lattice codeword.

In step (2), the source node simultaneously sends the mapped codeword information to the relay node.

In step (3), the relay node receives the composite signal from each source node, and decodes the received information into a linear combination equation of the Lattice codeword.

In step (4), the relay node broadcasts the Lattice equation to the first source node S ₁ and the second source node S ₂ , and each source node maps the Lattice code back to the finite field, and uses the information stored by itself to complete the decoding.

Beneficial effects: Compared with the prior art, a method for searching for a bidirectional cooperative relay channel calculation forwarding coding coefficient vector and a communication method provided by the present invention have the following beneficial effects:

Aiming at the characteristics of the calculation forwarding coding working mode in the bidirectional cooperative relay channel, the invention models the coding coefficient vector optimization problem of the relay node as an integer quadratic programming model with quadratic constraints; according to the characteristics of the optimization problem, The original optimization problem is transformed into a new relaxed planning problem that is easier to solve through the steps of lifting, convex relaxation, and cutting plane generation, and the optimal solution of the original problem can be effectively obtained by solving the relaxed planning problem. The selection of the coding coefficient vector has an important influence on the network reachability performance index; after simulation verification, the method proposed in the present invention can effectively obtain the optimal coefficient vector combination under the current channel state, and provides a good optimization foundation for the application of calculating forwarding coding .

Description of drawings

Fig. 1 is the block diagram of bidirectional relay channel calculation and forwarding strategy in the present invention;

Fig. 2 is the influence of coding coefficient vector on the reachable calculation rate in the present invention;

Fig. 3 is the calculation rate comparison of different coefficient vector search schemes in the present invention;

Fig. 4 is the influence of the channel coefficient on the achievable calculation rate when P=10dB in the present invention;

Fig. 5 is the influence of the channel coefficient on the achievable calculation rate when P=20dB in the present invention;

Fig. 6 is the influence of the channel coefficient on the attainable calculation rate when P=30dB in the present invention;

FIG. 7 is a schematic diagram of a bidirectional cooperative relay channel communication method.

Detailed ways

Below in conjunction with the accompanying drawings and specific embodiments, the present invention will be further clarified. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. Modifications in the form of valence all fall within the scope defined by the appended claims of the present application.

A method for searching forwarding coding coefficient vector for bidirectional cooperative relay channel calculation, as shown in Figure 1, in the bidirectional cooperative relay channel calculation and forwarding coding scheme, the optimization problem of calculating forwarding coding coefficient vector of relay nodes is modeled as a Quadratic Constrained Integer Quadratic Programming Model. An auxiliary variable is introduced according to the forwarding coding coefficient vector of the relay node to promote the quadratic term in the integer quadratic programming model to a new high-dimensional space. Through the convexization and relaxation process, the integer quadratic programming model upgraded to a new high-dimensional space is transformed into a new relaxation problem, and the relaxation problem is solved. If the obtained optimal solution satisfies the integer requirements, it is the optimal solution of the original problem. optimal solution. Otherwise, define a cutting plane constraint according to the introduction of auxiliary variables and the convexity and relaxation constraints of the previous step, and add it to the constraint set of the relaxation problem to cut off part of the feasible solutions that do not meet the requirements, reduce the feasible region, and then solve the new slack planning problem. Repeat the above process until the integer optimal solution is obtained.

As shown in Figure 1, the relay node uses the received signal obtained in the multiple access phase The estimated value of the linear combination equation of is broadcast to each source node. Each source node passes the decoder Map the received codeword back to the finite field and subtract the information stored by itself to recover the required estimated information

Specifically include the following steps:

Step 1: In the calculation and forwarding coding strategy of the bidirectional cooperative relay channel, the optimization objective function of the coefficient vector a of the relay node is obtained. If the coefficient vectors of the linear equations recovered by the relay node are different, the reachable calculation rate of each node is also different. In order to maximize the system capacity, the optimization problem of calculating forwarding coding coefficient vectors of relay nodes is modeled as an integer quadratic programming model with quadratic constraints. Among them, the optimization objective function of the coefficient vector a of the relay node is as follows:

a=argmin(a ^T Ga)

st‖a‖ ² ≤1+P‖h‖ ²

a ₁ ≠0,a ₂ ≠0

Among them, a represents the coefficient vector of the relay node, that is, the integer coefficient of the linear combination of network coding, a ₁ represents the integer coefficients of the network coding of the node S ₁ , a ₂ represents the integer coefficients of the network coding of the node S ₂ , represents the matrix transpose, P represents the constraint power, h=[h ₁ , h ₂ ] ^T , is the real-valued channel gain between nodes S ₁ , S ₂ and the relay, and I represents the identity matrix.

