Omnidirectional metasurface assisted covert communication method and system based on noise uncertainty

Abstract

The application provides an omnidirectional metasurface assisted covert communication method and system based on noise uncertainty, comprising the following steps: step 1: determining the working mode of the intelligent omnidirectional metasurface, and giving the mathematical expression of the transmission and reflection coefficients; step 2: deducing the condition that Alice can communicate normally with Willie and the condition that Alice cannot be detected by Willie with a probability of 100% in the covert transmission; step 3: analyzing the detection performance of Willie, obtaining the minimum detection error probability of Willie as the covert constraint of the system according to the probability density function of the noise power at Willie; step 4: analyzing the transmission from Alice to Bob, and obtaining the expression of the effective covert rate of the system; and step 5: establishing the optimization problem of the intelligent omnidirectional metasurface assisted covert communication system, jointly designing the optimal power of the transmitted covert message at Alice and the TARCs of the intelligent omnidirectional metasurface, and maximizing the effective covert rate of the system. The application of the technical scheme can effectively improve the covert performance of the system and ensure the efficient and safe transmission of information.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to an omnidirectional metasurface-assisted covert communication method and system based on noise uncertainty. Background Technology

[0002] To meet the high-frequency communication demands of post-5G services, the number of antennas will increase exponentially. However, traditional parabolic antennas and phased array antennas are unsuitable for large-scale, dense deployment due to their design complexity, high cost, and low efficiency. Novel antennas based on reconfigurable intelligent surfaces (RIS) possess passive, programmable, and beamforming characteristics, providing a low-cost, high-efficiency, and easily deployable solution for 6G communication to address these issues. Research indicates that this solution can be applied to various communication scenarios, including millimeter-wave communication, satellite communication, integrated sensing and communication, large-scale IoT, and vehicle-to-everything (V2X) communication. Despite rapid development, most RIS currently used in wireless communication systems are reflective or transmissive, thus only providing signal coverage and wireless transmission for the back or front half of the space, failing to achieve full-space signal coverage and intelligent transmission. This not only results in users in the other half of the space not receiving effective signal coverage but also wastes the space resources of that other half. To address these challenges, researchers have proposed the concept of intelligent omnidirectional metasurfaces. Compared to traditional reflective or transmissive RIS, intelligent omnidirectional metasurfaces can simultaneously transmit and reflect incident signals, thereby achieving full-space signal coverage and serving users on both sides at the same time.

[0003] Meanwhile, with the widespread adoption of wireless communication services, a large amount of private or confidential information is transmitted via electromagnetic waves and exposed to open environments, posing a significant risk of privacy breaches. Increased computing power has rendered traditional encryption techniques, reliant on algorithmic complexity, insufficient for information security. Physical layer security technologies leverage the dynamic nature of wireless media to minimize the information obtainable by eavesdroppers. However, these technologies, while aiming to ensure the security of communication content, overlook the fact that sometimes the exposure of user communication behaviors, such as node locations and transmission modes, can also lead to information leaks. To address this issue, scholars have proposed covert communication techniques, also known as low-probability detection techniques. Covert communication techniques not only protect communication content from eavesdropping but also ensure that the communication between the two parties remains undetected by monitors.

[0004] Although scholars both domestically and internationally have conducted extensive research on covert communication, the use of energy detection by illicit nodes typically results in low transmitter power and consequently low covert transmission rates in covert communication scenarios. Considering that smart reflectors can reshape wireless channels and have significant potential to improve the transmission rate, coverage, and energy efficiency of mobile communication systems, numerous studies in recent years have employed smart reflectors to enhance covert communication. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide an omnidirectional metasurface-assisted covert communication method and system based on noise uncertainty, which aims to enhance covert communication by utilizing noise uncertainty and intelligent omnidirectional metasurfaces to ensure efficient and secure information transmission.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: an omnidirectional metasurface-assisted covert communication method based on noise uncertainty, characterized by comprising the following steps:

[0007] Step 1: Determine the working mode of the intelligent omnidirectional metasurface and provide mathematical expressions for the transmission and reflection coefficients;

[0008] Step 2: Determine Alice's transmission strategy under different circumstances, namely, when she does not transmit covert messages and when she transmits covert messages. Derive the conditions under which Alice can communicate normally with Willie and the conditions under which Alice's covert transmission is not detected by Willie with a 100% probability.

[0009] Step 3: Analyze Willie's detection performance and obtain its minimum detection error probability as a hidden constraint of the system based on the probability density function of the noise power at Willie.

