CN113194072B - Legal monitoring implementation method assisted by intelligent reflecting surface - Google Patents

Legal monitoring implementation method assisted by intelligent reflecting surface Download PDF

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CN113194072B
CN113194072B CN202110362522.6A CN202110362522A CN113194072B CN 113194072 B CN113194072 B CN 113194072B CN 202110362522 A CN202110362522 A CN 202110362522A CN 113194072 B CN113194072 B CN 113194072B
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reflecting surface
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杜清河
王萌
张睿博
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Xian Jiaotong University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00Network architectures or network communication protocols for network security
    • H04L63/30Network architectures or network communication protocols for network security for supporting lawful interception, monitoring or retaining of communications or communication related information
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    • Y02DCLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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Abstract

The invention discloses an intelligent reflector-assisted legal monitoring implementation method, which comprises the following steps: in the reverse pilot transmission stage, a legal monitoring end performs pilot frequency spoofing, and pilot frequency sequences from a single-antenna suspicious receiving end are reflected by controlling a phase shift matrix of an intelligent reflecting surface, so that channel estimation of a multi-antenna suspicious transmitting end is wrong; in the data transmission stage, the legal monitoring end can maximize the signal-to-noise ratio of the legal monitoring end by controlling the phase shift matrix of the intelligent reflecting surface, and the legal monitoring assisted by the intelligent reflecting surface is completed.

Description

Legal monitoring implementation method assisted by intelligent reflecting surface
Technical Field
The invention belongs to the field of wireless information security, and relates to an intelligent reflector-assisted legal monitoring implementation method.
Background
The Intelligent Reflection Surface (IRS) is a brand new revolutionary technology in recent years, and a large number of low-cost passive reflection elements are integrated on the surface of the IRS, so that the wireless transmission environment can be intelligently configured, and the performance of a wireless communication network can be effectively improved. Each element on the IRS surface can cooperatively implement three-dimensional (3D) passive beamforming of directional signal enhancement or nulling by independently controlling the amplitude and phase of the incident signal. The intelligent reflection surface intelligently modifies the wireless channel through control signal reflection, and is in clear contrast with the wireless link adaptation of the existing transmitter and receiver, so that a new degree of freedom is provided for improving the performance of the wireless link, and a foundation is laid for realizing an intelligent programmable wireless environment. By intelligently adjusting passive beam forming, the reflected signals of the intelligent reflecting surface can be constructively added with signals from other paths, the power of the expected signals of a receiving end is enhanced, and undesired signals such as co-channel interference and the like can be destructively eliminated or suppressed. From an implementation point of view, intelligent emission surfaces are also of great advantage. The surface is made of low profile, lightweight, low cost, and conformal geometry, and is easily installed/removed on walls, building facades, ceilings, advertising panels, etc. The smart reflective surface is a complementary device in a wireless network, and deployment in existing wireless systems (e.g., cellular or WiFi) would not require modification of standards and hardware, only with the necessary modifications to the communication protocol. The integration of the smart reflective surface into the wireless network is transparent to the user, providing a high degree of flexibility and superior compatibility compared to existing wireless systems. The smart reflective surface may thus enable low cost deployment and integration. Smart reflective surfaces do not require the use of a transmit (RF) chain, but only operate over short distances. Therefore, the system can be densely deployed, has the characteristics of expandable cost and low energy consumption, and avoids complex interference management between intelligent reflecting surfaces.
In order to effectively monitor suspicious communications, many legal monitoring schemes have been applied to wireless suspicious information monitoring systems. The method can be divided into two main categories, namely passive monitoring and active monitoring according to whether legal monitoring parties participate in communication. Passive interception is the most direct and simplest way to realize the interception of suspicious information, and only the suspicious information needs to be intercepted and decoded. However, in a real listening scenario, his location is typically far from the suspicious communication link in order not to be found by both suspicious communication parties. In which case the channel state information is worse than for the suspicious communication link. However, successful interception can only be achieved if the interception link is of better quality than the suspicious communication link. In the active monitoring scheme based on cognitive interference, a monitoring party works in a full duplex mode, monitors a suspicious communication link and simultaneously transmits artificial noise interference to a suspicious transmitting end, so that the speed of transmitting signals of the transmitting end is slowed down, and the monitoring performance is improved. Active listening schemes, while capable of improving listening performance, are still limited to listening to link channel conditions. When the channel quality of the listening link is worse than the suspicious communication link or the listening party is far away from the suspicious communication link, the listening party is likely not to receive the signal from the suspicious sender. Even if the listener sends interference to the suspicious sender, the listener cannot realize the listening. How to improve the monitoring signal intensity in the legal monitoring system is the key for realizing successful monitoring, and is also a difficult problem to be solved in the legal monitoring field.
