Intelligent reflecting surface assisted covert communication method with unequal prior probabilities

Abstract

The present application belongs to the field of information security technology of wireless communication network, and relates to a smart reflecting surface assisted unequal prior probability covert communication method. a The present application optimizes the phase shift matrix Θ of the smart reflecting surface, so that the signal-to-interference-and-noise ratio at the legal receiving end is maximized. Under the condition of meeting the concealment, by jointly optimizing the transmitting power P a and the transmission codeword length L, the effective throughput η of the communication link between the transmitting end and the receiving end is maximized when the eavesdropper detects with the optimal detection threshold, and the optimal prior transmission probability for realizing the maximum effective throughput is given. The present application finds the optimal power detection threshold of the eavesdropper under the unequal prior probability, so as to realize the optimal detection. Under the most unfavorable condition for the legal communication parties, the optimal transmitting power, the optimal codeword length and the optimal prior transmission probability of the smart reflecting surface assisted covert communication are given under the limitation condition of the covert communication.

Description

Technical Field

[0001] This invention belongs to the field of information security technology of wireless communication networks, and relates to an intelligent reflector-assisted unequal prior probability covert communication method, specifically referring to the method by which the information source jointly optimizes the transmission power and the transmission codeword length to maximize the effective throughput of the communication link. Background Technology

[0002] With the deepening research into wireless communication technology, fifth-generation communication systems have developed rapidly. Compared to 1G cellular networks, communication speeds have been significantly improved, and a complex and vast wireless communication network is being built. Large amounts of information are transmitted through wireless networks, including confidential information such as personal identification information, bank account information, and various passwords. However, wireless communication channels have wide propagation characteristics, making information extremely vulnerable to eavesdropping. Even if information is encrypted, the transmission mode or bandwidth can still lead to information leakage and cause serious losses, raising significant concerns about the security of wireless communication.

[0003] Unlike information encryption and modern information hiding techniques, covert communication, as a promising technology, aims to interfere with eavesdroppers by exploiting uncertainties in the transmitter's power and channel conditions. This prevents eavesdroppers from correctly determining whether legitimate transmission is occurring, fundamentally solving wireless communication security problems and maintaining a high level of security. Currently, international research teams have derived and verified the basic theories of covert communication. Bash et al. proposed the famous square root rule, providing an upper limit for communication capacity under AWGN channel conditions. Smart reflectors can reconfigure the propagation environment by adjusting the phase shift of the incident signal through reflective elements on their surface. By rationally designing the reflection coefficient of smart reflectors, the quality of legitimate communication can be enhanced while degrading the eavesdropper's monitoring performance. Therefore, smart reflectors are widely used in covert communication.

[0004] Most current covert communication methods assume equal prior probabilities of the transmitter choosing to transmit information, neglecting the impact of the packet generation process on these prior probabilities. In some practical communication scenarios, such as real-time status monitoring systems, status packets are randomly generated and transmitted promptly to meet low latency requirements. Packet generation is controlled by a Poisson process, and studies have provided an upper limit on the number of packets that can achieve covert communication within a certain time interval and sufficient conditions regarding the Poisson process rate. The finite transmission time of the current packet has a significant impact on the generation of the next packet, thus greatly affecting the prior transmission probability in covert communication. Due to the influence of packet transmission, equal prior probabilities are not necessarily the optimal choice for achieving maximum effective throughput.

[0005] This invention proposes a specific strategy for covert communication with unequal prior probabilities using intelligent reflective surfaces, as illustrated in the schematic diagram below. Figure 1 As shown. By optimizing the phase shift matrix Θ of the smart reflector, the signal-to-interference-plus-noise ratio at the legitimate receiver is maximized. While satisfying the concealment requirement, this is achieved by jointly optimizing the transmit power P. a Given the transmission codeword length L, the system maximizes the effective throughput η of the communication link between the transmitter and receiver when the eavesdropper detects with the optimal detection threshold, and provides the optimal prior transmission probability for achieving the maximum effective throughput. Summary of the Invention

