Covert communication method based on STAR-RIS and full duplex cognitive interference

Abstract

The invention provides a covert communication method based on STAR-RIS and full-duplex cognitive interference. The method comprises the following steps: establishing a covert communication system model based on STAR-RIS and full-duplex cognitive interference; based on a binary hypothesis testing problem, evaluating a false alarm probability and a missed detection probability of hidden user UR spectrum interception; calculating the false alarm probability, the missed detection probability and the detection error probability of malicious monitor UW detection based on the average receiving power of the malicious monitor UW and the judgment criterion; obtaining the optimal detection threshold and the minimum detection error probability of the malicious monitor UW based on the definition of the detection error probability and the monotonicity of the false alarm probability and the missed detection probability under different classifications; the minimum average detection error probability of the malicious monitor UW is calculated based on the statistical magnitude of the channel hypothesis and the channel power gain. According to the method, the interference signal is transmitted by adopting the full-duplex hidden user, hidden communication is ensured, the inhibition effect of the interference of the direct and cascade double links on monitors in the same area is better, and the probability that information is detected can be effectively reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and relates to STAR-RIS (Simultaneously Transmitting And Reflecting Reconfigurable Intelligent Surface) and covert communication technologies, and particularly relates to a covert communication method based on STAR-RIS and full-duplex cognitive interference. Background Art

[0002] As an artificial electromagnetic surface structure with low cost, low power consumption, programmable and easy to deploy, RIS intelligently regulates the signal propagation direction through digital coding technology, breaks through the uncontrollable characteristics of traditional wireless channels, and then establishes a new intelligent programmable wireless environment. However, the characteristic that the classic RIS array can only regulate the unilateral reflection beam limits its application scenarios and cannot effectively meet the requirement of 360-degree signal full coverage, while STAR-RIS can effectively solve this problem. The traditional communication transceiver design only adapts passively to the wireless propagation environment. Integrating STAR-RIS can provide additional design degrees of freedom, intelligently regulate multi-dimensional parameters, and obtain more transmission paths, thereby enhancing the signal transmission quality and effectively improving the overall performance of the system. In addition, by using the transmission and reflection functions, STAR-RIS can effectively construct a blind area transmission link, thereby shortening the propagation distance, increasing the received signal strength, and achieving full-space coverage.

[0003] Due to the openness and broadcast nature of wireless channels, as well as the continuous emergence of new eavesdropping and attack methods, wireless communication is facing increasingly severe security threats. Different from traditional upper-layer encryption technologies that focus on protecting content security, the purpose of covert communication is to conceal the existence of legitimate transmission behaviors so that they cannot be detected by malicious monitors. Covert communication protects the security of communication networks by adopting various technical means, providing an important theoretical basis and practical application prospects for improving the privacy of communication systems. Existing research mainly adopts strategies such as channel and noise uncertainty, and cooperative interference of jammers to achieve higher covert performance. However, additional jammers will increase the system cost and power consumption; the use of an artificial noise-assisted full-duplex receiver can achieve covert communication but cannot effectively guarantee the energy efficiency of the receiver.

[0004] For a STAR-RIS-assisted covert communication network, the covert users in the STAR-RIS reflection area decide whether to transmit interference signals in a cognitive manner, which has a better suppression effect on malicious monitors in the same area, can avoid wasting energy when continuously transmitting interference, and reduce the detection probability of covert information; in addition, the base station superimposes and transmits user signals in a non-orthogonal multiple access manner, and the power allocated to the proximal covert user signal is lower than that of the distal ordinary user signal, which can further enhance the covert performance of the system.

[0005] In the prior art, there is no research on the method of using STAR-RIS and full-duplex cognitive interference assisted covert communication.

[0006] The invention with the application number 202410701189.0 discloses an optimization method for covert communication based on STAR-RIS and friendly interference, which mainly solves the problem of low covert transmission rate in the covert communication system of the prior art. The scheme includes: 1) building a covert communication system model assisted by STAR-RIS; 2) respectively obtaining the corresponding signal transmission rates according to the received signal expressions of the legitimate user side; 3) respectively obtaining the received signal observation values of the signal detection parties on both sides of STAR-RIS based on binary hypothesis testing, and obtaining the minimum average error detection probability of the detection parties; 4) obtaining the upper bound of the signal transmission rate of the legitimate user based on the definition of transmission outage probability and the signal transmission rate of the legitimate user; 5) establishing an optimization function expression of a multi-user covert communication system assisted by STAR-RIS and friendly interference, and maximizing the system transmission rate by jointly optimizing the transmission power and reflection power of the sender, as well as the transmission coefficient matrix and reflection coefficient matrix of STAR-RIS. However, the above method uses an external dedicated jammer to continuously send interference signals to the detection party to ensure the concealment of the system. However, the use of an external jammer will increase the system cost, and continuously transmitting interference signals will increase the system energy consumption. Summary of the Invention

[0007] Aiming at the technical problem that the detection probability of the covert information in the covert communication method of the existing STAR-RIS assisted system is relatively high, the present invention proposes a covert communication method based on STAR-RIS and full-duplex cognitive interference, which adopts a cognitive interference strategy in the STAR-RIS assisted non-orthogonal multiple access covert communication system to reduce the detection probability of malicious monitors; it can be used in the blind area covert communication scenario assisted by STAR-RIS in the 6G network. The present invention uses the internal nodes of the system as the interference transmitters, and uses a cognitive method to determine whether to transmit interference signals, which can not only effectively ensure the concealment of the system, but also reduce the system cost and energy consumption. The present invention can guide the setting of key parameters in the system, effectively suppress the monitoring performance of malicious monitors, and improve the system concealment.

[0008] In order to achieve the above object, the technical solution of the present invention is realized as follows: A covert communication method based on STAR-RIS and full-duplex cognitive interference, the steps are as follows:

[0009] Step 1: Establish a covert communication system model based on STAR-RIS and full-duplex cognitive interference, including a STAR-RIS equipped with N units, a base station BS located on the reflection side of the STAR-RIS, a covert user UR and a malicious monitor UW, and an ordinary user UT located on the transmission side;

[0010] Step 2: Based on the binary hypothesis testing problem, evaluate the false alarm probability and the miss detection probability of the covert user UR's spectrum listening.