[0010] Step 4: Analyze the transmission from Alice to Bob to obtain the expression for the system's effective covert rate;

[0011] Step 5: Establish the optimization problem of the intelligent omnidirectional metasurface-assisted covert communication system, jointly design the optimal power for transmitting covert messages at Alice and the TARCs of the intelligent omnidirectional metasurface, and maximize the effective covert rate of the system.

[0012] In a preferred embodiment, the mathematical expressions for the transmission and reflection coefficients of the smart omnidirectional metasurface are:

[0013]

[0014] Where l∈{t,r} indicates that the signal reaching Bob / Willie is transmitted or reflected through the intelligent omnidirectional metasurface; the intelligent omnidirectional metasurface consists of M units that can simultaneously transmit and reflect. Let these represent the transmission and reflection amplitudes of the m-th element, respectively. This represents the corresponding phase; according to the law of conservation of energy, we have

[0015] In a preferred embodiment, step 2 specifically comprises:

[0016] The channels from Alice to the intelligent omnidirectional metasurface, from the intelligent omnidirectional metasurface to Willie, and from the intelligent omnidirectional metasurface to Bob are respectively represented as h. as , and Assume the transmission rate R between Alice and Willie is... aw If this is predetermined, then the conditions under which Alice can communicate normally with Willie are:

[0017]

[0018] Among them, P max This indicates the maximum transmit power at Alice. In addition, u r =[u r,1 ,u r,2 ,…,u r,M ] T ,in

[0019] The condition under which Alice's covert transmission is not detected by Willie with 100% probability is:

[0020]

[0021] in, P b This indicates the power used by Alice to send covert messages.

[0022] In a preferred embodiment, the noise power at Willie is The probability density function is expressed as:

[0023]

[0024] Where ρ is a parameter representing the magnitude of the quantization noise uncertainty. Indicates the rated power of the noise;

[0025] The minimum detection error probability at Willie is:

[0026]

[0027] in, The system's hidden constraints are:

[0028] ξ * ≥1-ò

[0029] Wherein, ò is the concealment coefficient used to determine the level of concealment.

[0030] In a preferred embodiment, step 4 specifically involves: the signal-to-noise ratio at Bob is:

[0031]

[0032] in, This represents the noise power at Bob; furthermore, u t =[u t,1 ,u t,2 ,…,u t,M ] T ,in Alice achieves a stealth rate of R. b =log2(1+γ) b Define C as the condition that Alice is not detected by Willie's covert transmission with a 100% probability, and let P be the probability that condition C is satisfied. C The effective concealment rate of the system is then expressed as:

[0033]

[0034] In a preferred embodiment, step 5 specifically comprises:

[0035] Let B be the condition that Alice can communicate normally with Willie, and let P be the probability that condition B is satisfied. B Consider P C In the case where P = 1, P B =1, and according to the maximum power constraint at Alice, we can obtain Based on the above, the optimization problem for establishing an intelligent omnidirectional metasurface-assisted covert communication system is as follows:

[0036]

[0037] stC1:ξ * ≥1-ò

[0038] C2:

[0039] C3:

[0040] C4: A semidefinite relaxation algorithm was then used to obtain the optimal solution to the problem through alternating optimization.

[0041] This invention also provides an omnidirectional metasurface-assisted covert communication system based on noise uncertainty. The system operates the omnidirectional metasurface-assisted covert communication method based on noise uncertainty, including a transmitter Alice, a smart omnidirectional metasurface, a covert communication user Bob, and a normal communication user / monitor Willie. Alice, with the help of the smart omnidirectional metasurface, wants to send a covert message to Bob while communicating normally with Willie. Willie, acting as the monitor, wants to detect whether there is communication between Alice and Bob. Considering an infinite code length scenario, assuming the noise at Willie's location is uncertain, the system's effective covert rate is maximized by jointly optimizing Alice's transmission power and the TARCs of the smart omnidirectional metasurface, ensuring the covertness of transmission and the security of information.

[0042] Compared with existing technologies, this invention has the following advantages: This invention considers two transmission strategies at the transmitter and derives the condition that covert communication cannot be detected by the detector with a 100% probability based on the probability density function of noise at Willie's location. Furthermore, it considers energy detection at the detector Willie's location and, based on the above, obtains the minimum detection error probability for Willie as a covert constraint for subsequent problems. This invention also improves the system's covert performance by jointly designing transmitter power and intelligent omnidirectional metasurfaces (TARCs), ensuring secure information transmission. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of a scenario for a preferred embodiment of the present invention, which is a method for intelligent omnidirectional metasurface-assisted covert communication based on noise uncertainty.