[0006] The purpose of this invention is to maximize the effective throughput of the communication link while achieving covert communication. Considering communication in complex urban environments with dense obstacles leading to excessive ground transmission attenuation and very weak signal strength at the receiving end, this invention designs an intelligent reflector to maximize the signal strength at the receiving end by adjusting the signal phase. In a communication network equipped with a single-antenna transmitter, a single-antenna receiver, a single-antenna eavesdropper, and an intelligent reflector, the eavesdropper is set to detect the presence of legitimate communication using its optimal power detection threshold. Based on this, P is jointly optimized... a And L, to ensure that covert communication can still be achieved even if the eavesdropper chooses the most unfavorable situation for both parties in the legitimate communication, while maximizing the effective throughput η of the communication link.

[0007] The technical solution adopted by this invention to solve the technical problem is as follows:

[0008] A method for covert communication with unequal prior probabilities assisted by a smart reflective surface, comprising the following steps:

[0009] The first step is to build a system model:

[0010] 1) The transmitter (Alice) and the legitimate receiver (Bob) are conducting legitimate communication, hoping that this communication will not be detected by the eavesdropper (Willie). By deploying a smart reflector with M reflective elements, the signals received by Bob and Willie are both superimposed signals transmitted via the direct ground link and signals transmitted via the smart reflector's reflected link.

[0011] 2) In this model, three-dimensional space is considered, and the specific schematic diagram is as follows. Figure 1 The communication channels between Alice and Bob, and the eavesdropping channels between Alice and Willie, are both superpositions of large-scale fading and Rayleigh fading distributions. Where β0, α, h e represent the power gain per 1m reference distance, the large-scale fading factor, and the random distribution parameters of the Rayleigh channel, respectively, where h eIt follows a pattern with a mean of 0 and a variance of β. e The complex Gaussian distribution, e = ab, aw, d k Let k∈{ab,aw} represent the distance between nodes. The channel from Alice to the smart reflector is a superposition of large-scale fading and Rayleigh fading distributions. The channel from the smart transmitter to Bob and Willie is also a superposition of large-scale fading and Rayleigh fading distributions. Where h I and g m m = B, W are the M×1 and 1×M matrices representing Rayleigh fading, respectively, and d j Let k∈{ai,ib,iw} represent the distance between the smart reflector and the ground node. Consider additive white Gaussian noise. Let x[i] be the noise power at Willie and Bob, respectively. Alice sends a Gaussian information sequence x[i], i = 1, 2, ..., L.

[0012] 3) The transmitting power P of Alice at the transmitting end a Not exceeding the power limit P max The transmitted codeword length L does not exceed its upper codeword length limit L. max .

[0013] 4) Let R represent the information transmission rate between Alice and Bob:

[0014]

[0015] Where γ b It's the signal-to-interference-plus-noise ratio at Bob's location. Known as the Q-function, also called the right-tail function of the standard normal distribution, Qi -1 (x) is the inverse function of the Q function, and δ represents the average decoding error probability at Bob.

[0016] 5) By modeling the arrival of the data packet as a Poisson process with a rate of λ, we can give Alice's prior probability in each transmission cycle:

[0017] ρ1=1-e -λT (2)

[0018] ρ0=1-ρ1=e -λT (3)

[0019] Where ρ1 represents the probability that Alice chooses to transmit the signal, and ρ0 represents the probability that Alice chooses to remain silent.

[0020] Given a rate λ, the a priori transmission probability is determined solely by the packet transmission duration T. For a packet transmission duration T and a transmission system bandwidth of B, it can be rewritten as:

[0021]

[0022] 6) We know that in communication with finite transmission codeword length, the average decoding error probability at the receiver cannot be ignored. Based on (1), we can give the effective throughput η from the transmitter to the legitimate receiver:

[0023] η=ρ1R(1-δ) (5)

[0024] The second step is to list the optimization problems based on the system model:

[0025] 1) To determine whether legitimate communication behavior exists, Willie's binary hypothesis test is as follows:

[0026]

[0027] Willie wants to adopt the optimal detection strategy to minimize his average false detection probability. This can be achieved using the maximum likelihood criterion.

