Hidden NOMA communication method based on STAR-RIS partition cooperative interference

Abstract

The invention provides a hidden NOMA communication method based on STAR-RIS partition cooperative interference, and the method comprises the steps: building a STAR-RIS assisted hidden communication system, and enabling the STAR-RIS to be virtually divided into an enhanced transmission region and a cooperative interference region; calculating the communication interruption probability of the hidden user, and simplifying the communication interruption probability by utilizing the probability distribution of the intermediate variable; based on a binary hypothesis testing problem, determining a receiving signal and average receiving power of a malicious monitor, determining a minimum detection error probability of the malicious monitor adopting an optimal detection strategy, and calculating a lower bound of the minimum detection error probability; determining a concealment constraint; and establishing an optimization problem according to the communication interruption probability and the concealment constraint of the concealed user, and solving the optimization problem by adopting an alternating iterative optimization algorithm to obtain the optimal values of the power distribution coefficient and the area unit number of the enhanced transmission area. According to the invention, the transmission reliability and concealment can be improved by using the information relay and interference dual functions of STAR-RIS, and the spectrum utilization rate can be improved through regional cooperation.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, relates to STAR-RIS and covert communication technologies, and particularly relates to a covert NOMA communication method based on STAR-RIS. Background Art

[0002] With the rapid development of wireless communication technology, the problem of spectrum resource shortage has become increasingly prominent. At the same time, the requirements for communication security and concealment are also constantly increasing. As an emerging multiple access technology, Non-Orthogonal Multiple Access (NOMA) can effectively improve the spectrum utilization rate and meet the growing communication needs. However, in practical applications, the communication security and concealment of NOMA systems face many challenges. In particular, how to ensure the concealment of communication in the presence of malicious monitors has become an urgent problem to be solved.

[0003] As a new type of wireless communication technology, Reconfigurable Intelligent Surface (RIS) can optimize the propagation characteristics of wireless channels by dynamically adjusting the phase and amplitude of reflected signals, thereby improving the performance of communication systems. On this basis, the Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surface (STAR-RIS) further expands the application scenarios of RIS, enabling the simultaneous realization of signal reflection and transmission, and providing a new solution for covert communication. By dynamically adjusting the distribution of reflected and transmitted signals, STAR-RIS can effectively manage interference signals and enhance the concealment of communication.

[0004] In the field of covert communication, traditional NOMA systems mainly improve communication efficiency through power allocation and beamforming. However, in the face of complex wireless environments and malicious monitors, their concealment is still insufficient. The partition cooperative interference management ability of STAR-RIS can provide a more flexible interference management means for covert communication by dynamically adjusting the directions of reflected and transmitted signals. The partition cooperation technology can make full use of the spatial degrees of freedom and array resources of STAR-RIS by virtually dividing STAR-RIS into blocks, reasonably allocate the number of units in different regions, and accurately control the reflection and transmission of signals, thereby achieving more efficient covert communication.

[0005] In the prior art, there is no research on the method of using STAR-RIS partition cooperative interference to assist covert NOMA communication.

[0006] The invention patent with the application number 202410831101.7 discloses a method for covert communication in a STAR-RIS assisted NOMA network under non-ideal conditions. The steps are as follows: The base station sends multi-user information after superposition coding. After receiving the superposed information, the STAR-RIS device reflects and transmits it to different users simultaneously. Under non-ideal conditions, a method for enhancing the covert communication performance in the NOMA network by using the STAR-RIS device. The base station communicates with the users directly or through the STAR-RIS device, sends covert information to the near user, and sends public information to the far user. The illegal user detects whether the base station has sent covert information. The users decode the information they need by using non-orthogonal multiple access and serial interference cancellation. The STAR-RIS device enhances the information reception quality of the users through reflection and transmission, and at the same time interferes with the illegal users. This method introduces the STAR-RIS device without changing the original link, not only realizes the covert communication of the system, but also saves spectrum resources and improves the information transmission efficiency. However, the above patent only masks the transmission of covert signals with ordinary signals, and does not consider adopting the method of cooperative jamming to further reduce the probability of the covert information being detected, which will result in a relatively high malicious detection probability. Summary of the Invention

[0007] Aiming at the technical problem of low effective covert rate of the covert communication method in the existing STAR-RIS assisted system, the present invention proposes a covert NOMA communication method based on STAR-RIS partition cooperative jamming. A partition cooperation jamming strategy is adopted in a STAR-RIS assisted NOMA covert communication system to reduce the detection probability of malicious monitors, and it can be used in the blind area covert communication scenario assisted by STAR-RIS in a complex electromagnetic environment. The present invention adopts STAR-RIS partition cooperative jamming and jointly optimizes the power distribution coefficient of the base station and the number of regional units of STAR-RIS, which can not only utilize the information relay and interference dual functions of STAR-RIS to improve the transmission reliability and covertness, but also improve the spectrum utilization rate through regional cooperation, and then achieve a balance among the covert performance gain, system cost and design complexity.

[0008] In order to achieve the above object, the technical solution of the present invention is realized as follows: A covert NOMA communication method based on STAR-RIS partition cooperative jamming, the steps are as follows:

[0009] Step 1: Build a STAR-RIS assisted covert communication system. Covert users and malicious monitors are set on both the reflection side and the receiving side of STAR-RIS. STAR-RIS is virtually divided into an enhanced transmission ET area and a CJ area;

[0010] Step 2: Set two intermediate variables based on the coherent phase shift strategy, and use the moment-matching method to determine that the two intermediate variables follow a gamma distribution;

[0011] Step 3: According to the Signal-to-Interference-plus-Noise Ratio (SINR) at which the covert user decodes other covert user signals and its own signal, calculate the communication outage probability of the covert user, and simplify it using the probability distribution of the intermediate variables;

[0012] Step 4: Based on the binary hypothesis testing problem, determine the received signal and average received power of the malicious monitor. According to Pinsker's inequality, determine the minimum detection error probability when the malicious monitor adopts the optimal detection strategy, and calculate the lower bound of the minimum detection error probability; Use the central limit theorem and the statistical characteristics of the channel power gain to determine the covertness constraint;

[0013] Step 5: Jointly optimize the power allocation coefficient of the base station and the number of regional units in the ET area of the STAR-RIS to maximize the effective covert rate of the system. Establish an optimization problem based on the communication outage probability and covertness constraint of the covert user, and use the alternating iterative optimization algorithm to solve the optimization problem to obtain the optimal values of the power allocation coefficient and the number of regional units in the ET area.