The prior work has not considered the application of intelligent reflective surfaces in combination with lawful interception techniques in the field of information security. The intelligent reflecting surface deployed in large scale in the future can realize the monitoring function after authorization. Is a potential partner of legal interception technology. Therefore, research is needed in how to apply the smart reflective surface to the field of information security.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides an intelligent reflecting surface-assisted legal monitoring implementation method which can combine an intelligent reflecting surface with a legal monitoring technology to improve the monitoring performance of a legal monitoring end.
In order to achieve the above purpose, the method for implementing legal interception assisted by the intelligent reflecting surface of the invention comprises the following steps:
in the reverse pilot transmission stage, a legal monitoring end performs pilot frequency spoofing, and pilot frequency sequences from a single-antenna suspicious receiving end are reflected by controlling a phase shift matrix of an intelligent reflecting surface, so that channel estimation of a multi-antenna suspicious transmitting end is wrong;
in the data transmission stage, the legal monitoring end controls the phase shift matrix of the intelligent reflecting surface to maximize the signal to noise ratio of the legal monitoring end and complete the auxiliary legal monitoring of the intelligent reflecting surface.
The pilot sequence from the single-antenna suspicious receiving end is reflected by controlling the phase shift matrix of the intelligent reflecting surface, so that the channel estimation of the multi-antenna suspicious transmitting end is in error, and the specific process is as follows:
building an optimization problem P3:
P3:
Figure BDA0003006136460000031
s.t.
Figure BDA0003006136460000032
wherein h is b H and H AI Respectively representing fading channels from single antenna suspicious receiving end and IRS to multi-antenna suspicious transmitting end, h Ib Representing a single antenna suspect receiver to IRS channel.
Solving the optimization problem P3 to obtain the phase shift matrix phi of the intelligent reflecting surface in the reverse pilot transmission stage 0
Phase shift matrix Φ using smart reflective surfaces 0 So that the channel estimation of the multi-antenna suspicious transmitting end is wrong.
The optimization problem P3 is equivalently:
P4:
Figure BDA0003006136460000041
s.t.
Figure BDA0003006136460000042
wherein phi@phi 12 ,..,φ N ] H
Figure BDA0003006136460000043
h b H and H AI Respectively representing fading channels from single antenna suspicious receiving end and IRS to multi-antenna suspicious transmitting end, h Ib Representing a single antenna suspect receiver to IRS channel.
Solving the optimization problem P4 by using a minimum maximization algorithm to obtain a phase shift matrix phi of the intelligent reflecting surface in the reverse pilot transmission stage 0
The legal monitoring end controls the phase shift matrix of the intelligent reflecting surface, so that the specific process of maximizing the signal to noise ratio of the legal monitoring end is as follows:
construction of optimization problem P6:
P6:
Figure BDA0003006136460000044
s.t.
Figure BDA0003006136460000045
wherein h is Ik H is the channel between the intelligent reflecting surface and the legal monitoring end ek For the channels between the multi-antenna suspicious transmitting end ST and the legal monitoring ends LM, H AI Is a channel between the multi-antenna suspicious transmitting end ST and the intelligent reflecting surface;
solving the optimization problem P6, and obtaining a phase shift matrix phi of the intelligent reflecting surface in the data transmission stage 1 Wherein the phase shift matrix Φ of the smart reflective surface of the data transmission phase is utilized 1 So that the signal-to-noise ratio of the legal monitoring end is maximized.
Solving the optimization problem P6 by using a minimum maximization algorithm, and transmitting dataPhase shift matrix Φ of intelligent reflective surface of segment 1
The invention has the following beneficial effects:
in the specific operation, the legal monitoring terminal performs pilot frequency spoofing in the reverse pilot frequency transmission stage, and reflects the pilot frequency sequence from the single-antenna suspicious receiving terminal by controlling the phase shift matrix of the intelligent reflecting surface, so that the channel estimation of the multi-antenna suspicious transmitting terminal is wrong, namely, the active monitoring is realized by the pilot frequency spoofing, the energy consumption and the cost are lower, and in the data transmission stage, the legal monitoring terminal maximizes the signal to noise ratio of the legal monitoring terminal by controlling the phase shift matrix of the intelligent reflecting surface, so as to improve the monitoring performance. Compared with the traditional active and passive monitoring, the invention can intelligently configure the wireless propagation environment, break through the performance bottleneck of the passive monitoring, realize the improvement of the monitoring performance on the premise of hidden monitoring, and realize the remote monitoring at the same time.
