CN116976129A - Wireless hidden detection method and system based on intelligent reflecting surface assistance - Google Patents
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Abstract
The application discloses a wireless hidden detection method and system based on intelligent reflecting surface assistance. The method comprises the following steps: establishing a system model, and deducing detection error probability of legal receivers and illegal detectors; analyzing the expression of the detection error probability to obtain an optimal detection threshold value, and determining the detection error probability; establishing a joint optimization problem of an intelligent reflecting surface phase shift matrix and transmitting power; selecting the lower bound of the optimization problem to simplify the optimization problem, and obtaining the simplified optimization problem; solving the simplified optimization problem, determining an optimal intelligent reflecting surface phase shift matrix, and simultaneously selecting feasible transmitting power to meet the requirement of concealment constraint. The system comprises a model building module, a detection error probability determining module, a joint optimization problem building module, an optimization problem simplifying module and an optimal intelligent reflecting surface phase shift matrix determining module. The application improves the detection performance of the legal receiver and reduces the detection performance of illegal detectors, thereby meeting the requirement of concealment constraint.
Description
Technical Field
The application relates to the technical field of wireless communication, in particular to a wireless hidden detection method and system based on the assistance of an intelligent reflecting surface.
Background
The intelligent reflecting surface is an artificial electromagnetic surface structure with programmable electromagnetic characteristics and is made of superconducting materials. The intelligent reflecting surface is generally formed by arranging a large number of carefully designed electromagnetic units, and the electromagnetic properties of the electromagnetic units can be dynamically controlled by applying control signals to adjustable elements on the electromagnetic units, so that the intelligent control of the space electromagnetic waves in a programmable manner is realized, and electromagnetic fields with controllable parameters such as amplitude, phase, polarization and frequency are formed. In addition, as people increasingly rely on wireless devices to share private information, security and privacy concerns for wireless communications are raised due to the large amount of private information (e.g., email/bank account information and passwords, credit card details) being transmitted over wireless networks. In addition to confidentiality and integrity of transmitted information, in some cases, a user wishes to transmit a message over a wireless network without being detected.
Recently, in wireless communication networks, the use of smart reflective surfaces to assist in wireless communication has attracted increasing attention. When the intelligent reflecting surface auxiliary wireless hidden detection system is designed, the first intelligent reflecting surface only changes the wireless propagation environment and does not amplify or reduce the signal amplitude. Second, to ensure the concealment of the system, the probability of detection by an illegal user (the prison length) is negligible when detected by a legitimate user.
Smart reflective surface technology has excellent capabilities in achieving signal focusing or interference suppression by adapting to the phase shift of wireless signals, and the benefits of utilizing smart reflective surfaces for covert communication have been reported. For example, in intelligent reflective surface assisted multi-antenna covert communication systems, the combination of active and passive beam forming optimizations are used to improve covert communication performance. However, research of intelligent reflective surfaces in the context of covert detection has never been explicitly disclosed.
Disclosure of Invention
The application aims to provide a wireless hidden detection method and system based on the assistance of an intelligent reflecting surface, which improve the detection performance of a legal receiver and reduce the detection performance of a prison length simultaneously by optimizing the phase shift matrix and the transmitting power of the intelligent reflecting surface so as to meet the requirement of hidden constraint.
The technical solution for realizing the purpose of the application is as follows: a wireless hidden detection method based on intelligent reflecting surface assistance comprises the following steps:
step 1, establishing a system model, and deducing detection error probabilities of legal receivers and illegal detectors;
step 2, analyzing an expression of the detection error probability to obtain an optimal detection threshold value, and determining the detection error probability under the optimal detection threshold value;
step 3, establishing a joint optimization problem P1 of the intelligent reflection surface phase shift matrix and the transmitting power;
step 4, selecting a lower bound of the optimization problem P1 to simplify the optimization problem P1, and obtaining a simplified optimization problem P2;
and 5, solving the simplified optimization problem P2, determining an optimal intelligent reflecting surface phase shift matrix, and simultaneously selecting feasible transmitting power to meet the requirement of concealment constraint.