[0014] Preferably, the STAR-RIS assisted covert communication system includes a STAR-RIS configured with M units, a base station BS equipped with N antennas located on the reflection side of the STAR-RIS, a single-antenna covert user UR and a malicious monitor WR, and a single-antenna covert user UT and a malicious monitor WT located on the transmission side of the STAR-RIS; There is no direct link between the base station BS and the covert user UT and the malicious monitor WT; Assume that the covert user UR and the covert user UT are the proximal and distal users respectively, and the covert users UR and UT are a pair of NOMA users;

[0015] The STAR-RIS is virtually divided into an ET area containing M e units and a CJ area containing M c units. The ET area reflects / transmits the signal from the base station BS to enhance the communication intensity between the base station BS and the covert user UR and establish a communication link between the base station BS and the covert user UT; The CJ area modulates the signal from the base station BS into an interference signal to deteriorate the detection capabilities of the malicious monitor WR and the malicious monitor WT and improve the covert communication performance of the system.

[0016] Preferably, according to the NOMA principle, the signal transmitted by the base station BS is Therefore, the signals received by the covert user UR and the covert user UT and Can be respectively expressed as:

[0017]

[0018] Wherein, P b is the transmit power of the base station BS, 0 < φ < 0.5 is the power allocation factor, and are the covert signals sent by the base station BS to the covert user UR and the covert user UT respectively, n represents the number of channel uses, (·) H is the transpose operation, is the channel coefficient from the base station BS to the covert user UR, is the channel coefficient from the ET area of the STAR-RIS to the covert user UR, h be is the channel coefficient from the station BS to the ET area of the STAR-RIS, is the channel coefficient from the CJ area of the STAR-RIS to the covert user UR, is the channel coefficient from the ET area of the STAR-RIS to the covert user UT, is the channel coefficient from the CJ area of the STAR-RIS to the covert user UT; represents the vector of the reflected / transmitted interference signal; and are the coefficient matrices of reflection / transmission in the ET area and the CJ area respectively, and respectively represent the amplitude and phase shift of the th or th unit in the ET area and the CJ area of the STAR-RIS, and satisfy χ ∈ {r, t}, r and t respectively represent reflection and transmission; diag(·) is the diagonalization operation; and are the received noises of the covert user UR and the covert user UT respectively;

[0019] Based on the principle of successive interference cancellation, the covert user UR first decodes the signal of the covert user UT and subtracts it from the mixed signal, and then decodes its own signal The SINR of the signal decoded by the covert user UR is:

[0020]

[0021] Wherein, is the variance of the received noise of the covert user UR; represents the interference residual coefficient;

[0022] Considering the imperfect successive interference cancellation scenario, the covert user UR decodes its own signal The SINR of which is:

[0023]

[0024] where, represents the imperfect SIC factor;

[0025] Regarding the signal as interference, the SINR of the covert user UT directly decoding its own signal is:

[0026]

[0027] where, is the received noise of the covert user UT variance.

[0028] Preferably, it is assumed that the base station BS cannot obtain the instantaneous channel state information related to the malicious monitors WR / WT. Therefore, the base station BS adjusts the phase shifts and to align with the channels of the covert user UR and the covert user UT respectively, and adopts the coherent phase shift strategy to maximize the SINR of the users. The optimal phase shifts and are expressed as: where, respectively represent the phase shift of the channel coefficient and the phase shift of the be th unit of the channel coefficient h .

[0029] Preferably, the implementation method of the second step is: Since the coherent phase shift strategy is adopted in the ET region to maximize the received SINR of the covert user UR and the covert user UT, the intermediate variable According to the channel fading hypothesis, using the moment matching method, it is obtained that the intermediate variable X and the intermediate variable Y respectively follow the gamma distributions X ∼ Γ(s x , c x ) and Y ∼ Γ(s y , c y ), where, Γ(·,·) is the upper incomplete gamma function, the shape parameter scale parameter The intermediate variable

[0030] Preferably, when the covert user UR cannot recover the signal or cannot correctly decode its own signal When the communication interruption event of the covert user UR occurs; based on the definition of the interruption probability, the communication interruption probability of the covert user UR is as follows:

[0031]

[0032] where the decoding threshold R1 and R2 are the target rates of the signals and respectively; Pr{·} represents probability operation, is the SINR for the covert user UR to decode its own signal ; is the SINR for the covert user UR to decode the signal of the covert user UT ; is the SINR for the covert user UT to decode its own signal ;

[0033] Substitute the SINR for the covert user UR to decode the signal of the covert user UT and the SINR for the covert user UR to decode its own signal into the communication interruption probability of the covert user UR and perform simple operations to obtain:

[0034]

[0035] For simplicity of description, let the intermediate variable φ1 = 1 / (1 + γ th2 ); The intermediate variable Π can be solved in the following three cases:

[0036] Case 1: When the power allocation factor φ ≥ φ1 or φ < φ2, the intermediate variable Π is obtained as:

[0037]

[0038] Case 2: When φ3 ≤ φ < φ1, the intermediate variable The intermediate variable Π is obtained as:

[0039]

[0040] Case 3: When φ2 ≤ φ < φ3, the intermediate variable Π can be obtained as:

[0041]

[0042] Based on the above cases and according to the probability distribution of the intermediate variable X, the communication interruption probability of the covert user UR is obtained as:

[0043]

[0044] where, Γ(·) represents the gamma function, and γ(x, y) represents the lower incomplete gamma function;

[0045] When the covert user UT fails to correctly decode the signal a communication interruption event of the covert user UT occurs; the communication interruption probability of the covert user UT is:

[0046]

[0047] Substitute the SINR when the covert user UT decodes its own signal into the communication interruption probability of the covert user UT and perform simple calculations to obtain:

[0048]

[0049] According to the probability distribution of the intermediate variable Y, the communication interruption probability of the covert user UT is:

[0050]

