Method for maximizing minimum safety rate of ris-assisted uav relay system

Abstract

The application claims a kind of RIS-assisted unmanned aerial vehicle relay system minimum safety rate maximization method, the method considers fairness between legal users, under the constraints of meeting legal user service and quality, base station maximum transmit power, RIS phase shift and unmanned aerial vehicle location, the minimum safety rate maximization of RIS-assisted unmanned aerial vehicle relay system is realized.The application establishes the minimum safety rate maximization model based on RIS-assisted unmanned aerial vehicle relay system, first by introducing auxiliary variable, continuous convex approximation method is equivalent to convert non-convex optimization problem into convex optimization problem, then using alternating iterative algorithm, to maximize the minimum safety rate between legal users.The application can better realize the global fairness of resource allocation while ensuring the quality of service requirements of all legal users, with better practicability and feasibility.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of resource allocation of wireless communication systems, and particularly relates to a minimum safety rate maximization method for a RIS-assisted unmanned aerial vehicle relay system. BACKGROUND

[0002] With the rapid development of science and technology, wireless communication networks have gradually matured, but the security problems caused by the openness and broadcast nature of wireless channels still exist. How to improve the security of information transmission in wireless communication systems has become a key problem to be solved. Recently, Reconfigurable Intelligence Surface (RIS) has attracted widespread attention from academia and industry as a promising technology. The surface of RIS integrates a large number of passive reflecting elements, which can intelligently reconfigure the wireless propagation environment. Each reflecting element can control its amplitude and phase to reflect the incident signal. By jointly controlling the phase shift of all reflecting elements of RIS, the transmission direction of the reflected signal can be changed, thereby improving the security performance of the wireless communication system. In addition, unmanned aerial vehicles have the characteristics of low cost, flexibility, on-demand deployment, etc. Deploying RIS on unmanned aerial vehicles as an air relay can further improve the performance of wireless communication systems. In recent years, Rate-Splitting Multiple Access (RSMA) as a new multiple access technology can not only support large-scale connections, but also achieve higher spectral efficiency than Non-Orthogonal Multiple Access (NOMA) and Space Division Multiple Access (SDMA). By introducing RSMA into the RIS-assisted unmanned aerial vehicle relay system, the public message sent by the sender is not only the useful message required by the legitimate user, but also as AN to confuse the eavesdropper, thereby effectively enhancing the physical layer security performance of the system.

[0003] At present, many researches have been conducted on the resource allocation problem of physical layer security in RIS-assisted UAV relay system. ZHANG Y et al. published an article titled "Joint Optimization for Aerial Intelligent Reflecting Surface Assisted Secure Wireless Network" in 2022 IEEE 8th International Conference on Computer and Communications (ICCC), Chengdu, China, 2022: 1000-1004. The article studies the physical layer security problem in RIS-assisted UAV relay system, and maximizes the average security rate of the minimum user by jointly optimizing the phase shift matrix of RIS, communication scheduling and the trajectory of UAV. WEI W et al. published an article titled "Secure transmission design for aerial IRS assisted wireless networks" in IEEE Transactions on Communications, 2023, 71(6): 3528-3540. The article studies the case where there are multiple users and multiple eavesdroppers in RIS-assisted UAV relay system, and maximizes the sum security rate in the worst case by jointly optimizing the hovering position of UAV, the transmit beamforming of base station and the phase shift of RIS.

[0004] From the above results, it can be seen that most of the current researches on the physical layer security problem in RIS-assisted UAV relay system consider using Time Division Multiple Access (TDMA), SDMA or NOMA protocol, and do not consider using RSMA protocol. In a wireless secure communication system, using RSMA protocol not only supports multi-user access, but also effectively improves the security performance of the system. Therefore, the present invention considers the case where the base station and the legitimate user communicate using RSMA protocol, and studies the minimum security rate maximization method of RIS-assisted UAV relay system. SUMMARY

[0005] The present invention aims to solve the above problems of the prior art. A minimum security rate maximization method for RIS-assisted UAV relay system is proposed. The technical solution of the present invention is as follows:

[0006] A minimum security rate maximization method for RIS-assisted UAV relay system, comprising the following steps:

[0007] Step one: deploying RIS-aided UAV relay system with M reflecting elements, UAV carrying RIS as an aerial relay to assist the base station to communicate with the legitimate users, while there is an eavesdropper trying to eavesdrop the data information of the legitimate users;

[0008] Step two: considering fairness and communication reliability between legitimate users, constructing the minimum safe rate maximization problem of RIS-aided UAV relay system, and the optimization variables are base station transmit power P, common rate allocation C, RIS phase shift Θ and UAV position w u ;

