STAR-RIS assisted full-space covert communication system and method

Abstract

The invention provides an STAR-RIS assisted full-space covert communication system and method, which considers the 360-degree eavesdropping risk caused by eavesdroppers randomly located on the two sides of STAR-RIS, in order to limit the CC detection capability of the eavesdroppers, a covert user is designed into two antennas working in a full duplex mode, one antenna is used for receiving required covert information, and the other antenna is used for receiving the required covert information. And the other antenna transmits interference signals with different powers so as to hinder detection of an eavesdropper. Simulation results show that compared with other reference schemes, the scheme provided by the invention shows excellent performance in the aspect of resisting full-space eavesdropping.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication, specifically relating to a STAR-RIS-assisted all-space covert communication system and method to resist the randomness of eavesdroppers' locations. Background Technology

[0002] With the arrival of the 5G era, driven by advanced communication and data processing technologies, people are increasingly reliant on wireless communication. The transmission of large amounts of important and sensitive information, such as identity information and confidential documents, in open wireless networks increases the risk of eavesdropping. Therefore, information security issues are receiving increasing attention.

[0003] Physical layer security, as a key technology for protecting private information from eavesdropping attacks, has received widespread attention in recent years. However, because physical layer security technology can only protect the content information of wireless communication and cannot hide the existence of communication, it cannot function well in scenarios requiring secrecy, such as covert operations in specific scenarios. In recent years, covert communication technology has emerged as a new security mode, attracting widespread research interest in both civilian and military fields. It can protect communication between transceivers and provide a higher level of security for wireless communication systems. When the direct channel is blocked, the wireless channel propagation environment becomes uncontrollable and random. Therefore, researchers have introduced the Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surface (STAR-RIS). However, existing studies assume that the eavesdropper is deterministically located in the transmission or reflection region of the STAR-RIS. If the eavesdropper is more powerful, they can randomly be located in these two regions, which is detrimental to covert communication systems. Summary of the Invention

[0004] To address the problems of the prior art, the present invention provides a STAR-RIS-assisted all-space covert communication system and method, which exhibits excellent performance in resisting all-space eavesdropping.

[0005] This invention is achieved through the following technical solution:

[0006] In a first aspect, the present invention provides a STAR-RIS-assisted all-space covert communication method based on a covert communication system, the covert communication system including a transmitter Alice, STAR-RIS, a dual-antenna covert user Bob, a single-antenna eavesdropper Willie, and a single-antenna common auxiliary user User. One antenna of the covert user Bob is used to receive covert signals, and the other antenna is used to transmit interference signals that interfere with the detection of the eavesdropper Willie.

[0007] The method includes: solving an optimization problem under constraints of bandwidth, transmitter Alice transmit power, communication concealment, quality of service for common auxiliary users, and amplitude and phase constraints of STAR-RIS, to obtain the optimal communication bandwidth, transmitter precoding vector, and STAR-RIS reflection coefficient matrix and transmission coefficient matrix;

[0008] The optimization problem aims to maximize the stealth rate of the hidden user Bob.

[0009] Preferably, the optimization problem and constraints are as follows:

[0010]

[0011] B1+B2≤B max

[0012]

[0013] in, R b The concealment rate of the concealed user Bob; w b w u These are the pre-encoded vectors for the covert user Bob and the public auxiliary user User at the transmitter Alice; P tmax This refers to the maximum transmit power of transmitter Alice; B1, B2, B max These are the communication bandwidth of the hidden user Bob, the communication bandwidth of the public auxiliary user User, and the total bandwidth allocated by the system. R is the average asymptotic value of the minimum detection error probability for the eavesdropper Willie; ε is the concealment requirement; u , These are the communication rate and minimum communication rate for the public auxiliary user, User, respectively. The reflected and transmitted amplitudes of STAR-RIS are not specified. Let Θ be the reflection phase and transmission phase of STAR-RIS; r Θ ι These represent the reflection coefficient matrix and transmission coefficient matrix of STAR-RIS, respectively.

[0014] Furthermore, the average asymptotic value of the minimum detection error probability for the eavesdropper Willie is:

[0015]

[0016] in, as well as What is the probability that the eavesdropper Willie is randomly located in the STAR-RIS reflection region? The probability that the eavesdropper Willie is randomly located in the STAR-RIS transmission region, where χ AR h represents the large-scale path loss coefficient from transmitter Alice to STAR-RIS. rb For the wireless communication channel from STAR-RIS to the covert user Bob; P j max This represents the maximum power of the interference signal emitted by the covert user Bob; H represents the conjugate transpose of the matrix; * represents conjugate.

