A covert NOMA communication method assisted by STAR-RIS and fluid antenna

Abstract

This invention proposes a covert NOMA communication method assisted by STAR-RIS and fluid antennas. A system model is established, consisting of an access point, STAR-RIS nodes, covert user nodes, common user nodes, and eavesdropping nodes. Each node is equipped with a fluid antenna with multiple preset ports. A channel model is constructed and channel statistics are analyzed. Based on the communication system model and channel model, the outage probabilities of covert user nodes and common user nodes, as well as the detection error probability of eavesdropping nodes, are defined. An effective transmission rate maximization optimization problem is defined based on the outage and detection error probabilities, and a one-dimensional grid search combined with local refinement numerical optimization method is used to obtain the optimal communication system parameters. Based on the optimal communication system parameters, covert NOMA communication assisted by STAR-RIS and fluid antennas is implemented. This invention enhances the reliability of legitimate transmission by leveraging the positional freedom of the fluid antennas and reduces the probability of covert information being detected by eavesdroppers.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a covert non-orthogonal multiple access (NOMA) communication method. Background Technology

[0002] Fluid antennas, as a key technology for next-generation wireless communication, enhance communication performance by dynamically adjusting the effective position of the antenna within a limited space. Compared to traditional fixed-position antennas, fluid antennas offer adaptive port selection capabilities and superior spatial versatility, significantly improving spectral efficiency, energy efficiency, and anti-interference capabilities in complex propagation environments. This meets the stringent requirements of 6G mobile communication for high capacity and low latency. Furthermore, the flexibility of fluid antennas makes them highly compatible with emerging wireless paradigms such as inductively coupled communication, RIS (Reference Information System), and low-power IoT (Internet of Things), making them a crucial enabling technology for building future intelligent, sustainable, and efficient wireless communication systems.

[0003] Meanwhile, breakthroughs have also been made in the field of RIS-assisted communication in recent years. RIS possesses the ability to dynamically control the propagation of electromagnetic waves, and has the potential to fundamentally improve the coverage and transmission performance of existing wireless communication systems. Building on this, STAR-RIS further expands the application boundaries of RIS, enabling synchronous reflection and transmission of incident signals, providing a completely new technical path for covert communication. By flexibly adjusting the amplitude and phase of the reflection and transmission coefficients, STAR-RIS can effectively manage the spatial distribution of interference signals, thereby significantly enhancing the covertness of the communication process.

[0004] Although STAR-RIS and fluid antennas are functionally complementary—the former provides spatial diversity through dynamic antenna position switching, while the latter improves the signal propagation environment through electromagnetic wave modulation—the potential for their combined operation has not yet been fully explored. Currently, some literature has preliminarily explored the joint application of RIS and fluid antennas. For example, the paper FR Ghadi, K.-K. Wong, M. Kaveh, FJ Lopez-Martinez, WK New and H. Xu, SecrecyPerformance Analysis of RIS-Aided Fluid Antenna Systems, IEEE Wireless Communications and Networking Conference (WCNC), Milan, Italy, 2025, pp. 1-6, derives the equivalent channel distribution and delay interruption probability in a RIS-assisted base station and fluid antenna user communication system. It reveals that the RIS-fluid antenna system can provide dynamic spatial diversity, adapt to environmental changes in real time, thereby mitigating fading, improving signal quality, and enhancing system reliability, capacity, and energy efficiency. However, the aforementioned research only focuses on traditional reflective RIS, not STAR-RIS, and does not address covert communication in NOMA scenarios; the potential of STAR-RIS and fluid antennas in co-assisted covert communication remains to be further explored. Currently, there is no research on methods for using STAR-RIS and fluid antennas in co-assisted covert NOMA communication. Summary of the Invention

[0005] To address the technical problem that existing STAR-RIS-assisted covert communication systems lack integration with fluid antenna technology, thus failing to fully utilize the dynamic gain switching of antenna positions to improve transmission reliability and covertness, this invention proposes a covert NOMA communication method assisted by STAR-RIS and a fluid antenna. This method employs a collaborative strategy between STAR-RIS and a fluid antenna in the covert NOMA communication system to assist in the transmission of both covert and public signals, making it applicable to mixed indoor and outdoor communication scenarios with varying security requirements. This invention integrates STAR-RIS and a fluid antenna into the covert NOMA communication system, evaluating the system's reliability and covertness by analyzing the transmission interruption performance of legitimate users and the detection performance of eavesdroppers. This method leverages the full-space coverage of STAR-RIS to improve spectral efficiency and utilizes the positional freedom of the fluid antenna to enhance the reliability of legitimate transmission while reducing the probability of covert information being detected by eavesdroppers.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0007] A covert NOMA communication method assisted by STAR-RIS and a fluid antenna includes:

[0008] Step 1: Establish a covert NOMA communication system model based on STAR-RIS and fluid antenna collaboration. The system consists of access points, STAR-RIS nodes, covert user nodes, common user nodes, and eavesdropping nodes. Fluid antennas with multiple preset ports are configured for covert user nodes, common user nodes, and eavesdropping nodes.

[0009] Step 2: Construct a channel model from the access point to the hidden user node, the public user node, and the eavesdropper node, all of which pass through the STAR-RIS node, and analyze the channel statistics;

[0010] Step 3: Based on the communication system model and channel model, define the interruption probability of covert user nodes and public user nodes, as well as the detection error probability of eavesdropping nodes in covert communication. Based on the interruption probability and detection error probability, define the effective transmission rate maximization optimization problem. Use a one-dimensional grid search combined with local refinement numerical optimization method to solve the problem and obtain the optimal communication system parameters.

[0011] Step 4: Implement covert NOMA communication based on STAR-RIS and fluid antenna collaboration, using optimal communication system parameters.

[0012] The communication system model includes a single-antenna access point and a device equipped with... The STAR-RIS consists of a unit, a near-end covert user and a listener on the STAR-RIS reflection side, and a far-end public user on the transmission side; the covert user and the public user form a NOMA user pair; the STAR-RIS operates under a mode switching protocol, which will... The unit is divided into two parts, among which Each unit serves hidden users. Each unit serves public users; the access point hides its transmission behavior to the hidden user from the eavesdropper, while the eavesdropper listens to the communication from the access point to the STAR-RIS reflection unit and then to the hidden user. Public users only have transmission rate requirements and no concealment requirements; there are no direct links between the access point and the hidden user, public user, and eavesdropper.

