CN114826835B - Interference covariance matrix estimation method of IRS auxiliary wireless communication system in direction modulation - Google Patents
Interference covariance matrix estimation method of IRS auxiliary wireless communication system in direction modulation Download PDFInfo
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Abstract
The invention discloses an interference covariance matrix estimation method of an IRS auxiliary wireless communication system in directional modulation, which firstly establishes an optimization problem of minimizing the difference between a sample interference covariance matrix and a receiver noise variance matrix and the Euclidean distance of an estimation matrix under the constraint of an interference covariance matrix parameter structure; then, separating and reconstructing parameters of the interference covariance matrix according to a parameter expression of the interference covariance matrix to obtain a new optimization variable and an optimization problem; and decomposing the new optimization problem into two sub-problems aiming at the two groups of variables, solving the two sub-problems by using a KKT condition and a gradient descent method respectively, alternately updating the two groups of variables until the objective function converges to obtain a solution of the new optimization problem, and calculating a corresponding matrix according to the obtained solution to obtain an estimated interference covariance matrix. The method and the device are not only suitable for small sample scenes, but also have higher estimation precision, and are beneficial to reducing the influence caused by malicious interference at a legal user receiving end.
Description
Technical Field
The invention relates to the technical field of wireless communication, in particular to an interference covariance matrix estimation method of an IRS auxiliary wireless communication system in directional modulation.
Background
In recent years, wireless communication technology has rapidly developed, but in practical applications, high complexity, high hardware cost and high energy consumption remain key issues to be solved. The presence of intelligent reflective surfaces (INTELLIGENT REFLECTING surfaces, IRS) alleviates this problem well. The IRS is made up of a large number of reconfigurable, low cost passive reflecting units, each of which can independently alter the phase of the incoming signal, which makes it possible to artificially improve or reconstruct the wireless propagation environment. By controlling the IRS reflection unit, the IRS can coherently add the reflected signal with the signals of other paths at the desired receiver, destructively add at the receiver of an illegal user or further add artificial noise, enhancing the security of the communication.
The conventional direction modulation ensures that only a receiver in a target direction can receive a useful signal by designing a transmitting beam, adding artificial noise into a transmitting signal and the like, and constellation diagrams in other directions are distorted, thereby ensuring the safety of information transmission. However, the base station of the conventional direction modulation communication system can only send a single privacy bit stream to the user under the condition of using a plurality of antennas, and the IRS is introduced into the direction modulation communication system to well overcome the limitation, so that the safety of the communication system is further improved. However, when there is malicious interference in the environment, the IRS also reflects the interference signal, so that the interference received by the legal user is further enhanced. When the receiving end is multi-antenna, the interference can be eliminated by the receiving beam forming of the receiving end, however, since the information of the illegal user is generally unknown to the legal user, the legal user needs to estimate the received interference covariance matrix before eliminating the interference.
Disclosure of Invention
The invention aims to provide an interference covariance matrix estimation method of an IRS auxiliary wireless communication system in directional modulation, which reduces the complexity of the estimation method and improves the estimation precision.
The technical solution for realizing the purpose of the invention is as follows: an interference covariance matrix estimation method of an IRS-assisted wireless communication system in directional modulation, comprising the following steps:
step 1, combining a sample interference covariance matrix, and establishing a target optimization problem for minimizing R and S Euclidean distances, wherein R represents the interference covariance matrix, and S represents the difference between the sample interference covariance matrix and the noise variance matrix;
Step2, separating unknown parameters from known parameters in an interference covariance matrix R parameter expression, and reconstructing the parameters by utilizing the property that the line-of-sight channel matrix rank is one to obtain new optimized variables, and establishing a new target optimization problem according to the variables;
Step 3, decomposing the optimization problem into two sub-problems related to two scalar quantities and one vector, and solving the unknown scalar quantities according to the KKT condition when the unknown vector quantities are fixed; when the unknown scalar is fixed, a gradient descent method is applied to obtain an unknown vector, and the two groups of variables are alternately and iteratively updated until the objective function converges, so that a solution of the optimization problem is obtained;
And step 4, calculating an interference covariance matrix according to the obtained variation, namely obtaining an interference covariance matrix estimation result.
Compared with the prior art, the invention has the remarkable advantages that: (1) The known parameters and the unknown parameters in the interference covariance parameter structure are separated and reconstructed, so that the structural constraint of an interference covariance matrix is considered as much as possible, the dimension of a variable to be estimated is reduced, and the complexity of an estimation method is reduced; (2) The interference covariance matrix can be estimated under the condition of small samples, and the estimation accuracy is higher than that of directly using the sample interference covariance matrix as estimation.