[0017] Furthermore, the concealment rate of the concealed user Bob is:

[0018]

[0019] Among them, h rb For the wireless communication channel from STAR-RIS to the covert user Bob; H AR This is the wireless communication channel from transmitter Alice to STAR-RIS; P j To conceal the power of the jamming signal emitted by user Bob; For the self-interference channel of the concealed user Bob, μ∈(0,1), To mask the noise power of the additive white Gaussian noise received by user Bob.

[0020] Furthermore, the communication rate of the public auxiliary user (User) is:

[0021]

[0022] Among them, h ru For the wireless communication channel from STAR-RIS to the public auxiliary user (User); H AR This is the wireless communication channel from transmitter Alice to STAR-RIS; P j To conceal the power of the jamming signal emitted by user Bob; h rb This represents the wireless communication channel from STAR-RIS to the covert user Bob; H denotes the conjugate transpose, and * denotes the conjugate. The noise power of the additive white Gaussian noise received by the public auxiliary user.

[0023] Furthermore, an iterative algorithm based on the semi-finite relaxation method and the augmented Lagrange method is used to solve the optimization problem.

[0024] Furthermore, the optimization problem is divided into three sub-problems:

[0025] Given w b w cDesign B1 and B2 under the conditions of Θr and Θt. The first subproblem is:

[0026]

[0027] stB1+B2≤B max

[0028]

[0029] Given B1, B2, Θr, and Θ t Design w in the case b w c The corresponding second subproblem is:

[0030]

[0031] The second subproblem is solved using a semi-finite relaxation method;

[0032] B1, B2, w b and w c Using the solutions obtained from the first and second subproblems as a fixed point, a joint optimization design Θ is performed. r and Θ t The corresponding third subproblem is:

[0033]

[0034] The third subproblem is solved using an iterative algorithm based on the semi-finite relaxation method and the augmented Lagrange method.

[0035] Furthermore, the solution to the second subproblem is as follows:

[0036] The second subproblem is transformed into the following problem using a semi-finite relaxation method:

[0037]

[0038] sttr(W u )+tr(W b )≤P tmax

[0039]

[0040] in, and These are relative to W b and W u The concave function; Let be the penalty coefficient for the i-th iteration; h rbFor the wireless communication channel from STAR-RIS to the covert user Bob; H AR This is the wireless communication channel from transmitter Alice to STAR-RIS; h ru For the wireless communication channel from STAR-RIS to the public auxiliary user (User); χ AR The large-scale path loss coefficient from transmitter Alice to STAR-RIS; P j max The maximum power of the interference signal emitted by user Bob to conceal his identity; W represents the i-th iteration process. b ; τ∈{0,1}.

[0041] Furthermore, the solution to the third subproblem is as follows:

[0042] The third subproblem is transformed using semi-finite relaxation and augmented Lagrange methods:

[0043]

[0044] stdiag(V r )+diag(V r ) = I M

[0045]

[0046] in, ρ (i) , as well as Let β1, β2, and β3 be the penalty coefficients for the i-th iteration process, and let β1, β2, and β3 be Lagrange multipliers. v r =diag(Θ) r ), v t =diag(Θ) t ); E=(H rb H AR w b (H) rb H AR w b ) H F = (H ru H AR w u (H) ru H AR w u ) H , The noise power of the additive white Gaussian noise received by the public auxiliary user. x (i) and z (i) These are x and z, respectively, in the i-th iteration process, and P. j It is the power of the jamming signal emitted by the covert user Bob, P j max H is the maximum power of the interference signal emitted by the covert user Bob; rb =Diag(h rb ), H ru =Diag(h ru Diag(·) is an operation that converts the elements of a matrix diagonal matrix into a vector, and Diag(·) is an operation that converts the elements of a vector into a diagonal matrix.

[0047] Fixed V r V t Next, by jointly optimizing x, z, and w, the problem transformed from the third subproblem is further transformed into the following problem to be solved:

[0048]

[0049] Jointly optimize V with x, z, and w fixed. r V t The problem after transforming the third subproblem is further transformed into the following problem to be solved:

[0050]

[0051] stdiag(V r )+diag(V r ) = I M

[0052] .

[0053] Secondly, the present invention provides a STAR-RIS-assisted all-space covert communication system, including a transmitter Alice, STAR-RIS, a dual-antenna covert user Bob, a single-antenna eavesdropper Willie, and a single-antenna common auxiliary user User. One antenna of the covert user Bob is used to receive covert signals, and the other antenna is used to transmit interference signals that interfere with the detection of the eavesdropper Willie.