The system is used for realizing the wireless hidden detection method based on the assistance of the intelligent reflecting surface, and comprises a model building module, a detection error probability determining module, a joint optimization problem building module, an optimization problem simplifying module and an optimal intelligent reflecting surface phase shift matrix determining module, wherein:
the model building module is used for building a system model and deducing the detection error probability of a legal receiver and an illegal detector;
the detection error probability determining module is used for analyzing an expression of the detection error probability to obtain an optimal detection threshold and determining the detection error probability under the optimal detection threshold;
the joint optimization problem construction module is used for establishing a joint optimization problem P1 of the intelligent reflection surface phase shift matrix and the transmitting power;
the optimization problem simplification module is used for simplifying the optimization problem P1 by selecting the lower bound of the optimization problem P1 to obtain a simplified optimization problem P2;
and the optimal intelligent reflecting surface phase shift matrix determining module is used for solving the simplified optimization problem P2, determining the optimal intelligent reflecting surface phase shift matrix and simultaneously selecting feasible transmitting power to meet the requirement of concealment constraint.
A mobile terminal comprising a memory, a processor and a computer program stored in the memory and operable on the processor, wherein the processor implements the intelligent reflector-assisted wireless concealment method when executing the program.
A computer readable storage medium having stored thereon a computer program, wherein the program when executed by a processor implements the steps of the intelligent reflector-assisted wireless concealment method.
Compared with the prior art, the application has the remarkable advantages that: (1) Deducing detection error probability of legal receiver Bob and illegal detector Willie by establishing a system model, and then analyzing an expression of the detection error probability to obtain an optimal detection threshold; (2) By optimizing the phase shift matrix and the transmitting power of the intelligent reflecting surface, the detection performance of a legal receiver is improved, and meanwhile, the detection performance of an illegal detector is reduced so as to meet the requirement of concealment constraint.
Drawings
FIG. 1 is a diagram of an intelligent reflector-assisted wireless covert detection system model.
Fig. 2 is a schematic diagram showing the relationship between the probability of detection error of the legal detector Bob and the number of array elements of the intelligent reflection surface.
FIG. 3 shows the probability of detection error and the rice factor K of a legal detector ib Schematic of the relationship between the two.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present application. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
The application discloses a wireless hidden detection method based on intelligent reflecting surface assistance, which comprises the following steps:
step 1, establishing a system model, and deducing detection error probabilities of legal receivers and illegal detectors;
step 2, analyzing an expression of the detection error probability to obtain an optimal detection threshold value, and determining the detection error probability under the optimal detection threshold value;
step 3, establishing a joint optimization problem P1 of the intelligent reflection surface phase shift matrix and the transmitting power;
step 4, selecting a lower bound of the optimization problem P1 to simplify the optimization problem P1, and obtaining a simplified optimization problem P2;
and 5, solving the simplified optimization problem P2, determining an optimal intelligent reflecting surface phase shift matrix, and simultaneously selecting feasible transmitting power to meet the requirement of concealment constraint.
As a specific example, in step 1, a system model is built, and the detection error probability of the legal receiver and the illegal detector is deduced, which is specifically as follows:
establishing a wireless hidden detection system model assisted by an intelligent reflecting surface, wherein Alice represents a transmitter, bob represents a legal receiver and Willie represents an illegal detector, alice intends to send a signal to Bob, and allows Bob to detect the signal with the assistance of the intelligent reflecting surface, and Willie also tries to detect the existence of the sent signal;
assuming that Alice, bob and Willie each is provided with an antenna, the intelligent reflecting surface is provided with M reflecting elements; assuming a bounded uncertainty noise model, noise powerIs uniformly distributed in-> wherein />Representing the reference noise level ρ j Representing the noise uncertainty level, j e { b, w } corresponds to Bob and Willie, respectively; probability density function of noise powerThe expression is as follows:
wherein ,representing the lower bound of noise uncertainty, +.>An upper bound representing noise uncertainty;
the signal y received at Bob or Willie j [n]Expressed as:
wherein ,is to assume that Alice does not send a signal, +.>Is assumed that Alice transmits a signal, x [ n ]]Representing the signal sent by Alice, P a Is the power sent by Alice, +.>Indicating the channel of the smart reflecting surface to Bob or Willie, h ai Represents Alice to intelligent reflecting surface channel, h aj Representing Alice to Bob or Willie channels, i represents the smart reflective surface,representing the phase shift matrix of the intelligent reflecting surface, phi 1 ,φ 2 ,...,φ M The phases of the reflecting elements respectively corresponding to the intelligent reflecting surfaces, n j [n]Represents additive gaussian white noise, n=1,..n represents the index used by the different channels;
thus when N.fwdarw.infinity, bob or Willie receives the average power of the signalGiven by the formula:
wherein ,representing the variance of additive gaussian white noise;
assuming that radiometers are used at Bob and Willie to detect if Alice is sending a signal, the specific decision rules are as follows:
wherein ,τj Is the detection threshold value and, and />Respectively indicating that Alice is judging whether to send signals or not;
using error detection probability ζ j The detection performance is measured and defined as follows:
ξ j ＝α j +β j
wherein ,indicating false alarm rate->Indicating the leak detection rate;
the false alarm rate is given by:
the leak detection rate is approximately expressed as:
wherein ,represents the lower incomplete gamma function, and F (τ j) and H(τj ) The definition is as follows:
wherein ,a j and bj Is defined as follows:
wherein ,K z express rice factor, χ z Representing the large scale fading coefficients, z e { ai, ib, iw, ab, aw }, M e 1, 2..m, M is the total number of intelligent reflecting surfaces,/-a->Representing the line-of-sight channel of the smart reflector to Bob or Willie, < >>A line-of-sight channel representing Alice to Bob or Willie;
therefore, the detection error probability of Bob or Willie is expressed as:
as a specific example, the analysis of the expression of the detection error probability in step 2 yields an optimal detection threshold, and the detection error probability under the optimal detection threshold is determined as follows:
when (when)When xi j Along with tau j Increasing and increasing;
when (when)When xi j Relative to τ j The first derivative of (2) is as follows:
thus optimal detection thresholdObtaining the detection error probability xi under the optimal detection threshold value j * The formula is as follows:
as a specific example, the joint optimization problem P1 of the intelligent reflection surface phase shift matrix and the emission power is established in step 3, which is specifically as follows:
reducing the detection error probability of Bob by designing Alice emission power and intelligent reflection surface phase shift matrix Q, and ensuring that the detection error probability of Willie is not lower than a set constant, namelyWhere ε represents the parameter of required concealment, the joint optimization problem P1 is therefore represented as follows:
(P1):
in the formula Representing a covert constraint->Representing the unit mode constraint of the intelligent reflecting surface, +.>Representing Bob's probability of detection error.
As a specific example, the lower bound of the optimization problem P1 selected in step 4 simplifies the optimization problem P1 to obtain the simplified optimization problem P2, which is specifically as follows:
according to gamma (k+1, s) =kgamma (k, s) -s k e -s The following formula is obtained:
wherein ,
according toThe lower bound of the optimization problem P1 is expressed as follows:
(P2):
s.t.
wherein ,representing BobUpper bound of detection error probability,/-, for example>Representing the lower bound of the Willie detection error probability.
As a specific example, step 5 solves the simplified optimization problem P2, determines an optimal intelligent reflection surface phase shift matrix, and selects feasible transmitting power to meet the requirement of concealment constraint, which is specifically as follows:
is related to |a b | 2 Monotonically decreasing function of->Is related to |a w | 2 Is a monotonically decreasing function of (a) using |a b | 2 /|a w | 2 To determine the optimal smart reflector phase shift matrix Q while selecting the feasible Alice transmit power P a To satisfy the concealment constraint;
for this purpose, the optimization problem is expressed as follows:
wherein ,representing the line-of-sight channel of the smart reflector to Bob and Willie, respectively, +.>Respectively represent Alice's line-of-sight channel to the intelligent reflecting surface and Bob +.>Representing Alice's line-of-sight channels to the intelligent reflective surface and Willie, respectively;
the above optimization problem is rewritten as:
in the formula Hb and Hw The definition is as follows:
wherein ,u l is u < th > element;
since the above-mentioned optimization problem is non-convex, it is derived firstThen iteratively solving the optimization problem by using a continuous convex approximation algorithm;
the lower bound of (2) is expressed as follows:
wherein ,is an iteratively viable point;
further to |u l Relax |=1 to |u l The I is less than or equal to 1, and the original optimization problem is rewritten as follows:
the problem shown in the above formula is a convex optimization problem, solved with the CVX toolbox, then let u=e jarg(u) Thus obtaining the solution of the original problem.