Drawings
Fig. 1 is a flow chart of a method of interference covariance matrix estimation in an IRS-assisted wireless communication system in directional modulation in accordance with the present invention.
Detailed Description
The present application is further illustrated in the accompanying drawings and examples which are to be understood as being illustrative of the application and not limiting the scope of the application, and various equivalent modifications to the application will fall within the scope of the application as defined by the appended claims after reading the application.
In an IRS auxiliary direction modulation system, an illegal user works in a model in a full duplex mode, and in the communication system, communication between a base station and a legal user is considered to reduce the theft of privacy information by the illegal user and also considered to eliminate the influence caused by interference sent by the illegal user at a receiving end. In order to eliminate the influence of malicious interference as much as possible, it is important to estimate the interference covariance matrix. Therefore, the invention provides an interference covariance matrix estimation method of an IRS auxiliary wireless communication system in directional modulation, which comprises the steps of firstly establishing an optimization problem by combining a received sample interference covariance matrix, then separating and reconstructing known parameters and unknown parameters in an interference covariance matrix parameter expression, converting the estimation of the interference covariance matrix into the estimation of two scalar quantities and one vector, estimating the variables by using an alternate iterative method, and finally obtaining the estimated covariance matrix according to the obtained variables.
Referring to fig. 1, the interference covariance matrix estimation method of the IRS-assisted wireless communication system in the directional modulation of the present invention comprises the following steps:
step 1, combining a sample interference covariance matrix, and establishing a target optimization problem for minimizing R and S Euclidean distances, wherein R represents the interference covariance matrix, and S represents the difference between the sample interference covariance matrix and the noise variance matrix;
Step2, separating unknown parameters from known parameters in an interference covariance matrix R parameter expression, and reconstructing the parameters by utilizing the property that the line-of-sight channel matrix rank is one to obtain new optimized variables, and establishing a new target optimization problem according to the variables;
Step 3, decomposing the optimization problem into two sub-problems related to two scalar quantities and one vector, and solving the unknown scalar quantities according to the KKT condition when the unknown vector quantities are fixed; when the unknown scalar is fixed, a gradient descent method is applied to obtain an unknown vector, and the two groups of variables are alternately and iteratively updated until the objective function converges, so that a solution of the optimization problem is obtained;
And step 4, calculating an interference covariance matrix according to the obtained variation, namely obtaining an interference covariance matrix estimation result.
As a specific implementation manner, in the step1, the interference covariance matrix and the sample interference covariance matrix are constructed as follows:
An IRS assisted directional modulation communication system model is established, wherein a base station is provided with N A antennas, the IRS consists of M passive reflecting elements, a legal user has N B antennas, and an illegal user has N M antennas. In the model, an illegal user works in a full duplex mode, so that the illegal user can eavesdrop on the privacy information sent to a legal user by a base station, and can also send an interference signal to the legal user to interfere the receiving of useful signals by the legal user. The base band signal s A transmitted by the base station is represented as
Wherein P A is total transmitting power, and beta epsilon [0,1] is power distribution factor of privacy information and artificial noise; And/> Transmit beamforming vector and artificial noise projection matrix, respectively, and satisfy the conditions v H v=1 and/>X is a transmission symbol satisfying E [ |x| 2 ] =1; /(I)For transmitted artificial noise, obeys complex gaussian distribution, i.e. >
The interference signal s M sent by the illegal user is expressed as:
Wherein P M is the total power of the interference transmitted by the illegal user, For interference projection matrix,/>N J is the number of antennas transmitting interference, which satisfies N J∈[1,NM -1;
in a direction modulation communication system, a wireless communication channel is a line-of-sight channel, and a normalized channel vector is
Where N is the number of antennas of the transmitter or receiver, and the phase function ψ θ (N) is defined as
Wherein θ, n, d, λ represent the direction angle of arrival or departure, the index number of the antenna, the cell pitch in the transmitting antenna array, the wavelength, respectively; the wireless communication channel matrix is given by H H(θ)＝h(θr)hH(θt), where θ r and θ t are the arrival direction angle and the departure direction angle of the signal, respectively.