[0054] The control module is used to solve an optimization problem under constraints of bandwidth, transmitter Alice's transmit power, communication concealment, quality of service constraints for common auxiliary users, and amplitude and phase constraints of STAR-RIS, to obtain the optimal communication bandwidth, precoding vectors for concealed user Bob and common auxiliary user User at transmitter Alice, and reflection and transmission coefficient matrices of STAR-RIS; the optimization problem aims to maximize the concealment rate of concealed user Bob.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] This invention provides a full-space covert communication (CC) method assisted by reconfigurable smart surfaces (STAR-RIS) that simultaneously transmit and reflect. STAR-RISs can adjust reflected and transmitted signals by simultaneously controlling reflection and transmission coefficients. Compared to existing STAR-RIS-assisted CC schemes that assume a fixed eavesdropper location, the proposed CC scheme considers the 360° eavesdropping risk caused by eavesdroppers randomly located on either side of the STAR-RIS. To limit the eavesdropper's ability to detect the CC, the covert user is designed with two antennas operating in full-duplex mode. One antenna receives the required covert information, while the other transmits interference signals of different powers to hinder eavesdropper detection. This invention establishes robust covert constraints. Subsequently, this invention proposes an optimization problem: maximizing the system's covertness by jointly optimizing bandwidth allocation and the amplitude and phase constraints of the STAR-RIS, under the covert user's communication covertness constraints and the common auxiliary user's Quality of Service (QoS) constraints. Simulation results show that, compared with other benchmark schemes, the proposed STAR-RIS-assisted CC scheme exhibits superior performance in resisting all-space eavesdropping, thus verifying the effectiveness of the proposed scheme and the superiority of STAR-RIS in improving CC performance.

[0057] Furthermore, to solve the optimization problem, this invention proposes an iterative algorithm based on the semi-finite relaxation (SDR) method and the augmented Lagrange method, which can effectively solve the proposed optimization problem. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1This is a schematic diagram of the all-space covert communication system of the present invention;

[0060] Figure 2 This illustrates the relationship between the concealment rate and the number of elements (M) in STAR-RIS in this embodiment of the invention.

[0061] Figure 3 This illustrates the relationship between the concealment rate and the number of antennas (N) at the base station in this embodiment of the invention. Detailed Implementation

[0062] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0063] It should be noted that the process equipment or apparatus not specifically mentioned in the following embodiments are all conventional equipment or apparatus in the art.

[0064] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products, or apparatuses. Furthermore, unless otherwise stated, the numbering of each method step is merely a convenient tool for identifying each method step, and not intended to limit the order of the method steps or define the scope of the invention. Changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0065] This invention provides a full-space covert communication scheme assisted by reconfigurable smart surfaces that simultaneously transmit and reflect. When an incident signal arrives at a STAR-RIS, it is split into two parts: one part is reflected back to the same side of the incident signal, and the other part is transmitted to the other side. STAR-RISs can adjust the reflected and transmitted signals by simultaneously controlling the reflection and transmission coefficients, which helps to establish a more flexible 360-degree coverage full-space smart radio environment. The STAR-RIS-assisted full-space covert communication scheme resists the randomness of eavesdropper locations. Compared to existing STAR-RIS-assisted CC schemes that assume fixed eavesdropper locations, the CC scheme proposed in this invention considers eavesdroppers randomly located on both sides of the STAR-RIS, resulting in a 360-degree eavesdropping risk. To limit the eavesdropper's ability to detect the CC, the covert user is designed with two antennas operating in full-duplex mode. One antenna is used to receive the desired covert information, while the other antenna transmits interference signals of different power to hinder eavesdropper detection. In addition to the covert user, the base station also needs to provide services to public users; the two users operate using orthogonal bandwidths to avoid interference. For the worst-case scenario, this invention analyzes and derives a closed-form expression for the minimum detection error probability (DEP) of the eavesdropper, and uses this to construct a robust concealment constraint. Subsequently, this invention proposes an optimization problem: maximizing the system concealment rate by jointly optimizing bandwidth allocation and the amplitude and phase constraints of STAR-RIS, under the communication concealment constraints of the concealed user and the service quality constraints of the public auxiliary user. To solve this non-convex optimization problem, an iterative algorithm based on a semi-finite relaxation method and an augmented Lagrangian method is proposed. Simulation results show that, compared with other benchmark schemes, the proposed STAR-RIS-assisted CC scheme exhibits superior performance in resisting all-space eavesdropping, thus verifying the effectiveness of the proposed scheme and the superiority of STAR-RIS in improving CC performance.