The application also provides a wireless hidden detection system based on the assistance of the intelligent reflecting surface, which is used for realizing the wireless hidden detection method based on the assistance of the intelligent reflecting surface, and comprises a model building module, a detection error probability determining module, a joint optimization problem building module, an optimization problem simplifying module and an optimal intelligent reflecting surface phase shift matrix determining module, wherein:
the model building module is used for building a system model and deducing the detection error probability of a legal receiver and an illegal detector;
the detection error probability determining module is used for analyzing an expression of the detection error probability to obtain an optimal detection threshold and determining the detection error probability under the optimal detection threshold;
the joint optimization problem construction module is used for establishing a joint optimization problem P1 of the intelligent reflection surface phase shift matrix and the transmitting power;
the optimization problem simplification module is used for simplifying the optimization problem P1 by selecting the lower bound of the optimization problem P1 to obtain a simplified optimization problem P2;
and the optimal intelligent reflecting surface phase shift matrix determining module is used for solving the simplified optimization problem P2, determining the optimal intelligent reflecting surface phase shift matrix and simultaneously selecting feasible transmitting power to meet the requirement of concealment constraint.
The application also provides a mobile terminal, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the wireless hidden detection method based on the assistance of the intelligent reflecting surface when executing the program.
The application also provides a computer readable storage medium, on which a computer program is stored, which when being executed by a processor implements the steps in the intelligent reflector-assisted wireless concealment method.
The application will be described in further detail with reference to the accompanying drawings and specific examples.
Examples
As shown in fig. 1, the present example provides a wireless hidden detection method based on intelligent reflection surface assistance, which specifically includes the following steps:
consider first a smart reflector assisted wireless covert detection system in which a transmitter (Alice) intends to transmit a signal to a legitimate receiver (Bob) and let it accurately detect the signal with the aid of a smart reflector, while a prison (Willie) also attempts to detect the presence of the transmitted signal.
Suppose Alice, bob and Willie each have an antenna and the smart reflective surface has M reflective elements. In a practical wireless environment, the noise power received by the receiver may also be affected by uncertainty due to variations in background noise. Assuming a bounded uncertainty noise model, wherein noise powerIs uniformly distributed in-> wherein Representing the reference noise level ρ j Representing the noise uncertainty level, j e { b, w } corresponds to Bob and Willie, respectively. Thus, the probability density function of the noise power can be expressed as follows:
wherein ,representing the lower bound of noise uncertainty, +.>Representing the upper bound of noise uncertainty.
The signal y received at Bob or Willie j [n]Can be expressed as:
wherein ,is to assume that Alice does not send a signal, +.>Is assumed that Alice transmits a signal, x [ n ]]Representing the signal sent by Alice, P a Is the power sent by Alice, +.>Indicating the channel of the smart reflecting surface to Bob or Willie, h ai Represents Alice to intelligent reflecting surface channel, h aj Representing Alice to Bob or Willie channels, i represents the smart reflective surface,representing the phase shift matrix of the intelligent reflecting surface, phi 1 ,φ 2 ,...,φ M The phases of the reflecting elements respectively corresponding to the intelligent reflecting surfaces, n j [n]Represents additive gaussian white noise, n=1.
Thus when N.fwdarw.infinity, bob or Willie receives the average work of the signalRate ofGiven by the formula:
wherein ,representing the variance of the additive gaussian white noise.
Assuming that radiometers are used at Bob and Willie to detect if Alice is sending a signal, the specific decision rules are as follows:
wherein ,τj Is the detection threshold value and, and />Respectively indicate whether Alice transmits a signal or not.
We use the error detection probability ζ j To measure the detection performance, it is defined as follows:
ξ j ＝α j +β j
wherein ,expressed as false alarm rate, and +.>Expressed as leak detection rate.