[0011] Step 3: The malicious monitor UW detects whether there is covert communication between the base station BS and the covert user UR. Based on the average received power of the malicious monitor UW and the decision criterion, calculate the false alarm probability miss detection probability and the detection error probability ξ;

[0012] Step 4: Based on the definition of the detection error probability and the monotonicity of the false alarm probability and the miss detection probability under different classifications, obtain the optimal detection threshold τ * of the malicious monitor UW and the minimum detection error probability ξ * ;

[0013] Step 5: Based on the channel hypothesis and the statistic of the channel power gain, calculate the minimum average detection error probability of the malicious monitor UW

[0014] Preferably, the base station BS is equipped with M antennas, the covert user UR is a single-antenna covert user, and there is no direct link between the base station BS and the covert user UR, the ordinary user UT, and the malicious monitor UW; the covert user UR and the ordinary user UT are the proximal user and the distal user respectively, the covert user UR is a law enforcement user, and the base station BS needs to hide its transmission behavior to the covert user UR from the malicious monitor UW; the ordinary user UT only has service quality requirements and no concealment requirements; the covert user UR equipped with a sensing module operates in full duplex mode and is equipped with two antennas, one for receiving signals and the other for transmitting interference signals;

[0015] Express the channel coefficients from the base station BS to the STAR-RIS, from the STAR-RIS to the covert user UR / ordinary user UT / malicious monitor UW, and from the covert user UR to the malicious monitor UW as: and where the subscript G b is the line of sight, and g j represent small-scale Rice and Rayleigh fading respectively, represents the complex domain; is the large-scale path loss coefficient, ο ∈ (b, r, t, w, j), ρ0 is the reference path loss at unit distance, α is the path loss exponent, d οDenote the distance between nodes, \(N\) represents the total number of cells of the STAR-RIS, and \(M\) is the total number of antennas of the base station BS; the subscripts \(b\), \(r\), \(t\), \(w\), \(j\) represent the base station BS, the receiver of the covert user UR, the ordinary user UT, the malicious monitor UW, and the transmitter of the covert user UR, respectively.

[0016] The self-interference channel of the covert user UR is where \(g\) rr follows a circularly symmetric complex Gaussian distribution with zero mean and unit variance, and \(\mathbf{\Theta}\) is the self-interference cancellation coefficient; the reflection / transmission coefficient matrix of the STAR-RIS is expressed as where \(\chi\in\{r,t\}\), and are the reflection / transmission amplitude and phase shift of the \(n\)-th STAR-RIS cell, respectively.

[0017] Preferably, the covert user UR faces a binary hypothesis testing problem: the null hypothesis \(H_0\) means that the base station BS does not transmit covert information to the covert user UR, and the alternative hypothesis \(H_1\) means that the base station BS transmits covert information to the covert user UR; based on the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\), the received signal \(y\) of the covert user UR r is expressed as:

[0018]

[0019] where, is the channel use index, is the superimposed signal transmitted by the base station BS, \(P\) b is the transmit power of the base station BS, \(x\) χ and are the signals transmitted by the base station BS to the UR / UT and the beamforming vector of the base station BS, respectively, \(\chi\in\{r,t\}\), \(\omega>0.5\) represents the power allocation factor; \(P\) j is the interference power of the covert user UR, which follows a uniform distribution, i.e., is the maximum transmit power of the UR; \(x\) j is the interference signal transmitted by the covert user UR, \(n\) r is the received noise at the covert user UR, which follows a circularly symmetric complex Gaussian distribution with zero mean and variance ; \(\delta\) is an indicator variable, \(\delta = 1\) indicates the presence of interference, and \(\delta = 0\) indicates the absence of interference; \(\mathbf{\Phi}\) r is the reflection coefficient matrix of the STAR-RIS, \(\mathbf{H}\) b and \(\mathbf{h}\) r represent the channel coefficients from the BS to the STAR-RIS and from the STAR-RIS to the UR, respectively.

[0020] Preferably, the false alarm probability of the covert user UR spectrum sensing is a function of the missed detection probability and:

[0021]

[0022] where γ j is the spectrum sensing signal-to-noise ratio; f j is the sampling frequency, Q -1 (x) is the inverse function of the Gaussian Q function; κ s is the sensing ratio of the covert user UR, and T is the total transmission symbol period.

[0023] Preferably, the covert user UR uses successive interference cancellation technology to decode the signals x t of the ordinary user UT and its own signal x r in sequence. The signal-to-interference-plus-noise ratios of the decoded signals x t and its own signal x r under the alternative hypothesis H1 are respectively expressed as:

[0024]

[0025] The covert user UR decides whether to transmit an interference signal according to its sensing result. Let D r,0 and D r,1 respectively represent the decision results of the covert user UR on the null hypothesis H0 and the alternative hypothesis H1; when the covert user UR believes that the base station BS does not transmit covert information, the judgment result is D r,0 , otherwise the judgment result is D r,1 ;

[0026] The malicious monitor UW faces a binary hypothesis testing problem. The observed value y w of the received signal is expressed as:

[0027]

[0028] where P b is the transmission power of the base station BS, h w and h j respectively represent the channel coefficients from the STAR-RIS to the malicious monitor UW and from the covert user UR to the malicious monitor UW, x t is the signal sent by the base station BS to the ordinary user UT, x j is the interference signal transmitted by the covert user UR, and n w is the received noise at the malicious monitor UW.