[0051] Preferably, the malicious monitors WR and WT face a binary hypothesis testing problem: the null hypothesis H0 means that the base station BS does not transmit covert information, and the alternative hypothesis H1 means that the base station BS transmits covert information, and the prior probabilities of H0 and H1 are equal;

[0052] Based on the binary hypothesis testing problem, the received signal observations obtained at the malicious monitors WR and WT are respectively expressed as:

[0053]

[0054] where, and respectively represent the received noises of the malicious monitors WR and WT; is the channel coefficient from the CJ area of the STAR-RIS to the malicious monitor WR, is the channel coefficient from the ET area of the STAR-RIS to the malicious monitor WR, is the channel coefficient from the CJ area of the STAR-RIS to the malicious monitor WT, is the channel coefficient from the ET area of the STAR-RIS to the malicious monitor WT;

[0055] Assume that all channels are independent and identically distributed, and the number of channel uses N→∞; the average received powers of the malicious monitors WR and WT are respectively calculated as:

[0056]

[0057] Among them, and are the variances of the received noise of the malicious monitors WR and WT, respectively;

[0058] The minimum detection error probability of the malicious monitors WR and WT adopting the optimal detection strategy is calculated as:

[0059]

[0060] Among them, represents the probability distribution P ι and the probability distribution Q ι The total variation distance between ι ∈ {w1, w2}; P ι and Q ι represent the probability distributions of the average received power of the malicious monitors WR / WT under the null hypothesis H0 and the alternative hypothesis H1, respectively;

[0061] Using Pinsker's inequality, an easy-to-process upper bound of the total variation distance is obtained, expressed as:

[0062]

[0063] Among them, D KL (P ι ||Q ι ) is the KL divergence of the probability distribution P ι and the probability distribution Q ι ;

[0064] Substituting the minimum detection error probability ξ * , we can get

[0065] Preferably, the method for determining the concealment constraint using the central limit theorem and the statistical characteristics of the channel power gain is: when the minimum detection error probability ξ * ≥1 - ε 1 / 2 , covert communication can be achieved, where ε1 and ε2 represent the preset concealment thresholds; the concealment constraint is expressed as

[0066] According to the definition of the KL divergence, the KL divergence of the probability distribution and the KL divergence of the probability distribution and and are calculated respectively as:

[0067] ​

[0068]

[0069] Among them, the intermediate variable

[0070] Adopt the expectation of KL divergence Evaluate the concealment of the system by the expectations of the channels related to the malicious monitors WR and WT: Assume that the malicious monitors WR and WT cannot obtain the working mode of the STAR-RIS and the phase shift settings of the two regions. According to the central limit theorem, the intermediate variable and are exponential distribution random variables with means of the intermediate variables and respectively; the intermediate variable is the sum of two independent exponential distribution random variables with means of the intermediate variables and respectively, is the sum of two independent exponential distribution random variables with means of and respectively;

[0071] Utilize the central limit theorem and the statistical characteristics of the channel power gain, and the expectations of the KL divergences and are calculated respectively as:

[0072]

[0073] Among them, represents the expectation operation, and Ei(·) represents the exponential integral function.

[0074] To sum up, through equivalent transformation, the concealment constraint of the STAR-RIS partition cooperation interference-assisted NOMA system is

[0075] Preferably, the optimization problem is:

[0076]

[0077] Among them, τ is the effective concealment rate of the system, ε1 and ε2 are preset concealment thresholds, R1 and R2 are the target rates of the signals and respectively, φ is the power allocation coefficient of the base station BS, M e is the number of regional units in the ET area of the STAR-RIS, M c is the number of regional units in the CT area of the STAR-RIS, and M represents the total number of units of the STAR-RIS; and are the communication interruption probabilities of the hidden users UR and UT, respectively.

[0078] Preferably, the method for solving the optimization problem by using the alternating iteration optimization algorithm is as follows:

[0079] Decompose the optimization problem into two sub-problems: Sub-problem 1 is to solve the optimal power allocation coefficient φ of the base station BS given the number of regional units M in the ET area of the STAR-RIS, that is e , and

[0080] Sub-problem 2 is to solve the optimal number of regional units M in the ET area of the STAR-RIS given the power allocation coefficient φ of the base station BS, that is e , and

[0081] Solve Sub-problem 1 through the golden section method to obtain its optimal value, and use the comparison method to solve Sub-problem 2: When only considering the equality constraint, the objective function is monotonically increasing with respect to the number of regional units M e ; therefore, solve the two inequality constraints to obtain the two upper bounds of the number of regional units M e , compare the sizes of the two upper bounds, and obtain the optimal solution of Sub-problem 2;

[0082] Use the alternating iteration method to update the solutions of the two sub-problems and obtain the local optimal value of the optimization problem.

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] First, the present invention uses STAR-RIS partition cooperative interference to assist in covert communication. The STAR-RIS is divided into an Enhanced Transmission (ET) area and a Cooperative Jamming (CJ) area. The ET area enhances / establishes the channel from the base station BS to the user by adjusting the phase configuration, improving the signal strength and communication quality; the CJ area generates interference signals through reflection / transmission modulation, deteriorating the received signal quality of the monitor, effectively ensuring the concealment of the communication system.

[0085] Second, the present invention makes full use of the signal enhancement and interference assistance dual functions of STAR-RIS. Through partitioning, its reflection and transmission capabilities can be utilized more effectively. Compared with the single-function scheme, the overall performance of the system is better.

[0086] Third, the present invention adopts a partition unit dynamic adjustment strategy, which can adaptively adjust the number of partition units according to different communication requirements and environmental conditions, improving the design flexibility and adaptability. Description of the Drawings

[0087] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0088] Figure 1 It is a flowchart of the present invention.

[0089] Figure 2 It is a system model diagram of the present invention.

[0090] Figure 3 It is the transmit power P of the base station BS of the present invention b Simulation result diagram of the impact on the user outage probability.

[0091] Figure 4 It is the simulation result diagram of the impact of the power allocation factor φ of the base station BS of the present invention on the user outage probability.

[0092] Figure 5 It is the transmit power P of the base station BS of the present invention b Simulation result diagram of the impact on the expected value of KL divergence.