[0013] In the communication system model, the covert user, the public user, and the eavesdropper are each equipped with a mesh-structured fluid antenna with multiple preset ports. Each fluid antenna is connected to only one radio frequency link. The single-radio frequency link fluid antennas equipped on the covert user, the public user, and the eavesdropper have... One preset port , These represent the number of ports contained in each row and each column of the fluid antenna, respectively, and all ports are in... Evenly distributed across the region , The length and width of the region are given by the given information. Indicates the wavelength related to the carrier frequency. , To conceal users, For public users, For listening; port spacing less than Furthermore, at the receiving end, the fluid antenna switches between ports via an internal reconfigurable feed network.

[0014] Step two includes:

[0015] Modeling the spatial correlation between ports of a fluid antenna: Assuming the fluid antenna has a half-space receiving coverage, then any two ports... and The spatial correlation between them can be expressed as:

[0016] ;

[0017] in, A one-dimensional index for the port. For the row or column index of the port, The row or column representing the port; This represents the sinc function. A mapping function to convert a two-dimensional index of a port location into a one-dimensional index;

[0018] Define the port with optimal channel quality metrics and the power gain of the cascaded channels:

[0019] Select the port index that maximizes the channel gain as the optimal port to activate. , Represents a node The optimal port index selected in the selection process. Indicates access point and node The Channel coefficients between ports and cascaded via STAR-RIS ;

[0020] Access Points and Nodes The The power gain of the cascaded channels between ports and via STAR-RIS is .

[0021] Furthermore, step two includes: modeling the equivalent cascaded channel power gain between the access point and covert users, public users, and eavesdroppers, and through STAR-RIS. The cumulative distribution function is obtained as follows:

[0022] A1. Assuming the channel coefficients follow an independent and identically distributed quasi-static Rayleigh fading pattern, the access point and the eavesdropper, the hidden user, and the public user are... The equivalent concatenated channel coefficients between ports and via STAR-RIS are uniformly expressed as follows:

[0023] ;

[0024] in, The imaginary unit, This is the channel coefficient vector from the access point to STAR-RIS. From STAR-RIS to Node The channel coefficient vector, For the first time from the access point to STAR-RIS Channel coefficients of each unit, For the first time from STAR-RIS Units to nodes The channel coefficient, and These are the channel coefficients. With channel coefficient phase, This represents the reflection or transmission coefficient matrix of STAR-RIS. Indicates the working mode index. It is in reflection mode. Transmission mode; and These represent the STAR-RIS number 1, 2, 3, 4, 5, 6, 7, 8 The reflection / transmission amplitude and phase shift of each unit, ; This represents the diagonalization operation; through phase alignment, STAR-RIS is controlled to achieve ideal phase shift adjustment, i.e. , Indexing for user nodes, To conceal users, For public users, From STAR-RIS Units to nodes Channel coefficient The phase;

[0025] A2. Based on the channel assumption of quasi-static Rayleigh fading, and according to the central limit theorem, the equivalent concatenated channel coefficients between the access point and a port of the hidden user and the public user, and through STAR-RIS, are... It can be approximated as the mean. ,variance The Gaussian random variable; therefore, based on the probabilistic and statistical properties of the Gaussian random variable, the equivalent cascaded channel coefficients It follows a non-central chi-square distribution with 1 degree of freedom; therefore, the equivalent cascaded channel power gain The cumulative distribution function can be expressed as:

[0026] ;

[0027] in, For non-central parameters, Indicates the order is The parameters are and The MarcumQ function;

[0028] A3. According to the Central Limit Theorem, the access point and the listener's... The equivalent concatenated channel coefficients between ports and via STAR-RIS It can be approximated as the mean. ,variance If the Gaussian random variable is used, then the equivalent cascaded channel power gain is... Follow the mean The exponential distribution; based on the distribution characteristics of the exponential distribution, the equivalent cascaded channel power gain. The cumulative distribution function can be expressed as:

[0029] ;

[0030] A4. A Gaussian Copula model, combined with an approximate Jakes model, is used to describe the spatial correlation between the ports of the fluid antenna. , Using the definition of the cumulative distribution function and with the help of Sklar's theory, then The cumulative distribution function is:

[0031] ;

[0032] in, The unit cube is defined. The joint cumulative distribution function of d random vectors with uniform marginal distribution. For the channel correlation matrix of the fluid antenna port of the eavesdropper, It has a mean of 0 and a correlation matrix of The cumulative distribution function of the joint multivariate normal distribution, It is an error function inverse function, The Gaussian Copula dependency parameter for the listener.

[0033] Furthermore, step two includes:

[0034] Transmitted signal modeling: Based on the superposition coding principle in NOMA technology, the signal transmitted by the access point is as follows: ,in It is the power allocation factor. and These are the concealed signals sent from the access point to concealed users and the public signals sent to public users, respectively, satisfying... ;

[0035] Received signal modeling: Covert users and public users using the first The signals received by each port can be uniformly represented as:

[0036] ;

[0037] in, It is the transmit power of the access point. , Indexing for user nodes, To conceal users, For public users, For user nodes The received signal at the location, Indicates access point and user node The Channel coefficients between ports and cascaded via STAR-RIS For user nodes Additive white Gaussian noise at a given location, with a mean of 0 and a variance of 0. The complex Gaussian distribution; This indicates the distance from STAR-RIS to the user node. The channel coefficient vector, For the first time from STAR-RIS Unit to user node The channel coefficient.