[0066] The STAR-RIS-assisted all-space covert communication method for resisting the randomness of eavesdropper locations as described in this invention includes:

[0067] Step 1, refer to Figure 1 A covert communication system is constructed, mainly consisting of Alice (N-antenna transmitter), STAR-RIS (M-unit), Bob (dual-antenna covert user), Willie (single-antenna eavesdropper), and User (single-antenna common auxiliary user); the probability that Willie is randomly located in the reflection zone of STAR-RIS is... The probability of the launch area is Assume that the eavesdropper Willie and the public auxiliary user User are both in half-duplex mode, while the covert user Bob is in full-duplex mode. Furthermore, assume that Bob's covert user has one antenna for receiving covert information and another antenna for transmitting noise to interfere with Willie's detection. In the considered scenario, assume that there are no direct links between existing nodes due to obstacles such as buildings. Additionally, deploying STAR-RIS near the users can improve communication performance between the transmitter Alice and the legitimate users (covert user Bob and public auxiliary user User), while hindering Willie's detection of CC. Assume that STAR-RIS operates using an energy separation (ES) protocol, meaning that all its components can operate simultaneously in reflection and transmission modes.

[0068] Step 2: The eavesdropper Willie constructs a binary hypothesis model by detecting the signals he receives to determine whether the transmitter Alice sends a signal to the covert user Bob. In order to make the model more practical, the detection error probability of the eavesdropper Willie is optimized and the optimal detection threshold and the minimum detection error probability are given.

[0069] The signal expressions received by the covert user Bob and the public auxiliary user User are as follows:

[0070]

[0071] in, This represents the sampling time with a maximum usage of L within a time slot; the wireless communication channels from transmitter Alice to STAR-RIS, STAR-RIS to covert user Bob, public auxiliary user User, and eavesdropper Willie are respectively... and G AR g rb g ru and g rw It is the small-scale Rayleigh fading coefficient, which follows a complex Gaussian distribution with zero mean and unit variance; This is the large-scale path loss coefficient, where ρ0 represents the reference power gain per meter, α represents the path loss exponent, d is the corresponding node distance, and β∈{AR,rb,ru,rw}; for full-duplex covert user Bob, his self-interference channel is... μ∈(0,1); P j To conceal the interference signal emitted by user Bob, the power follows a uniform distribution, and the maximum value of the interference signal power is P. j max ; ι∈{r,t}, Θ when ι is r ιThis represents the reflection coefficient matrix of STAR-RIS, where ι represents Θ at time t. ι Denotes the transmission coefficient matrix of STAR-RIS, where for All have amplitude phase ι∈{r,t}, The reflected and transmitted amplitudes of STAR-RIS are not specified. Let be the reflection phase and transmission phase of STAR-RIS; Diag(a) represents a diagonal matrix with diagonal elements of vector a; w b , These are the pre-encoded vectors for the covert user Bob and the public auxiliary user User at the transmitter Alice; x b and These are signals sent by transmitter Alice to covert user Bob and public auxiliary user User, respectively. It is a jamming signal sent by the covert user Bob. and These are the additive white Gaussian noise received by the covert user Bob and the public auxiliary user User, respectively. and Here, H represents the corresponding noise power. H denotes the conjugate transpose, and * denotes the conjugate. Based on the received signals from the covert user Bob and the common auxiliary user User, the corresponding covert rate and communication rate can be obtained: B1 and B2 represent the communication bandwidth of the hidden user Bob and the communication bandwidth of the public auxiliary user User, respectively.

[0072] The signal expression received by the eavesdropper Willie is as follows

[0073]

[0074] in, This indicates that Willie, the eavesdropper, only received interference signals sent by the covert user Bob, while The eavesdropper Willie not only received the interference signal sent by the covert user Bob, but also the covert signal sent by the transmitter Alice to the covert user Bob; The additive white Gaussian noise received by the eavesdropper Willie. The corresponding noise power; the average power of the signal received by the eavesdropper Willie over a certain period of time is Suppose that the eavesdropper Willie uses an infinite number of signal samples to achieve binary detection over a period of time, i.e., L→∞, then:

[0075]

[0076] Where Θ κ =bΘ r +(1-b)Θ t b is a Bernoulli variable; set the detection threshold τ. dt >0, assuming the eavesdropper Willie's detection decision is and Indicates when The eavesdropper Willie determined the received signal to be Indicates when The eavesdropper Willie determined the received signal to be

[0077] Considering that the eavesdropper Willie can optimize its detection threshold to minimize the detection error probability, we will now analyze its minimum detection error probability.

[0078] First, we derive the false alarm (FA) probability and the false detection (MD) probability. The false alarm probability refers to the probability that the eavesdropper Willie receives a signal that is false. In this situation, the decision is to determine the outcome. The probability of a missed detection refers to the probability that the eavesdropper Willie receives a signal of... In this situation, the decision is to determine the outcome. The probabilities of false alarms (FA) and false misses (MD) are as follows:

[0079]

[0080] in, as well as P j max The maximum power of the interference signal emitted by the concealed user Bob.