[0029] Preferably, the ultimate goal of the malicious monitor UW is to analyze its average received power P wto determine the observation value y of the received signal w Whether it is under the null hypothesis H0 or the alternative hypothesis H1, the decision criterion is τ is the energy detection threshold of the malicious monitor UW, D w,0 and D w,1 are the decision results supporting the null hypothesis H0 and the alternative hypothesis H1 respectively; assuming that all channels are independent and identically distributed, and the number of channel uses is infinite, i.e., I→∞; the average received power of the malicious monitor UW is:

[0030]

[0031] where κ j =T j / T=(T - T s ) / T = 1 - κ s is the transmission ratio of the covert user UR, κ s is the sensing time slot ratio of the covert user UR, T is the total transmission symbol period, T s is the symbol time slot length for the covert user UR to perform sensing, T j is the symbol time slot length for the covert user UR to transmit interference signals; is the variance of the received noise n w

[0032] The base station BS uses maximum ratio transmission for beamforming, and the beamforming vectors of the base station BS for the covert and ordinary signals can be obtained as and where Φ t is the transmission coefficient matrix of the STAR - RIS; the reflection and transmission coefficient matrices of the STAR - RIS are and h t is the channel coefficient from the STAR - RIS to the UT, diag(·) represents the diagonalization operation, a N,b represents the phase shift corresponding to the channel H b

[0033] Preferably, when the malicious monitor UW detects whether the base station BS is performing covert information transmission, based on the definitions of the false alarm probability and the miss - detection probability, the false alarm probability and the miss - detection probability detected by the malicious monitor UW are respectively:

[0034]

[0035] where Pr{·} represents the probability operation, κ j is the interference time slot ratio of the covert user UR.

[0036] ​​Let the intermediate variable

[0037] Through classification analysis, the false alarm probability and the miss detection probability The calculation results are respectively:

[0038]

[0039] The detection error probability is When the intermediate variable ρ1 < ρ2, that is At this time, the detection error probability of the malicious monitor UW is:

[0040]

[0041] Preferably, analyze the optimal detection threshold selection of the malicious monitor UW:

[0042] (1) When the energy detection threshold τ ≤ ρ0 or τ > ρ3, the detection error probability ξ = 1, there is no optimal detection threshold or the minimum ξ value;

[0043] (2) When ρ0 < τ ≤ ρ1, the detection error probability ξ is a monotonically decreasing function with respect to the energy detection threshold τ;

[0044] (3) When ρ1 < τ ≤ ρ2, the detection error probability ξ = 0, which means that τ * = ρ2 is the optimal value in the interval ρ0 < τ ≤ ρ2;

[0045] (4) When ρ2 < τ ≤ ρ3, the detection error probability ξ is a monotonically increasing function with respect to the energy detection threshold τ;

[0046] Then the optimal detection threshold of the malicious monitor UW is τ * = ρ2, and the minimum detection error probability is ξ * = 0;

[0047] When the intermediate variable ρ2 ≤ ρ1, that is At this time, the detection error probability of the malicious monitor UW is:

[0048]

[0049] Among them,

[0050] Analyze the optimal detection threshold selection of the malicious monitor UW:

[0051] 1) When τ ≤ ρ0 or τ > ρ3, the detection error probability ξ = 1, there is no optimal detection threshold or the minimum ξ value;

[0052] 2) When ρ0 < τ ≤ ρ2, the detection error probability ξ is a monotonically decreasing function with respect to the energy detection threshold τ;

[0053] 3) When ρ2 < τ ≤ ρ1, since the first-order partial derivative of the detection error probability ξ with respect to the energy detection threshold τ is

[0054]

[0055] then the detection error probability ξ is a monotonically decreasing function with respect to the energy detection threshold τ;

[0056] 4) When ρ1 < τ ≤ ρ3, the detection error probability ξ is a monotonically increasing function with respect to the energy detection threshold τ;

[0057] The optimal detection threshold of the malicious monitor UW is τ * = ρ1, and the minimum detection error probability is

[0058] which ensures that the malicious monitor UW cannot achieve a zero error detection probability.

[0059] Preferably, based on the expression of the minimum detection error probability ξ * it is found that the minimum detection error probability ξ * is related to the sensing time slot ratio κ s = 1 - κ j of the covert user UR and the miss detection probability ; as the miss detection probability increases, the value of the minimum detection error probability ξ * decreases; the miss detection probability is a monotonically decreasing function with respect to the false alarm probability , so the minimum detection error probability ξ * is a monotonically increasing function with respect to the false alarm probability ; according to the definition of the mean value, the minimum average detection error probability of the malicious monitor UW is expressed as:

[0060]

[0061] where, denotes the expectation operation;

[0062] Based on the channel statistics of the intermediate variables X and Y, through probability operations, we get

[0063]

[0064] where, M a,b(·) is the Whittaker function, 2F1(·,·;·;·) is the Gauss hypergeometric function, and f Y (y) is the probability density function of the intermediate variable Y;

[0065] The minimum average detection error probability of the malicious monitor UW is:

[0066]

[0067] where the intermediate parameter

[0068] σ is the Rice factor, d is the element spacing, λ is the signal wavelength, is the azimuth angle from the STAR-RIS to the UR / UW, is the elevation angle from the STAR-RIS to the UR / UW, L a (·) represents the Laguerre polynomial.

[0069] Preferably, the intermediate variable is set based on the reflection and transmission coefficient matrix of the STAR-RIS to obtain the intermediate variable The intermediate variable Y is a random variable subject to an exponential distribution with an expectation of l j +Nl w l r , that is, Y~exp(1 / (l j +Nl w l r )); the intermediate variable is a random variable subject to a non-central chi-square distribution with 2 degrees of freedom and a non-central parameter of and respectively represent the conjugates of the m-th components of the channels h w and h r ; the cumulative distribution function and probability density function of the intermediate variable X are respectively:

[0070]

[0071] where Q1(·,·) is the first-order Marcum Q function and I0(·) is the modified Bessel function of the first kind.

[0072] The present invention has the following beneficial effects compared with the prior art:

[0073] First, the present invention uses a full-duplex covert user to transmit interference signals with a sensing module installed in the reflection area to ensure covert communication. The suppression effect of the direct and cascaded double-link interference on the same-area monitor is better, and the probability of information being detected can be effectively reduced.