[0038] Furthermore, based on the communication system model and channel model, the outage probabilities of covert user nodes and public user nodes are defined, including:

[0039] B1. A Gaussian Copula model, combined with an approximate Jakes model, is used to describe the spatial correlation between the ports of the fluid antenna, thus concealing the signal-to-interference-plus-noise ratio (SNR) of the user decoding their own signal. The cumulative distribution function can be expressed as:

[0040] ;

[0041] in, The channel correlation matrix for the fluid antenna port of the concealed user. This indicates that the mean is 0 and the correlation matrix is... The cumulative distribution function of the joint multivariate normal distribution, To conceal the user's Gaussian Copula dependency parameters, This represents the average transmit signal-to-noise ratio. To conceal the variance of noise received by the user;

[0042] B2. According to the definition of the cumulative distribution function, the signal-to-interference-plus-noise ratio (SINR) of a public user decoding its own signal. The cumulative distribution function can be calculated as:

[0043] ;

[0044] in, Represents the probability of a random event occurring. This represents the average transmit signal-to-noise ratio. The variance of noise received by public users;

[0045] B3. According to the definition of the cumulative distribution function, the signal-to-interference-plus-noise ratio (SINR) of a covert user decoding a public user signal. The cumulative distribution function is:

[0046] ;

[0047] B4. According to the definition of communication interruption probability, when the hidden user cannot restore the public user signal... Or unable to correctly decode covert user signals At that time, a communication interruption event occurs for the covert user; therefore, the probability of communication interruption for the covert user is... It can be calculated as follows:

[0048] ;

[0049] in, The signal-to-noise ratio threshold for concealed signals. The signal-to-interference-plus-noise ratio (SIR) threshold for public signals. and These are covert user signals With public user signals The target rate;

[0050] B5. When public users cannot correctly decode public signals At that time, a public user communication interruption event occurred; based on intermediate variables. The probability distribution of communication interruption probability for public users It can be calculated as follows:

[0051] .

[0052] Furthermore, based on the communication system model and channel model, the probability of a listener making a false detection of covert communication is defined, including:

[0053] C1. Based on binary hypothesis testing, the eavesdropper's first... The received signal observations obtained from each port can be expressed as:

[0054] ;

[0055] in, The noise at the listener's location is additive white Gaussian noise with a mean of 0 and a variance of 1. The complex Gaussian distribution; The channel index indicates the time slot occupied. The null hypothesis means that no covert information is transmitted between the access point and the covert user. As an alternative hypothesis, it indicates that covert information is transmitted between the access point and the covert user;

[0056] C2. Assume all channels are independent and identically distributed, and consider the number of times each channel is used. Infinitely many, that is Therefore, under both assumptions, the average received power of the eavesdropper... It can be represented as:

[0057] ;

[0058] in, It is the variance of the noise received by the listener;

[0059] C3. Based on the definitions of false alarm and false detection probabilities, the probability of a false alarm detected by the eavesdropper can be calculated. With the probability of missed detection They are respectively:

[0060] ;

[0061] ;

[0062] Among them, false alarm probability Indicates the null hypothesis The judgment was made as The probability of detection; the probability of missed detection Indicating in the alternative hypothesis The judgment was made as The probability of;

[0063] C4. Assume the null hypothesis and alternative hypothesis Since the prior probabilities are equal, based on this assumption, the error probability of the eavesdropper's detection is:

[0064] .

[0065] Furthermore, the optimization problem for maximizing the effective transmission rate, defined based on the probability of interruption and the probability of detection error, is as follows:

[0066] ;

[0067] in, To determine the effective transmission rate as the objective function, constraints are applied. For concealment constraints, It is a very small positive number, representing the allowable concealment loss, a constraint. Power allocation factor Boundary constraints.

[0068] Furthermore, a numerical optimization method combining one-dimensional grid search and local refinement is employed to solve the problem, including:

[0069] D1. Initialize search parameters and set search step size. In the feasible region Generate an evenly spaced set of grid points within the inner area. ,in , Indicates rounding down;

[0070] D2. Coarse grid feasible point filtering, parameter settings For each grid point Calculate the detection error probability of the eavesdropper. And check whether the concealment constraint is met. Record all grid points that satisfy the constraints to form a feasible set. ;

[0071] D3. Coarse-grid optimal value estimation, calculating the optimal value for each grid point. For the corresponding effective transmission rate, select the grid point that maximizes the effective transmission rate. ;

[0072] D4. Local refinement search, using grid points Centered on, within the interval The search employs the golden ratio to improve accuracy when the search interval width is less than a preset threshold. The process terminates at a certain time, yielding the optimal power allocation factor. .

[0073] The beneficial effects of this invention are as follows:

[0074] First, this invention introduces a fluid antenna into a STAR-RIS-assisted covert NOMA communication system for the first time. Utilizing the dynamic position-switching capability of the fluid antenna within a limited space, additional spatial diversity gain is achieved, effectively combating multipath fading. Compared to traditional fixed antenna solutions, this invention significantly reduces the probability of transmission interruption for legitimate users, ensuring reliable reception of both covert and public signals.

[0075] Secondly, the adaptive port selection of the fluid antenna in this invention further increases the detection uncertainty for eavesdroppers, thereby achieving stricter concealment constraints while ensuring the quality of legitimate communication. Furthermore, the power allocation of the near-end concealed user signal is lower than the power of the far-end ordinary user signal; in this case, public information can play a concealment role, further enhancing the system's concealment.

[0076] Third, this invention, based on the NOMA mechanism, supports the superposition and transmission of concealed signals and public signals on the same time-frequency resources, improving the system's spectrum utilization. Simultaneously, STAR-RIS's synchronous reflection and transmission capabilities enable this invention to be flexibly applied to mixed indoor and outdoor communication scenarios. Attached Figure Description

[0077] 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 only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0078] Figure 1 This is a flowchart of the present invention.

[0079] Figure 2 This is a system model diagram of the present invention.

[0080] Figure 3 The detection threshold for Willie, the eavesdropper in this invention. Simulation results of the impact on false alarm probability, missed detection probability, and detection error probability.

[0081] Figure 4 The power allocation factor of the access point (AP) in this invention Simulation results showing the impact on the interruption probability of the hidden user Bob.

[0082] Figure 5 The target rate for Carol, a public user of this invention. Simulation results of the impact on the interruption probability of public user Carol. Detailed Implementation

[0083] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0084] like Figure 1 As shown, a covert NOMA communication method assisted by STAR-RIS and a fluid antenna is proposed. This method utilizes an Access Point (AP), a Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surface (STAR-RIS), a covert user (Bob), a public user (Carol), and a listener (Willie) to construct a covert communication system. The AP transmits covert signals to the covert user Bob and public signals to the public user Carol using superposition coding. The listener Willie monitors whether covert communication has occurred between the AP and the covert user Bob. All three users—Bob, Carol, and Willie—are equipped with fluid antennas, selecting the optimal fluid port. STAR-RIS employs a mode-switching protocol and aligns the phases of the covert user Bob and the public user Carol, thereby improving the system's transmission reliability and covertness.