The false alarm rate is given by:
the leak detection rate is approximately expressed as:
wherein ,represents the lower incomplete gamma function, and F (τ j) and H(τj ) The definition is as follows:
wherein ,a j and bj Is defined as follows:
wherein ,K z express rice factor, χ z Representing the large scale fading coefficients, z e { ai, ib, iw, ab, aw }, M e 1, 2..m, M is the total number of intelligent reflecting surfaces,/-a->Representing intelligent reflecting surfaceLine-of-sight channel to Bob or Willie,>a line-of-sight channel representing Alice to Bob or Willie; therefore, the detection error probability of Bob or Willie is expressed as:
note that whenWhen xi j Along with tau j Increasing and increasing. However, when +.>When xi j Relative to τ j The first derivative of (2) is as follows:
thus, an optimal detection thresholdFrom this, the detection error probability ζ under the optimal detection threshold can be derived j * Given by the formula:
reducing the detection error probability of Bob by designing Alice emission power and intelligent reflection surface phase shift matrix Q, and ensuring that the detection error probability of Willie is not lower than a specific constant, namelyWhere e represents the parameters of the required concealment. Thus, the optimization problem can be expressed as follows:
(P1):
in the formula Representing a covert constraint->Representing the unit mode constraint of the intelligent reflecting surface, +.>Representing Bob's probability of detection error.
Since the P1 problem involves the following incomplete gamma functions, it is generally difficult to solve directly. Therefore, to solve the P1 problem, we choose the lower bound of the P1 problem to simplify the P1 problem. According to gamma (k+1, s) =kgamma (k, s) -s k e -s We can obtain the following formula:
wherein ,according to->The lower bound of the P1 problem can be expressed as follows:
(P2):
wherein ,representing the upper bound of the probability of Bob detection error,/->Representing the lower bound of the Willie detection error probability.
However, the P2 problem is also not well solved directly, but we noteIs related to |a b | 2 Monotonically decreasing function of->Is related to |a w | 2 Is a monotonically decreasing function of (a) using |a b | 2 /|a w | 2 To determine the optimal smart reflector phase shift matrix Q while selecting the feasible Alice transmit power P a To satisfy the concealment constraint.
To this end, the optimization problem can be expressed as follows:
wherein ,representing the line-of-sight channel of the smart reflector to Bob and Willie, respectively, +.>Respectively represent Alice's line-of-sight channel to the intelligent reflecting surface and Bob +.>Representing Alice's line-of-sight channels to the intelligent reflective surface and Willie, respectively;
the above optimization problem can be rewritten as:
in the formula Hb and Hw The definition is as follows:
wherein ,u l is u < th > element.
Since the above-described optimization problem is non-convex, for ease of solution, we first deriveAnd then iteratively solving the optimization problem using a continuous convex approximation algorithm. First->The lower bound of (2) may be expressed as follows:
wherein ,is an iteratively viable point.
Further, we will |u l Relax |=1 to |u l The I is less than or equal to 1, and the original optimization problem can be rewritten as:
note that this problem is a convex optimization problem that can be solved with existing CVX toolboxes, then let u=e jarg(u) The solution of the original problem can be obtained.
Fig. 2 shows a schematic diagram of the relationship between the probability of detection error of the legal detector Bob and the number of array elements of the intelligent reflection surface. FIG. 3 shows the probability of detection error and the rice factor K of a legal detector ib Schematic of the relationship between the two.
In summary, the application derives the detection error probability of legal receiver Bob and illegal detector Willie by establishing a system model, and then analyzes the expression of the detection error probability to obtain the optimal detection threshold; by optimizing the phase shift matrix and the transmitting power of the intelligent reflecting surface, the detection performance of a legal receiver is improved, and meanwhile, the detection performance of an illegal detector is reduced so as to meet the requirement of concealment constraint.
The above description is only a preferred embodiment of the present application, and is not intended to limit the application in any way, and any person skilled in the art may make modifications or alterations to the disclosed technical content to the equivalent embodiments. However, any simple modification, equivalent variation and variation of the above embodiments according to the technical substance of the present application still fall within the protection scope of the technical solution of the present application.
