CN112929062B - MIMO interference channel network interference alignment method based on group sparsity - Google Patents

MIMO interference channel network interference alignment method based on group sparsity Download PDF

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CN112929062B
CN112929062B CN202110090058.XA CN202110090058A CN112929062B CN 112929062 B CN112929062 B CN 112929062B CN 202110090058 A CN202110090058 A CN 202110090058A CN 112929062 B CN112929062 B CN 112929062B
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刘伟
石钰林
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

A method for aligning interference of MIMO interference channel network based on group sparsity aims to separate a desired signal received by each receiver from an interference signal under the MIMO interference channel network, thereby eliminating the interference signal received by the receiver and increasing the degree of freedom of the network. The method comprises the following implementation steps: constructing an objective function with a group sparse structure; solving the optimal solution of the objective function by using an iterative solution method; each transmitter in the network uses a precoding matrix in the optimal solution of the objective function to precode signals transmitted by the transmitter, each receiver uses a decoding matrix in the optimal solution of the objective function to decode the signals received by the receiver, and interference signals received by the receiver are eliminated; the method can obtain higher degree of freedom in the same scene, and has wider application scene due to the use of a low-complexity solving method for the objective function.

Description

MIMO interference channel network interference alignment method based on group sparsity
Technical Field
The invention belongs to the technical field of communication, and further relates to a group sparsity-based Multiple Input Multiple Output (MIMO) interference channel network interference alignment method in the technical field of wireless communication. The invention can be used in an interference channel IC (interference channel) consisting of a plurality of transmitting-receiving pairs, and achieves the aim of interference alignment by designing a precoding matrix of a transmitter and a decoding matrix of a receiver on the premise that the transmitter knows global channel state information.
Background
Interference alignment is an effective interference management mechanism for eliminating network interference, and interference is overlapped at a receiving end by precoding a transmitting signal so as to completely eliminate the influence of the interference on a desired signal. Unlike existing methods of handling interference, which treat interference as noise, interference cancellation, and orthogonal access, interference alignment allows the network to gain maximum freedom by compressing the signal dimension occupied by interference. The interference alignment method is a key content of research in the technical field of interference alignment, and the traditional interference alignment method can only ensure partial sparsity of system interference vectors, can not completely make the system interference vectors be 0, and can not generate the required interference-free signal dimension under partial conditions.
An Interference alignment method based on manifold optimization for a MIMO Interference channel network is proposed in a paper published by Chen Zhang, Ziwei Liu and Gengxin Zhang, wherein the paper is 'Interference alignment schemes for k-user Interference channel based on optimization' (EURASIP Journal on Wireless Communications and Networking,2019 (1)). The method comprises the following implementation steps: firstly, setting parameters of a MIMO interference channel network with multiple inputs and multiple outputs; secondly, calculating the characteristic value of an interference covariance matrix of an interference channel network on the premise that a transmitting end and a receiving end know complete channel state information; thirdly, jointly designing a precoding and decoding matrix through the sum of the eigenvalues of the minimum interference covariance matrix; and fourthly, performing precoding operation on the transmitting signal of each transmitter in the MIMO interference channel system, and performing decoding operation on the receiving signal of each receiver to realize the effect of interference alignment. Although the method can realize the purpose of interference alignment in the MIMO interference channel, the method still has the defects that the mapping relation between the system degree of freedom and the group sparse level of the network interference vector under the MIMO interference channel is not considered, the sparse structure of the interference vector is not clear, only partial sparsity of the network interference vector can be realized, and the obtained network degree of freedom is lower.
The patent document "interference cancellation method associated with joint base station user" (publication number: CN108923879B, application number: CN201810738133.7) applied by the university of sienna electronics technology discloses an interference alignment method for joint interference cancellation for MIMO interference channel networks. The method comprises the following steps: firstly, setting a network model; secondly, constructing a target function, and converting the design problem of the pre-coding matrix into a mixed integer linear programming problem; thirdly, solving an objective function to obtain the association relation between each user and the base station and the number of data streams transmitted by each user; fourthly, the user transmits data stream to the base station associated with the user; and eliminating the interference signal of the base station to obtain the expected signal of the base station. However, the method still has the disadvantages that the mixed integer linear programming problem needs recursive operation for solving, the complexity of the algorithm grows exponentially along with the increase of the network scale, and the method is limited in application scenes and is not suitable for scenes with more transmitters and receivers in practical situations.
Disclosure of Invention
The invention aims to provide an interference alignment method based on group sparsity under an MIMO interference channel network, aiming at overcoming the defects in the prior art, and solving the problems that the sparse structure of an interference vector in the existing interference alignment method is not clear, only partial sparsity of the interference vector can be realized, the obtained network has low degree of freedom and high algorithm complexity, and the method is not suitable for a scene with more transmitters and receivers.