Step 2: Introduce auxiliary variable A _ij according to the coefficient vector a of the relay node, and upgrade the quadratic term of the optimization objective function formula (1) of the coefficient vector a of the relay node to a new high-dimensional space, let A _ij =a _i a _j (1≤i, j≤2), the symmetric matrix A can be expressed as A=aa ^T , and <A,B> represents the Frobenius inner product of the symmetric matrix A and B, that is, tr(A ^T B). Then the quadratic term a ^T Ga in the original problem (formula (1)) can be expressed as <G, aa ^T >. Therefore, the optimization objective function of the coefficient vector a of the new relay node is obtained:

and

Among them, I is a 2×2 identity matrix, S ² is a 2×2 symmetric matrix set, and b=1+P‖h‖ ² . The symmetric matrix A can be expressed as A=aa ^T . <A,B> represents the Frobenius inner product of symmetric matrices A and B, ie tr(A ^T B). Then the quadratic term a ^T Ga in the original problem can be expressed as <G, aa ^T >.

It can be seen from the above formula (2) that the improved minimization problem is transformed from the original quadratic function and quadratic constraints to a linear integer optimization problem about (a, A), which reduces the difficulty of solving.

Step 3: Use the PSD relaxation method to perform convex relaxation of the non-convex constraints in the original problem in step 2, and rewrite the optimization objective function of the coefficient vector a of the new relay node obtained in step 2 as a relaxation problem.

In the original problem (1), the quadratic constraint is a convex constraint. However, the constraint A=aa ^T introduced in the lifting process is not convex, and an appropriate relaxation method is used to make the optimization problem convex. The original problem (1) can be written in the following equivalent form

in, express The convex envelope of .

Not considering A=aa ^T and Two constraints, the problem constraints can be expressed as follows:

make Indicates that A is a symmetric positive semi-definite matrix, which can be obtained by A=aa ^T Therefore, on this basis, the PSD relaxation method can be used to convexly relax the non-convex constraints in the original problem.

for Satisfy:

Therefore, the linear positive semi-definite inequality apply to The PSD constraints are defined as follows:

After adding the PSD relaxation constraint,

make

Then the relaxed objective function formula (2) can be expressed as:

because is a semi-positive definite matrix, that is:

The PSD constraint in equation (3) can be replaced by the following form (relaxation problem):

where v represents an arbitrary real vector.

Step 4: Solve the relaxation problem in Step 3. If the obtained optimal solution satisfies the integer requirement, it is the optimal solution of the original problem, and skip to Step 6. Otherwise skip to step 4.

Step 5: In the constraint set of the relaxation problem obtained in Step 3, add the cutting plane constraints according to the introduction of auxiliary variables and the convexity and relaxation constraints of the previous step to cut off a part of the feasible solutions that do not meet the requirements, reduce the feasible region, and then , to solve a new relaxed programming problem.

make express any point in the variable space of . able to pass feature decomposition to discriminate Whether it is within the constrained region of the PSD cone. Let _{λk and vk denote} respectively The eigenvalues of and their corresponding eigenvectors, k=1,2. Without loss of generality, it is assumed that λ ₁ ≤ ₂ , λ _t <0≤λ _t+1 , t∈0,1,2. If t=0, it means that all eigenvalues are non-negative, is a positive semi-definite matrix; if t≠0, then k=1,...,t, which cannot be satisfied is the requirement for a positive definite matrix.

Therefore, the following formula can be used as a cutting plane constraint and added to the original constraint set to solve a new relaxed programming problem.

Among them, v _k respectively represent The eigenvalues of the corresponding eigenvectors, express Any point in the variable space of , k=1,2.

Step 6: Return and output the optimal solution.

A two-way cooperative relay channel communication method, as shown in Figure 7, includes the following steps:

In step (1), in the bidirectional cooperative relay channel calculation forwarding coding scheme, the source nodes map their respective information from a finite field to a nested Lattice codeword.

In step (2), the source node simultaneously sends the mapped codeword information to the relay node.