Drawings
FIG. 1 is a schematic diagram of a system architecture of the present invention;
FIG. 2 is a system actual simulation model of the present invention;
FIG. 3 is a diagram showing the signal-to-noise ratio of a suspicious receiving end and a legal monitoring end according to the number N of intelligent reflection units;
FIG. 4 is a graph showing the influence of the threshold value of the noise ratio of the suspicious receiver to the average signal to noise ratio of the legal monitoring end and the number N of reflection units in the invention;
fig. 5 is a graph of the signal-to-noise ratio of a lawful interception terminal as a function of the distance between a suspicious receiving terminal and the lawful interception terminal.
Detailed Description
In order to make the present invention better understood by those skilled in the art, the following description will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments, but not intended to limit the scope of the present disclosure. In addition, in the following description, descriptions of well-known structures and techniques are omitted so as not to unnecessarily obscure the concepts of the present disclosure. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
In the accompanying drawings, there is shown a schematic structural diagram in accordance with a disclosed embodiment of the invention. The figures are not drawn to scale, wherein certain details are exaggerated for clarity of presentation and may have been omitted. The shapes of the various regions, layers and their relative sizes, positional relationships shown in the drawings are merely exemplary, may in practice deviate due to manufacturing tolerances or technical limitations, and one skilled in the art may additionally design regions/layers having different shapes, sizes, relative positions as actually required.
The method for realizing legal interception assisted by the intelligent reflecting surface comprises the following steps:
referring to fig. 1, the system includes a multi-antenna suspicious transmitting end ST, a single-antenna suspicious receiving end SR, a plurality of remote single-antenna mobile internet-of-things devices as lawful interception ends LM, and an intelligent reflection surface IRS having N independent reflection units, and a channel between the multi-antenna suspicious transmitting end ST and the intelligent reflection surface is set to be H AI The channel between the multi-antenna suspicious transmitting end ST and the single-antenna suspicious receiving end SR is h b The channel between the multi-antenna suspicious transmitting end ST and the legal monitoring ends LM is h ek The channel between the intelligent reflecting surface and the single-antenna suspicious receiving end SR is h Ib Channel h between intelligent reflecting surface and legal monitoring end LM Ik
Assuming that channels in the system are quasi-static fading channels, channel states cannot change in one reverse pilot sequence transmission and data transmission time block, and channel parameter changes of different transmission time blocks are independently and uniformly distributed. The system works in a TDD mode, the channel diversity exists, and in the system, the channel of the legal monitoring terminal is unknown to both suspicious communication parties. This assumption is practical because it is difficult for both parties of the suspicious communication to detect the presence of the legal interception terminal LM, especially under the active interception scheme assisted by the intelligent reflection surface, the single-antenna suspicious reception terminal SR transmits the pilot sequence to the multi-antenna suspicious transmission terminal ST for channel estimation, the legal interception terminal LM performs pilot spoofing in the reverse pilot transmission stage, and controls the intelligent reflection surface phase shift matrix to reflect the pilot sequence from the single-antenna suspicious reception terminal SR, so that the channel estimation of the multi-antenna suspicious transmission terminal ST is wrong, resulting in information leakage. And the legal monitoring end LM in the data transmission stage controls the intelligent reflection surface phase shift matrix, so that the average and signal-to-noise ratio maximization of the monitoring end are realized, and the monitoring capability is improved.
Specifically, the multi-antenna suspicious transmitting end and the single-antenna suspicious receiving end communicate with each other, the single-antenna suspicious receiving end transmits a pilot sequence to the multi-antenna suspicious transmitting end for channel estimation, the legal monitoring end performs pilot spoofing in a reverse pilot transmission stage, and the pilot sequence from the single-antenna suspicious receiving end is reflected by controlling an intelligent reflection surface IRS phase shift matrix, so that the channel estimation of the multi-antenna suspicious transmitting end is wrong to cause information leakage; in the data transmission stage, the legal monitoring end controls the intelligent reflection surface phase shift matrix to maximize the signal-to-noise ratio of the monitoring end so as to improve the monitoring capability.