After channel transmission and receive beamforming, the received signal at legal user Bob is expressed as
Wherein,Is the receive beamforming vector at Bob; /(I)Is additive white Gaussian noise and obeys the distribution/>Furthermore,/> Channel matrixes from IRS to legal user Bob, from base station Alice to IRS, from Alice to Bob, from illegal user Mallly to IRS and Mallly to Bob respectively; diagonal matrix/>The phase shift of the IRS is shown, wherein phi i is the phase shift of the signal after reflection by the ith passive reflection unit on the IRS; g AIB、gAB、gMIB、gMB represents the path loss of four paths from Alice to Bob via IRS, from Alice to Bob, from Mallory to Bob via IRS, and from Mallory to Bob, respectively.
For convenience of representation, H A1、HM1 is defined as Alice to Bob, mallly to Bob equivalent channel matrices, respectively, i.e
The portion of the malicious interference from Mallly in the signal received by Bob is obtained by equation (5)
In order to eliminate the influence of interference sent by Mallory on Bob received signals by a method of receiving beam forming in subsequent processing, an interference covariance matrix received by Bob from Mallory needs to be estimated, and an ideal interference covariance matrix R i is:
in order to estimate the interference covariance matrix, in a communication system, once the base station detects an interference signal, the base station does not transmit any signal, and then a legal user receives the interference signal and estimates the interference covariance matrix, where the received signal at the legal user Bob is
Using y B [ K ] to represent the signal received in the kth time slot, when the K sample signals are received at Bob, the sample interference covariance matrixRepresented as
When K approaches infinity, the sample interference covariance matrix can estimate the interference covariance matrix, at this time
However, when the number of samples is small, the estimation error of the sample interference covariance matrix becomes large. Thus, in order to make accurate estimates of the interference covariance matrix even with a small number of samples, we have established the following optimization objective function
Wherein,The difference between the sample interference covariance matrix and the receiver noise variance matrix;
Furthermore, in equation (12), in order to make the estimation of the interference covariance matrix R as accurate as possible, the optimization variable R should be constrained by the properties satisfied by R i, i.e., by the parameter structure (8). In order to make estimation accurate by utilizing the property of an ideal interference covariance matrix R i as much as possible, an optimization problem under the constraint of an interference covariance matrix parameter structure is established, unknown parameters and known parameters in the interference covariance matrix are separated and recombined to obtain new optimization variables, the optimization problem is converted into two sub-problems, and the two sub-problems are solved through alternate iteration to obtain a solution of a target optimization problem.
And (3) establishing a target optimization problem of minimizing the Euclidean distance between the interference covariance matrix R and the difference S between the sample interference covariance matrix and the receiver noise covariance matrix, wherein the interference covariance matrix is constrained by the parameter structure, namely the formula (8).
Taking the parameter expression of an ideal interference covariance matrix R i into consideration, establishing the following target optimization problem for accurately estimating R
As a specific embodiment, the step2 specifically includes the following steps:
let R i＝FFH, according to equation (8), obtain an expression for F while separating the unknown and known parameters in matrix F, which can be written as
Wherein the matrixAnd/>Representing an unknown portion of the covariance interference matrix; at the same time, due to channel matrix/>And/>The ranks of the matrices T 1 and T 2 are 1, and the matrices T 1＝αβH and T 2＝ωνH are decomposed to satisfy/>And/>The interference covariance matrix can be expressed as
Since the optimization problem for four vectors is still complex and the number of interfering transmit antennas N J for Mallory is generally unknown, we again construct the variables to simplify the original problem.
Let beta Hβ＝c1,νHβ＝c2,νHν＝c3 know that there is a relationship between these three new variablesWhere θ is the angle between vectors β and v. Furthermore, due to/>Wherein/>For the arrival and departure direction angles of IRS to Bob, we can let/>The interference covariance matrix may be expressed as
Looking at the above equation, it can be found that the dimension of the variable can be further reduced. Order theThe expression of the interference covariance matrix is converted into
Wherein,The new optimization problem is that
As a specific embodiment, the step 3 specifically includes:
Decomposing the optimization problem into terms respectively And/>Is a two-part problem with (a) and (b). When/>When fixed, can be solved according to KKT condition/>When/>When the gradient descent method is used for fixation, the/>Alternate update/>And/>Until the objective function converges, the estimated/>And/>
When givenWhen regarding the variables/>The optimization problem of (c) can be written as
Wherein the objective function is
In the formula (20), to simplify the expression, letAnd/>
The optimization problem (19) can be solved directly with the KKT condition. Setting Lagrangian multiplier of constraint condition as v, and letting m=aa * -e-v/2, then applying KKT condition to solveIs that
Three variables l 1,l2 and l 3 are set as
When l 3 is equal to or greater than 0, v=0; when l 3 < 0, the lagrangian multiplier v is the positive real root of equation v 3+l1v2+l2v+l3 =0. Substituting the obtained v into m and the formula (21), and obtaining the variable in the formula (22)Is a solution to the optimization of (3).