[0044] Figure 2 This invention provides a preferred embodiment for comparing the signal-to-noise ratio γ at Bob when using different numbers of intelligent omnidirectional metasurface units M and different concealment coefficients ω. b Simulation diagram.

[0045] Figure 3 The power P used for sending covert messages at Alice is compared with different numbers of intelligent omnidirectional metasurface units M and different concealment coefficients ò in the preferred embodiment of the present invention. b The simulation diagram. Detailed Implementation

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0047] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, 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 pertains.

[0048] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0049] Reference Figure 1 This invention provides a schematic diagram of a scenario for a method of covert communication assisted by an intelligent omnidirectional metasurface based on noise uncertainty. The scenario consists of a transmitter Alice, an intelligent omnidirectional metasurface, a covert communication user Bob, and a normal communication user / monitor Willie. Alice, with the help of the intelligent omnidirectional metasurface, wants to send a covert message to Bob while communicating normally with Willie. Willie also acts as a monitor, aiming to detect whether communication occurs between Alice and Bob. The invention considers an infinite code length scenario, i.e., the total number of channels N→∞. Furthermore, due to temperature changes, environmental noise variations, and calibration errors, noise uncertainty is almost unavoidable; therefore, this invention considers the uncertainty of noise present at Willie's location.

[0050] In this embodiment, Alice, Bob, and Willie are each equipped with a single antenna. The intelligent omnidirectional metasurface has M elements that can simultaneously transmit and reflect, and the transmission and reflection coefficients of each element can be dynamically adjusted according to the propagation environment. The channels from Alice to the intelligent omnidirectional metasurface, from the intelligent omnidirectional metasurface to Bob, and from the intelligent omnidirectional metasurface to Willie are respectively represented as h. as , and

[0051] In wireless communication systems, intelligent omnidirectional metasurfaces have three operating modes: energy distribution, mode switching, and time switching. In this embodiment, the intelligent omnidirectional metasurface operates in energy distribution mode, and its transmission and reflection coefficients are mathematically expressed as follows:

[0052]

[0053] Where l∈{t,r} indicates that the signal reaching Bob / Willie is transmitted or reflected through the intelligent omnidirectional metasurface. Let these represent the transmission and reflection amplitudes of the m-th element, respectively. This indicates the corresponding phase. According to the law of conservation of energy, we have...

[0054] Next, by analyzing the transmission between Alice and Willie, we determine Alice's transmission strategy under different conditions (i.e., no covert message transmission and covert message transmission), where the transmission rate R between Alice and Willie is... aw This is predetermined. Furthermore, when transmission between Alice and Willie is interrupted, Alice will not send any messages. First, based on the received signal at Willie's location when Alice is not transmitting a covert message, we can derive the conditions under which Alice can communicate normally with Willie:

[0055]

[0056] Among them, P max u represents the maximum transmit power at Alice. r =[u r,1 ,u r,2 ,…,u r,M ] T , Let condition B be the condition that Alice can communicate normally with Willie, and let P be the probability that condition B is true. B .

[0057] Next, based on the signal received by Willie when Alice transmits the covert message, the condition for Alice's covert transmission not to be detected by Willie with a 100% probability is:

[0058]

[0059] in, P b This represents the power used by Alice to send the covert message. Subsequently, the condition that Alice is not detected by Willie with a 100% probability of covert transmission is denoted as condition C, and the probability that condition C holds is P. C .

[0060] In this embodiment, considering noise uncertainty, it is assumed that the exact noise power at Willie is unknown, but the statistics of the noise uncertainty at Willie are known, that is, the probability density function of the noise power at Willie is known, specifically expressed as:

[0061]

[0062] in, Let represent the rated power of the noise at Wille, and ρ be a parameter quantifying the magnitude of the noise uncertainty. Based on this probability density function, the probabilities P that guarantee conditions B and C hold can be obtained respectively. B and P C .

[0063] In covert communication, Willie needs to distinguish between the null hypothesis H0 (i.e., Alice did not send a covert message) and the alternative hypothesis H1 (i.e., Alice sent a covert message), specifically expressed as follows:

[0064]

[0065] Among them, y w [i] represents Willie's received signal in the i-th channel. x w [i] and x b [i] represent the signals Alice sends to Willie and Bob on the i-th channel, respectively, both following a complex Gaussian distribution with mean 0 and variance 1, i.e., x w [i]~CN(0,1), x b [i]~CN(0,1). and These represent Alice's method of sending x in cases H0 and H1, respectively. w Power, P b This indicates that Alice is used to send x. b The power. n w This represents the uncertain additive white Gaussian noise (AWGN) at Willie.