[0028]

[0029] Find the optimal power detection threshold Γ * Willie compared the received signal power measured by its power detector radiometer with Γ. * This is used to determine the communication status between Alice and Bob. If the received signal power is greater than a preset detection threshold, communication is considered to have occurred; otherwise, it is not.

[0030] 2) To ensure covert communication, the following constraints need to be specified:

[0031]

[0032] Where ε is the tolerance value. By further scaling the relative entropy, the final expression for the hidden constraint is obtained.

[0033]

[0034] 3) For any given transmit power P a And the optimal transmission codeword length L The goal is always to maximize the received signal strength at Bob's location. That is, to require... The modulus length reaches its maximum due to h ab It is a complex scalar with a phase angle. It is also a complex scalar, as long as g B Θh I and h ab If the phase angles are the same, then it can be The modulus reaches its maximum. Therefore, the optimal phase can be obtained:

[0035] θ n =arg(h ab )-arg(g B ,n)-arg(h I ,n) (10)

[0036] Where arg(a) is the phase angle of the complex scalar a, g B n and h I n represents g B and h I The nth element.

[0037] 4) The optimization objective is to maximize the effective throughput of the communication system. Based on this model, the following optimization problem can be constructed:

[0038]

[0039] The constraints are concealment, maximum transmit power, and maximum codeword length. Since the concealment constraint is closely related to the relative magnitude of the prior probability, the next step focuses on maximizing the system's effective throughput under different scenarios.

[0040] The third step is to solve the optimization problem through scenario-based discussion:

[0041] By classifying the magnitudes of prior probabilities, the optimization problem (11) is decomposed into two sub-optimization problems.

[0042] Scenario 1: ρ0 > ρ1

[0043] Substituting the specific expressions for the prior probability and information transmission rate into (11), we obtain the first sub-optimization problem as follows:

[0044]

[0045]

[0046] It is easy to see that η is monotonically increasing with respect to L. Furthermore, η is monotonically increasing with respect to γ. b The first derivative is as follows:

[0047]

[0048] When the signal-to-interference-plus-noise ratio γ of the received signal at Bob b When >1, then there is Since the inverse Q function is monotonically decreasing with respect to the bit error rate δ, as long as δ > 2.66 × 10 -4 Then you can get At this time, η with respect to γb If the first derivative is greater than 0, the objective function is optimized with respect to γ. b It is monotonically increasing. At the same time, γ... b Regarding P a It is also monotonically increasing, so we can obtain η with respect to P. a Monotonically increasing. Because the objective function is related to P... a Since both L and L are monotonically increasing, the optimal transmit power is always the maximum value within its range, regardless of the value of L. Therefore, we can first obtain the optimal transmit power and then solve for the optimal transmission codeword length based on this. The optimal transmit power and optimal transmission codeword length for scenario 1 are given below:

[0049]

[0050]

[0051] in It is to satisfy The maximum value within the possible range.

[0052] Scenario 2: ρ0≤ρ1

[0053] Similarly, substituting the specific expressions for the prior probability and the information transmission rate into (11), we obtain the second sub-optimization problem as follows:

[0054]

[0055] Similar to the analysis method in Scenario 1, the transmit power P of Alice can be solved using the concealment constraint. a Given the constraints, and based on the maximum power constraint, we obtain information about P. a The preliminary optimal solution is as follows:

[0056]

[0057] Substituting this preliminary optimal solution back into the objective function, we further analyze the monotonicity of the objective function with respect to L, thus obtaining the optimal solution for L. The optimal transmit power and optimal transmission codeword length for scenario 2 are given below:

[0058]

[0059]

[0060] in It is to satisfy The maximum value,

[0061]

[0062] L pIt is Substituting the zeros of the first derivative of L into the objective function, and satisfying Bln2 / λ≤L p ≤L max .

[0063] Substituting the optimal solutions obtained in scenarios 1 and 2 into the expression (2) of the prior transmission probability, we can obtain the optimal prior transmission probability for maximizing the effective throughput.