[0009] Step three: initializing base station transmit power P, common rate allocation C, RIS phase shift Θ and UAV position w u , setting the maximum iteration number n max , and convergence precision ε;

[0010] Step four: fixing RIS phase shift Θ and UAV position w u , solving base station transmit power P and common rate allocation C;

[0011] Step five: fixing base station transmit power P, common rate allocation C and UAV position w u , solving RIS phase shift Θ;

[0012] Step six: fixing base station transmit power P, common rate allocation C and RIS phase shift Θ, solving UAV position w u ;

[0013] Step seven: alternately iterating and optimizing base station transmit power P, common rate allocation C, RIS phase shift Θ and UAV position w u , until the minimum safe rate error value is less than the threshold value or the maximum iteration number is reached.

[0014] Further, in the step one, the UAV relay system model is as follows:

[0015] Considering an RIS-aided UAV relay secure communication system, the model is composed of a base station, a UAV carrying RIS, K legitimate users and an eavesdropper, wherein the base station, the legitimate users and the eavesdropper are all equipped with a single antenna, and the base station communicates with the legitimate users using the RSMA protocol;

[0016] The transmission signal at the base station is represented as:

[0017]

[0018] s c and s k represent the common message and the private message of the kth legitimate user transmitted at the base station, respectively, p c and pk They are s c and s k Given the transmission power, the signals received at the legitimate user k and the eavesdropper are respectively represented as:

[0019]

[0020] Among them, h k h e and h r These represent the channel gains from RIS to legitimate user k, from RIS to the eavesdropper, and from the base station to RIS, respectively. Let k represent the additive white Gaussian noise at the legitimate user's location and the eavesdropper's location, respectively.

[0021] According to the RSMA principle, the instantaneous signal-to-interference-plus-noise ratio (SIRR) for decoding public and private messages at legitimate user k is expressed as follows:

[0022]

[0023] in, Let be the noise variance at the legitimate user k. Therefore, the instantaneous reach rate of legitimate user k decoding public and private messages per unit bandwidth is expressed as follows:

[0024] R kc =log2(1+Γ c,k )

[0025] R kp =log2(1+Γ p,k )

[0026] To ensure that public messages can be successfully decoded by all users, the actual transmission rate R of public messages is... c The rate does not exceed the minimum reachability of public messages among all legitimate users, i.e., R. c Satisfy R c ≤min k∈K R kc Additionally, R c Shared by all legitimate users, each legitimate user k is assigned to R. c Part of C k Common rate allocation vectors C1, C2, ..., C K It should satisfy ∑ k∈K C k =R c Therefore, the total reachability rate of a legitimate user k is expressed as:

[0027] R k,tot =C k +R kp

[0028] The achievable wiretapping rate of the eavesdropper to decode the common message and the private message of the legitimate user k is denoted as

[0029] R ec = log2(l + Γ ec )

[0030]

[0031] wherein and denote the signal-to-interference-plus-noise ratio (SINR) of the eavesdropper to decode the common message and the private message of the legitimate user k, respectively, which are denoted as

[0032]

[0033] wherein is the noise variance at the eavesdropper; assuming that the achievable wiretapping rate of the common message at the eavesdropper is evenly distributed to each legitimate user, the total achievable wiretapping rate of the eavesdropper to the legitimate user k can be denoted as

[0034]

[0035] Finally, the security rate of the legitimate user k is defined as follows:

[0036]

[0037] wherein [x] + = max{x, 0}, [·] + may be omitted, the reason is that in the optimal solution, the security rate R s,k of each legitimate user corresponding to it is at least 0.

[0038] Further, in the step two, the constructed minimum security rate maximization optimization problem is:

[0039]

[0040] C7: 0≤ x u ≤ X, 0≤ y u ≤ Y

[0041] wherein the constraint C1 is the minimum rate requirement constraint of each legitimate user, denotes the minimum rate requirement of each legitimate user, the constraint C2 is the maximum transmit power constraint at the base station, p maxis the maximum transmit power at the base station, constraint C3 ensures that each legitimate user is able to decode the common stream, constraint C4 ensures that the common stream cannot be completely decoded by an eavesdropper, constraint C5 indicates that the common rate allocated to each legitimate user is non-negative; constraint C6 indicates the phase shift constraint of each reflecting element of RIS, Θ m represents the reflection phase of each reflecting element of RIS; constraint C7 indicates that the UAV is deployed within a certain area range, x u represents the horizontal abscissa of the UAV position, y u represents the horizontal ordinate of the UAV position, X represents the maximum value of the horizontal abscissa of the UAV position, and Y represents the maximum value of the horizontal ordinate of the UAV position.