[0085] A covert NOMA communication method assisted by STAR-RIS and a fluid antenna, such as Figure 1 As shown, it includes:

[0086] Step 1: Establish a concealed non-orthogonal multiple access (NOMA) communication system model based on the simultaneous transmission and reflection reconfigurable smart surface STAR-RIS and the coordinated assistance of fluid antennas. The system consists of an access point, a STAR-RIS node, a concealed user Bob node, a public user Carol node, and a listener Willie node. Fluid antennas with multiple preset ports are configured for the concealed user Bob node, the public user Carol node, and the listener Willie node.

[0087] In the embodiments of this application, such as Figure 2 As shown, the communication system model includes a single-antenna access point (AP) and a device equipped with... The STAR-RIS consists of a unit with Bob, a near-end covert user, and Willie, a listener, located on the reflective side, and Carol, a far-end public user, located on the transmissive side. Bob and Carol form a NOMA user pair. The STAR-RIS operates under a mode-switching protocol. The unit is divided into two parts, among which One unit serves Bob, a covert user in the reflection zone, while Willie, an eavesdropper, is also in the reflection zone, monitoring communication from the AP to the STAR-RIS reflection unit and then to Bob. Each unit serves the public user Carol in the transmission area; the access point AP needs to hide its transmission behavior to the covert user Bob from the eavesdropper Willie, while the public user Carol only has transmission rate requirements and no covertness requirements; due to the existence of the building, there is no direct link between the access point AP and the covert user Bob, the public user Carol, and the eavesdropper Willie. During operation, the fluid antenna ports are traversed and switched within the channel coherence time, and the port with the best channel quality index is selected as the active port to determine the optimal cascaded channel between nodes. Based on the cascaded channel state information of the covert user Bob and the public user Carol, and the optimal active port, the access point (AP) adjusts the reflection phase and transmission phase of each unit of STAR-RIS to reflect the signal to the covert user Bob and transmit it to the public user Carol. At the same time, the equivalent cascaded channel power gain between the access point (AP) and the eavesdropper Willie follows a preset random statistical distribution. The access point (AP) superimposes and encodes the covert information of the covert user Bob and the public information of the public user Carol in the power domain to generate a superimposed signal. The covert user Bob decodes the signal using a serial interference cancellation mechanism, and the public user Carol directly decodes its own public information, completing the parallel transmission of covert and public communication.

[0088] STAR-RIS is a bidirectional RIS that can simultaneously perform reflection and transmission. In actual operation, whether each STAR-RIS unit reflects, transmits, or can simultaneously reflect and transmit depends on the STAR-RIS's operating mode. STAR-RIS has three operating modes: Energy Split (ES), Mode Switching (MS), and Time Switching (TS). In Energy Split (ES) mode, each unit can simultaneously reflect and transmit. The energy of the incident signal is divided into two parts in real time within each unit, and the two parts, carrying their respective information, are emitted simultaneously. In Mode Switching (MS) mode, all units are divided into two parts: one part is dedicated to transmission, and the other part is dedicated to reflection, each performing its own function. In Time Switching (TS) mode, all units take turns transmitting or reflecting in different time slots.

[0089] In this embodiment, the covert user Bob, the public user Carol, and the eavesdropper Willie are each equipped with a mesh-structured fluid antenna with multiple preset ports, and each fluid antenna is connected to only one radio frequency link. The single-RF-link fluid antennas equipped on the covert user Bob, the public user Carol, and the eavesdropper Willie have… One preset port , These represent the number of ports contained in each row and each column of the fluid antenna, respectively, and all ports are in... Evenly distributed across the region , The length and width of the region are given by the given information. Indicates the wavelength related to the carrier frequency. , To conceal the identity of user Bob, For public user Carol, Willie, the listener; port spacing less than Furthermore, at the receiving end, the fluid antenna switches between ports via an internal reconfigurable feed network, such as a pixel reconstruction layer or a liquid metal switch topology.

[0090] Step 2: Construct a channel model from the access point to the covert user Bob node, the public user Carol node, and the eavesdropper Willie node, all of which pass through the STAR-RIS node, and analyze the channel statistics.

[0091] In this embodiment of the application, step two includes:

[0092] Modeling the spatial correlation between ports of a fluid antenna: Since the ports of a fluid antenna can be freely switched and can be arbitrarily close to each other, spatial correlation exists between the corresponding channels. Therefore, assuming the fluid antenna has a half-space receiving coverage range, any two ports... and The spatial correlation between them can be expressed as:

[0093] ;

[0094] in, A one-dimensional index for the port. For the row or column index of the port, The row or column representing the port; This represents the sinc function. This is a mapping function that converts a two-dimensional index of a port location into a one-dimensional index.

[0095] Define the port with optimal channel quality metrics and the power gain of the cascaded channels:

[0096] Select the port index that maximizes the channel gain as the optimal port to activate. , Represents a node The optimal port index selected in the selection process. Indicates the access point (AP) and node The Channel coefficients between ports and cascaded via STAR-RIS ;

[0097] Access Point (AP) and Node The The power gain of the cascaded channels between ports and via STAR-RIS is .

[0098] In this embodiment of the application, step two further includes:

[0099] Model the equivalent cascaded channel power gain between the access point (AP) and covert user Bob, public user Carol, and eavesdropper Willie, and via STAR-RIS. The cumulative distribution function is obtained as follows:

[0100] A1. Assuming the channel coefficients follow independent and identically distributed quasi-static Rayleigh fading, the equivalent concatenated channel coefficients between the access point (AP) and a port of the eavesdropper Willie, the covert user Bob, and the public user Carol, and after passing through STAR-RIS, are uniformly expressed as follows:

[0101] ;

[0102] in, The imaginary unit, This is the channel coefficient vector from the access point (AP) to STAR-RIS. From STAR-RIS to Node The channel coefficient vector, For the first time from the access point AP to STAR-RIS Channel coefficients of each unit, For the first time from STAR-RIS Units to nodes The channel coefficient, and These are the channel coefficients. With channel coefficient phase, This represents the reflection or transmission coefficient matrix of STAR-RIS. Indicates the working mode index. It is in reflection mode. Transmission mode; and These represent the STAR-RIS number 1, 2, 3, 4, 5, 6, 7, 8 The reflection / transmission amplitude and phase shift of each unit, ; This represents the diagonalization operation; through phase alignment, STAR-RIS is controlled to achieve ideal phase shift adjustment, i.e. , Indexing for user nodes, To conceal users, For public users, From STAR-RIS Units to nodes Channel coefficient The phase.