[0064] The beneficial effects of this invention are:

[0065] This invention determines the optimal power detection threshold for eavesdroppers under unequal prior probabilities, thereby achieving optimal detection. Under this most unfavorable condition for both parties in legitimate communication, and within the constraints of covert communication, it provides the optimal transmit power, optimal codeword length, and optimal prior transmission probability for smart reflector-assisted covert communication, demonstrating that the optimal prior transmission probability for achieving maximum effective throughput is not necessarily 0.5. This invention provides a reference method for how to deploy smart reflectors and how to set the optimal codeword length and optimal transmit power. Attached Figure Description

[0066] Figure 1 This is a diagram of a covert communication system based on unequal prior probabilities using intelligent reflective surfaces.

[0067] Figure 2 It is the effect of changes in the eavesdropper's power detection threshold and transmission power on its average detection error probability.

[0068] Figure 3 This refers to the impact of changes in the maximum codeword length and tolerance value on the optimal transmission codeword length.

[0069] Figure 4 It describes the impact of variations in maximum codeword length and tolerance on optimal transmit power and maximized effective throughput.

[0070] Figure 5 This relates to the impact of maximum codeword length and average decoding error probability on maximizing effective throughput.

[0071] Figure 6 This describes the effect of variations in Poisson rate and maximum transmit power on the optimal transmission codeword length and optimal transmit power.

[0072] Figure 7 This refers to the impact of variations in Poisson rate and maximum transmit power on maximum effective throughput and optimal prior transmission probability. Detailed Implementation

[0073] To better understand the above technical solution, a detailed analysis is provided below in conjunction with the accompanying drawings and specific implementation methods.

[0074] A covert communication method using a smart reflector to assist in unequal prior probabilities is proposed. This method first optimizes the phase shift matrix of the smart reflector to maximize the signal-to-interference-plus-noise ratio (SNR) at the legitimate receiver, and then jointly optimizes the transmit power P at the transmitter. a The method uses a transmission codeword length L to achieve covert communication that prevents eavesdropping by an eavesdropper with optimal detection capabilities, and maximizes effective throughput while maintaining covertness. The specific steps are as follows:

[0075] The first step is to make the following settings:

[0076] 1) The positions of the transmitter Alice, the legitimate receiver Bob, the eavesdropper Willie, and the smart reflector are fixed as Alice (0,0,0), Bob (180,10,0), Willie (-300,300,0) and the smart reflector (180,0,30), respectively.

[0077] 2) The number of reflective elements, system bandwidth, and decoding error probability of the intelligent reflector are set as follows: M = 36, B = 15kHz, δ = 0dBm. The channel Rayleigh fading, large-scale fading parameters, and Rayleigh fading parameters are: β0 = -20dBdB, α = 4.4, β... ab =β aw =1. Noise power is set to:

[0078] The second step involved analyzing the best detection methods for the eavesdropper Willie:

[0079] Figure 2 The impact of different power detection thresholds and transmit powers on Willie's average detection error probability was analyzed. As shown in the figure, as the power detection threshold increases, the average detection error probability decreases from a stable value to a minimum point, then increases again until another stable point, indicating that Willie does indeed have an optimal detection threshold that maximizes its detection accuracy. Furthermore, as the transmit power increases, the minimum average detection error probability decreases continuously. This is because increasing the transmit power also increases the relative entropy, which is more advantageous for eavesdroppers. Therefore, Alice's transmit power needs to be carefully selected.

[0080] The third step involves analyzing the impact of different parameters on the optimal solution:

[0081] Figure 3This study demonstrates the impact of different tolerance values ​​and different maximum transmission codeword lengths on the optimal transmission codeword length. Five sets of tolerance values ​​were compared in the experiment. The data in the figure shows that the tolerance value has no effect on the optimal transmission codeword length. This is because the tolerance value in the implicit constraint has no effect on the optimal transmission codeword length. Secondly, as the maximum transmission codeword length increases, the optimal transmission codeword length initially increases and then remains constant. This is inconsistent with the conclusion that the optimal transmission codeword length obtained from most equal prior probabilities is the maximum transmission codeword length. Since the optimal prior transmission probability monotonically increases with the optimal transmission codeword length, this also indicates that the optimal prior probability is not necessarily 0.5 at all times.