[0074] Second, the use of user cooperation-based covert communication within the system in the present invention can reduce the system cost, and the cognitive function enables users to decide whether to transmit interference signals according to their detection results, which can avoid wasting energy by continuously transmitting interference and reduce the possibility of being detected.

[0075] Third, in the present invention, the base station superimposes and transmits user signals in a non-orthogonal multiple access manner, and the power allocation of the proximal covert user signal is lower than that of the distal ordinary user signal. At this time, ordinary information can play a covert role, further enhancing the covert performance of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0077] Figure 1 It is a flowchart for the implementation of the present invention.

[0078] Figure 2 It is a system model diagram of the present invention.

[0079] Figure 3 It is the false alarm probability of UR of the present invention Effect simulation result diagram of the average minimum detection error probability for UW

[0080] Figure 4 It is the effect simulation result diagram of the ratio κ of the UR sensing time slot of the present invention s on the average minimum detection error probability for UW

[0081] Figure 5 It is a schematic diagram of the optimal detection threshold selection for UW when ρ1 < ρ2 in the present invention.

[0082] Figure 6 It is a schematic diagram of the optimal detection threshold selection for UW when ρ2 ≤ ρ1 in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0083] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention. ​​

[0084] As shown Figure 1 in the figure, a covert communication method based on STAR-RIS and full-duplex cognitive interference uses a base station BS, a covert user UR, and a malicious monitor UW located on the reflection side of the STAR-RIS, and a general user UT located on the transmission side of the STAR-RIS to construct a covert communication model; the malicious monitor UW on the reflection side determines whether the base station BS sends covert information according to the received signal, and the covert user UR on the reflection side decides whether to transmit interference signals through cognitive functions to confuse the signal detection of the malicious monitor UW. The specific implementation steps of the present invention are as follows:

[0085] Step 1: Establish a covert communication system model based on STAR-RIS and full-duplex cognitive interference, including a STAR-RIS equipped with N units, a base station BS, a covert user UR, and a malicious monitor UW located on the reflection side of the STAR-RIS, and a general user UT located on the transmission side.

[0086] As shown Figure 2 in the figure, a covert communication system model based on STAR-RIS and full-duplex cognitive interference is established. The system consists of a STAR-RIS equipped with N units, a base station BS equipped with M antennas, a single-antenna covert user UR, a malicious monitor UW located on the reflection side of the STAR-RIS, and a general user UT located on the transmission side of the STAR-RIS; due to the existence of buildings, there is no direct link between the base station BS and the covert user UR, the general user UT, and the malicious monitor UW; it is assumed that the covert user UR and the general user UT are the proximal and distal users respectively; the covert user UR is a law enforcement user, and the base station BS needs to hide its transmission behavior to the covert user UR from the malicious monitor UW; the general user UT only has quality of service requirements and no covertness requirements.

[0087] The channel coefficients from the base station BS to the STAR-RIS, from the STAR-RIS to the covert user UR / general user UT / malicious monitor UW, and from the covert user UR to the malicious monitor UW are respectively expressed as: and where the subscript G b is the line of sight, and g j respectively represent small-scale Ricean and Rayleigh fading, represents the complex domain, represents an a×b-dimensional complex matrix; is the large-scale path loss coefficient, ο∈(b,r,t,w,j), ρ0 is the reference path loss at unit distance, α is the path loss exponent, d οdenote the distance between nodes, \(N\) represents the total number of STAR-RIS units, and \(M\) is the total number of antennas of the base station BS. For ease of description, the subscript letters \(b\), \(r\), \(t\), \(w\), \(j\) represent the base station BS, the receiver of the covert user UR, the ordinary user UT, the malicious monitor UW, and the transmitter of the covert user UR, respectively; the self-interference channel of the covert user UR is modeled as where \(g\) rr obeys a circularly symmetric complex Gaussian distribution with zero mean and unit variance, i.e., is the self-interference cancellation coefficient; the reflection / transmission coefficient matrix of STAR-RIS is uniformly denoted as where \(\chi\in\{r,t\}\), and are the reflection / transmission amplitude and phase shift of the \(n\)-th STAR-RIS unit, respectively,

[0088] Step 2: Based on the binary hypothesis testing problem, evaluate the false alarm probability and the miss detection probability of the spectrum sensing of the covert user UR.

[0089] The covert user UR equipped with a sensing module operates in full-duplex mode and is equipped with two antennas, one for receiving signals and the other for transmitting interference signals to weaken the detection ability of the malicious monitor UW. The covert user UR decides whether to transmit interference signals according to its detection results; when the covert user UR determines that the base station BS does not send covert information, it transmits interference signals; otherwise, it remains silent. Therefore, the covert user UR faces a binary hypothesis testing problem: the null hypothesis \(H_0\) represents that the base station BS does not transmit covert information to the covert user UR, and the alternative hypothesis \(H_1\) represents that the base station BS transmits covert information to the covert user UR. Based on the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\), the received signal \(y\) of the covert user UR r can be expressed as:

[0090]

[0091] where is the channel use index, is the superimposed signal transmitted by the base station BS, \(P\) b is the transmission power of the base station BS, \(x\) χ and are the signals transmitted by the base station BS to UR / UT and the beamforming vector of the base station BS, respectively, \(\chi\in\{r,t\}\), \(\omega\gt0.5\) represents the power allocation factor; \(P\) j is the interference power of the covert user UR, which follows a uniform distribution, i.e., is the maximum transmission power of UR; \(x\) j is the interference signal transmitted by the covert user UR, is the received noise at the covert user UR, which follows a circularly symmetric complex Gaussian distribution with zero mean and variance ; δ is an indicator variable, where δ = 1 indicates the presence of interference and δ = 0 indicates the absence of interference; Φ r is the reflection coefficient matrix of the STAR-RIS, and H b and h r represent the channel coefficients from the BS to the STAR-RIS and from the STAR-RIS to the UR, respectively.