The technical idea for realizing the aim of the invention is as follows: establishing an objective function with a group sparse structure according to the mapping relation between the degree of freedom of the interference channel network system and the interference vector sparse structure; and determining the optimal solution of the objective function by using an iterative solution with smaller algorithm complexity, precoding the transmitting vector of each transmitter by using the optimal solution of the objective function, decoding the receiving vector of each receiver, eliminating the interference signal received by the receiver and realizing interference alignment.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) an objective function with a group sparse structure is constructed using the following equation:
Figure GDA0003294642240000021
wherein, P represents an objective function with a group sparse structure, min represents the minimum value operation, and { } represents an aggregate symbol, UkA decoding matrix representing the vector of the received signal by the kth receiver, K ∈ {1, 2., K }, [ epsilon ] representing symbols, K represents the total number of receivers in the MIMO interference channel network, K ≧ 2, VlDenotes the l thA transmitter precoding matrix for the transmitted signal vector, L ∈ {1, 2., L }, L representing the total number of transmitters in the network, L ═ K, Σ representing the accumulation operation, | | | | i2Which means a 2-norm operation is shown,
Figure GDA0003294642240000031
represents the interference vectors received by all but the ith transmitter in the MIMO interfering channel network for the mth expected data stream of the kth receiver, where l is k, M is e {1, 2.. multidata., d }, d represents the total number of data streams transmitted by each transmitter, and d is ≦ min { M ≦ for the mth transmitterl,Nk}，MlIndicating the number of antennas with which the ith transmitter is equipped, NkIndicating the number of antennas equipped in the kth receiver;
(2) solving an objective function P:
(2a) randomly selecting a value from (0,1), substituting the value into the elements of the decoding matrix of each receiver, and solving the precoding matrix in the objective function to obtain the precoding matrix of each transmitter;
(2b) respectively executing Schmidt orthogonalization operation on each precoding matrix, substituting all orthogonalized precoding matrices in current iteration into an objective function updated in last iteration, and solving a decoding matrix in the objective function to obtain a decoding matrix updated in current iteration of each receiver;
(2c) respectively executing Schmidt orthogonalization operation on each decoding matrix, substituting all orthogonalized decoding matrices in the current iteration into the target function updated in the last iteration, and solving the precoding matrix in the target function to obtain the precoding matrix updated in the current iteration of each transmitter;
(2d) judging whether the values of elements in all interference vectors are less than 10-5If so, obtaining the optimal solution of the target function P, and executing the step (3), otherwise, executing the step (2 b);
(3) each transmitter simultaneously transmits a data stream:
(3a) using the formula sl＝V'lxlPerforming a precoding operation on a transmission vector to be transmitted by each transmitter, wherein slTo representThe l transmitter precoded transmit vector, V'lThe l-th precoding matrix, x, representing the optimal solution of the objective function PlA transmit vector representing the ith transmitter;
(3b) each transmitter transmits the precoded transmission vector to a corresponding receiver;
(4) interference signal elimination of the receiver:
(4a) each receiver receives a pre-coded expected signal vector transmitted by a corresponding transmitter and simultaneously receives pre-coded interference signal vectors transmitted by other transmitters;
(4b) using the formula yk＝(U'k)HpkPerforming a decoding operation on the signal vector received by each receiver to separate its desired signal vector from the interfering signal vector, wherein ykRepresents the desired signal vector for the kth receiver, H represents the conjugate transpose operation, U'kRepresenting the kth decoding matrix, P, in the optimal solution of the objective function PkRepresenting a vector of signals received by the kth receiver;
(5) a non-interfering desired signal is obtained at each receiver, ending the interference alignment.
Compared with the prior art, the invention has the following advantages:
firstly, the invention constructs an objective function with a group sparse structure, can enable interference vectors in an interference channel network to have group sparsity by solving the optimal solution of the objective function, and overcomes the problem that the prior art can only realize partial sparsity of the interference vectors, so that the degree of freedom of the network is low, and the degree of freedom of the interference channel network in the invention is higher.
Secondly, the invention solves the optimal solution of the objective function by using an iterative solution, has low algorithm complexity, and overcomes the problems that the algorithm complexity is exponentially increased along with the increase of the network scale and the practical application scene is limited in the prior art, so that the invention can be suitable for the condition of large network scale and expands the application range.
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FIG. 1 is a flow chart of the present invention;
fig. 2 is a graph of simulation results of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The steps of the present invention will be described in further detail with reference to fig. 1.
Step 1, constructing an objective function with a group sparse structure as follows by using the following formula:
Figure GDA0003294642240000041
wherein, P represents an objective function with a group sparse structure, min represents the minimum value operation, and { } represents an aggregate symbol, UkA decoding matrix representing the K-th receiver on the received signal vector, K ∈ {1, 2., K }, K represents the total number of receivers in the MIMO interfering channel network, K ═ 4, VlA precoding matrix representing the L-th transmitter to the transmitted signal vector, L ∈ {1, 2., L }, L representing the total number of transmitters in the network, L ═ 4, Σ representing the accumulation operation, | | | | | y2Which means a 2-norm operation is shown,
Figure GDA0003294642240000042