[0103] For ease of explanation, let's assume... , Following quasi-static Rayleigh fading with independent and identically distributed characteristics, the access point AP and the eavesdropper Willie's... Between the ports, and between the access point AP and the hidden user Bob, and the public user Carol. The equivalent concatenated channel coefficients between ports via STAR-RIS can be reformulated as:

[0104] ;

[0105] ;

[0106] A2. Based on the quasi-static Rayleigh fading channel assumption, when the number of STAR-RIS units is large, according to the central limit theorem, the equivalent concatenated channel coefficient between the access point (AP) and a port of the concealed user Bob and the public user Carol, and passing through STAR-RIS, is... It can be approximated as the mean. ,variance The Gaussian random variable; therefore, based on the probabilistic and statistical properties of the Gaussian random variable, the equivalent cascaded channel power coefficient Following a non-central chi-square distribution with 1 degree of freedom, the equivalent cascaded channel power gain The cumulative distribution function can be expressed as:

[0107] ;

[0108] in, For non-central parameters, Indicates the order is The parameters are and The MarcumQ function.

[0109] A3. According to the Central Limit Theorem, what is the equivalent cascaded channel coefficient between the access point (AP) and a port of the eavesdropper Willie, and through STAR-RIS? It can be approximated as the mean. ,variance The Gaussian random variable; therefore, the equivalent cascaded channel power gain Follow the mean The exponential distribution, based on the distribution characteristics of the exponential distribution, the equivalent cascaded channel power gain The cumulative distribution function can be expressed as:

[0110] ;

[0111] A4. A Gaussian Copula model, combined with an approximate Jakes model, is used to describe the spatial correlation between the ports of the fluid antenna. , Using the definition of the cumulative distribution function and with the help of Sklar's theory, then The cumulative distribution function is:

[0112] ;

[0113] in, The unit cube is defined. The joint cumulative distribution function of d random vectors with uniform marginal distribution. For Willie's fluid antenna port, the channel correlation matrix is... It has a mean of 0 and a correlation matrix of The cumulative distribution function of the joint multivariate normal distribution, It is an error function inverse function, The Gaussian Copula dependency parameter for the listener Willie.

[0114] Step two includes:

[0115] Transmitted signal modeling: Based on the superposition coding principle in NOMA technology, the signal transmitted by the access point (AP) is as follows: ,in It is the power allocation factor. and These are the covert signals sent by the access point (AP) to the covert user Bob and the public signals sent to the public user Carol, respectively, satisfying... .

[0116] Received signal modeling: Covert user Bob and public user Carol use the first The signals received by each port can be uniformly represented as:

[0117] ;

[0118] in, It is the transmit power of the access point (AP). , Indexing for user nodes, To conceal users, For public users, For user nodes The received signal at the location, Indicates the access point (AP) and user node The Channel coefficients between ports and cascaded via STAR-RIS For user nodes Additive white Gaussian noise at a given location, with a mean of 0 and a variance of 0. The complex Gaussian distribution; This indicates the distance from STAR-RIS to the user node. The channel coefficient vector, For the first time from STAR-RIS Unit to user node The channel coefficient.

[0119] Step 3: Based on the communication system model and channel model, define the interruption probability of the covert user Bob node and the public user Carol node, as well as the error probability of the eavesdropper Willie in detecting the covert communication. Based on the interruption probability and the error probability, define the optimization problem of maximizing the effective transmission rate. Use a one-dimensional grid search combined with a local refinement numerical optimization method to solve the problem and obtain the optimal communication system parameters.

[0120] Based on the principle of serial interference cancellation, the covert user Bob first decodes the signal from the public user Carol. After subtracting it from the mixed signal, the signal itself is then decoded. Therefore, Bob decodes the signal. The signal-to-interference-plus-noise ratio is:

[0121] ;

[0122] in, This represents the average transmit signal-to-noise ratio. The variance of the noise received by user Bob is used to conceal the noise.

[0123] Considering perfect serial interference cancellation, the covert user Bob decodes his own signal. The signal-to-noise ratio is:

[0124] .

[0125] In addition, user Bob's signal will be hidden. Considered interference, public user Carol directly decodes her own signal. The signal-to-interference-plus-noise ratio is:

[0126] ;

[0127] in, This represents the average transmit signal-to-noise ratio. The variance of the noise received by the public user Carol.

[0128] In this embodiment of the application, the outage probabilities of the covert user Bob node and the public user Carol node are defined based on the communication system model and the channel model, including:

[0129] B1. A Gaussian Copula model, combined with an approximate Jakes model, is used to describe the spatial correlation between the ports of the fluid antenna, thus concealing the signal-to-interference-plus-noise ratio (SNR) of user Bob decoding his own signal. The cumulative distribution function can be expressed as:

[0130] ;

[0131] ;

[0132] in, Channel correlation matrix for the fluid antenna port of the concealed user Bob. This indicates that the mean is 0 and the correlation matrix is... The cumulative distribution function of the joint multivariate normal distribution, To conceal user Bob's Gaussian Copula dependency parameters, This represents the average transmit signal-to-noise ratio. Let be the variance of the noise received by Bob.

[0133] B2. According to the definition of the cumulative distribution function, the signal-to-interference-plus-noise ratio (SIR) of the public user Carol decoding her own signal is... The cumulative distribution function can be calculated as:

[0134] ;

[0135] in, Represents the probability of a random event occurring. This represents the average transmit signal-to-noise ratio. The variance of the noise received by the public user Carol.

[0136] B3. Based on the definition of the cumulative distribution function, the signal-to-interference-plus-noise ratio (SIR) of the signal decoded by the covert user Bob from the public user Carol's signal is... The cumulative distribution function is:

[0137] .

[0138] B4. According to the definition of communication interruption probability, when the hidden user Bob cannot recover the signal from the public user Carol... Or unable to correctly decode the hidden user Bob's signal At that time, the communication interruption event of the covert user Bob occurred; therefore, the probability of the communication interruption of the covert user Bob is... It can be calculated as follows:

[0139] ;

[0140] The probability of communication interruption for the covert user Bob can be obtained through simple calculations. for:

[0141] ;

[0142] in, The signal-to-noise ratio threshold for concealed signals. The signal-to-interference-plus-noise ratio (SIR) threshold for public signals. and These are the signals from the hidden user Bob. With public user Carol signal The target rate.