[0082] Figure 4 The graph illustrates the impact of different tolerance values ​​and maximum transmitted codeword lengths on optimal transmit power and maximum effective throughput. As the maximum codeword length increases, the optimal transmit power initially increases and then stabilizes. While increasing transmit power improves throughput, it also increases the risk of detection by eavesdroppers, thus requiring a balance to be maintained. Furthermore, as the tolerance value increases, the optimal transmit power also continuously increases until a stable value is reached. This is because as the tolerance value increases, the concealment constraints become less stringent, providing more room for variation in transmit power.

[0083] Figure 5 This demonstrates the impact of maximum codeword length and mean decoding error probability on maximum effective throughput, given a tolerance value. As the mean decoding error probability increases, the maximum effective throughput also increases. This is because an increase in the mean decoding error probability leads to a higher information transmission rate between legitimate communicators, thus affecting the effective throughput.

[0084] Figure 6 and Figure 7 The effects of variations in Poisson rate and maximum transmit power on optimal transmitted codeword length, optimal transmit power, maximum effective throughput, and optimal a priori transmission probability were analyzed. As the maximum transmit power increases, the optimal transmit power initially increases and then stabilizes. This is because when the maximum transmit power reaches a certain level, the concealment constraint takes effect, limiting the transmit power value. Since the effective throughput is affected by both the signal-to-interference-plus-noise ratio (SNR) at Bob's location and the transmit power, the dominant parameter varies at different times, resulting in a trend of initial increase followed by decrease in maximum effective throughput. When the Poisson rate is low, only the maximum transmitted codeword length constraint takes effect. Even if the optimal transmitted codeword length reaches its maximum value, the maximum effective throughput at this rate is lower than that at other rates due to the low optimal a priori transmission probability.

[0085] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A covert communication method based on unequal prior probabilities using intelligent reflective surfaces, characterized in that, Includes the following steps: The first step is to build a system model: 1) Alice, the transmitter, and Bob, the legitimate receiver, are conducting legitimate communication, hoping that this communication will not be detected by Willie, the eavesdropper; this is achieved by deploying [equipment / facilities]. The intelligent reflective surface of the reflective element, the signals received by Bob and Willie are both superimposed from the signals transmitted by the ground direct link and the signals transmitted by the intelligent reflective surface reflection link; 2) Both the communication channel between Alice and Bob and the eavesdropping channel between Alice and Willie are superpositions of large-scale fading and Rayleigh fading distributions. ;in , , These represent the power gain per 1m reference distance, the large-scale fading factor, and the random distribution parameters of the Rayleigh channel, respectively. It follows a mean of 0 and a variance of . The complex Gaussian distribution, ; Indicates the distance between nodes. ; The channel from Alice to the smart reflector is a superposition of large-scale fading and Rayleigh fading distributions. The channel from the smart transmitter to Bob and Willie is also a superposition of large-scale fading and Rayleigh fading distributions. ,in and , These are the characteristics of Rayleigh decay. and matrix, This indicates the distance between the smart reflector and the ground node. Considering additive white Gaussian noise, The noise power at Willie and Bob are respectively; Alice sends a Gaussian information sequence. ; 3) Alice's transmission power Not exceeding the power limit Transmission codeword length Not exceeding its codeword length limit ; 4) Let This indicates the information transmission rate between Alice and Bob: （1）； in, It's the signal-to-interference-plus-noise ratio at Bob's location. , is known as The function, also called the right-tail function of the standard normal distribution, yes The inverse function of a function This represents the average error probability of decoding at Bob's location; 5) By modeling the arrival of the data packet as a rate of The Poisson process can give Alice's prior probability in each transmission cycle: （2）； （3）； in, This refers to the probability that Alice chooses to transmit the signal. This represents the probability that Alice chooses to remain silent; At a given rate Under the premise that the prior transmission probability is determined solely by the packet transmission duration, Determine; for packet transmission duration The bandwidth of the transmission system is Rewrite it as: （4）； 6) Given that in communication with finite transmission codeword length, the average decoding error probability at the receiver cannot be ignored, based on (1), give the effective throughput from the transmitter to the legitimate receiver. : （5） The second step is to list the optimization problems based on the system model: 1) To determine whether legitimate communication behavior exists, Willie's binary hypothesis test is as follows: （6）； Willie aims to employ the optimal detection strategy to minimize his average false detection probability; based on the maximum likelihood criterion... （7）； Find the optimal power detection threshold Willie compared the received signal power measured by the power detector radiometer with... This is used to determine the communication status between Alice and Bob; if the received signal power is greater than a preset detection threshold, then communication is determined to have occurred, otherwise it is not. 2) To ensure covert communication, the following constraints need to be specified: （8）； in, This is the tolerance value; by further scaling the relative entropy, the final hidden constraint expression is obtained. （9）； 3) For any given transmit power and transmission codeword length ,optimal The goal is always to maximize the received signal strength at Bob's location; that is, to require... The modulus length reaches its maximum due to It is a complex scalar with a phase angle. It is also a complex standard, as long as and If the phase angles are the same, then it can be The modulus reaches its maximum; therefore, the optimal phase can be obtained: （10）； in, It is a composite standard quantity phase angle, and They represent and The One element; 4) The optimization objective is to maximize the effective throughput of the communication system. Based on this model, the following optimization problem is constructed: （11）； ； ； The third step is to solve the optimization problem.

