CN114928383B - Reconfigurable intelligent surface-assisted beam attack method - Google Patents

Abstract

The invention belongs to the technical field of information and communication, and particularly relates to a Reconfigurable Intelligent Surface (RIS) assisted beam attack method. The objective of the invention is that the attacker (Wyn) minimizes the achievable rate at the receiver (Bob) by adjusting the Phase Shift (PS) matrix of the RIS. For the non-convex optimization problem of RIS-assisted beam forming, the invention provides a low-complexity alternating direction (LAD) algorithm. The algorithm decomposes the problem of solving the PS matrix of the RIS into the problem of sequentially solving each element in the matrix, and can obtain the closed solution of each reflection unit PS, thereby reducing the computational complexity of solving the non-convex optimization problem. Meanwhile, simulation results show that the solving algorithm provided by the invention has better convergence; compared with a random scheme and a RIS-free scheme, the method can achieve better effect on minimizing the reachable rate of the receiver.

Description

Reconfigurable intelligent surface-assisted beam attack method

Technical Field

The invention belongs to the technical field of information and communication, and particularly relates to a reconfigurable intelligent surface-assisted beam attack method.

Background

Reconfigurable intelligent interface (RIS) is a potential technology for future sixth-generation mobile communication due to its ability to control Phase Shift (PS) of reflected signals. Existing research has shown that RIS can achieve considerable multipath diversity gain without the need for expensive hardware equipment. In recent years, with the aid of RIS, various algorithms such as semi-definite relaxation, OM algorithm, MM algorithm, block coordinate descent, and ADMM algorithm have been proposed for the problem of maximizing the receiver reachability. Meanwhile, RIS is also regarded as a key technology that can improve the security of the physical layer.

It is worth mentioning that most of the existing research focuses on the performance gain from RIS, with little attention paid to the potential risks of this technology. As a low cost passive device, the RIS may also be controlled by an illegal attacker. Compared with active attack, the RIS-assisted passive beamforming attack can achieve the attack purpose without additional transmission power. For example, "k.huang and h.wang," Intelligent reflection Surface air polluted Attack attach and Its coutersearch, "IEEE trans. Wire.Commun., vol.20, no.1, pp.345-359, jan.2021," proposes a Pilot pollution Attack mode in which an eavesdropper controls an RIS; "J.Yang, X.Ji, F.Wang, K.Huang and L.Guo," A novel pitch painting scheme via the interpretation of the design parameter based on the static CSI, "IEEE trans. Ven.Technol., doi:10.1109/TVT.2021.3120602" realizes the minimization of the privacy capacity by changing the phase shift parameters of the RIS uplink and downlink. It can be seen that the two documents mentioned above disclose to us that an eavesdropper can eavesdrop on information using the RIS.

However, the receiver may also take corresponding measures to prevent the eavesdropper from eavesdropping on the information. In fact, for an attacker (Wyn), it is possible to completely concentrate on reducing the communication quality of the receiver and minimize the reachable rate of the receiver by controlling the RIS to achieve the purpose of attack.

Disclosure of Invention

The invention aims to provide an algorithm for solving the non-convex optimization problem involved in RIS-assisted beam forming. The technical scheme of the invention is based on a RIS auxiliary passive beam forming attack model controlled by Wyn, provides an optimization problem for minimizing the accessibility of a receiving party and provides a low-complexity alternating direction (LAD) algorithm.

Consider a RIS assisted multiple-input multiple-output (MIMO) wireless communication system as shown in fig. 1. The sender (Alice) and the receiver (Bob) communicate with each other via a direct path and a RIS. Since RIS is controlled by an attacker (Wyn), wyn can obtain Channel State Information (CSI) of a channel. Specifically, there are N at Alice and Bob, respectively _t And N _r The root antenna, RIS department has N reflection element. Assuming that each reflecting unit in the RIS can independently adjust the PS of the incident signal by its reflection coefficient, alice actually provides performance gain for communication with Bob by setting a beamforming vectorWyn interferes with Alice and Bob's communication by adjusting the reflective elements of the RIS. The link channel between Alice and RIS, the link channel between RIS and Bob, and the link channel between Alice and Bob are used respectively

To indicate that>

Representing a complex field. The baseband signal s sent by Alice satisfies s ^H s＝E _s ，E _s Representing the signal power.

Based on the above channel model, the signal received at Bob can be represented as:

in the formula

PS matrix, θ, representing RIS _i Epsilon [0,2 pi) represents the PS of the ith reflection unit; w satisfies | | w | non-conducting phosphor ² =1 represents beamforming vector at Alice; />

Representing complex additive white Gaussian noise, σ ² Representing noise power, I represents N _r An order unit matrix.