In step (3), the relay node receives the composite signal from each source node, and decodes the received information into a linear combination equation of the Lattice codeword.

In step (4), the relay node broadcasts the Lattice equation to the first source node S ₁ and the second source node S ₂ , and each source node maps the Lattice code back to the finite field, and uses the information stored by itself to complete the decoding.

FIG. 2 shows the influence of the coding coefficient vector on the achievable calculation rate in the present invention. The search problem of the linear combination coefficient vector of the codeword is the key problem in calculating the forwarding coding strategy. Under the condition that the channel coefficients are fixed, different coding coefficient vectors will have an important impact on the network achievable rate index. It is assumed that the transmission rates of each source node in the bidirectional cooperative relay network are symmetrical, that is, R ₁ =R ₂ . Let the channel coefficient vector h=[1,h ₂ ] ^T , h ₂ ∈ [0,1], and the power constraint P is 10dB. Figure 2 shows the influence of coefficient vectors of different codeword linear combinations on the information rate. In this paper, the achievable calculation rates of three coefficient vectors, a=[0,1] ^T , a=[-1,-1] ^T , and a=[1,2] ^T , are compared respectively. As can be seen from the figure, the achievable calculation rate is closely related to the selection of the coding coefficient vector. When the encoding coefficient vector matches the current channel coefficients, the network achievable computation rate is maximized. When h ₂ =1, a=[-1,-1] The matching state of ^T and the channel coefficient is the best, so the achievable calculation rate is the largest. Therefore, in order to ensure the maximization of the system calculation rate, it is necessary to make an optimal selection of the encoding coefficient vector.

FIG. 3 is a comparison of calculation rates of different coefficient vector search schemes in the present invention. Using the Monte-Carlo method, 1000 random experiments were performed, and the obtained results were statistically averaged. The real-valued channel gains h ₁ , h ₂ between nodes S ₁ , S ₂ and relays are independent of each other and obey distribution, the power constraint P varies from 0dB to 30dB. Figure \3 shows the comparison of the reachable calculation rate under several different schemes of the method proposed in this paper, the upper bound of the reachable calculation rate, the exhaustive search algorithm and the coefficientless vector search PNC. The upper bound of the reachable computation rate for computing the forwarding strategy can be expressed as The exhaustive search algorithm exhaustively searches all integer combinations of the coding coefficient vectors within the constraint range, and the solution that satisfies the current maximum calculation rate is the optimal coefficient vector in the current channel state. The LRCP algorithm represents the coefficient vector search algorithm proposed in this paper. The uncoded coefficient vector search PNC scheme is defined that the relay node directly decodes and forwards the information x ₁ +x ₂ to each source node without performing the coefficient vector search. As can be seen from the figure, the achievable computing rates obtained by different coding strategies are significantly different. Since the solution obtained by the exhaustive search algorithm is the optimal coefficient vector, it is the closest to the theoretical bound. The results obtained by the LRCP algorithm are consistent with the exhaustive search algorithm, indicating that the algorithm proposed in this paper can effectively obtain the optimal coefficient vector combination of the network. The coefficientless vector search PNC scheme has the worst performance because there is no corresponding adjustment of the coefficient vector for the change of the channel coefficient, and there is a large performance gap under the condition of high signal-to-noise ratio.

Figures 4, 5, and 6 show the influence of channel coefficient changes on the achievable calculation rate when the power constraint P is 10dB, 20dB, and 30dB, respectively. Let the channel coefficient vector h=[1,h ₂ ] ^T , h ₂ ∈[0,1], first obtain the optimal coefficient vector by the method proposed in this paper, and then calculate the achievable calculation rate under the optimal coefficient vector. It can be seen from the figure that under the condition of low signal-to-noise ratio, the performance of the method proposed in this paper, the exhaustive search algorithm and the coefficientless vector search PNC scheme are relatively close, and they are all close to the upper bound of the achievable calculation rate. However, with the increase of signal-to-noise ratio, the performance of the method and the exhaustive search algorithm proposed in this paper will be significantly better than the coefficientless vector search PNC scheme. It should be noted that the default coding coefficient vector of the non-coding coefficient vector search PNC scheme is a=[1,1] ^T . When h ₂ ≥ 0.8, the matching degree of this scheme with the channel coefficients is improved, so its performance is similar to the one presented in this paper. The proposed method is equivalent to the exhaustive search algorithm. Meanwhile, when h ₂ =0.5, the method proposed in this paper can reach the theoretical bound of the calculation rate.