Claims (9)
1. The wireless hidden detection method based on the assistance of the intelligent reflecting surface is characterized by comprising the following steps of:
step 1, establishing a system model, and deducing detection error probabilities of legal receivers and illegal detectors;
step 2, analyzing an expression of the detection error probability to obtain an optimal detection threshold value, and determining the detection error probability under the optimal detection threshold value;
step 3, establishing a joint optimization problem P1 of the intelligent reflection surface phase shift matrix and the transmitting power;
step 4, selecting a lower bound of the optimization problem P1 to simplify the optimization problem P1, and obtaining a simplified optimization problem P2;
and 5, solving the simplified optimization problem P2, determining an optimal intelligent reflecting surface phase shift matrix, and simultaneously selecting feasible transmitting power to meet the requirement of concealment constraint.
2. The method for wireless hidden detection based on intelligent reflecting surface assistance according to claim 1, wherein in step 1, a system model is built to derive detection error probabilities of legal receivers and illegal detectors, specifically comprising the following steps:
establishing a wireless hidden detection system model assisted by an intelligent reflecting surface, wherein Alice represents a transmitter, bob represents a legal receiver and Willie represents an illegal detector, alice intends to send a signal to Bob, and allows Bob to detect the signal with the assistance of the intelligent reflecting surface, and Willie also tries to detect the existence of the sent signal;
assuming that Alice, bob and Willie each is provided with an antenna, the intelligent reflecting surface is provided with M reflecting elements; assuming a bounded uncertainty noise model, noise powerIs uniformly distributed in-> wherein />Representing the reference noise level ρ j Representing the noise uncertainty level, j e { b, w } corresponds to Bob and Willie, respectively; probability density function of noise powerThe expression is as follows:
wherein ,representing the lower bound of noise uncertainty, +.>An upper bound representing noise uncertainty;
the signal y received at Bob or Willie j [n]Expressed as:
wherein ,is to assume that Alice does not send a signal, +.>Is assumed to be Alice sends a signal x [ n ]]Representing the signal sent by Alice, P a Is the power sent by Alice, +.>Indicating the channel of the smart reflecting surface to Bob or Willie, h ai Represents Alice to intelligent reflecting surface channel, h aj Representing Alice to Bob or Willie channels, i represents the smart reflective surface,representing the phase shift matrix of the intelligent reflecting surface, phi 1 ,φ 2 ,...,φ M The phases of the reflecting elements respectively corresponding to the intelligent reflecting surfaces, n j [n]Represents additive gaussian white noise, n=1,..n represents the index used by the different channels;
thus when N.fwdarw.infinity, bob or Willie receives the average power of the signalGiven by the formula:
wherein ,representing the variance of additive gaussian white noise;
assuming that radiometers are used at Bob and Willie to detect if Alice is sending a signal, the specific decision rules are as follows:
wherein ,τj Is the detection threshold value and, and />Respectively indicating that Alice is judging whether to send signals or not;
using error detection probability ζ j The detection performance is measured and defined as follows:
ξ j ＝α j +β j
wherein ,indicating false alarm rate->Indicating the leak detection rate;
the false alarm rate is given by:
the leak detection rate is approximately expressed as:
wherein ,represents the lower incomplete gamma function, and F (τ j) and H(τj ) The definition is as follows:
wherein ,a j and bj Is defined as follows:
wherein ,K z express rice factor, χ z Representing the large scale fading coefficients, z e { ai, ib, iw, ab, aw }, M e 1, 2..m, M is the total number of intelligent reflecting surfaces,/-a->Representing the line-of-sight channel of the smart reflector to Bob or Willie, < >>A line-of-sight channel representing Alice to Bob or Willie;
therefore, the detection error probability of Bob or Willie is expressed as:
3. the wireless hidden detection method based on intelligent reflection surface assistance according to claim 2, wherein the analysis of the expression of the detection error probability in step 2 obtains an optimal detection threshold, and the detection error probability under the optimal detection threshold is determined as follows:
when (when)When xi j Along with tau j Increasing and increasing;
when (when)When xi j Relative to τ j The first derivative of (2) is as follows:
thus optimal detection thresholdObtaining the detection error probability xi under the optimal detection threshold value j * The formula is as follows:
4. the wireless hidden detection method based on intelligent reflecting surface assistance according to claim 3, wherein the joint optimization problem P1 of the intelligent reflecting surface phase shift matrix and the transmitting power is established in step 3, specifically as follows:
reducing the detection error probability of Bob by designing Alice emission power and intelligent reflection surface phase shift matrix Q, and ensuring that the detection error probability of Willie is not lower than a set constant, namelyWhere ε represents the parameter of required concealment, the joint optimization problem P1 is therefore represented as follows:
(P1):
in the formula Representing a covert constraint->Representing the unit mode constraint of the intelligent reflecting surface,representing Bob's probability of detection error.