represents the interference vectors received by all but the ith transmitter in the MIMO interfering channel network for the mth expected data stream of the kth receiver, where l is k, M is e {1, 2.. multidata., d }, d represents the total number of data streams transmitted by each transmitter, and d is ≦ min { M ≦ for the mth transmitterl,Nk}，d＝1，MlIndicating the number of antennas with which the ith transmitter is equipped, Ml＝3，NkIndicating the number of antennas with which the kth receiver is equipped, Nk＝3。
And 2, solving the objective function P.
And step 1, randomly selecting a value from (0,1), substituting the value into the elements of the decoding matrix of each receiver, and solving the precoding matrix in the objective function to obtain the precoding matrix of each transmitter.
And 2, respectively executing Schmitt orthogonalization operation on each precoding matrix to ensure the full rank of each precoding matrix, substituting all orthogonalized precoding matrices in the current iteration into the target function updated in the last iteration, and solving a decoding matrix in the target function to obtain the decoding matrix updated in the current iteration of each receiver.
And 3, respectively executing Schmidt orthogonalization operation on each decoding matrix to ensure the full rank of each decoding matrix, substituting all the orthogonalized decoding matrices in the current iteration into the target function updated in the last iteration, and solving the precoding matrix in the target function to obtain the precoding matrix updated in the current iteration of each transmitter.
Step 4, judging whether the values of elements in all interference vectors are less than 10-5If so, obtaining the optimal solution of the target function P, and executing the step 3, otherwise, executing the step 2 of the step.
And 3, each transmitter simultaneously transmits the data stream.
Step 1, using formula sl＝V'lxlPerforming a precoding operation on a transmission vector to be transmitted by each transmitter, wherein slRepresents the precoded transmit vector, V 'of the l-th transmitter'lThe l-th precoding matrix, x, representing the optimal solution of the objective function PlRepresenting the transmit vector of the ith transmitter.
And step 2, each transmitter transmits the precoded transmission vector to a corresponding receiver.
And 4, eliminating the interference signal of the receiver.
Step 1, each receiver receives a precoded expected signal vector transmitted by a corresponding transmitter, and simultaneously receives precoded interference signal vectors transmitted by other transmitters.
Step 2, using formula yk＝(U'k)HpkPerforming a decoding operation on the signal vector received by each receiver to separate its desired signal vector from the interfering signal vector, wherein ykRepresents the desired signal direction of the k-th receiverQuantity, H represents the conjugate transpose operation, U'kRepresenting the kth decoding matrix, P, in the optimal solution of the objective function PkRepresenting the vector of signals received by the kth receiver.
And 5, obtaining a non-interference expected signal at each receiver, and finishing interference alignment.
The effect of the present invention is further explained by combining the simulation experiment as follows:
1. simulation experiment conditions are as follows:
the hardware platform of the simulation experiment of the invention is as follows: the processor is an Intel i 78700 k CPU, the main frequency is 3.5GHz, and the memory is 8 GB.
The software of the simulation experiment of the invention is as follows: windows 10 operating system and Matlab R2018b emulation software.
2. Simulation content and result analysis thereof:
the simulation experiment of the invention is to simulate a multi-input multi-output MIMO interference channel network by programming in Matlab R2018b simulation software, wherein the network comprises 4 transmitters and 4 receivers, each transmitter in the network is respectively provided with 3 antennas, and each receiver is respectively provided with 3 antennas.
The simulation experiment of the invention is to adopt the invention and a prior art (interference alignment method under the interference channel based on manifold optimization), carry on 10 data transmission experiments to the interference channel network of MIMO separately, the transmitting power of the transmitter simulated by each experiment is 0dB, 5dB, 10dB, 15dB, 20dB, 25dB, 30dB, 35dB, 40dB, 45dB sequentially, each transmitter transmits 1 data stream in each simulation experiment, have obtained the total degree of freedom of the interference channel network of MIMO when the transmitting power of the transmitter is 0dB, 5dB, 10dB, 15dB, 20dB, 25dB, 30dB, 35dB, 40dB, 45dB respectively, its result is as shown in figure 2.
In the simulation experiment, one prior art adopted means:
the Interference alignment method under the Interference channel based on manifold optimization proposed in the article "Interference alignment schemes for k-user Interference channel based on optimization" (EURASIP Journal on Wireless Communications and networks, 2019 (1)) published by Gengxin Zhang et al.
The effect of the present invention will be further described with reference to the simulation diagram of fig. 2.
Fig. 2 is a comparison diagram of total degrees of freedom of networks respectively obtained by the method of the present invention and the method of the prior art under the same configuration of MIMO interference channel networks. The abscissa in fig. 2 represents the transmit power in dB for each transmitter in the MIMO interfering channel network. The ordinate represents the total degree of freedom of the MIMO interfering channel network. In fig. 2, a curve indicated by a square indicates a simulation result curve using the prior art, and a curve indicated by a circle indicates a simulation result curve using the method of the present invention.
As can be seen from the two simulation curves in fig. 2, when the transmission power of each transmitter in the MIMO interference channel network is less than 20dB, the total degree of freedom of the MIMO interference channel network obtained by the present invention is higher than that of the MIMO interference channel network obtained by the prior art.
The simulation experiment results show that under the condition that the transmitting power of each transmitter in the network is the same, the total degree of freedom of the MIMO interference channel network obtained by the method is higher than that of the MIMO interference channel network obtained by the prior art under the condition that the transmitting power of each transmitter is lower; the invention has wider application range and is a high-efficiency data transmission method.