[0093] Figure 6 It is the transmit power P of the base station BS of the present invention b Simulation result diagram of the impact on the effective secrecy rate τ. Specific implementation manners

[0094] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0095] As Figure 1 shown, a covert NOMA communication method based on STAR-RIS partition cooperative interference uses a base station BS, a covert user UR, and a malicious monitor WR located on the reflection side of the STAR-RIS, as well as a covert user UT and a malicious monitor WT located on the transmission side of the STAR-RIS to construct a covert NOMA communication system; the malicious monitor WR and the malicious monitor WT judge whether the base station BS sends covert information according to the received signals; the STAR-RIS enhances the reliability of legitimate transmission and reduces the probability of the covert information being detected by the monitors in a partition cooperative interference manner. The specific implementation method of the present invention is as follows:

[0096] Step 1: Build a covert communication system assisted by STAR-RIS. Covert users and malicious monitors are set on both the reflection side and the receiving side of STAR-RIS. STAR-RIS is virtually divided into an ET area and a CJ area.

[0097] As Figure 2 shown, build a covert NOMA communication system based on STAR-RIS partition collaborative interference. The system includes a STAR-RIS with M units, a base station BS equipped with N antennas located on the reflection side of STAR-RIS, a single-antenna covert user UR and a malicious monitor WR, and a single-antenna covert user UT and a malicious monitor WT located on the transmission side of STAR-RIS. Due to the existence of buildings, there is no direct link between the base station BS and the covert user UT and the malicious monitor WT; assume that the covert user UR and the covert user UT are the proximal and distal users respectively; the covert user UR and UT are a pair of NOMA users, and both are covert users. The base station BS needs to hide its transmission behavior to the covert users UR and UT from the malicious monitors WR and WT.

[0098] STAR-RIS is virtually divided into an ET area containing M e units and a CJ area containing M c units. The ET area reflects / transmits the signal from the base station BS to enhance the communication intensity between the base station BS and the covert user UR and establish a communication link between the base station BS and the covert user UT; the CJ area modulates the signal from the base station BS into an interference signal to deteriorate the detection capabilities of the malicious monitors WR and WT and improve the covert communication performance of the system.

[0099] Denote the channel coefficients from the base station BS to the ET area / CJ area of STAR-RIS, from the ET area to the malicious monitors WR / WT, from the ET area to the covert users UR / UT, from the CJ area to the malicious monitors WR / WT, from the CJ area to the covert users UR / UT, and from the base station BS to the malicious monitor WR and the covert user UR as: h be 、h bc 、 and Among them, the channel coefficient is the large-scale path loss coefficient, g ij represents the small-scale fading coefficient, ρ0 is the reference path loss per unit distance, α is the path loss exponent, d ij is the reference distance between node i and node j, and the nodes nodes b, respectively represent the base station BS, the units, the th unit, subscript subscript Assume that the channels associated with STAR-RIS follow Nakagami-m fading, i.e., there is a small-scale fading coefficient g ij ~ Nakagami(m ij , 1), where m ij represents the fading parameter; all direct channels follow Rayleigh fading, i.e., the small-scale fading coefficient

[0100] According to the NOMA principle, the signal transmitted by the base station BS is where P b is the transmission power of the base station BS, 0 < φ < 0.5 is the power allocation factor, and are the covert signals sent by the base station BS to the covert user UR and the covert user UT, respectively. Therefore, the signals received by the covert user UR and the covert user UT and can be expressed as:

[0101]

[0102] where n represents the number of channel uses, represents the vector of reflected / transmitted interference signals; are the coefficient matrices of reflection / transmission in the ET region and the CJ region, respectively, and represent the amplitude and phase shift of the th or th unit in the ET region and the CJ region of STAR-RIS, respectively, and satisfy χ ∈ {r, t}, where r and t represent reflection and transmission, respectively; diag(·) is the diagonalization operation; and are the received noises of the covert user UR and the covert user UT, respectively.

[0103] Based on the principle of successive interference cancellation (SIC), the covert user UR first decodes the signal of the covert user UT and subtracts it from the mixed signal, and then decodes its own signal Therefore, the SINR of the covert user UR for decoding the signal is:

[0104]

[0105] where is the variance of the received noise of the covert user UR ; represents the interference residual coefficient, which means that the interference influence in the CJ region is completely eliminated between the covert user UR and UT.

[0106] Considering the imperfect SIC situation, the SINR of the covert user UR decoding its own signal is:

[0107]

[0108] where, represents the imperfect SIC factor, which means perfect SIC.

[0109] Regarding the signal as interference, the SINR of the covert user UT directly decoding its own signal is:

[0110]

[0111] where, is the variance of the received noise of the covert user UT ;

[0112] Assume that the base station BS cannot obtain the instantaneous channel state information (CSI) related to the malicious monitors WR / WT. Therefore, the base station BS adjusts the phase shifts and to align with the channels of the covert user UR and the covert user UT respectively, that is, adopts the coherent phase shift strategy to maximize the SINR of the users. Thus, the optimal phase shifts and can be expressed as: where, and represent the phase shifts of the channel coefficients and the phase shift of the be -th and element of the channel coefficient h

[0113] Step 2: Based on the coherent phase shift strategy, set two intermediate variables and use the moment matching method to determine that the two intermediate variables follow the gamma distribution.

[0114] Since the coherent phase shift strategy is adopted in the ET region to maximize the received SINR of the covert user UR and the covert user UT, the intermediate variables According to the channel fading hypothesis, using the moment - matching method, the intermediate variables X and Y respectively follow gamma distributions X ∼ Γ(s x , c x ) and Y ∼ Γ(s y , c y ), where Γ(·,·) is the upper incomplete gamma function, the shape parameter scale parameter intermediate variable

[0115] Step 3: Calculate the communication outage probability of the covert user according to the SINR of the covert user decoding other covert user signals and its own signal, and simplify it using the probability distribution of the intermediate variable.

[0116] Analysis of the outage performance of the covert users UR and UT: When the covert user UR cannot recover the signal or cannot correctly decode its own signal , the communication outage event of the covert user UR occurs; therefore, based on the definition of the outage probability, the communication outage probability of the covert user UR can be calculated as:

[0117]

[0118] where the decoding threshold R1 and R2 are the target rates of the signals and respectively. Pr{·} represents the probability operation, is the SINR of the covert user UR decoding its own signal , is the SINR of the covert user UR decoding the signal of the covert user UT , is the SINR of the covert user UT decoding its own signal . According to the channel statistics, the analytical expressions of the communication outage probabilities of the covert users UR and UT can be calculated.