The specific implementation scheme is as follows:
pilot decoy stage
In the system, a legal monitoring end keeps silent in a reverse pilot transmission stage, and pilot sequences u transmitted from a single-antenna suspicious receiving end to a multi-antenna suspicious transmitting end are reflected by controlling IRS composed of N reflecting units H Pilot frequency transmitting power of single antenna suspicious receiving end is P b The signal Y received by the single antenna suspected receiving end is:
Figure BDA0003006136460000081
wherein h is b H and H AI Represents the fading channels from the single antenna suspicious receiving end and IRS to the multi-antenna suspicious transmitting end respectively, h Ib Representing the channel from a suspected receiving end of a single antenna to an IRS, phi 0 =diag{φ 12 ,...,φ N }∈£ N×N Consists of IRS reflection coefficient, and is more than or equal to 0 and less than or equal to |phi i 1 for 1 i N, where N is equal to or greater than 1 i N a Additive complex Gaussian white noise representing the reception of suspicious multi-antenna transmitters, with a mean value of 0 and a variance of
Figure BDA0003006136460000082
Channel estimation phase
The multi-antenna suspicious transmitting end obtains channel CSI by least square estimation, the multi-antenna suspicious transmitting end knows pilot frequency transmitting power and pilot frequency sequence, pilot frequency decoy causes channel estimation deviation at the multi-antenna suspicious transmitting end, information is leaked to the IRS surface, and a channel h estimated at the multi-antenna suspicious transmitting end is:
Figure BDA0003006136460000083
data transmission stage
The pilot frequency decoy scheme in the invention can not detect the existence of legal monitoring end by the traditional method, so the multi-antenna suspicious transmitting end adopts Maximum Ratio Transmission (MRT) and P under the limit of maximum transmitting power a Representing the transmitting power of the multi-antenna suspicious transmitting end, wherein the transmitting beam forming vector w of the multi-antenna suspicious transmitting end is as follows:
Figure BDA0003006136460000091
data reception phase
Is provided with
Figure BDA0003006136460000092
Representing a direct channel between a multi-antenna suspicious sender and a single-antenna suspicious receiver +.>
Figure BDA0003006136460000093
Representing multi-antenna suspicious transmitting end-intelligent reflecting surface-single-antenna suspicious receiving endX represents a suspicious information signal with unit power, n b N is as follows ek Additive complex Gaussian white noise signals respectively representing a single antenna suspicious receiving end and a legal monitoring end, wherein the average value is 0, and the variance is +.>
Figure BDA0003006136460000094
Is->
Figure BDA0003006136460000095
Signal y received by suspicious single-antenna receiver b The method comprises the following steps:
Figure BDA0003006136460000096
legal monitoring end:
Figure BDA0003006136460000097
Figure BDA0003006136460000098
Figure BDA0003006136460000099
wherein y is e,1 For the signal received by the first lawful interception receiver y e,k For the signal received by the kth legal interception, y Ε For all the legal monitoring terminals, k is the number of legal monitoring terminals, and the signal to noise ratio gamma of the single antenna suspicious receiving terminal and the legal monitoring terminal b Gamma-ray e The method comprises the following steps:
Figure BDA00030061364600000910
Figure BDA00030061364600000911
when gamma is e ≥γ b And if the suspicious information is received, the legal monitoring terminal can successfully decode the suspicious information and can realize successful monitoring, and the monitoring rate is the suspicious communication rate. When gamma is e <γ b The legal monitoring end cannot guarantee that suspicious information is decoded without errors, monitoring cannot be achieved, at the moment, the monitoring rate is 0, and therefore the legal monitoring end monitoring event is represented as follows by an indication function:
Figure BDA0003006136460000101
r=1 indicates that the lawful interception terminal successfully intercepts suspicious information; r=0 indicates that the lawful interception end fails to intercept suspicious information.
System optimization objective:
according to the description, in the data transmission stage, not only the legal monitoring end can receive the information source signal reflected by the intelligent reflecting surface so as to improve the signal to noise ratio, but also the single-antenna suspicious receiving end can receive the information reflected by the intelligent reflecting surface so as to improve the signal strength of the received suspicious information. Therefore, not only information leakage caused by the design of the phase shift matrix of the intelligent reflecting surface in the reverse pilot transmission stage is considered, but also optimization of the phase shift matrix of the intelligent reflecting surface in the data transmission stage is considered, so that signals are concentrated in the direction of the legal monitoring end.