Claims (1)

1. A MIMO interference channel network interference alignment method based on group sparsity is characterized in that an objective function P is constructed by utilizing the relation between the system degree of freedom and the group sparsity level of a network interference vector under a multi-input multi-output MIMO interference channel network, and a problem P is solved to obtain a precoding matrix and a decoding matrix, and the method comprises the following steps:
(1) an objective function with a group sparse structure is constructed using the following equation:
Figure FDA0003294642230000011
wherein, P represents an objective function with a group sparse structure, min represents the minimum value operation, and { } represents an aggregate symbol, UkA decoding matrix representing the vector of the received signal by the kth receiver, K ∈ {1, 2., K }, [ epsilon ] representing symbols, K represents the total number of receivers in the MIMO interference channel network, K ≧ 2, VlA precoding matrix representing the L-th transmitter to the transmitted signal vector, L ∈ {1, 2., L }, L representing the total number of transmitters in the network, L ═ K, Σ representing the accumulation operation, | | | | | y2Which means a 2-norm operation is shown,
Figure FDA0003294642230000012
represents the interference vectors received by all but the ith transmitter in the MIMO interfering channel network for the mth expected data stream of the kth receiver, where l is k, M is e {1, 2.. multidata., d }, d represents the total number of data streams transmitted by each transmitter, and d is ≦ min { M ≦ for the mth transmitterl,Nk}，MlIndicating the number of antennas with which the ith transmitter is equipped, NkIndicating the number of antennas equipped in the kth receiver;
(2) solving an objective function P:
(2a) randomly selecting a value from (0,1), substituting the value into the elements of the decoding matrix of each receiver, and solving the precoding matrix in the objective function to obtain the precoding matrix of each transmitter;
(2b) respectively executing Schmidt orthogonalization operation on each precoding matrix, substituting all orthogonalized precoding matrices in current iteration into an objective function updated in last iteration, and solving a decoding matrix in the objective function to obtain a decoding matrix updated in current iteration of each receiver;
(2c) respectively executing Schmidt orthogonalization operation on each decoding matrix, substituting all orthogonalized decoding matrices in the current iteration into the target function updated in the last iteration, and solving the precoding matrix in the target function to obtain the precoding matrix updated in the current iteration of each transmitter;
(2d) judging whether the values of elements in all interference vectors are less than 10-5If yes, obtaining the maximum of the target function PPreferably, executing the step (3), otherwise, executing the step (2 b);
(3) each transmitter simultaneously transmits a data stream:
(3a) using the formula sl＝V′lxlPerforming a precoding operation on a transmission vector to be transmitted by each transmitter, wherein slRepresents the precoded transmit vector, V 'of the l-th transmitter'lThe l-th precoding matrix, x, representing the optimal solution of the objective function PlA transmit vector representing the ith transmitter;
(3b) each transmitter transmits the precoded transmission vector to a corresponding receiver;
(4) interference signal elimination of the receiver:
(4a) each receiver receives a pre-coded expected signal vector transmitted by a corresponding transmitter and simultaneously receives pre-coded interference signal vectors transmitted by other transmitters;
(4b) using the formula yk＝(U'k)HpkPerforming a decoding operation on the signal vector received by each receiver to separate its desired signal vector from the interfering signal vector, wherein ykRepresents the desired signal vector for the kth receiver, H represents the conjugate transpose operation, U'kRepresenting the kth decoding matrix, P, in the optimal solution of the objective function PkRepresenting a vector of signals received by the kth receiver;
(5) a non-interfering desired signal is obtained at each receiver, ending the interference alignment.
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