[0066] Willie typically uses energy detection, and its performance is measured by the probability of detection errors, which consists of the false alarm rate α and the false negative rate β, expressed as:

[0067] ξ=α+β

[0068] According to the Neyman-Pearson criterion, the optimal detection method at Willie's location is likelihood ratio detection, and the corresponding decision rule is:

[0069]

[0070] Among them, T w τ represents the average power of the signal Willie receives in the time slot, τ is a predetermined threshold, and D0 and D1 are the factors that favor H0 and H1, respectively.

[0071] By discussing the false alarm rate and false negative rate under different conditions, a mathematical analytical expression for the detection error probability at Willie's location can be obtained. Furthermore, the optimal detection threshold τ at Willie's location is derived. * The minimum detection error probability ξ can be obtained. * Minimum detection error probability ξ at Willie. * The mathematical expression is:

[0072]

[0073] in,

[0074] Based on the above, ξ will be adopted in subsequent work. * ≥1-ò serves as a concealment constraint for the system, where ò represents the concealment coefficient, used to determine the level of concealment.

[0075] Next, by analyzing the covert transmission process from Alice to Bob, the expression for the system's effective covert rate is obtained. The received signal at Bob's location is represented as:

[0076]

[0077] Where, n b Let represent the additive white Gaussian noise at Bob's location. Based on the expression for Bob's received signal, the signal-to-noise ratio at Bob's location is:

[0078]

[0079] Among them, u t =[u t,1 ,u t,2 ,…,u t,M ] T , Let R represent the noise power at Bob's location. Therefore, Alice's stealth rate is R. b =log2(1+γ) b Furthermore, the effective concealment rate of the system is expressed as:

[0080]

[0081] In this embodiment, P is considered C In the case where P = 1, P B =1, and according to the maximum power constraint at Alice, we can obtain Based on the above, the optimization problem for establishing an intelligent omnidirectional metasurface-assisted covert communication system is as follows:

[0082]

[0083] stC1:ξ * ≥1-ò

[0084] C2:

[0085] C3:

[0086] C4: Among them, constraint C1 represents the hidden constraint of the system, constraint C2 represents the power constraint at Alice, and constraints C3 and C4 represent the amplitude and phase constraints of the intelligent omnidirectional metasurface unit.

[0087] To solve the above problem, a semidefinite relaxation algorithm is subsequently employed to transform the problem into a more easily solvable form. Furthermore, since the optimization variables in the constraints are mutually coupled, an alternating optimization algorithm is used for iterative solution. The algorithm consists of two phases: In the first phase, given the TARCs of the intelligent omnidirectional metasurface, the optimization at Alice is used to emit the covert message x. b The power. In the second phase, given Alice, the power used to transmit the covert message x. b The power is optimized for TARCs of the intelligent omnidirectional metasurface. The above two steps are then repeated until the algorithm converges.

[0088] Furthermore, since the semidefinite relaxation algorithm used in solving the problem introduces the constraint that the matrix rank is 1, the above alternating optimization algorithm needs to be Gaussian randomized after convergence to obtain the optimal solution of the TARCs of the intelligent omnidirectional metasurface to obtain a rank 1 solution that meets the conditions.

[0089] Figure 2 To illustrate this invention, we compare the signal-to-noise ratio γ at Bob's location with different numbers of intelligent omnidirectional metasurface units M and different concealment coefficients ò. b Simulation diagram. From Figure 2 First, it can be observed that γ b The value decreases as the concealment coefficient ω decreases, because a smaller concealment coefficient indicates a stricter concealment constraint. Furthermore, it can be observed that γ decreases as the number of intelligent omnidirectional metasurface units M increases. b The value of M also increases accordingly, because a larger M allows Bob to receive a stronger transmitted signal.

[0090] Figure 3 To illustrate this invention, we compare the power P used for sending covert messages at Alice when there are different numbers of intelligent omnidirectional metasurface units M and different concealment coefficients ò. b Simulation diagram. From Figure 3 It can be observed that the power P used by Alice to send the covert message is... bThe concealment coefficient decreases as the concealment coefficient ò decreases, because a smaller concealment coefficient leads to more stringent concealment requirements. Furthermore, according to... Figure 2 The signal-to-noise ratio at Bob increases with the increase of M. Therefore, when the number of intelligent omnidirectional metasurface units M increases, only a smaller P is needed at Alice. b This enables covert communication.