[0081] Therefore, the detection error probability of the eavesdropper Willie is:

[0082]

[0083] To achieve covert communication, it is necessary to ensure P e ≥1-ε, where ε∈(0,1) is a very small value required by the system performance index. Next, the detection error probability of the eavesdropper Willie is optimized to achieve the minimum detection error probability. The optimal detection threshold, which minimizes the detection error probability, is expressed as:

[0084]

[0085] Substituting formula (9) into formula (8) yields the minimum detection error probability. Right now:

[0086]

[0087] However, in formula (11), v and λ are both random variables and they are coupled together, so they cannot be calculated directly. First, using large-scale system analysis techniques, we derive the asymptotic equation for λ, namely:

[0088]

[0089] Here, tr(.) represents the trace of the matrix.

[0090] Will Substituting into formula (10), we get:

[0091]

[0092] Since v ~ exp(λ) v ),in pass Taking the average over v yields the average asymptotic analytical result of the minimum detection error probability:

[0093]

[0094] Finally, through Taking the average over b yields the final asymptotic analytical result of the minimum detection error:

[0095]

[0096] in as well as

[0097] Step 3: For the covert communication system of STAR-RIS assisted single-antenna common auxiliary user, with the optimization objective of maximizing the covert rate of covert user Bob, the constraints include bandwidth constraints, transmitter Alice transmit power constraints, communication covert constraints, quality of service (QoS) constraints of common auxiliary users, and amplitude and phase constraints of STAR-RIS, to construct the optimization problem of multi-antenna covert communication system.

[0098] The optimization problem of a multi-antenna covert communication system is shown in equation (15):

[0099]

[0100] in, Formula (15a) is the transmitter Alice's transmit power constraint, P tmaxis the maximum transmit power of transmitter Alice; Equation (15b) is the bandwidth constraint for covert user Bob and common auxiliary user User; Equation (15c) is the communication covert constraint; Equation (15d) is the QoS constraint at common auxiliary user User; Equation (15e) is the amplitude and phase constraint of STAR-RIS. max The total bandwidth allocated to the system; ε is the concealment requirement; The minimum communication rate for public auxiliary users (User).

[0101] Step 4: The optimization problem constructed in Step 3 is divided into three sub-problems. For these three non-convex sub-problems, an iterative algorithm based on the semi-finite relaxation (SDR) method and the augmented Lagrangian method is proposed.

[0102] In the optimization problem constructed in step 3, B1, B2, and Θ r Θ t w b w c The objective function, communication concealment constraints, and QoS constraints are all strongly coupled. Furthermore, the presence of STAR-RIS introduces an amplitude constraint (Equation (15e)), then Θ r With Θ t The amplitudes are interdependent. Therefore, this optimization problem cannot be directly solved using traditional convex optimization algorithms. To solve this problem, an optimization algorithm is designed using an alternating strategy, dividing the optimization problem into three subproblems. Two of these subproblems deal with bandwidth allocations B1 and B2 and the active beamformer variable w, respectively. b w c Another sub-problem is related to the passive beamformer variable Θ. r Θ t After the algorithm converges, a joint B1, B2, w is finally obtained. b w c Θ r and Θ t The solution.

[0103] Specifically, firstly, given w b w c Θ r and Θ t Given the circumstances, design B1 and B2. Then the subproblem can be described as:

[0104]

[0105] It's not hard to see that this problem is a linear programming problem. The optimal closed-form solution can be derived as follows: as well as

[0106] Then, given B1, B2, Θ r and Θ t Design w in the case b w c Then the subproblem can be described as:

[0107]

[0108] This invention utilizes SDR (Sequential Direct Reduction) technology to address the nonconvex optimization problem of equation (17). By defining... as well as The problem can be transformed into:

[0109]

[0110] in,

[0111] The problem with Equation (18) is nonconvex due to the presence of the nonconvex constraint (Equation (18b)) and the rank-one constraint (Equation (18e)). For the nonconvex constraint (Equation (18b)), logarithmic operations can be applied to transform it into two convex-subtractive-convex forms. Therefore, by performing a first-order Taylor expansion in the i-th iteration of the iterative algorithm, the nonconvex function can be transformed into a convex upper bound:

[0112]

[0113] in,

[0114] Furthermore, in order to resolve the rank-one constraint (formula (18e)), an equivalent transformation is required, namely...