As previously described, alice affects communication at Alice and Bob by designing a beamforming vector w to maximize the achievable rate at Bob, and Wyn minimizes the achievable rate at Bob by designing the PS matrix Θ of RIS. Therefore, the optimization problem can be expressed as:

in the formula, R represents the reachable rate at Bob, and the calculation formula is as follows:

R＝log ₂ (1+γ _SNR ) (3)

in the formula of gamma _SNR Representing the received signal-to-noise ratio, according to equation (1), the expression is:

therefore, problem (P) ₀ ) Can be converted into:

since the Θ, w parameters in the optimization function are highly coupled, the problem (P) ₁ ) It is difficult to solve. In addition, problem (P) ₁ ) The constraint of (2) is also non-convex, and some conventional solution methods such as semi-definite relaxation and the like have high computational complexity. Therefore, next, a low complexity alternating direction (LAD) algorithm will be presented herein to solve such problems, which is also the core of the present invention.

1) Determination of beamforming vector w at Alice.

For a given PS matrix Θ, the problem (P) ₁ ) Can be rewritten as:

problem (P) ₂ ) Is equivalent to:

because of the matrix H ^H H is N ^t Hermite order, so:

in the formula of _max (H ^H H) Representation matrix H ^H The maximum eigenvalue of H, and w is now the matrix H ^H H corresponds to the feature vector with the maximum feature value and satisfies | | w | | luminance ² ＝1。

2) Determination of PS matrix Θ at Wyn.

According to equation (8), problem (P) ₁ ) Can be converted into:

the matrix theory knowledge can be used for obtaining:

therefore, problem (P) ₄ ) Can be converted into:

in order to deduce theta _i Closed-form solution of (i =1,2, …, N), problem (P) when other parameters are fixed ₅ ) Can be decomposed into N subproblems, where N represents the number of reflector elements, where the nth subproblem is:

definition matrix

The expressions are respectively:

wherein i =1,2, …, N, j =1,2, …, N _t ,k＝1,2,…,N _r ，|P _i,j,k I represents the element P _i,j,k The amplitude of (a) is determined,

indicating its phase. | Q _j,k I and phi _j,k Also respectively represent elements Q _j,k Amplitude and phase of (c).

Order to

The equation has two roots, respectively:

in the formula:

/>

in>

The solution with smaller value is the problem (P) ₅ N). And sequentially calculating N sub-problems to obtain the PS matrix theta at the RIS.

And (3) LAD algorithm calculation complexity analysis:

since the closed-form solution of the PS for each reflection unit is available, the computational complexity of the algorithm is greatly reduced. Specifically, the calculation process of the LAD algorithm mainly includes two parts. The first part is the solution of the parameters J and L, each with a solution complexity of

The second part is the solution of the parameters K and M, each having a solution complexity of ≦>

Therefore, the calculation ^ is based on the formulas (15) and (16)>

And &>

In total->

Since N =1,2, …, N, the computational complexity of each iteration is ≦ ≦ for the next iteration>

Assuming P represents the number of iterations, then the overall complexity of the algorithm is ≧>

The invention has the beneficial effect that for the non-convex optimization problem of RIS-assisted beam forming, the invention provides a low-complexity alternating direction algorithm. The algorithm decomposes the problem of solving the PS matrix of the RIS into the problem of sequentially solving each element in the matrix, and can obtain the closed solution of each reflection unit PS, thereby reducing the computational complexity of solving the non-convex optimization problem. Meanwhile, simulation results show that the solving algorithm provided by the invention has better convergence; compared with a random scheme and a RIS-free scheme, the method can achieve better effect on minimizing the reachable rate of the receiver.

Drawings

Fig. 1 is a RIS assisted MIMO passive beam attack diagram.

Fig. 2 is a simulation diagram of the convergence situation of the LAD algorithm under the condition of a single channel.

FIG. 3 is a simulation diagram of the convergence of the LAD algorithm under average channel conditions.

Fig. 4 is a graph of a simulation comparing the performance of the LAD algorithm and the other two algorithms.

Detailed Description

The steps and features of the present invention are described in detail below in conjunction with the attached drawing figures so that those skilled in the art can better understand the present invention.

FIG. 1 is a general system diagram of the application of the present invention. The goal of this communication system is Wyn to minimize the achievable rate at Bob by adjusting the PS matrix of the RIS. Under the channel model, the specific implementation steps of the invention are as follows:

a) Respectively inputting a channel fading coefficient matrix T, R, D between Alice and RIS, between RIS and Bob, and between Alice and Bob, and a maximum iteration number iter _max Initialization of the PS matrix theta of the RIS _in ；

b) Respectively calculate according to the formulas (15) and (16)