[0119] Substitute the SINR of the covert user UR decoding the signal of the covert user UT in Equation (3) and the SINR of the covert user UR decoding its own signal in Equation (4) into the communication outage probability in Equation (6) and perform simple operations to obtain:

[0120]

[0121] For simplicity of description, let the intermediate variable φ1 = 1 / (1 + γ th2 ) Thus, the intermediate variable Π in Equation (7) can be solved in the following three cases.

[0122] Case 1: When the power allocation factor φ ≥ φ1 or φ < φ2, the intermediate variable Π can be obtained as:

[0123]

[0124] Case 2: When φ3 ≤ φ < φ1, where the intermediate variable The intermediate variable Π can be obtained as:

[0125]

[0126] Case 3: When φ2 ≤ φ < φ3, the intermediate variable Π can be obtained as:

[0127]

[0128] From the above cases, it can be seen that the prerequisite for Case 2 to hold is: φ < φ1 and φ ≥ φ2; if we want to get φ2 ≤ φ < φ1, we must satisfy That is, satisfying φ3 ≤ φ < φ1 means the intermediate variable Similarly, satisfying φ2 ≤ φ < φ3 means In short, In another case, when φ2 > φ1, that is At this time, the communication outage probability

[0129] Substituting Equations (8) to (10) into Equation (7), and according to the probability distribution of the intermediate variable X, the communication outage probability of the covert user UR can be obtained as:

[0130]

[0131] where Γ(·) represents the gamma function, and γ(x, y) represents the lower incomplete gamma function.

[0132] When the covert user UT cannot correctly decode the signal the communication outage event of the covert user UT occurs; therefore, the communication outage probability of the covert user UT can be calculated as:

[0133]

[0134] Substituting the SINR of the covert user UT decoding its own signal in Equation (5) into the communication outage probability in Equation (12) and performing simple operations, we can obtain:

[0135]

[0136] According to the probability distribution of the intermediate variable Y, the communication outage probability of the covert user UT can be obtained. It is:

[0137]

[0138] Step 4: Based on the binary hypothesis testing problem, determine the received signal and the average received power of the malicious monitor. According to the Pinsker's inequality and the expression of the minimum detection error probability when the malicious monitor adopts the optimal detection strategy, calculate the lower bound of the minimum detection error probability; use the central limit theorem and the statistical characteristics of the channel power gain to determine the covertness constraint.

[0139] Analysis of the detection error probability of the malicious monitors WR and WT: The malicious monitors WR and WT on both sides of the STAR-RIS attempt to use energy detectors to detect whether there is a covert communication behavior between the base station BS and the covert users UR and UT respectively. To avoid the malicious monitors WR and WT detecting the transmission of covert information, the CJ area of the STAR-RIS modulates the input signal from the base station BS into an interference signal to confuse the detection of the malicious monitors. Therefore, the malicious monitors WR and WT are uncertain whether the base station BS has sent a covert signal, that is, the malicious monitors WR and WT are faced with a binary hypothesis testing problem: the null hypothesis H0 means that the base station BS has not transmitted covert information, and the alternative hypothesis H1 means that the base station BS has transmitted covert information. The prior probabilities of H0 and H1 are equal.

[0140] Based on the binary hypothesis testing problem, the observed values of the received signals obtained at the malicious monitors WR and WT can be respectively expressed as:

[0141]

[0142] where and respectively represent the received noises of the malicious monitors WR and WT.

[0143] The ultimate goal of the malicious monitors WR and WT is to analyze their average received power and to determine whether the received signals and are under the hypothesis H0 or the hypothesis H1. Assume that all channels are independent and identically distributed, and the number of channel uses N→∞; the average received powers of the malicious monitors WR and WT are respectively calculated as:

[0144]

[0145]

[0146] Among them, and are the variances of the received noises of the malicious monitors WR and WT, respectively.

[0147] To maximize the detection performance, the malicious monitors WR and WT adopt an optimal detection strategy. At this time, the corresponding minimum detection error probability can be calculated as:

[0148]

[0149] Among them, represents the probability distribution P ι and the probability distribution Q ι The total variation distance between ι ∈ {w1, w2}; P ι and Q ι represent the probability distributions of the average received power of the malicious monitors WR / WT under the null hypothesis H0 and the alternative hypothesis H1, respectively, and are respectively expressed as P(x|y) represents the probability distribution of x under the condition y.

[0150] Due to the total variation distance is difficult to solve, so using the Pinsker inequality, an easy-to-process upper bound of the total variation distance can be obtained, which is expressed as follows:

[0151]

[0152] Among them, D KL (P ι ||Q ι ) is the KL divergence of the probability distributions P ι and Q ι and represents the degree of difference between the two distributions.

[0153] Substituting the above inequality into the minimum detection error probability ξ * , we can get Generally speaking, when the minimum detection error probability ξ * ≥1 - ε 1 / 2 , covert communication can be achieved, where ε1 and ε2 represent the preset covertness thresholds. Therefore, the covertness constraint can be further expressed as

[0154] According to the definition of the KL divergence, the KL divergence between and and the KL divergence between and can be calculated respectively as:

[0155]

[0156] Among them, the intermediate variable

[0157] Since the instantaneous CSI related to the malicious monitors WR and WT cannot be obtained, the base station BS does not know the intermediate variable and the value of. Therefore, the expected value of the KL divergence is used to evaluate the secrecy of the system with respect to the channels related to the malicious monitors WR and WT. It is assumed that the malicious monitors WR and WT cannot obtain the operating mode of the STAR-RIS and the phase shift settings of the two zones, so their phase shifts are random for the malicious monitors WR and WT. According to the central limit theorem, the intermediate variable and are exponentially distributed random variables with means being the intermediate variable and respectively; the intermediate variable is the sum of two independent exponentially distributed random variables with means being the intermediate variable and respectively, and is the sum of two independent exponentially distributed random variables with means being and respectively.