[0115]

[0116] Where ||W||² is the spectral norm of W, and is a convex function with respect to W. Therefore and These are relative to W b and W u The concave function. This can be obtained using a first-order Taylor expansion, therefore... and The linear lower bounds are:

[0117]

[0118] and They are and The eigenvectors corresponding to the largest eigenvalues ​​are obtained in the i-th iteration. Finally, they are penalized into the objective function, and the problem of formula (18) is transformed into:

[0119]

[0120] Finally, B1, B2, and w b and w c The solutions obtained by formulas (16) and (25) are fixed to be used for joint optimization design of Θ. r and Θ t .

[0121]

[0122] Next, the problem with formula (26) will be addressed using SDR technology.

[0123] Similarly, using SDR technology, v r =diag(Θ) r ), v t =diag(Θ) t ), as well as Therefore, the problem with formula (26) can be transformed into:

[0124]

[0125] in

[0126] E=(H rb H AR w b (H) rb H AR w b ) H F = (H ru H AR w u (H) ru H AR w u ) H , H rb =Diag(h rb ), H ru =Diag(h ru Diag(·) is an operation that converts the elements of a matrix diagonal matrix into a vector, and Diag(·) is an operation that converts the elements of a vector into a diagonal matrix.

[0127] The fractional forms in formulas (27a) and (27b) are difficult to handle directly. Therefore, it is necessary to introduce auxiliary variables, namely... and

[0128] The optimization problem of formula (26) is reformulated as:

[0129]

[0130] For the form For the function ω, it is a concave function, therefore a first-order Taylor expansion can be performed on the left side of the constraint inequality (28a). Its linear upper bound is:

[0131]

[0132] in as well as

[0133] Furthermore, the spectral norm penalty is still used for the rank-one constraint (27c).

[0134]

[0135] and They are V r (i) and V t (i) The eigenvectors corresponding to the largest eigenvalues ​​are obtained in the i-th iteration of the inner loop and then penalized in the objective function.

[0136] For the equality constraint (28c), the augmented Lagrangian method is used to handle the constraint. In the i-th iteration, problem (26) is transformed into:

[0137]

[0138] in, ρ (i) , Let β1, β2, and β3 be the penalty coefficients for the i-th iteration, and let β1, β2, and β3 be the Lagrange multipliers. The problem is then solved in two iterative steps (33).

[0139] Step 1: Fix V r V t Next, jointly optimize x, z, and w. Problem (33) is transformed into:

[0140]

[0141] It can be proven that the objective function of this problem is convex, and both constraints (28b) and (33a) are convex. To solve this convex optimization problem, KKT (Karush-Kuhn-Tucker) conditions are used. Given that both the objective function and constraints are convex, the KKT conditions are both necessary and sufficient conditions for this problem. Therefore, closed-form solutions for x, z, and w can be obtained:

[0142]

[0143]

[0144] here

[0145] Step 2: With x, z, and w fixed, jointly optimize V. r V t Problem (33) is transformed into:

[0146]

[0147] This problem can be solved directly using CVX.

[0148] For the algorithm of the optimization problem of formula (27), c1 represents the accuracy tolerance of the outer loop, h1(x (p) ,z (p) ,w (p) () indicates a violation of a constraint, which is defined as:

[0149]

[0150] It is worth noting that when At that time, the penalty parameter will be ρ (p+1) =eρ (p) The way to reduce it is such that, in the simulation, e is set to 0.7. Conversely, when At that time, the Lagrange multiplier is updated according to the following formula:

[0151]

[0152] The algorithm for solving problem (33) is summarized as follows:

[0153] Set initial values x (0) z (0) w (0) ρ (0) >0, h2, c1, c2, 0 < e < 1 and p = 1.

[0154] When h1(x) (p),z (p) ,w (p) Repeat the following loop if c ≥ c1:

[0155] When h2 ≥ c2, repeat the following second loop: based on the given... To solve problem (38), the obtained solution is used to update... Solve problem (34) based on the results obtained, and make j = j + 1. End the second loop.

[0156] if Update the Lagrange multipliers using formula (40) and make ρ (p+1) =ρ (p) Conversely, ρ (p+1) =eρ (p) p = p + 1.

[0157] The algorithm for solving the overall optimization problem (15) of the STAR-RIS-assisted covert communication system is summarized as follows:

[0158] Initialize feasible points Define the tolerance precision ε, and set the iteration index i = 0. Repeat the following loop:

[0159] When v≥z0, set the inner loop index m=0 and initialize ρ. b and ρ u When v1≥z1, under given conditions In time, resolve the problem (25) and update based on the results. Calculate based on the results Update penalty coefficient ρ b =ξ1ρ b , ρ u =ξ2ρ u Let m = m + 1. Exit the loop when the loop condition is no longer met, and update the result accordingly.