The invention maximizes listener and signal-to-noise ratio by jointly optimizing the intelligent reflective surface phase shift matrices for the reverse pilot transmission stage and the data transmission stage, wherein,
the optimization problem of the system is as follows:
P1:
Figure BDA0003006136460000102
s.t.γ b ≥γ 0
||w|| 2 ≤P T
constraint gamma b ≥γ 0 The method is used for ensuring that the signal-to-noise ratio of the single-antenna suspicious receiving end is higher than a given threshold, namely ensuring that the single-antenna suspicious receiving end can correctly decode information and cannot detect the existence of a legal monitoring end, and ensuring that the receiving signal-to-noise ratio of the legal monitoring end is larger than that of the suspicious receiving end. Constraint w 2 ≤P T When the total power cannot meet the signal-to-noise ratio requirement of the single-antenna suspicious receiving end, the multi-antenna suspicious sending end stops sending suspicious information, and at the moment, the signal-to-noise ratio of the single-antenna suspicious receiving end and the legal monitoring end is 0.
The optimization problem P1 is equivalently expressed as:
P2:
Figure BDA0003006136460000111
s.t.
Figure BDA0003006136460000112
||w|| 2 ≤P T
wherein, the IRS phase shift matrix phi in the reverse pilot transmission stage 0 Optimizing:
the legal monitoring end controls the IRS phase shift matrix phi to reflect the pilot frequency sequence from the single-antenna suspicious receiving end, so that the channel estimation result of the multi-antenna suspicious transmitting end is wrong, and information leakage is caused as much as possible, namely, the optimization problem P3 is as follows:
P3:
Figure BDA0003006136460000113
s.t.
Figure BDA0003006136460000114
the optimization problem P3 is equivalently:
P4:
Figure BDA0003006136460000115
s.t.
Figure BDA0003006136460000116
wherein phi@phi 12 ,..,φ N ] H
Figure BDA0003006136460000117
Because the unit mode is not convex, the optimization problem P4 is still a non-convex problem, the invention adopts a Minimum Maximization (MM) algorithm to solve the optimization problem P4, and the specific solving process is as follows:
the core idea of the minimization and maximization algorithm is to first calculate the approximate upper bound of the objective function, then iteratively calculate the optimal value of the upper bound under constraint conditions, and the convergence point is the local optimal point.
Phi-shaped k To satisfy the feasible solution of the optimization problem P4, the next iteration point φ k+1 The upper bound of the objective function is expressed as:
Figure BDA0003006136460000121
/>
wherein α@λ (λ max (A)I-A)φ k +n, the optimization problem P4 is equivalently:
P5:
Figure BDA0003006136460000122
i.e. if and only if phi i And alpha is i When the phases are equal to each other,
Figure BDA0003006136460000123
the maximum, therefore, closed-form optimal solution of the optimization problem P5 is:
Figure BDA0003006136460000124
let k=k+1 and update Φ k Until the objective function converges, initializing a feasible point phi 0 And applying MM algorithm to iteratively solve the optimization problem P3 to obtainLocal optimal solution Φ of optimization problem P3 0
IRS phase shift matrix phi in data transmission stage 1 Optimization
The legal monitoring end controls the IRS phase shift matrix phi to maximally realize the monitoring and the signal-to-noise ratio of the legal monitoring end, namely, the method is equivalent to the optimization problem P6:
P6:
Figure BDA0003006136460000125
s.t.