[0158] According to the definition of expectation and the convolution formula, using the central limit theorem and the statistical characteristics of the channel power gain, the expected value of the KL divergence can be calculated respectively as:

[0159]

[0160] where denotes the expectation operation and Ei(·) denotes the exponential integral function.

[0161] In summary, through equivalent transformation, the secrecy constraint of the STAR-RIS partition cooperative interference-assisted NOMA system can be reformulated as

[0162] Step 5: Jointly optimize the power allocation coefficient of the base station and the number of regional units in the ET area of the STAR-RIS to maximize the effective secrecy rate of the system. An optimization problem is established based on the communication outage probability of the secrecy users, and an alternating iterative optimization algorithm is used to solve the optimization problem to obtain the optimal values of the power allocation coefficient and the number of regional units in the ET area.

[0163] Analysis of the effective covert rate of the system: In the downlink NOMA network, the base station BS aims to send covert signals to the covert users UR and UT with the help of STAR-RIS without being detected by the malicious detectors WR and WT. The effective covert rate (ECR) of the system can be defined as To improve the covert performance of the STAR-RIS partition cooperation interference-assisted downlink NOMA system, while satisfying the constraints such as the power of the signals of the covert users UR and UT, the covertness of the network, and the number of STAR-RIS units, by jointly optimizing the power allocation coefficient φ of the base station BS and the number of regional units M in the ET area of the STAR-RIS e , to maximize the ECR of the network. Therefore, the optimization problem can be formulated as follows:

[0164]

[0165] where ε1 and ε2 are preset covertness thresholds. R1 and R2 are the target rates of the signals and respectively. The constraint conditions from top to bottom represent the covertness constraint of covert communication, the power allocation coefficient constraint of the base station BS, and the total number of units constraint of the STAR-RIS. M represents the total number of units of the STAR-RIS.

[0166] To solve the above problem, the optimization problem is decomposed into two sub-problems: Sub-problem 1 is to solve the optimal power allocation coefficient φ of the base station BS given the number of regional units M in the ET area of the STAR-RIS e , and Sub-problem 2 is to solve the optimal number of regional units M in the ET area of the STAR-RIS given the power allocation coefficient φ of the base station BS e . Then, the golden section method is used to solve Sub-problem 1, and the comparison method is used to solve Sub-problem 2. Finally, the alternating iteration algorithm is used to obtain the local optimal value of the optimization problem. The two sub-problems are solved alternately until convergence. Next, the two sub-problems are solved in turn.

[0167] Thus, Sub-problem 1 can be formulated as follows:

[0168]

[0169] Since the objective function of Sub-problem 1 is a complex non-linear unimodal function, its optimal value can be obtained by the golden section method.

[0170] Sub-problem 2 can be formulated as follows:

[0171]

[0172] Since the objective function of sub-problem 2 is a complex non-linear function, and there are both inequality and equality constraints in the constraints; when only considering the equality constraints, the objective function is monotonically increasing with respect to the variable M e Therefore, solve the two inequality constraints to obtain two upper bounds of the variable M e of and Compare the magnitudes of the two, and the optimal solution of sub-problem 2 can be obtained as

[0173] After solving the above two sub-problems, the alternating iteration method is used to update the solutions of the two sub-problems to obtain the local optimal value of the original optimization problem, i.e., equation (25).

[0174] Next, Matlab simulation is used to verify the effectiveness of the proposed STAR-RIS partition cooperative interference-assisted covert NOMA communication method. The parameters are set as follows: the total number of STAR-RIS units M = 100, the variances of the received noises of WR and WT The preset covertness thresholds ε1 = ε2 = 0.001, the target rates of signals and are R1 = 0.6 bps / Hz and R2 = 0.4 bps / Hz, the SIC factor

[0175] Figure 3 is the transmit power P of the base station BS b The simulation curve of the influence of the transmit power P of the base station BS on the user outage probability. The theoretical and simulation results are basically the same, indicating that the theoretical derivation is correct. It can be seen from Figure 3 that as the transmit power of the base station BS increases, the outage probabilities of the covert users UR and UT gradually decrease; in addition, when the total number of STAR-RIS units is fixed at 100, as the number of units in the ET area increases, the outage performances of the covert UR and UT are both improved.

[0176] Figure 4 The simulation curve of the influence of the power allocation factor φ of the base station BS on the user outage probability. The theoretical and simulation results are basically the same, indicating that the theoretical derivation is correct. It can be seen from Figure 4 that as the power allocation factor φ increases, the outage probability of the covert user UR gradually decreases, while the outage probability of the covert user UT gradually increases; this is because as the power allocation factor φ increases, it means that the power allocated to the signal of the covert user UR becomes larger, while the power allocated to the signal of the covert user UT decreases.

[0177] Figure 5 is the transmit power P of the base station BS b The simulation curve of the influence of the transmit power P of the base station BS on the expected value of the KL divergence. The theoretical and simulation results are basically the same, indicating that the theoretical derivation is correct. It can be seen from Figure 5It can be seen that as the transmission power of the base station BS increases, the expected value of the KL divergence gradually increases to its upper limit. The larger the KL divergence value, the greater the difference between the two distributions, and the higher the probability of successful detection by the malicious monitors WR and WT. This fully shows that increasing the transmission power of the base station BS increases the probability of the malicious monitors WR and WT detecting the covert information transmission, that is, their detection error probability decreases; however, when the transmission power P b increases to a certain value, due to the existence of cooperative jamming, the detection error probability of the monitors no longer continues to decrease, which fully demonstrates the effectiveness of the proposed method.

[0178] Figure 6 is the transmission power P of the base station BS b The simulation curve of the influence of the effective covert rate τ. From Figure 6 it can be seen that when jointly optimizing the power allocation factor φ of the base station BS and the number M of ET area units e the effective covert rate of the entire system is higher than the scheme of only optimizing the power allocation factor φ of the base station BS or only optimizing the number M of ET area units e and is significantly higher than the scheme without optimization. In addition, from Figure 6 it can also be seen that as the transmission power of the base station BS increases, the effective covert rate gradually increases, indicating an improvement in the covert performance of the system.

[0179] In summary, the proposed STAR-RIS partition cooperative jamming-assisted covert NOMA communication method of the present invention can effectively increase the covertness of the communication system, and the simulation results fully illustrate its effectiveness.