[0143] B5. When public user Carol is unable to correctly decode public signals. At that time, a communication interruption event occurred for public user Carol; based on intermediate variables. The probability distribution of communication interruption for public user Carol It can be calculated as follows:

[0144] .

[0145] Furthermore, the effective transmission rate of the STAR-RIS-assisted fluid covert NOMA communication system studied can be defined as:

[0146] .

[0147] In this embodiment of the application, the probability of false detection of the covert user Bob by the eavesdropper Willie is defined based on the communication system model and the channel model, including:

[0148] C1. Based on the binary hypothesis test, the listener Willie's... The received signal observations obtained from each port can be expressed as:

[0149] ;

[0150] in, The noise at the listener Willie is additive white Gaussian noise with a mean of 0 and a variance of 1. The complex Gaussian distribution; The channel index indicates the time slot occupied. The null hypothesis indicates that no covert information was exchanged between the access point (AP) and the covert user Bob. As an alternative hypothesis, it is assumed that covert information was exchanged between the access point (AP) and the covert user Bob.

[0151] Willie's ultimate goal was to analyze its average received power. To determine the observed values ​​of the received signal. Under the null hypothesis Under the alternative hypothesis The decision-making criteria are as follows: ,express The judgment was made at that time. , The judgment was made at that time. , It is a pre-set energy detection threshold. and They support the null hypothesis. and alternative hypothesis The verdict.

[0152] C2. Assume all channels are independent and identically distributed, and consider the number of times each channel is used. Infinitely many, that is Therefore, under both assumptions, the average received power of the eavesdropper Willie... It can be represented as:

[0153]

[0154] in, It is the variance of the noise received by the listener Willie.

[0155] C3. Based on the definitions of false alarm and false negative probabilities, the probability of a false alarm detected by the eavesdropper Willie can be calculated. With the probability of missed detection They are respectively:

[0156] ;

[0157] ;

[0158] in, Let be the false alarm probability, representing the probability under the null hypothesis. The judgment was made as The probability of; Let be the probability of a missed detection, representing the probability under the alternative hypothesis. The judgment was made as The probability of.

[0159] C4. Assume the null hypothesis and alternative hypothesis Since the prior probabilities are equal, based on this assumption, the error probability of the eavesdropper Willie is:

[0160] ;

[0161] In this embodiment of the application, under the constraints of concealment and power allocation fairness, the power allocation factor is optimized. The optimization problem for maximizing the effective transmission rate of a STAR-RIS-assisted fluid covert NOMA communication system is as follows:

[0162] ;

[0163] in, To determine the effective transmission rate as the objective function, constraints are applied. For concealment constraints, It is a very small positive number, representing the allowable concealment loss, a constraint. Power allocation factor Boundary constraints.

[0164] In this embodiment of the application, due to the objective function With constraints The cumulative distribution functions of the joint multivariate normal distributions are all complex in form, and their analytical forms are highly nonlinear and nonconvex, making it impossible to directly obtain the monotonic analytical conditions and closed-form solutions. A numerical optimization method combining one-dimensional grid search and local refinement is employed to solve the problem, including:

[0165] D1. Initialize search parameters and set search step size. In the feasible region Generate an evenly spaced set of grid points within the inner area. ,in , Indicates rounding down;

[0166] D2. Coarse grid feasible point filtering, parameter settings For each grid point Calculate the detection error probability of the eavesdropper Willie. And check whether the concealment constraint is met. Record all grid points that satisfy the constraints to form a feasible set. ;

[0167] D3. Coarse-grid optimal value estimation, calculating the optimal value for each grid point. For the corresponding effective transmission rate, select the grid point that maximizes the effective transmission rate. ;

[0168] D4. Local refinement search, using grid points Centered on, within the interval The search employs the golden ratio to improve accuracy when the search interval width is less than a preset threshold. The process terminates at a certain time, yielding the optimal power allocation factor. .

[0169] The effectiveness of the proposed covert NOMA communication method based on STAR-RIS and a fluid antenna is verified through Matlab simulation. The parameters are set as follows: total number of STAR-RIS elements. The variances of the received noise at Willie, Bob, and Carol are respectively dB.

[0170] Figure 3 The detection threshold of Willie in this invention Simulation curves showing the impact of the proposed scheme on the probability of false alarms, false negatives, and detection errors are presented. The scheme presented in the figure is represented by a Fluid Antenna System (FAS), while the contrasting scheme is represented by a Traditional Antenna System (TAS). The theoretical and simulation results are largely consistent, indicating that the theoretical derivation is correct. As can be seen from the figure, with the detection threshold... As the threshold increases, the false alarm probability gradually decreases, while the missed detection probability gradually increases. Both the proposed scheme and the TAS scheme exhibit a decrease followed by an increase in the detection error probability, with a minimum detection error probability existing. However, the minimum detection error probability under the proposed scheme is higher than that under the TAS scheme. Furthermore, there is a performance overlap in the detection error probabilities of the two schemes. This is because Willie, Bob, and Carol are all equipped with fluid antennas. Fluid antennas improve channel quality for both legitimate users and eavesdroppers. However, when eavesdroppers use energy detection, the false alarm probability increases significantly due to the multi-port noise maximum effect, leading to a higher detection error probability in low-threshold regions. Traditional antennas have a lower false alarm probability in low-threshold regions but a higher missed detection probability in high-threshold regions. By appropriately setting the detection threshold, the proposed scheme will enable the NOMA communication system to achieve better concealment performance.

[0171] Figure 4 Power allocation factor for AP Probability of Bob's interruption The simulation curves show the impact of the power allocation factor. The theoretical and simulation results are basically consistent, indicating that the theoretical derivation is correct. The graph shows that as the power allocation factor... The increase in Bob's interruption probability It first drops and then rises rapidly. This is because, according to the NOMA principle, Bob needs to decode the hidden signal. First decode the common signal .when At that time, signal The transmit power compared to the signal The larger the value, the better Carol's communication quality, while The low transmission power leads to Approaching 1. With... The increase in signal The transmission power will decrease. Within this range, there must exist a value that makes... It reaches a minimum value, then rapidly approaches 1. Furthermore, a suitable value is selected through numerical optimization. The proposed scheme is significantly superior to the comparative TAS scheme, which shows that the proposed STAR-RIS and fluid antenna synergy scheme can effectively improve the reliability of the system.