When givenWhen regarding the variables/>The optimization problem of (a) is an unconstrained optimization problem, and we directly apply a gradient descent method to solve the variable/>Objective function with respect to optimization variables/>The gradient of (2) is
During gradient descent, the optimization variables are as followsUpdating until convergence; wherein/>And/>The variables updated in the m-th step and the m-1 th step are respectively,/>For the gradient direction of the mth step,/>For the update step size of the m-th step, the step size is determined by a backtracking linear search method, and the objective function is ensured to be reduced in each update.
Thus, the update is alternately performed according to the above methodAnd/>Until convergence, a solution to the optimization problem (18) can be obtained.
S4, according to the variablesAnd/>Calculation/>The resulting matrix is the estimated interference covariance matrix.
In summary, the method separates and reconstructs the known parameters and the unknown parameters in the interference covariance parameter structure, so that the structural constraint of the interference covariance matrix is considered as much as possible, the dimension of the variable to be estimated is reduced, and the complexity of the estimation method is reduced. In addition, the invention can estimate the interference covariance matrix under the condition of small samples, has higher estimation precision compared with the method of directly using the sample interference covariance matrix as estimation, and is beneficial to reducing the influence caused by malicious interference at the receiving end of legal users.
Claims (1)
1. An interference covariance matrix estimation method of an IRS-assisted wireless communication system in directional modulation, comprising the following steps:
step 1, combining a sample interference covariance matrix, and establishing a target optimization problem for minimizing R and S Euclidean distances, wherein R represents the interference covariance matrix, and S represents the difference between the sample interference covariance matrix and the noise variance matrix;
Step 2, separating unknown parameters and known parameters in an interference covariance matrix R parameter expression, reconstructing the parameters by utilizing the property that the line-of-sight channel matrix rank is one to obtain new optimization variables, and establishing a new target optimization problem according to the variables;
Step 3, decomposing the optimization problem into two sub-problems related to two scalar quantities and one vector, and solving the unknown scalar quantities according to the KKT condition when the unknown vector quantities are fixed; when the unknown scalar is fixed, a gradient descent method is applied to obtain an unknown vector, and the two groups of variables are alternately and iteratively updated until the objective function converges, so that a solution of the optimization problem is obtained;
step 4, calculating an interference covariance matrix according to the obtained variation, namely, obtaining an interference covariance matrix estimation result;
in the step 1, the interference covariance matrix and the sample interference covariance matrix are constructed as follows:
Establishing an IRS-assisted direction modulation communication system model, wherein a base station is provided with N A antennas, the IRS consists of M passive reflecting elements, a legal user has N B antennas, and an illegal user has N M antennas; in the model, an illegal user works in a full duplex mode, and the illegal user can eavesdrop on the privacy information sent to a legal user by a base station and also can send an interference signal to the legal user to interfere the receiving of useful signals by the legal user; the base band signal s A transmitted by the base station is represented as
Wherein P A is total transmitting power, and beta epsilon [0,1] is power distribution factor of privacy information and artificial noise; And/> Transmit beamforming vector and artificial noise projection matrix, respectively, and satisfy the conditions v H v=1 andX is a transmission symbol satisfying E [ |x| 2 ] =1; /(I)For transmitted artificial noise, obeys complex gaussian distribution, i.e. >
The interference signal s M sent by the illegal user is expressed as:
Wherein P M is the total power of the interference transmitted by the illegal user, For interference projection matrix,/>N J is the number of antennas transmitting interference, which satisfies N J∈[1,NM -1;
in a direction modulation communication system, a wireless communication channel is a line-of-sight channel, and a normalized channel vector is
Where N is the number of antennas of the transmitter or receiver, and the phase function ψ θ (N) is defined as
Wherein θ, n, d, λ represent the direction angle of arrival or departure, the index number of the antenna, the cell pitch in the transmitting antenna array, the wavelength, respectively; the wireless communication channel matrix is given by H H(θ)＝h(θr)hH(θt), where θ r and θ t are the arrival direction angle and the departure direction angle of the signal, respectively;