[0092] The covert user UR uses successive interference cancellation technology to decode the signals x t of the ordinary user UT and its own signal x r in sequence. The signal-to-interference-plus-noise ratios of its decoded signal x t and its own signal x r under the alternative hypothesis H1 are respectively expressed as:

[0093]

[0094] The covert user UR decides whether to transmit an interference signal according to its sensing result. Let D r,0 and D r,1 represent the decision results of the covert user UR for the null hypothesis H0 and the alternative hypothesis H1, respectively; when the covert user UR believes that the base station BS has not transmitted covert information, the judgment result is D r,0 , otherwise it is D r,1 . and represent the false alarm probability and the miss detection probability of the spectrum sensing of the covert user UR, respectively. Among them, the false alarm probability as a function of the miss detection probability can be expressed as:

[0095]

[0096] where γ j is the spectrum sensing signal-to-noise ratio, which can be obtained according to formulas (2) and (3); f j is the sampling frequency, Q -1 (x) is the inverse function of the Gaussian Q function; κ s is the sensing ratio of the covert user UR, and T is the total transmission symbol period.

[0097] Step 3: The malicious monitor UW detects whether there is covert communication between the base station BS and the covert user UR. Based on the average received power and decision criterion of the malicious monitor UW, calculate the false alarm probability the miss detection probability and the detection error probability ξ of the malicious monitor UW.

[0098] The malicious monitor UW attempts to use an energy detector to detect whether there is covert communication between the base station BS and the covert user UR. Therefore, the malicious monitor UW also faces a binary hypothesis testing problem, and the observed value y of its received signal w can be expressed as:

[0099]

[0100] where P b is the transmission power of the base station BS, h w and h j represent the channel coefficients from the STAR-RIS to the malicious monitor UW and from the covert user UR to the malicious monitor UW respectively, x t is the signal sent by the base station BS to the ordinary user UT, x j is the interference signal transmitted by the covert user UR, and n w is the received noise at the malicious monitor UW.

[0101] The ultimate goal of the malicious monitor UW is to analyze its average received power P w to determine whether the observed value y of the received signal w is under the null hypothesis H0 or the alternative hypothesis H1, and its decision criterion is τ is the energy detection threshold preset by the malicious monitor UW, D w,0 and D w,1 are the decision results supporting the null hypothesis H0 and the alternative hypothesis H1 respectively. Assuming that all channels are independent and identically distributed, and the number of channel uses is infinite, i.e., I→∞; the average received power of the malicious monitor UW is calculated as

[0102]

[0103] where κ j =T j / T=(T - T s ) / T = 1 - κ s is the transmission ratio of the covert user UR, κ s is the sensing time slot ratio of the covert user UR, T is the total transmission symbol period, T s is the symbol time slot length for the covert user UR to perform sensing, and T j is the symbol time slot length for the covert user UR to transmit the interference signal. is the variance of the received noise n w . Based on the average received power P w and the decision criterion of the malicious monitor UW, the false alarm and miss detection probabilities can be calculated subsequently.

[0104] To maximize the received signal quality of the covert user UR and the ordinary user UT, the base station BS performs beamforming using maximum ratio transmission. Therefore, the beamforming vectors of the base station BS for the covert and ordinary signals are respectively and where Φ t is the transmission coefficient matrix of the STAR-RIS; the reflection and transmission coefficient matrices of the STAR-RIS are respectively and h t is the channel coefficient from the STAR-RIS to the UT, diag(·) represents the diagonalization operation, and a N,b represents the phase shift corresponding to the channel H b .

[0105] Let the intermediate variable Then, based on the settings of the reflection and transmission coefficient matrices of the STAR-RIS, we can obtain Y is a random variable following an exponential distribution with an expectation of l j +Nl w l r , that is, Y ~ exp(1 / (l j +Nl w l r )) is a random variable following a non-central chi-square distribution with 2 degrees of freedom and a non-central parameter of and respectively represent the conjugates of the m-th components of the channels h w and h r . The cumulative distribution function and probability density function of the intermediate variable X are respectively

[0106]

[0107] where the corresponding intermediate parameters can be successively expressed as is the azimuth angle from the STAR-RIS to the UR / UW, is the elevation angle from the STAR-RIS to the UR / UW, σ is the Rice factor, d is the element spacing, λ is the signal wavelength, Q1(·,·) is the first-order Marcum Q function, I0(·) is the first-order modified Bessel function, and L a (·) represents the Laguerre polynomial with parameter a. Based on the cumulative distribution function F X (x) and the probability density function f X (x), the false alarm and miss detection probabilities of the malicious monitor UW can be calculated subsequently

[0108] When the malicious monitor UW detects whether the base station BS is performing covert information transmission, based on the definitions of false alarm and miss detection probabilities, the false alarm probability detected by the malicious monitor UW is calculated and the miss detection probability are respectively:

[0109]

[0110] where Pr{·} represents probability operation, and κ j is the interference time slot ratio of the covert user UR.

[0111] Let the intermediate variable Through classification analysis, the false alarm probability and the miss detection probability of the specific calculation results are respectively:

[0112]

[0113] The detection performance of the malicious monitor UW is evaluated using the detection error probability, and the definition formula of the detection error probability is When the intermediate variable ρ1 < ρ2, that is , the expression of the detection error probability of the malicious monitor UW can be obtained as:

[0114]

[0115] Step 4: Based on the definition of the detection error probability and the monotonicity of the false alarm probability and the miss detection probability under different classifications, obtain the optimal detection threshold τ * of the malicious monitor UW and the minimum detection error probability ξ * .