[0172] Figure 5 Carol's target rate Probability of interruption for Carol The simulation curves show the impact of the theory. The theoretical and simulation results are basically consistent, indicating that the theoretical derivation is correct. The graph shows that as the target speed increases... The increase in Carol's interruption probability The rate gradually increases. This is because a higher target rate raises the decoding threshold, making Carol more prone to interruption under given channel conditions. Furthermore, the proposed scheme significantly outperforms the comparative TAS scheme, indicating that the proposed scheme can improve the system's interrupt performance.

[0173] In summary, the covert NOMA communication method with STAR-RIS and fluid antenna assisted by the present invention can effectively improve the covertness and reliability of the communication system, and the simulation results fully demonstrate its effectiveness.

[0174] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0175] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A covert NOMA communication method assisted by STAR-RIS and a fluid antenna, characterized in that, include: Step 1: Establish a covert NOMA communication system model based on STAR-RIS and fluid antenna collaboration. The system model consists of access point, STAR-RIS node, covert user node, common user node and eavesdropper node, and configures fluid antennas with multiple preset ports for covert user node, common user node and eavesdropper node. Step 2: Construct a channel model from the access point to the covert user node, the public user node, and the eavesdropper node, all of which pass through the STAR-RIS node, and analyze the channel statistics; Step 3: Based on the communication system model and channel model, define the interruption probability of covert user nodes and public user nodes, as well as the detection error probability of eavesdropping nodes in covert communication. Based on the interruption probability and detection error probability, define the effective transmission rate maximization optimization problem. Use a one-dimensional grid search combined with local refinement numerical optimization method to solve the problem and obtain the optimal communication system parameters. Step 4: Implement covert NOMA communication based on STAR-RIS and fluid antenna collaboration, using optimal communication system parameters.

2. The covert NOMA communication method assisted by STAR-RIS and a fluid antenna according to claim 1, characterized in that, The communication system model includes a single-antenna access point and a device equipped with... The STAR-RIS consists of a unit, a near-end covert user and a listener on the STAR-RIS reflection side, and a far-end public user on the transmission side; the covert user and the public user form a NOMA user pair; the STAR-RIS operates under a mode switching protocol, which will... The unit is divided into two parts, among which Each unit serves hidden users. Each unit serves public users; The access point hides its transmission behavior to the hidden user from the eavesdropper, while the eavesdropper listens to the communication from the access point to the STAR-RIS reflection unit and then to the hidden user. The public user only has the requirement of transmission rate and no requirement of concealment. There are no direct links between the access point and hidden users, public users, or eavesdroppers.

3. The covert NOMA communication method assisted by STAR-RIS and a fluid antenna according to claim 2, characterized in that, In the communication system model, the covert user, the public user, and the eavesdropper are each equipped with a mesh-structured fluid antenna with multiple preset ports. Each fluid antenna is connected to only one radio frequency link. The single-radio frequency link fluid antennas equipped on the covert user, the public user, and the eavesdropper have... One preset port , These represent the number of ports contained in each row and each column of the fluid antenna, respectively, and all ports are in... Evenly distributed across the region , The length and width of the region are given by the given information. Indicates the wavelength related to the carrier frequency. , To conceal users, For public users, For listening; port spacing less than Furthermore, at the receiving end, the fluid antenna switches between ports via an internal reconfigurable feed network.

4. The covert NOMA communication method assisted by STAR-RIS and fluid antenna according to claim 3, characterized in that, Step two includes: Modeling the spatial correlation between ports of a fluid antenna: Assuming the fluid antenna has a half-space receiving coverage, then any two ports... and The spatial correlation between them can be expressed as: ； in, A one-dimensional index for the port. For the row or column index of the port, The row or column representing the port; This represents the sinc function. A mapping function to convert a two-dimensional index of a port location into a one-dimensional index; Define the port with optimal channel quality metrics and the power gain of the cascaded channels: Select the port index that maximizes the channel gain as the optimal port to activate. , Represents a node The optimal port index selected in the selection process. Indicates access point and node The Channel coefficients between ports and cascaded via STAR-RIS ; Access Points and Nodes The The power gain of the cascaded channels between ports and via STAR-RIS is .

5. The covert NOMA communication method assisted by STAR-RIS and a fluid antenna according to claim 4, characterized in that, Step two includes: modeling the equivalent cascaded channel power gain between the access point and covert users, public users, and eavesdroppers, and through STAR-RIS. The cumulative distribution function is obtained as follows: A1. Assuming the channel coefficients follow an independent and identically distributed quasi-static Rayleigh fading pattern, the access point and the eavesdropper, the hidden user, and the public user are... The equivalent concatenated channel coefficients between ports and via STAR-RIS are uniformly expressed as follows: ； in, The imaginary unit, This is the channel coefficient vector from the access point to STAR-RIS. From STAR-RIS to Node The channel coefficient vector, For the first time from the access point to STAR-RIS Channel coefficients of each unit, For the first time from STAR-RIS Units to nodes The channel coefficient, and These are the channel coefficients. With channel coefficient phase, This represents the reflection or transmission coefficient matrix of STAR-RIS. Indicates the working mode index. It is in reflection mode. Transmission mode; and These represent the STAR-RIS number 1, 2, 3, 4, 5, 6, 7, 8 The reflection / transmission amplitude and phase shift of each unit, ; This represents the diagonalization operation; by adjusting the phase alignment, STAR-RIS achieves ideal phase shift adjustment, i.e. , Indexing for user nodes, To conceal users, For public users, From STAR-RIS Units to nodes Channel coefficient The phase; A2. Based on the channel assumption of quasi-static Rayleigh fading, and according to the central limit theorem, the equivalent concatenated channel coefficients between the access point and a port of the hidden user and the public user, and through STAR-RIS, are... It can be approximated as the mean. ,variance The Gaussian random variable; therefore, based on the probabilistic and statistical properties of the Gaussian random variable, the equivalent cascaded channel coefficients It follows a non-central chi-square distribution with 1 degree of freedom; therefore, the equivalent cascaded channel power gain The cumulative distribution function is expressed as: ； in, For non-central parameters, Indicates the order is The parameters are and Marcum Q function; A3. According to the Central Limit Theorem, the access point and the listener's... The equivalent concatenated channel coefficients between ports and via STAR-RIS It can be approximated as the mean. ,variance If the Gaussian random variable is used, then the equivalent cascaded channel power gain is... Follow the mean The exponential distribution; based on the distribution characteristics of the exponential distribution, the equivalent cascaded channel power gain. The cumulative distribution function is expressed as: ； A4. A Gaussian Copula model, combined with an approximate Jakes model, is used to describe the spatial correlation between the ports of the fluid antenna. , Using the definition of the cumulative distribution function and with the help of Sklar's theory, then The cumulative distribution function is: ； in, The unit cube is defined. The joint cumulative distribution function of d random vectors with uniform marginal distribution. The channel correlation matrix for the fluid antenna port of the eavesdropper. It has a mean of 0 and a correlation matrix of The cumulative distribution function of the joint multivariate normal distribution, It is an error function inverse function, The Gaussian Copula dependency parameter for the listener.