Claims

1. An omnidirectional metasurface-assisted covert communication method based on noise uncertainty, characterized in that, Includes the following steps: Step 1: Determine the working mode of the intelligent omnidirectional metasurface and provide mathematical expressions for the transmission and reflection coefficients; Step 2: Determine Alice's transmission strategy under different circumstances, namely, when she does not transmit covert messages and when she transmits covert messages. Derive the conditions under which Alice can communicate normally with Willie and the conditions under which Alice's covert transmission is not detected by Willie with a 100% probability. Step 3: Analyze Willie's detection performance and obtain its minimum detection error probability as a hidden constraint of the system based on the probability density function of the noise power at Willie. Step 4: Analyze the transmission from Alice to Bob to obtain the expression for the system's effective covert rate; Step 5: Establish the optimization problem of the intelligent omnidirectional metasurface-assisted covert communication system, jointly design the optimal power for transmitting covert messages at Alice and the TARCs of the intelligent omnidirectional metasurface, and maximize the effective covert rate of the system.

2. The omnidirectional metasurface-assisted covert communication method based on noise uncertainty according to claim 1, characterized in that, The mathematical expressions for the transmission and reflection coefficients of the intelligent omnidirectional metasurface are: Where l∈{t,r} indicates that the signal reaching Bob / Willie is transmitted or reflected through the intelligent omnidirectional metasurface; the intelligent omnidirectional metasurface consists of M units that can simultaneously transmit and reflect. Let these represent the transmission and reflection amplitudes of the m-th element, respectively. This represents the corresponding phase; according to the law of conservation of energy, we have 3. The omnidirectional metasurface-assisted covert communication method based on noise uncertainty according to claim 1, characterized in that, Step 2 specifically involves: The channels from Alice to the intelligent omnidirectional metasurface, from the intelligent omnidirectional metasurface to Willie, and from the intelligent omnidirectional metasurface to Bob are respectively represented as h. as , and Assume the transmission rate R between Alice and Willie is... aw If this is predetermined, then the conditions under which Alice can communicate normally with Willie are: Among them, P max This indicates the maximum transmit power at Alice. In addition, u r =[u r,1 ,u r,2 ,…,u r,M ] T ,in The condition under which Alice's covert transmission is not detected by Willie with 100% probability is: in, P b This indicates the power used by Alice to send covert messages.

4. The omnidirectional metasurface-assisted covert communication method based on noise uncertainty according to claim 1, characterized in that, The noise power at Willie The probability density function is expressed as: Where ρ is a parameter representing the magnitude of the quantization noise uncertainty. Indicates the rated power of the noise; The minimum detection error probability at Willie is: in, The system's hidden constraints are: x * ≥1-ò Wherein, ò is the concealment coefficient used to determine the level of concealment.

5. The omnidirectional metasurface-assisted covert communication method based on noise uncertainty according to claim 1, characterized in that, Step 4 specifically involves: the signal-to-noise ratio at Bob's location is: in, This represents the noise power at Bob; furthermore, u t =[u t,1 ,u t,2 ,…,u t,M ] T ,in Alice achieves a stealth rate of R. b =log2(1+γ) b Define C as the condition that Alice is not detected by Willie's covert transmission with a 100% probability, and let P be the probability that condition C is satisfied. C The effective concealment rate of the system is then expressed as:

6. The omnidirectional metasurface-assisted covert communication method based on noise uncertainty according to claim 1, characterized in that, Step 5 specifically involves: Let B be the condition that Alice can communicate normally with Willie, and let P be the probability that condition B is satisfied. B Consider P C In the case where P = 1, P B =1, and according to the maximum power constraint at Alice, we can obtain Based on the above, the optimization problem for establishing an intelligent omnidirectional metasurface-assisted covert communication system is as follows: s.t.C1:ξ * ≥1-ò C2: C3: C4: A semidefinite relaxation algorithm was then used to obtain the optimal solution to the problem through alternating optimization.

7. An omnidirectional metasurface-assisted covert communication system based on noise uncertainty, characterized in that, The noise uncertainty-based omnidirectional metasurface-assisted covert communication system operates the noise uncertainty-based omnidirectional metasurface-assisted covert communication method according to any one of claims 1 to 6, including a transmitter Alice, a smart omnidirectional metasurface, a covert communication user Bob, and a normal communication user and monitor Willie; the transmitter Alice wants to send a covert message to another user Bob while communicating normally with Willie, with the help of the smart omnidirectional metasurface; Willie also acts as a monitor, hoping to detect whether there is communication behavior between Alice and Bob; Considering the scenario of infinite code length, assuming that the noise at Willie is uncertain, we can maximize the effective concealment rate of the system by jointly optimizing Alice's transmit power and the TARCs of the intelligent omnidirectional metasurface, thus ensuring the concealment of transmission and the security of information.

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