[0160] When v2≥z2, set the inner loop index m=0 and initialize ρ. b and ρ u When v1≥z1, under given conditions At that time, the problem is solved according to the above algorithm (33), and the results are updated. Calculate based on the results Update penalty coefficient ρ r =ξ3ρ r , ρ t =ξ4ρ t Let n = n + 1. Exit the loop when the loop condition is no longer met, and update the result accordingly.

[0161] In the given Next, resolve the issue (16) and update. calculate renew Let i=i+1.

[0162] Example

[0163] This invention validates the effectiveness of the proposed algorithm through numerical results. In the numerical results, this invention evaluates the average concealment rate of the considered STAR-RIS-assisted system and compares it with benchmarks for random Θ (i.e., non-optimized Θ), maximum transmission ratio (MRT), and conventional RIS.

[0164] Figure 2 The relationship between the concealment rate and the number of cells M in the STAR-RIS is shown under different concealment requirements ε. On the one hand, as the concealment requirement ε decreases, the system needs to meet higher concealment requirements, which in turn leads to a decrease in the concealment rate. On the other hand, as the number of cells M increases, the concealment rate also increases, indicating that the more cells in the STAR-RIS, the more degrees of freedom are provided to improve system performance. However, it should be noted that the concealment rate also decreases as M increases, which may be due to inherent limitations in other system settings. Furthermore, compared with the other two schemes, the performance improvement of the present invention is most significant when M is small, while the performance improvement of the RIS-assisted scheme is negligible. As M increases, the performance improvement of the RIS-assisted scheme becomes more significant, but it is still far inferior to the present invention. After comparing these schemes, it is found that the present invention exhibits the best performance in all cases.

[0165] Figure 3 The relationship between concealment rate and the number of antennas at the base station is shown under different levels of concealment requirement ε. As N increases, the concealment rate of all schemes increases, but the rate of increase decreases. Similarly, even when N is small, there is a significant performance gap between the proposed scheme and other schemes. Furthermore, when N is small, the RIS-assisted scheme outperforms the MRT scheme, while when N is greater than 16, the MRT scheme outperforms the RIS-assisted scheme, but the gap between these two schemes decreases as N increases. Finally, under both concealment requirements, the proposed scheme achieves better solutions than other schemes.

[0166] The results show that the proposed solution has significantly improved performance compared to the benchmark, and its advantages are even more pronounced when the number of STAR-RIS units increases.

Claims

1. A STAR-RIS-assisted all-space covert communication method, characterized in that, Based on the covert communication system, the covert communication system includes a transmitter, STAR-RIS, a dual-antenna covert user, a single-antenna eavesdropper, and a single-antenna common auxiliary user. One antenna of the covert user is used to receive covert signals, and the other antenna is used to transmit interference signals to interfere with the detection of the eavesdropper. The method includes: solving an optimization problem under constraints of bandwidth, transmitter transmit power, communication concealment, quality of service for common auxiliary users, and amplitude and phase constraints of STAR-RIS, to obtain the optimal communication bandwidth, transmitter precoding vector, and STAR-RIS reflection coefficient matrix and transmission coefficient matrix; The optimization problem aims to maximize the stealth rate of the hidden user.

2. The STAR-RIS-assisted all-space covert communication method according to claim 1, characterized in that, The optimization problem and its constraints are as follows: B1+B2≤B max in, R b To conceal the user's concealment rate; w b w u These are the pre-coded vectors for the covert user and the public auxiliary user (User) at the transmitter; P tmax This refers to the transmitter's maximum transmission power; B1, B2, B max These are the communication bandwidth for covert users, the communication bandwidth for public auxiliary users, and the total bandwidth allocated by the system. R is the average asymptotic value of the minimum detection error probability of the eavesdropper; ε is the concealment requirement; u , These are the communication rate and minimum communication rate for public auxiliary users, respectively; The reflected and transmitted amplitudes of STAR-RIS are not specified. Let Θ be the reflection phase and transmission phase of STAR-RIS; r Θ ι These represent the reflection coefficient matrix and transmission coefficient matrix of STAR-RIS, respectively.

3. The STAR-RIS-assisted all-space covert communication method according to claim 2, characterized in that, The average asymptotic value of the minimum detection error probability of the eavesdropper is: in, as well as The probability that an eavesdropper is randomly located in the STAR-RIS reflection region. The probability that an eavesdropper is randomly located in the STAR-RIS transmission region, where χ AR h represents the large-scale path loss coefficient from the transmitter to STAR-RIS. rb This is the wireless communication channel from STAR-RIS to the covert user; P j max The maximum power of the interference signal transmitted by the concealed user; H represents the conjugate transpose of the matrix; * represents conjugate.