2. The covert communication method based on unequal prior probabilities using a smart reflective surface as described in claim 1, characterized in that, The third step, solving the optimization problem, is carried out as follows: By classifying the relationships between prior probabilities, Scenario 1: Substituting the specific expressions for the prior probability and the information transmission rate into (11), we obtain the optimization problem as follows: （12）； ； ； ； about It is monotonically increasing; in addition, about The first derivative is as follows: （13）； When the signal-to-interference-plus-noise ratio of the received signal at Bob's location At that time, there is ,because Inverse function with respect to bit error rate Monotonically decreasing, as long as it is guaranteed Then you can get ; at this time, about If the first derivative is greater than 0, the objective function is optimized with respect to... It is monotonically increasing; at the same time about It is also monotonically increasing, so we can obtain about Monotonically increasing; because the objective function is about and They are all monotonically increasing, therefore regardless of Regardless of the value chosen, the optimal transmission power is always the maximum value within its range; therefore, the optimal transmission power can be obtained first. Based on this, the optimal transmission codeword length is then determined; the optimal transmit power and optimal transmission codeword length for scenario 1 are given below: （14）； （15）； in, , It is to satisfy , The maximum value within the possible range; Substituting the obtained optimal solution into the expression (2) of the prior transmission probability, we obtain the optimal prior transmission probability that maximizes the effective throughput.

3. The covert communication method based on unequal prior probabilities using a smart reflective surface as described in claim 1, characterized in that... The third step, solving the optimization problem, is carried out as follows: By classifying the relationships between prior probabilities, Scenario 2: Substituting the specific expressions for the prior probability and the information transmission rate into (11), we obtain the optimization problem as follows: （16）； The transmit power of Alice is solved by using concealment constraints. Given the constraints, and based on the maximum power constraint, we obtain the following... The preliminary optimal solution is as follows: （17）； Substitute this preliminary optimal solution back into the objective function, and again discuss and analyze the objective function with respect to... The monotonicity, thus obtaining The optimal solution for scenario 2 is given below; the optimal transmit power and optimal transmission codeword length are as follows: （18）； （19）； in , It is to satisfy , The maximum value, （20）； It is After substituting into the objective function, regarding The zeros of the first derivative of , and satisfying ; Substituting the obtained optimal solution into the expression (2) of the prior transmission probability, we obtain the optimal prior transmission probability that maximizes the effective throughput.

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