[0180] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A covert NOMA communication method based on STAR-RIS partition collaborative interference, characterized in that, The steps are as follows: Step 1: Build a STAR-RIS-assisted covert communication system. Covert users and malicious monitors are set on both the reflection side and the receiving side of the STAR-RIS. The STAR-RIS is virtually divided into an enhanced transmission (ET) area and a CJ area; Step 2: Set two intermediate variables based on the coherent phase shift strategy, and use the moment matching method to determine that the two intermediate variables follow a gamma distribution; Step 3: Calculate the communication outage probability of the covert users according to the signal-to-interference-plus-noise ratio (SINR) of the covert users decoding other covert users' signals and their own signals, and simplify it using the probability distribution of the intermediate variables; Step 4: Based on the binary hypothesis testing problem, determine the received signal and the average received power of the malicious monitors. According to the Pinsker inequality, determine the minimum detection error probability of the malicious monitors adopting the optimal detection strategy, and calculate the lower bound of the minimum detection error probability; Use the central limit theorem and the statistical characteristics of the channel power gain to determine the covertness constraint; Step 5: Jointly optimize the power allocation coefficient of the base station and the number of regional units in the ET area of the STAR-RIS to maximize the effective covert rate of the system. Establish an optimization problem according to the communication outage probability and the covertness constraint of the covert users, and use the alternating iterative optimization algorithm to solve the optimization problem to obtain the optimal values of the power allocation coefficient and the number of regional units in the ET area.

2. The covert NOMA communication method based on STAR-RIS partitioned cooperative interference according to claim 1, wherein The STAR-RIS-assisted covert communication system includes a STAR-RIS configured with M units, a base station BS equipped with N antennas located on the reflection side of the STAR-RIS, a single-antenna covert user UR and a malicious monitor WR, and a single-antenna covert user UT and a malicious monitor WT located on the transmission side of the STAR-RIS; There is no direct link between the base station BS and the covert user UT and the malicious monitor WT; Assume that the covert user UR and the covert user UT are the proximal and distal users respectively, and the covert users UR and UT are a pair of NOMA users; The STAR-RIS is virtually partitioned into an ET region containing M e cells and a CJ region containing M c cells. The ET region reflects / transmits signals from the base station BS to enhance the communication strength between the base station BS and the hidden user UR and establish a communication link between the base station BS and the hidden user UT; The CJ area modulates the signal from the base station BS into an interference signal to deteriorate the detection capabilities of the malicious monitors WR and WT and improve the covert communication performance of the system.

3. The covert NOMA communication method based on STAR-RIS partitioned cooperative interference according to claim 2, wherein, According to the NOMA principle, the signal transmitted by the base station BS is Therefore, the signals received by the covert user UR and the covert user UT and can be respectively expressed as: Among them, P b is the transmission power of the base station BS, 0<φ<0.5 is the power allocation factor, and are the concealed signals sent by the base station BS to the concealed user UR and the concealed user UT, respectively. n represents the number of channels used, (·) H is the transpose operation, is the channel coefficient from the base station BS to the hidden user UR, h is the channel coefficient from the STAR-RIS ET region to the hidden user UR, be is the channel coefficient of the ET zone from station BS to STAR-RIS, is the channel coefficient from the CJ region of STAR-RIS to the hidden user UR, is the channel coefficient from the STAR-RIS ET region to the hidden user UT, is the channel coefficient from the CJ region of STAR-RIS to the hidden user UT; represents the reflected / transmitted interference signal vector; and are the reflection / transmission coefficient matrices of the ET region and the CJ region, and Represents the ET region and CJ region of STAR-RIS or The amplitude and phase shift of each unit, and satisfy r and t represent reflection and transmission, respectively; diag(·) is the diagonalization operation; and are the receiving noise of the hidden user UR and the hidden user UT respectively; Based on the principle of successive interference cancellation, the covert user UR first decodes the signal of the covert user UT and subtracts it from the mixed signal, and then decodes its own signal The signal-to-interference-plus-noise ratio of the decoded signal of the covert user UR is as follows: Among them, is the variance of the hidden user UR reception noise ; represents the interference residual coefficient; Considering the imperfect successive interference cancellation scenario, the covert user UR decodes its own signal The signal-to-interference-plus-noise ratio of which is as follows: Among them, represents the imperfect SIC factor; Treat the signal as interference and let the hidden user UT directly decode its own signal with the signal-to-interference-plus-noise ratio of: Among them, is the variance of the noise received by the hidden user UT .

4. The covert NOMA communication method based on STAR-RIS partitioned cooperative interference according to claim 3, wherein Assume that the base station BS cannot obtain the instantaneous channel state information related to the malicious monitor WR / WT. Therefore, the base station BS adjusts the phase shift of the ET region and are respectively aligned with the channels of the covert user UR and the covert user UT, and a coherent phase shift strategy is adopted to maximize the signal-to-interference-plus-noise ratio of the users. The optimal phase shifts and are expressed as: where respectively represent the phase shifts of the channel coefficients and the phase shift of the be th and element of the channel coefficient h 5. The covert NOMA communication method based on STAR-RIS partitioned collaborative interference according to claim 3, wherein The implementation method of the second step is as follows: Since the ET region adopts a coherent phase shift strategy to maximize the received signal-to-interference-plus-noise ratio of the covert user UR and the covert user UT, the intermediate variable can be obtained. According to the channel fading assumption and using the moment matching method, the intermediate variable X and the intermediate variable Y respectively follow the gamma distributions X ∼ Γ(s x , c x ) and Y ∼ Γ(s y , c y ), where Γ(·, ·) is the upper incomplete gamma function, the shape parameter scale parameter intermediate variable 6. The covert NOMA communication method based on STAR-RIS partitioned cooperative interference according to claim 5, characterized in that, When the covert user UR cannot recover the signal or cannot correctly decode its own signal a communication interruption event of the covert user UR occurs; based on the definition of the interruption probability, the communication interruption probability of the covert user UR is as follows: Among them, the decoding threshold R1 and R2 are the target rates of the signals and respectively; Pr{·} represents the probability operation, is the signal-to-interference-plus-noise ratio for the covert user UR to decode its own signal ; is the signal-to-interference-plus-noise ratio for the covert user UR to decode the signal of the covert user UT ; is the signal-to-interference-plus-noise ratio for the covert user UT to decode its own signal ; Decode the signal of the hidden user UT from the hidden user UR The signal-to-interference-plus-noise ratio and the SINR for the hidden user UR to decode its own signal are substituted into the communication outage probability of the hidden user UR and through simple calculations, we obtain: For simplicity of description, let the intermediate variable φ1 = 1 / (1 + γ th2 ). The intermediate variable Π can be solved in the following three cases: Case 1: When the power allocation factor φ ≥ φ1 or φ < φ2, the intermediate variable Π is obtained as: Case 2: When φ3 ≤ φ < φ1, the intermediate variable The intermediate variable Π obtained is: Case 3: When φ2 ≤ φ < φ3, the intermediate variable Π can be obtained as: Based on the above situation and according to the probability distribution of the intermediate variable X, the communication interruption probability of the hidden user UR is obtained as follows: where, Γ(·) represents the gamma function, and γ(x, y) represents the lower incomplete gamma function; When the hidden user UT fails to correctly decode the signal a communication interruption event of the hidden user UT occurs; the communication interruption probability of the hidden user UT is as follows Decode the signal of the hidden user UT by itself Signal-to-interference-plus-noise ratio Substitute it into the communication interruption probability of the hidden user UT And perform a simple calculation to obtain: According to the probability distribution of the intermediate variable Y, the communication outage probability of the hidden user UT is obtained as follows:

7. The covert NOMA communication method based on STAR-RIS partitioned cooperative interference according to any one of claims 3-6, characterized in that The malicious monitors WR and WT face a binary hypothesis testing problem: The null hypothesis H0 means that the base station BS does not transmit covert information, and the alternative hypothesis H1 means that the base station BS transmits covert information. The prior probabilities of H0 and H1 are equal; Based on the binary hypothesis testing problem, the received signal observations obtained at the malicious monitors WR and WT are respectively expressed as: Among them, and respectively represent the received noises of malicious monitors WR and WT; is the channel coefficient from the CJ region of STAR-RIS to malicious monitor WR, is the channel coefficient from the ET region of STAR-RIS to malicious monitor WR, is the channel coefficient from the CJ region of STAR-RIS to malicious monitor WT, is the channel coefficient from the ET region of STAR-RIS to malicious monitor WT; Assume that all channels are independent and identically distributed, and the number of channel uses N → ∞; The average received powers of the malicious monitors WR and WT are respectively calculated as: Among them, and are the variances of the received noises of malicious monitors WR and WT, respectively. The minimum detection error probability of the malicious monitors WR and WT adopting the optimal detection strategy is calculated as: Among them, represents the probability distribution P ι and the probability distribution Q ι The total variation distance between ι ∈ {w1, w2}; P ι and Q ι respectively represent the probability distributions of the average received power of the malicious monitors WR / WT under the null hypothesis H0 and the alternative hypothesis H1; Using Pinsker's inequality, obtain a tractable upper bound on the total variation distance which is given by: Among them, D KL (P ι ||Q ι ) is the KL divergence between the probability distribution P ι and the probability distribution Q ι ; Substitute the minimum detection error probability ξ * , and we can obtain 8. The covert NOMA communication method based on STAR-RIS partitioned cooperative interference according to claim 7, wherein The method for determining the concealment constraint by using the central limit theorem and the statistical characteristics of the channel power gain is as follows: When the minimum detection error probability ξ * ≥1 - ε 1 / 2 is satisfied, covert communication can be achieved, where ε1 and ε2 represent preset concealment thresholds; the concealment constraint is expressed as According to the definition of KL divergence, the probability distribution and of the KL divergence The probability distribution and of the KL divergence are calculated respectively as follows: Among them, intermediate variable Expected value of KL divergence Evaluate the concealment of the system by taking the expectations of the channels related to the malicious monitors WR and WT: Assume that the malicious monitors WR and WT cannot obtain the working mode of the STAR-RIS and the phase shift settings of the two zones. According to the central limit theorem, the intermediate variables and are exponential distribution random variables with means of the intermediate variables and respectively; the intermediate variable is the sum of two independent exponential distribution random variables with means of the intermediate variables and respectively, is the sum of two independent exponential distribution random variables with means of and respectively; Using the central limit theorem and the statistical characteristics of the channel power gain, the KL divergence and are calculated as the expectations respectively as follows: Among them, represents the desired operation, and Ei(·) represents the exponential integral function. In summary, through equivalent transformation, the secrecy constraint of the NOMA system assisted by STAR-RIS partitioned cooperative jamming is 9. The covert NOMA communication method based on STAR-RIS partitioned cooperative interference according to claim 8, wherein The optimization problem is: where, τ is the effective secrecy rate of the system, ε1 and ε2 are the preset secrecy thresholds, R1 and R2 are the target rates of the signals and respectively, φ is the power allocation coefficient of the base station BS, M e is the number of regional units in the ET area of the STAR-RIS, M c is the number of regional units in the CT area of the STAR-RIS, and M represents the total number of units of the STAR-RIS; and are the communication outage probabilities of the legitimate users UR and UT, respectively.

10. The covert NOMA communication method based on STAR-RIS partitioned cooperative interference according to claim 9, wherein, The method of using the alternating iterative optimization algorithm to solve the optimization problem is: The optimization problem is decomposed into two sub-problems: Sub-problem 1 is to solve the optimal power allocation coefficient φ of the base station BS given the number of regional units M in the ET area of the STAR-RIS, that is e , Sub - problem 2 is to solve for the optimal number of regional units \(M\) in the ET area of the STAR - RIS with the power allocation coefficient \(\varphi\) of the given base station BS e , that is The optimal value of sub-problem 1 is obtained by the golden section method, and the sub-problem 2 is solved by the comparison method: when only considering the equality constraints, the objective function is monotonically increasing with respect to the number of regional units M e Therefore, by solving the two inequality constraints, the two upper bounds of the number of regional units M e are obtained, and by comparing the magnitudes of the two upper bounds, the optimal solution of sub-problem 2 is obtained; The solutions of the two sub-problems are updated by the alternating iteration method to obtain the local optimal value of the optimization problem.

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