after channel transmission and receive beamforming, the received signal at legal user Bob is expressed as
Wherein,Is the receive beamforming vector at Bob; /(I)Is additive white Gaussian noise and obeys the distribution/>Furthermore,/> Channel matrixes from IRS to legal user Bob, from base station Alice to IRS, from Alice to Bob, from illegal user Mallly to IRS and Mallly to Bob respectively; diagonal matrix/>The phase shift of the IRS is shown, wherein phi i is the phase shift of the signal after reflection by the ith passive reflection unit on the IRS; g AIB、gAB、gMIB、gMB represents the path loss of four paths from Alice to Bob via IRS, from Alice to Bob, from Mallory to Bob via IRS, from Mallory to Bob, respectively;
Definition H A1、HM1 is Alice to Bob, mallly to Bob equivalent channel matrix, respectively, i.e
The portion of the malicious interference from Mallly in the signal received by Bob is obtained by equation (5)
The ideal interference covariance matrix R i is:
in order to estimate the interference covariance matrix, in a communication system, once the base station detects an interference signal, the base station does not transmit any signal, and then a legal user receives the interference signal and estimates the interference covariance matrix, where the received signal at the legal user Bob is
Using y B [ K ] to represent the signal received in the kth time slot, when the K sample signals are received at Bob, the sample interference covariance matrixRepresented as
When K approaches infinity, the sample interference covariance matrix can estimate the interference covariance matrix, at this time
In step 1, a target optimization problem for minimizing R and S euclidean distances is established, specifically as follows:
Establishing the following optimized objective function
Wherein,The difference between the sample interference covariance matrix and the receiver noise variance matrix;
in equation (12), in order to accurately estimate the interference covariance matrix R, the optimization variable R should be constrained by the properties satisfied by R i, i.e., by parameter formula (8), the following objective optimization problem is established
The step2 specifically comprises the following steps:
let R i＝FFH, according to equation (8), obtain the expression of F, at the same time separate the unknown and known parameters in matrix F, the matrix is written as
Wherein the matrixAnd/>Representing an unknown portion of the covariance interference matrix; at the same time, due to channel matrix/>And/>The ranks of the matrices T 1 and T 2 are 1, and the matrices T 1＝αβH and T 2＝ωνH are decomposed to satisfy/>And/>The interference covariance matrix is expressed as
The number of interfering transmitting antennas N J of Mallory is unknown, and the variables are constructed again: let beta Hβ＝c1,νHβ＝c2,νHν＝c3 there be a relationship between these three new variablesWherein θ is the angle between vectors β and v; in addition, due toWherein/> For the arrival and departure direction angles of IRS to Bob, we can let/>The interference covariance matrix is expressed as
Order theThe expression of the interference covariance matrix is converted into
Wherein,The new optimization problem is that
The step 3 specifically comprises the following steps:
Decomposing the optimization problem into terms respectively And/>Is a sub-problem of (2); when/>Solving according to KKT condition when fixingWhen/>When fixed, the gradient descent method is applied to obtain/>Alternate update/>And/>Until the objective function converges to obtain the estimated/>And/>
When givenWhen regarding the variables/>Is written as an optimization problem of (1)
Wherein the objective function is
In the formula (20), letAnd/>
The optimization problem (19) is directly solved by using KKT conditions; setting Lagrangian multiplier of constraint condition as v, and letting m=aa * -e-v/2, then applying KKT condition to solveIs that
Three variables l 1,l2 and l 3 are set as
When l 3 is equal to or greater than 0, v=0; when l 3 < 0, the lagrangian multiplier v is the positive real root of equation v 3+l1v2+l2v+l3 =0; substituting the obtained v into m and the formula (21), and obtaining the variable in the formula (22)Is the optimal solution of (a);
When given When regarding the variables/>Is an unconstrained optimization problem, and a gradient descent method is applied to solve the variable/>Objective function with respect to optimization variables/>The gradient of (2) is
During gradient descent, the optimization variables are as followsUpdating until convergence; wherein/>AndThe variables updated in the m-th step and the m-1 th step are respectively,/>For the gradient direction of the mth step,/>The step length is the updating step length of the m step, and the step length is determined by a backtracking linear search method, so that the objective function is ensured to be reduced in each updating;
alternate updates according to the above method And/>Until convergence, a solution to the optimization problem (18) is obtained.
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