4. The STAR-RIS-assisted all-space covert communication method according to claim 2, characterized in that, The concealment rate of the concealed user is: Among them, h rb For STAR-RIS to the covert user's wireless communication channel; H AR This is the wireless communication channel from the transmitter to STAR-RIS; P j To conceal the power of interference signals emitted by users; For concealing users' self-interference channels, μ∈(0,1), To mask the noise power of additive white Gaussian noise received by the user.

5. The STAR-RIS-assisted all-space covert communication method according to claim 2, characterized in that, The communication rate of the public auxiliary user (User) is: Among them, h ru For the wireless communication channel from STAR-RIS to the public auxiliary user (User); H AR This is the wireless communication channel from the transmitter to STAR-RIS; P j To conceal the power of interference signals emitted by users; h rb This is the wireless communication channel from STAR-RIS to the covert user; H represents the conjugate transpose, and * represents the conjugate. The noise power of additive white Gaussian noise received by public auxiliary users.

6. The STAR-RIS-assisted all-space covert communication method according to claim 2, characterized in that, The optimization problem is solved using an iterative algorithm based on the semi-finite relaxation method and the augmented Lagrange method.

7. The STAR-RIS-assisted all-space covert communication method according to claim 6, characterized in that, The optimization problem is divided into three sub-problems: Given w b w c Θ r and Θ t Given the circumstances, design B1 and B2, and the first subproblem corresponding to them is: stB1+B2≤B max Given B1, B2, Θ r and Θ t Design w in the case b w c The corresponding second subproblem is: The second subproblem is solved using a semi-finite relaxation method; B1, B2, w b and w c Using the solutions obtained from the first and second subproblems as a fixed point, a joint optimization design Θ is performed. r and Θ t The corresponding third subproblem is: The third subproblem is solved using an iterative algorithm based on the semi-finite relaxation method and the augmented Lagrange method.

8. The STAR-RIS-assisted all-space covert communication method according to claim 7, characterized in that, The solution to the second subproblem is as follows: The second subproblem is transformed into the following problem using a semi-finite relaxation method: s.t.tr(W u )+tr(W b )≤P tmax in, and They are relative to W b and W u The concave function; Let be the penalty coefficient for the i-th iteration; h rb For STAR-RIS to the covert user's wireless communication channel; H AR This is the wireless communication channel from transmitter Alice to STAR-RIS; h ru This is a wireless communication channel from STAR-RIS to public auxiliary users; χ AR The large-scale path loss coefficient from the transmitter to STAR-RIS; P j max The maximum power of the interference signal transmitted by the concealed user; W represents the i-th iteration process. b ; τ∈{0,1}.

9. The STAR-RIS-assisted all-space covert communication method according to claim 7, characterized in that, The solution to the third subproblem is as follows: The third subproblem is transformed using semi-finite relaxation and augmented Lagrange methods: s.t.diag(V r )+diag(V r )=I M in, ρ (i) , as well as Let β1, β2, and β3 be the penalty coefficients for the i-th iteration process, and let β1, β2, and β3 be Lagrange multipliers. v r =diag(Θ) r ), v t =diag(Θ) t ); E=(H rb H AR w b (H) rb H AR w b ) H F = (H ru H AR w u (H) ru H AR w u ) H , The noise power of the additive white Gaussian noise received by the public auxiliary user. x (i) and z (i) These are x and z, respectively, in the i-th iteration process, and P. j It is the power of the interference signal emitted by the covert user, P j max It is the maximum power of the interference signal emitted by the covert user; H rb =Diag(h rb ), H ru =Diag(h ru Diag(·) is an operation that converts the elements of a matrix diagonal matrix into a vector, and Diag(·) is an operation that converts the elements of a vector into a diagonal matrix. Fixed V r V t Next, by jointly optimizing x, z, and w, the problem transformed from the third subproblem is further transformed into the following problem to be solved: Jointly optimize V with x, z, and w fixed. r V t The problem after transforming the third subproblem is further transformed into the following problem to be solved: s.t.diag(V r )+diag(V r )=I M 10. A STAR-RIS-assisted all-space covert communication system, characterized in that, It includes a transmitter, STAR-RIS, a dual-antenna covert user, a single-antenna eavesdropper, and a single-antenna common auxiliary user. One antenna of the covert user is used to receive covert signals, and the other antenna is used to transmit interference signals to interfere with the detection of the eavesdropper. The control module is used to solve the optimization problem under the constraints of bandwidth, transmitter transmit power, communication concealment, quality of service constraints for common auxiliary users, and amplitude and phase constraints of STAR-RIS, so as to obtain the optimal communication bandwidth, precoding vectors for concealed users and common auxiliary users at the transmitter, and reflection coefficient matrix and transmission coefficient matrix of STAR-RIS. The optimization problem aims to maximize the stealth rate of the hidden user.

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