[0116] By analyzing, obtain the optimal detection threshold and the minimum detection error probability of the malicious monitor UW on the reflection side of the STAR-RIS. Based on Figure 3 shown, analyze the selection of the optimal detection threshold of the malicious monitor UW:

[0117] (1) When the energy detection threshold τ ≤ ρ0 or τ > ρ3, the detection error probability ξ = 1, and there is no optimal detection threshold or minimum ξ value;

[0118] (2) When ρ0 < τ ≤ ρ1, the detection error probability ξ is a monotonically decreasing function with respect to the energy detection threshold τ;

[0119] (3) When ρ1 < τ ≤ ρ2, the detection error probability ξ = 0, which means that τ * = ρ2 is the optimal value in the interval ρ0 < τ ≤ ρ2;

[0120] When ρ2 < τ ≤ ρ3, the detection error probability ξ is a monotonically increasing function with respect to the energy detection threshold τ;

[0121] In summary, the optimal detection threshold for the malicious monitor UW is τ * = ρ2. Correspondingly, the minimum detection error probability is ξ * = 0.

[0122] When the intermediate variable ρ2 ≤ ρ1, that is According to formulas (11) and (12), the detection error probability expression for the malicious monitor UW can be obtained as:

[0123]

[0124] where

[0125] Based on Figure 4 as shown, analyze the optimal detection threshold selection for the malicious monitor UW:

[0126] (1) When τ ≤ ρ0 or τ > ρ3, the detection error probability ξ = 1, and there is no optimal detection threshold or minimum ξ value;

[0127] (2) When ρ0 < τ ≤ ρ2, the detection error probability ξ is a monotonically decreasing function with respect to the energy detection threshold τ;

[0128] (3) When ρ2 < τ ≤ ρ1, since the first-order partial derivative of the detection error probability ξ with respect to the energy detection threshold τ is

[0129]

[0130] Therefore, the detection error probability ξ is a monotonically decreasing function with respect to the energy detection threshold τ;

[0131] (4) When ρ1 < τ ≤ ρ3, the detection error probability ξ is a monotonically increasing function with respect to the energy detection threshold τ;

[0132] In summary, the optimal detection threshold for the malicious monitor UW is τ * = ρ1. Correspondingly, substituting ρ1 into formula (14), the minimum detection error probability can be obtained as

[0133] In the above results, It is ensured that the malicious monitor UW cannot achieve a zero error detection probability, which means that in order to achieve covert communication, the interference power received at the malicious monitor UW should be no less than the power of the covert signal transmitted by the base station BS. According to the expressions and establishment conditions of the optimal detection threshold and the minimum detection error probability, the relationship between the power of the covert signal transmitted by the base station BS and the power of the interference signal transmitted by the covert user is given.

[0134] Step 5: Calculate the minimum average detection error probability of the malicious monitor UW based on the channel hypothesis and the statistic of the channel power gain

[0135] Based on the expression of the minimum detection error probability ξ * it can be found that the minimum detection error probability ξ * is related to the sensing time slot ratio κ s = 1 - κ j of the covert user UR and the miss detection probability ; obviously, as the miss detection probability increases, the value of the minimum detection error probability ξ * decreases; while the miss detection probability is a monotonically decreasing function of the false alarm probability . Therefore, the minimum detection error probability ξ * is a monotonically increasing function of the false alarm probability . According to the definition of the mean value, the minimum average detection error probability of the malicious monitor UW can be expressed as:

[0136]

[0137] where, denotes the expectation operation.

[0138] Based on the channel statistics of the intermediate variables X and Y, through probability operations, we can obtain

[0139]

[0140]

[0141] where, M a,b (·) is the Whittaker function, 2F1(·,·;·;·) is the Gaussian hypergeometric function, and f Y (y) is the probability density function of the intermediate variable Y.

[0142] To sum up, the minimum average detection error probability of the malicious monitor UW is calculated as:

[0143]

[0144] Among them,

[0145] σ is the Rice factor, d is the element spacing, λ is the signal wavelength, L a (·) represents the Laguerre polynomial.

[0146] Next, MATLAB simulation is used to verify the effectiveness of the STAR-RIS and full-duplex cognitive interference-assisted covert communication method proposed in the present invention. The parameters are set as follows: the number of elements N of the STAR-RIS is 64, the number of antennas M of the base station BS is 5, the power allocation coefficient ω of the base station BS is 0.7, the Rice factor σ is 2, the element spacing is taken as λ / 2, and the sensing time slot ratio κ s = 0.3.

[0147] Figure 5 is the false alarm probability of the covert user UR The minimum average detection error probability for the malicious monitor UW Influence simulation curve graph. It can be seen from the figure that is a monotonically increasing function of the false alarm probability This is because when the false alarm probability increases, according to the receiver operating characteristic curve of spectrum sensing, the corresponding miss detection probability decreases, which results in a higher probability for the covert user UR of the cognitive interference receiver to assist the covert communication of the proposed STAR-RIS assisted system. Therefore, the minimum average detection error probability increases as the false alarm probability increases. In addition, The larger, the larger the minimum average detection error probability The larger, which means the higher the interference power, the more conducive to realizing covert communication.

[0148] Figure 6 is the sensing time slot ratio κ of the covert user UR s Influence simulation curve graph of the minimum average detection error probability for the malicious monitor UW Set It can be seen from the figure that when the sensing time slot ratio κ s increases from 0 to 1, first increases and then decreases. This is because as the sensing time slot ratio κ s increases, the covert user UR of the cognitive interference receiver can obtain higher sensing quality, which means there is a higher chance to help with covert transmission. However, when the sensing time slot ratio κ sWhen it exceeds its optimal value, it also means that there is a great chance for the malicious monitor UW to detect the covert communication behavior during the sensing period. Therefore, when the sensing time slot ratio κ s exceeds its optimal value, the average minimum detection error probability of the malicious monitor UW is decreasing. The sensing time slot ratio κ s = 0 means that the sensing time slot is 0, which is equivalent to a continuous or all-time interference receiver. The sensing time slot ratio κ s = 1 means that κ j = 0, that is, no interference is sent, and the performance is the worst. There exists an optimal sensing time slot ratio κ s value, which means that the cognitive interference receiver has a performance advantage in improving the system's concealment.