6. The covert NOMA communication method assisted by STAR-RIS and a fluid antenna according to claim 5, characterized in that, Step two includes: Transmitted signal modeling: Based on the superposition coding principle in NOMA technology, the signal transmitted by the access point is as follows: ,in It is the power allocation factor. and These are the concealed signals sent from the access point to concealed users and the public signals sent to public users, respectively, satisfying... ; Received signal modeling: Covert users and public users using the first The signals received by each port are uniformly represented as: ； in, It is the transmit power of the access point. , Indexing for user nodes, To conceal users, For public users, For user nodes The received signal at the location, Indicates access point and user node The Channel coefficients between ports and cascaded via STAR-RIS For user nodes Additive white Gaussian noise at a given location, with a mean of 0 and a variance of 0. The complex Gaussian distribution; This indicates the distance from STAR-RIS to the user node. The channel coefficient vector, For the first time from STAR-RIS Unit to user node The channel coefficient.

7. The covert NOMA communication method assisted by STAR-RIS and a fluid antenna according to claim 6, characterized in that, Based on the communication system model and channel model, the outage probabilities of concealed user nodes and public user nodes are defined, including: B1. A Gaussian Copula model, combined with an approximate Jakes model, is used to describe the spatial correlation between the ports of the fluid antenna, thus concealing the signal-to-interference-plus-noise ratio (SNR) of the user decoding their own signal. The cumulative distribution function is expressed as: ； in, The channel correlation matrix for the fluid antenna port of the concealed user. This indicates that the mean is 0 and the correlation matrix is... The cumulative distribution function of the joint multivariate normal distribution, To conceal the user's Gaussian Copula dependency parameters, This represents the average transmit signal-to-noise ratio. To conceal the variance of noise received by the user; B2. According to the definition of the cumulative distribution function, the signal-to-interference-plus-noise ratio (SINR) of a public user decoding its own signal. The cumulative distribution function is calculated as follows: ； in, Represents the probability of a random event occurring. This represents the average transmit signal-to-noise ratio. The variance of noise received by public users; B3. According to the definition of the cumulative distribution function, the signal-to-interference-plus-noise ratio (SINR) of a covert user decoding a public user signal. The cumulative distribution function is: ； B4. According to the definition of communication interruption probability, when the hidden user cannot restore the public user signal... Or unable to correctly decode covert user signals At that time, a communication interruption event occurs for the covert user; therefore, the probability of communication interruption for the covert user is... The calculation is as follows: ； in, The signal-to-noise ratio threshold for concealed signals. The signal-to-interference-plus-noise ratio (SIR) threshold for public signals. and These are covert user signals With public user signals The target rate; B5. When public users cannot correctly decode public signals At that time, a public user communication interruption event occurred; based on intermediate variables. The probability distribution of communication interruption probability for public users The calculation is as follows: 。 8. The covert NOMA communication method assisted by STAR-RIS and a fluid antenna according to any one of claims 5-7, characterized in that, Based on the communication system model and channel model, the probability of a listener making a false detection of covert communication is defined, including: C1. Based on binary hypothesis testing, the eavesdropper's first... The received signal observations obtained from each port are represented as follows: ； in, The noise at the listener's location is additive white Gaussian noise with a mean of 0 and a variance of 1. The complex Gaussian distribution; The channel index indicates the time slot occupied. The null hypothesis indicates that no covert information is transmitted between the access point and the covert user. As an alternative hypothesis, it indicates that covert information is transmitted between the access point and the covert user; C2. Assume all channels are independent and identically distributed, and consider the number of times each channel is used. Infinitely many, that is Therefore, under both assumptions, the average received power of the eavesdropper... It can be represented as: ； in, It is the variance of the noise received by the listener; C3. Based on the definitions of false alarm and false detection probabilities, calculate the false alarm probability detected by the eavesdropper. With the probability of missed detection They are respectively: ； ； Among them, false alarm probability Indicates the null hypothesis The judgment was made as The probability of detection; the probability of missed detection Indicating in the alternative hypothesis The judgment was made as The probability of; C4. Assume the null hypothesis and alternative hypothesis Since the prior probabilities are equal, based on this assumption, the error probability of the eavesdropper's detection is: 。 9. The covert NOMA communication method assisted by STAR-RIS and a fluid antenna according to claim 8, characterized in that, The optimization problem for maximizing the effective transmission rate, defined by the probability of interruption and the probability of detection error, is as follows: ； in, To determine the effective transmission rate as the objective function, constraints are applied. For concealment constraints, It is a very small positive number, representing the allowable concealment loss, a constraint. Power allocation factor Boundary constraints.

10. The covert NOMA communication method assisted by STAR-RIS and a fluid antenna according to claim 9, characterized in that, A numerical optimization method combining one-dimensional grid search and local refinement is employed to solve the problem, including: D1. Initialize search parameters and set search step size. In the feasible region Generate an evenly spaced set of grid points within the inner area. ,in , Indicates rounding down; D2. Coarse grid feasible point filtering, parameter settings For each grid point Calculate the detection error probability of the eavesdropper. And check whether the concealment constraint is met. Record all grid points that satisfy the constraints to form a feasible set. ; D3. Coarse-grid optimal value estimation, calculating the optimal value for each grid point. For the corresponding effective transmission rate, select the grid point that maximizes the effective transmission rate. ; D4. Local refinement search, using grid points Centered on, within the interval The search employs the golden ratio to improve accuracy when the search interval width is less than a preset threshold. The process terminates at a certain time, yielding the optimal power allocation factor. .

Images