The above simulation results show that the selection of coding coefficient vectors has an important impact on the network reachability performance indicators. The method proposed in this paper can effectively obtain the optimal combination of coefficient vectors under the current channel state, which provides a good optimization basis for the application of computing forwarding coding. .

The above is only the preferred embodiment of the present invention, it should be pointed out that: for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can also be made, and these improvements and modifications are also It should be regarded as the protection scope of the present invention.

Claims (2)

1. a two-way cooperative relay channel calculation forwarding coding coefficient vector search method, is characterized in that, comprises the following steps: Step 1: In the calculation and forwarding coding strategy of the bidirectional cooperative relay channel, the optimization objective function of the forwarding coding coefficient vector a of the relay node is obtained; the optimization problem of calculating the forwarding coding coefficient vector of the relay node is modeled as a Constrained integer quadratic programming model; Among them, a represents the forwarding coding coefficient vector of the relay node, a ₁ represents the integer coefficient of the network coding of the node S ₁ , a ₂ represents the integer coefficient of the network coding of the node S ₂ , T represents the matrix transpose, P represents the constraint power, h=[h ₁ , h ₂ ] ^T , is the real-valued channel gain between nodes S ₁ , S ₂ and the relay, and I represents the identity matrix; Step 2: According to the forwarding coding coefficient vector a of the relay node, the auxiliary variable A _ij is introduced to promote the quadratic term in the integer quadratic programming model obtained in step 1 to a new high-dimensional space, and obtain the new relay node’s The optimization objective function of forwarding the encoding coefficient vector a; and where I is a 2×2 identity matrix, is a set of symmetric matrices of 2×2, b=1+P‖h‖ ² ; symmetric matrix A is promoted as A=aa ^T ; <A, B> represents the Frobenius inner product of symmetric matrix A and symmetric matrix B, denoted as tr(A ^T B); then the quadratic term a ^T Ga in equation (1) is expressed as <G, aa ^T >; Step 3: Using the PSD relaxation method, the non-convex constraints in the optimization objective function of the forwarding coding coefficient vector a of the new relay node obtained in step 2 are convexly relaxed, and the forwarding of the new relay node obtained in step 2 is performed. The optimization objective function of the encoding coefficient vector a is rewritten as a relaxation problem; for Satisfy: Therefore, the linear positive semi-definite inequality apply to express The convex envelope of , the PSD constraint is defined as follows: After adding the PSD relaxation constraint, make Then the relaxed objective function formula (2) is expressed as: because is a positive semi-definite matrix: Replace the PSD constraint in Eq. (3) with a relaxation problem of the following form: Among them, v represents any real vector; Step 4: Solve the relaxation problem obtained in step 3. If the obtained optimal solution satisfies the integer requirement, it is the optimal solution of the optimization objective function of the forwarding coding coefficient vector a of the new relay node obtained in step 2, and skips Go to step 6; otherwise, go to step 5; Step 5: In the constraint set of the relaxation problem obtained in step 3, add cutting plane constraints according to the introduction of auxiliary variables and the convexity and relaxation constraints in step 3, so as to cut off part of the feasible solutions that do not meet the requirements, and reduce the feasible region to obtain a new slack programming problem, then, solve the new slack programming problem; The cutting plane constraint obtained in the step 5 is expressed as: Among them, v _k respectively represent The eigenvalues of the corresponding eigenvectors, express Any point in the variable space of , k=1,2; Step 6: Return and output the optimal solution. 2. A bidirectional cooperative relay channel communication method based on the bidirectional cooperative relay channel calculation forwarding coding coefficient vector search method according to any one of claim 1, characterized in that, comprising the following steps: Step (1), in the bidirectional cooperative relay channel calculation forwarding coding scheme, the source node maps the respective information from the finite field to a nested Lattice codeword; Step (2), the source node sends the mapped codeword information to the relay node at the same time; Step (3), the relay node receives the composite signal from each source node, and decodes the received information into a linear combination equation of the Lattice codeword; In step (4), the relay node broadcasts the Lattice equation to the first source node S ₁ and the second source node S ₂ , and each source node maps the Lattice code back to the finite field, and uses the information stored by itself to complete the decoding.