Figure BDA0003006136460000126
optimizing phi 0 In the same way, obtain phi 1 The algorithm for solving the system optimization problem according to the key steps is summarized as shown in table 1:
TABLE 1
Figure BDA0003006136460000127
/>
Figure BDA0003006136460000131
Simulation experiment
The actual simulation model of the system is shown in fig. 2, and the number of antennas 5 of the multi-antenna suspicious sender ST is (0 m,30 m). And the plurality of LM mobile Internet of things devices with the single-antenna legal monitoring ends are randomly distributed in an area with the radius of 10m by taking (160 m,0 m) as the center of a circle to perform collaborative monitoring. The intelligent reflective surface is located at (100 m,30 m). The single antenna suspected receiving end SR is at (100 m,0 m). The intelligent reflecting surface is used to reflect the pilot sequence and enhance the link between the multi-antenna suspicious sender ST to the lawful listener LM. Setting multi-antenna suspicious transmitting end ST, single-antenna suspicious receiving end SR and legal monitoring end LM with noise variance of all
Figure BDA0003006136460000132
To contain as many cases as possibleWe proceed altogether 10 5 And (5) secondary simulation. The path loss model is represented by pl= (PL 0 -10ρlog 10 (d/d 0 ) A) is given. PL (PL) 0 = -30dB at reference distance d 0 In the simulation, we set two suspicious communication parties, a multi-antenna suspicious transmitting end ST and a legal monitoring end LM, the multi-antenna suspicious transmitting end ST and an intelligent reflecting surface, the intelligent reflecting surface and a single-antenna suspicious receiving end SR respectively, and the path loss index and the distance between the legal monitoring ends LM are ρ respectively b =ρ ek =3,ρ AI =2,ρ Ib =ρ Ik =2.5。
The simulation verification of the invention is shown as fig. 3, fig. 4 and fig. 5 respectively, wherein fig. 3 shows the condition that the signal to noise ratio of the single-antenna suspicious receiving end SR and the legal monitoring end LM changes along with the number N of intelligent reflecting units under the condition that the single-antenna suspicious receiving end SR has a certain receiving signal to noise ratio threshold. Fig. 4 shows the influence of the signal-to-noise ratio threshold received by the single-antenna suspicious receiving end SR and the number N of reflecting units on the average and the signal-to-noise ratio of the legal monitoring end LM. Fig. 5 shows that the performance of the present invention is better than conventional passive listening and that remote listening can be achieved.

Claims (2)

1. The method for realizing legal interception assisted by the intelligent reflecting surface is characterized by comprising the following steps of:
in the reverse pilot transmission stage, a legal monitoring end performs pilot frequency spoofing, and pilot frequency sequences from a single-antenna suspicious receiving end are reflected by controlling a phase shift matrix of an intelligent reflecting surface, so that channel estimation of a multi-antenna suspicious transmitting end is wrong;
in the data transmission stage, the legal monitoring end controls the phase shift matrix of the intelligent reflecting surface to maximize the signal-to-noise ratio of the legal monitoring end and complete the auxiliary legal monitoring of the intelligent reflecting surface;
the pilot sequence from the single-antenna suspicious receiving end is reflected by controlling the phase shift matrix of the intelligent reflecting surface, so that the channel estimation of the multi-antenna suspicious transmitting end is in error, and the specific process is as follows:
building an optimization problem P3:
Figure FDA0004187372980000011
Figure FDA0004187372980000012
wherein phi is i For the phase of the ith reflecting element of the intelligent reflecting surface, phi 0 For the pilot transmission stage intelligent reflecting surface phase shift matrix, diag (·) is diagonalization, N is the total reflecting unit number of the intelligent reflecting surface, () H Representing a conjugate transpose operation, |·| representing the modulus of the scalar, |·| representing the euclidean norm, h b H and H AI Respectively representing fading channels from single antenna suspicious receiving end and IRS to multi-antenna suspicious transmitting end, h Ib Representing the channel from the suspicious receiving end of the single antenna to the IRS;
solving the optimization problem P3 to obtain the phase shift matrix phi of the intelligent reflecting surface in the reverse pilot transmission stage 0
Phase shift matrix Φ using smart reflective surfaces 0 The channel estimation of the multi-antenna suspicious transmitting end is made to have errors;
the legal monitoring end controls the phase shift matrix of the intelligent reflecting surface, so that the specific process of maximizing the signal to noise ratio of the legal monitoring end is as follows:
construction of optimization problem P6:
Figure FDA0004187372980000021
Figure FDA0004187372980000022
wherein K represents the kth legal listeners, K is the total legal listener number, h Ik H is the channel between the intelligent reflecting surface and the legal monitoring end ek For multi-antenna suspicious sender ST and multiple legal monitorsChannel between hearing-side LMs, H AI Is a channel between the multi-antenna suspicious transmitting end ST and the intelligent reflecting surface;
solving the optimization problem P6, and obtaining a phase shift matrix phi of the intelligent reflecting surface in the data transmission stage 1 Wherein the phase shift matrix Φ of the smart reflective surface of the data transmission phase is utilized 1 So that the signal-to-noise ratio of the legal monitoring end is maximized.
2. The method for implementing legal interception with the assistance of an intelligent reflecting surface according to claim 1, characterized in that the optimization problem P6 is solved by using a minimization and maximization algorithm, and the phase shift matrix Φ of the intelligent reflecting surface in the data transmission stage 1
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