[0149] In summary, the STAR-RIS and the full-duplex cognitive interference-assisted covert communication method proposed in the present invention can effectively increase the concealment of communication and reduce the detection effect of malicious detectors. The simulation results fully illustrate its effectiveness.

[0150] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A covert communication method based on STAR-RIS and full-duplex cognitive interference, characterized in that The steps are as follows: Step 1: Establish a covert communication system model based on STAR-RIS and full-duplex cognitive interference, including a STAR-RIS equipped with N units, a base station BS located on the reflection side of the STAR-RIS, a covert user UR and a malicious monitor UW, as well as an ordinary user UT located on the transmission side; Step 2: Based on the binary hypothesis testing problem, evaluate the false alarm probability and miss detection probability of the spectrum sensing of the covert user UR; Step 3: The malicious monitor UW detects whether there is covert communication between the base station BS and the covert user UR, and calculates the false alarm probability detected by the malicious monitor UW based on the average received power of the malicious monitor UW and the decision criterion miss detection probability and the detection error probability ξ; Step 4: Based on the definition of the detection error probability and the monotonicity of the false alarm probability and the missed detection probability obtain the optimal detection threshold τ * of the malicious monitor UW and the minimum detection error probability ξ * ; Step 5: Calculate the minimum average detection error probability of the malicious monitor UW based on the statistics of the channel hypothesis and the channel power gain 2. The covert communication method based on STAR-RIS and full-duplex cognitive interference according to claim 1, wherein, The base station BS is equipped with M antennas. The covert user UR is a single-antenna covert user. There is no direct link between the base station BS and the covert user UR, the ordinary user UT, and the malicious monitor UW. The covert user UR and the ordinary user UT are the proximal user and the distal user respectively. The covert user UR is a law enforcement user. The base station BS needs to hide its transmission behavior to the covert user UR from the malicious monitor UW; The ordinary user UT only has quality of service requirements and no covertness requirements. The covert user UR equipped with a sensing module operates in full-duplex mode and is equipped with two antennas, one for receiving signals and the other for transmitting interference signals; The channel coefficients from the base station BS to the STAR-RIS, from the STAR-RIS to the covert user UR / ordinary user UT / malicious monitor UW, and from the covert user UR to the malicious monitor UW are respectively expressed as: and where the subscript G b is the line-of-sight, and g j respectively represent small-scale Rice and Rayleigh fading, represents the complex domain; is the large-scale path loss coefficient, ο ∈ (b, r, t, w, j), ρ0 is the reference path loss at unit distance, α is the path loss exponent, d ο represents the distance between nodes, N represents the total number of elements of the STAR-RIS, M is the total number of antennas of the base station BS; the subscripts b, r, t, w, j respectively represent the base station BS, the receiving end of the covert user UR, the ordinary user UT, the malicious monitor UW, and the transmitting end of the covert user UR; The self-interference channel of the hidden user UR is where g rr follows a circularly symmetric complex Gaussian distribution with zero mean and unit variance, is the self-interference cancellation coefficient; the reflection / transmission coefficient matrix of the STAR-RIS is expressed as where χ ∈ {r, t}, and are the reflection / transmission amplitude and phase shift of the nth STAR-RIS element, respectively, 3. The covert communication method based on STAR-RIS and full-duplex cognitive interference according to claim 2, wherein The covert user UR faces a binary hypothesis testing problem: The null hypothesis H0 means that the base station BS does not transmit covert information to the covert user UR, and the alternative hypothesis H1 means that the base station BS transmits covert information to the covert user UR; Based on the null hypothesis H0 and the alternative hypothesis H1, the received signal y of the covert user UR r is expressed as: Among them, is the channel usage index, is the superimposed signal transmitted by the base station BS, P b is the transmission power of the base station BS, x χ and are the signal transmitted by the base station BS to the UR / UT and the beamforming vector of the base station BS respectively, χ ∈ {r, t}, ω > 0.5 represents the power allocation factor; P j is the interference power of the hidden user UR, which follows a uniform distribution, that is is the maximum transmission power of the UR; x j is the interference signal transmitted by the hidden user UR, n r is the received noise at the hidden user UR, which follows a circularly symmetric complex Gaussian distribution with zero mean and variance ; δ is an indicator variable, δ = 1 indicates interference, δ = 0 indicates no interference; Φ r is the reflection coefficient matrix of the STAR-RIS, H b and h r represent the channel coefficients from the BS to the STAR-RIS and from the STAR-RIS to the UR respectively.

4. The covert communication method based on STAR-RIS and full-duplex cognitive interference according to any one of claims 1-3, characterized in that The false alarm probability of the covert user's UR spectrum sensing is a function of the missed detection probability and: Among them, γ j is the spectrum sensing signal-to-noise ratio; f j is the sampling frequency, Q -1 (x) is the inverse function of the Gaussian Q function; κ s is the sensing ratio of the covert user UR, and T is the total transmission symbol period.

5. The covert communication method based on STAR-RIS and full-duplex cognitive interference according to claim 4, characterized in that, The hidden user UR uses successive interference cancellation technology to decode the signal x of the ordinary user UT in sequence t and its own signal x r , and the signal-to-interference-plus-noise ratios of the decoded signal x t and its own signal x r under the alternative hypothesis H1 are respectively expressed as: The hidden user UR decides whether to transmit an interference signal according to its perception result, denoted by D r,0 and D r,1 respectively represent the judgment results of the hidden user UR on the null hypothesis H0 and the alternative hypothesis H1; when the hidden user UR believes that the base station BS does not transmit hidden information, the judgment result is D r,0 , otherwise the judgment result is D r,1 ; The malicious monitor UW faces a binary hypothesis testing problem and receives the observation value y of the signal w which is expressed as: where, P b is the transmission power of the base station BS, h w and h j respectively represent the channel coefficients from the STAR-RIS to the malicious monitor UW and from the covert user UR to the malicious monitor UW, x t is the signal sent by the base station BS to the ordinary user UT, x j is the interference signal transmitted by the covert user UR, and n w is the received noise at the malicious monitor UW.