Then taken so as to->

Smaller than>

And assigned a value of theta _n ；

c) Repeating the step b), calculating the PS values of the N reflection units and obtaining a PS matrix theta of the RIS;

d) Let theta _in ＝Θ；

e) Repeating the steps b) c) d) until the value of the objective function in the formula (12) is lower than a preset threshold value epsilon or the maximum iteration number iter is reached _max . Taking the theta value of the last iteration as the optimal solution theta of the PS matrix at the RIS _opt ；

f) Calculating to obtain the most beamforming vector w at Alice according to a formula (8) _opt ；

g) Output theta _opt ，w _opt 。

Fig. 2 shows the convergence of the LAD algorithm under both single and average channels. As shown in FIGS. 2 and 3, after each iteration, the reachable rate at Bob is reduced or unchanged, which shows that the algorithm has better convergence. Meanwhile, the large-scale RIS can make the convergence rate of the algorithm faster and the reachable rate at Bob smaller.

Fig. 4 compares the performance of three different methods. Specifically, the LAD algorithm is the content of the present invention, the random scheme represents PS matrix random assignment of RIS, and the RIS-free scheme represents a traditional communication system without RIS. As can be seen from FIG. 3, compared with the random scheme and the RIS-free scheme, the LAD algorithm can greatly reduce the reachable rate at Bob along with the increase of the number of the reflecting surface units, so as to achieve the purpose of RIS-assisted interference on the normal communication of Alice and Bob.

Claims (1)

1. A reconfigurable intelligent surface-assisted beam attack method is used for a multi-input multi-output wireless communication system with RIS, a sender (Alice) and a receiver (Bob) in the system communicate with the RIS through a direct path, the RIS is controlled and defined by an attacker (Wyn), and N are respectively arranged at the Alice and the Bob _t And N _r The system comprises a root antenna, N reflection units are arranged at an RIS, each reflection unit in the RIS can independently adjust PS of an incident signal, alice provides performance gain for communication with Bob by setting a beam forming vector, and Wyn interferes with the communication of Alice and Bob by adjusting the reflection units of the RIS; the link channel between Alice and RIS, the link channel between RIS and Bob and the link channel between Alice and Bob are used respectively

To indicate that>

Representing complex number field, the baseband signal s sent by Alice satisfies s ^H s＝E _s ，E _s Represents the signal power; the signal received at Bob is represented as:

in the formula

PS matrix, θ, representing RIS _i Epsilon [0,2 pi) represents PS of the ith reflection unit, w satisfies | | w | pre-calculation ² =1 denotes beamforming vector at Alice @>

Representing complex additive white Gaussian noise, σ ² Representing the noise power, I representing the identity matrix; the method is characterized in that the beam forming attack method comprises the following steps:

alice maximizes the reachable rate at Bob by designing a beamforming vector w, and Wyn minimizes the reachable rate at Bob by designing PS, so as to influence the communication at Alice and Bob, and then an optimization problem is established as follows:

P ₀ :

s.t.||w|| ² ＝1

θ _i ∈[0,2π),i＝1,2,…,N

r represents the achievable rate at Bob:

R＝log ₂ (1+γ _SNR )

γ _SNR representing the received signal-to-noise ratio:

will question P ₀ Conversion to:

P ₁ :

s.t.||w|| ² ＝1

θ _i ∈[0,2π),i＝1,2,…,N

determining a beamforming vector w at Alice:

for a given PS matrix Θ, the problem P ₁ The rewrite is:

P ₂ :

s.t.||w|| ² ＝1

problem P ₂ Is equivalent to:

P ₃ :

s.t.||w|| ² ≠0

matrix H ^H H is N ^t An Hermite order matrix, then:

in the formula of _max (H ^H H) Representation matrix H ^H The maximum eigenvalue of H, and w is now the matrix H ^H H corresponds to the eigenvector with the largest eigenvalue and satisfies | | w | calry ² ＝1；

Determine the PS matrix Θ at Wyn:

will question P ₁ Conversion to:

P ₄ :

s.t.θ _i ∈[0,2π),i＝1,2,…,N

from the knowledge of matrix theory:

will question P ₄ Conversion to:

P ₅ :

s.t.θ _i ∈[0,2π),i＝1,2,…,N

when other parameters are fixed, the problem P is solved ₅ The method is divided into N subproblems, wherein N is the number of reflecting units of the RIS, and the nth subproblem is as follows:

s.t.θ _n ∈[0,2π)

definition matrix

Wherein i =1,2, …, N, j =1,2, …, N _t ,k＝1,2,…,N _r ，|P _i,j,k I represents the element P _i,j,k The amplitude of (a) is determined,

represents its phase, | Q _j,k I and phi _j,k Respectively represent an element Q _j,k Amplitude and phase of;

order to

The nth sub-problem has two roots, respectively:

in the formula:

/>

in or>

The solution with smaller value is the problem P ₅ And (4) sequentially calculating N subproblems to obtain the PS matrix theta at the RIS. />

Images