5. The wireless hidden detection method based on intelligent reflecting surface assistance according to claim 4, wherein the lower bound of the optimization problem P1 selected in step 4 simplifies the optimization problem P1 to obtain a simplified optimization problem P2, which is specifically as follows:
according to gamma (k+1, s) =kgamma (k, s) -s k e -s The following formula is obtained:
wherein ,
according toThe lower bound of the optimization problem P1 is expressed as follows:
(P2):
wherein ,representing the upper bound of the probability of Bob detection error,/->Representing the lower bound of the Willie detection error probability.
6. The intelligent reflector-assisted wireless concealment detection method as in claim 5 wherein in step 5, the reduced optimization problem P2 is solved, an optimal intelligent reflector phase shift matrix is determined, and at the same time, the feasible transmit power is selected to meet the concealment constraint requirement, specifically as follows:
is related to |a b | 2 Monotonically decreasing function of->Is related to |a w | 2 Is a monotonically decreasing function of (a) using |a b | 2 /|a w | 2 To determine the optimal smart reflector phase shift matrix Q while selecting the feasible Alice transmit power P a To satisfy the concealment constraint;
for this purpose, the optimization problem is expressed as follows:
wherein ,representing the line-of-sight channel of the smart reflector to Bob and Willie, respectively, +.>Respectively represent Alice's line-of-sight channel to the intelligent reflecting surface and Bob +.>Representing Alice's line-of-sight channels to the intelligent reflective surface and Willie, respectively;
the above optimization problem is rewritten as:
in the formula Hb and Hw The definition is as follows:
wherein ,u l is u < th > element;
since the above-mentioned optimization problem is non-convex, it is derived firstThen iteratively solving the optimization problem by using a continuous convex approximation algorithm;
the lower bound of (2) is expressed as follows:
wherein ,is an iteratively viable point;
further to |u l Relax |=1 to |u l The I is less than or equal to 1, and the original optimization problem is rewritten as follows:
the problem shown in the above formula is a convex optimization problem, solved with the CVX toolbox, then let u=e jarg(u) Thus obtaining the solution of the original problem.
7. The wireless hidden detection system based on the intelligent reflection surface assistance is characterized in that the system is used for realizing the wireless hidden detection method based on the intelligent reflection surface assistance according to any one of claims 1 to 6, and the system comprises a model building module, a detection error probability determining module, a joint optimization problem building module, an optimization problem simplifying module and an optimal intelligent reflection surface phase shift matrix determining module, wherein:
the model building module is used for building a system model and deducing the detection error probability of a legal receiver and an illegal detector;
the detection error probability determining module is used for analyzing an expression of the detection error probability to obtain an optimal detection threshold and determining the detection error probability under the optimal detection threshold;
the joint optimization problem construction module is used for establishing a joint optimization problem P1 of the intelligent reflection surface phase shift matrix and the transmitting power;
the optimization problem simplification module is used for simplifying the optimization problem P1 by selecting the lower bound of the optimization problem P1 to obtain a simplified optimization problem P2;
and the optimal intelligent reflecting surface phase shift matrix determining module is used for solving the simplified optimization problem P2, determining the optimal intelligent reflecting surface phase shift matrix and simultaneously selecting feasible transmitting power to meet the requirement of concealment constraint.
8. A mobile terminal comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the intelligent reflector-assisted wireless concealment method according to any of claims 1-6 when executing the program.
9. A computer readable storage medium having stored thereon a computer program, wherein the program when executed by a processor implements the steps of the intelligent reflector-assisted wireless concealment method according to any of claims 1-6.
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