6. The covert communication method based on STAR-RIS and full-duplex cognitive interference according to claim 5, wherein The ultimate goal of the malicious monitor UW is to analyze its average received power P w to determine the observed value y of the received signal w under the null hypothesis H0 or the alternative hypothesis H1, and the decision criterion is τ is the energy detection threshold of the malicious monitor UW, and D w,0 and D w,1 are the decision results supporting the null hypothesis H0 and the alternative hypothesis H1 respectively; assuming that all channels are independent and identically distributed and the number of channel uses is infinite, i.e., I → ∞; the average received power of the malicious monitor UW is: Among them, κ j = T j / T = (T - T s ) / T = 1 - κ s is the transmission ratio for concealing the user UR, κ s is the sensing time slot ratio for concealing the user UR, T is the total transmission symbol period, T s is the symbol time slot length for the user UR to perform sensing, T j is the symbol time slot length for the user UR to transmit the interference signal; is the variance of the received noise n w . The base station BS uses maximum ratio transmission for beamforming. The beamforming vectors of the base station BS for the covert and ordinary signals can be obtained as and where Φ t is the transmission coefficient matrix of the STAR-RIS; the reflection and transmission coefficient matrices of the STAR-RIS are and h t is the channel coefficient from the STAR-RIS to the UT, diag(·) represents the diagonalization operation, and a N,b represents the phase shift corresponding to the channel H b .

7. The covert communication method based on STAR-RIS and full-duplex cognitive interference according to claim 5 or 6, characterized in that, When the malicious monitor UW detects whether the base station BS performs covert information transmission, based on the definitions of the false alarm probability and the missed detection probability, calculate the false alarm probability of the malicious monitor UW's detection and the missed detection probability respectively as follows: where Pr{·} represents a probability operation, and κ j is the interference time slot ratio of the covert user UR. Let the intermediate variable Through classification analysis, the false alarm probability and the missed detection probability are calculated as follows: The detection error probability is When the intermediate variable ρ1 < ρ2, that is the detection error probability of the malicious monitor UW is:

8. The covert communication method based on STAR-RIS and full-duplex cognitive interference according to claim 7, characterized in that, Analyze the optimal detection threshold selection of the malicious monitor UW: (1) When the energy detection threshold τ ≤ ρ0 or τ > ρ3, the detection error probability ξ = 1, and there is no optimal detection threshold or minimum ξ value; (2) When ρ0 < τ ≤ ρ1, the detection error probability ξ is a monotonically decreasing function with respect to the energy detection threshold τ; (3) When ρ1 < τ ≤ ρ2, the detection error probability ξ = 0, which means that τ * = ρ2 is the optimal value in the interval ρ0 < τ ≤ ρ2; (4) When ρ2 < τ ≤ ρ3, the detection error probability ξ is a monotonically increasing function with respect to the energy detection threshold τ; Then the optimal detection threshold of the malicious monitor UW is τ * = ρ2, and the minimum detection error probability is ξ * = 0; When the intermediate variable ρ2 ≤ ρ1, that is the detection error probability of the malicious monitor UW is: Among them, Analyze the optimal detection threshold selection of the malicious monitor UW: 1) When τ ≤ ρ0 or τ > ρ3, the detection error probability ξ = 1, and there is no optimal detection threshold or minimum ξ value; 2) When ρ0 < τ ≤ ρ2, the detection error probability ξ is a monotonically decreasing function with respect to the energy detection threshold τ; 3) When ρ2 < τ ≤ ρ1, since the first-order partial derivative of the detection error probability ξ with respect to the energy detection threshold τ is then the detection error probability ξ is a monotonically decreasing function with respect to the energy detection threshold τ; 4) When ρ1 < τ ≤ ρ3, the detection error probability ξ is a monotonically increasing function with respect to the energy detection threshold τ; The optimal detection threshold of the malicious monitor UW is τ * = ρ1, and the minimum detection error probability is Ensure that the malicious monitor UW cannot achieve a zero error detection probability.

9. The covert communication method based on STAR-RIS and full-duplex cognitive interference according to claim 1 or 8, characterized in that, Based on the expression of the minimum detection error probability ξ * to find the minimum detection error probability ξ * and the sensing time slot ratio κ of the covert user UR s = 1 - κ j and the miss detection probability are related; as the miss detection probability increases, the value of the minimum detection error probability ξ * decreases; the miss detection probability is a monotonically decreasing function of the false alarm probability , so the minimum detection error probability ξ * is a monotonically increasing function of the false alarm probability ; according to the definition of the mean, the minimum average detection error probability of the malicious monitor UW is expressed as: Among them, represents an expected operation; Based on the channel statistics of the intermediate variables X and Y, through probability operations, obtain Among them, M a,b (·) is the Whittaker function, 2F1(·, ·; ·; ·) is the Gaussian hypergeometric function, and f Y (y) is the probability density function of the intermediate variable Y; The minimum average detection error probability of the malicious monitor UW is: Among them, the intermediate parameter σ is the Rice factor, d is the element spacing, λ is the signal wavelength, is the azimuth angle from the STAR-RIS to the UR / UW, is the elevation angle from the STAR-RIS to the UR / UW, L a (·) represents the Laguerre polynomial.

10. The covert communication method based on STAR-RIS and full-duplex cognitive interference according to claim 9, wherein, The intermediate variable The intermediate variable can be obtained based on the setting of the reflection and transmission coefficient matrices of the STAR-RIS The intermediate variable Y is a random variable following an exponential distribution with an expectation of That is The intermediate variable is a random variable following a non-central chi-square distribution with 2 degrees of freedom and a non-central parameter of and respectively represent the conjugates of the m-th components of the channels h w and h r ; The cumulative distribution function and probability density function of the intermediate variable X are respectively where Q1(·, ·) is the first-order Marcum Q function and I0(·) is the modified Bessel function of the first kind.

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