[0042] Further, in the fourth step, the joint optimization sub-problem of the base station transmit power P and the common rate allocation C is obtained, and the step of converting it into an equivalent convex optimization problem is:

[0043] First, fix the RIS phase shift Θ and the UAV position w u , and obtain the joint optimization sub-problem of the base station transmit power P and the common rate allocation C:

[0044]

[0045] s.t.C1~C5

[0046]

[0047] wherein τ1 is a relaxation variable introduced, C2 and C5 are affine with respect to the optimization variables P and C under the given RIS phase shift Θ and the UAV position w u , and C1, C3, C4 and C8 are all non-convex, so the sub-problem is a non-convex optimization problem;

[0048] Let R s,k =C k +(f kp -g kp )-(f ec -g ec ) / K-(f ep -g ep ), R kc =f kc -g kc ; wherein f kc , g kc , f kp , g kp , f ec , g ec , f ep , g ep are respectively:

[0049]

[0050] f kc g kc They are R kc The first and second terms after transforming into the form of the subtraction of two functions, f kp g kp They are R kp The first and second terms after transforming into the form of the subtraction of two functions, f ec g ec They are R ec The first and second terms after transforming into the form of the subtraction of two functions, f ep g ep They are R ep The first and second terms after transforming into the form of subtracting two functions.

[0051] Then, the optimization problem P2 can be rewritten as:

[0052]

[0053] stC2、C5

[0054]

[0055] Using the SCA method, respectively for g kp g kc f ec and f ep At the initial feasible point P (n) Performing a first-order Taylor expansion at the given point yields the upper bound. The optimization problem P 2.1 g kp g kc f ec and f ep Replacing them with their upper bounds respectively, we can obtain an equivalent convex optimization problem:

[0056]

[0057] stC2、C5

[0058]

[0059] Furthermore, in step five, the method for obtaining the RIS phase shift Θ optimization subproblem and converting it into an equivalent convex optimization problem is as follows:

[0060] First, fix the base station transmit power P, the common rate allocation C, and the drone location w. u Let the channel gain η k =|v H Hk | 2 , η e = |v H H e | 2 where is introduced, the RIS phase shift Θ optimization subproblem is obtained:

[0061]

[0062] s.t. C1, C3, C4, C6

[0063] The objective function and constraints C1, C3 and C4 of optimization problem P3 are all non-convex with respect to variable v, which needs to be processed; R kc , R kp and R ec , R ep are replaced by lower bound and upper bound respectively;

[0064] Therefore, the objective function can be rewritten as:

[0065]

[0066] Optimization problem P3 can be equivalently converted into a convex optimization subproblem:

[0067] P 3.1 : max τ2

[0068] v, τ2

[0069]

[0070]

[0071] where τ2 is the introduced relaxation variable.

[0072] Further, in step six, the UAV position w u optimization subproblem is obtained, and it is converted into an equivalent convex optimization problem:

[0073] First, fix the base station transmit power P, the common rate allocation C and the RIS phase shift Θ, and obtain the UAV position w u optimization subproblem:

[0074]

[0075] s.t. C1, C3, C4, C7

[0076] Since the objective function and constraints C1, C3 and C4 in optimization problem P4 are all non-convex with respect to optimization variable w uAll are non-convex, so the optimization problem P4 is a non-convex optimization problem, which cannot be directly solved and needs to be processed;

[0077] For easy processing, R kc , R kp and R ec , R ep are simplified, respectively, and have:

[0078]

[0079] Where d r , d k , d e represent the distance between the base station and the RIS, the distance between the RIS and the legitimate user k, and the distance between the RIS and the eavesdropper, respectively; β0 represents the path loss exponent; B kc , D kc are the second terms of the numerator and denominator of the fraction after simplification and transformation of R kc ; B kp , D kp are the second terms of the numerator and denominator of the fraction after simplification and transformation of R kp ; B ec , D ec are the second terms of the numerator and denominator of the fraction after simplification and transformation of R ec ; B ep , D ep are the second terms of the numerator and denominator of the fraction after simplification and transformation of R ep ; B kc , B kp , B ec , B ep and D kc , D kp , D ec , D ep are represented as:

[0080]

[0081]

[0082] Due to the non-convexity of and , the relaxation variable is introduced to convert the optimization problem P4 into:

[0083]

[0084] s.t.C7

[0085]

[0086] where the optimization problem P 4.1 The objective function can be written as:

[0087]

[0088] Since the change of the optimization variable w u will also affect the values of φ r , φ k and φ e , B kc , B kp , B ec , B ep and D kc , D kp , D ec , D ep are complicated functions of the optimization variable w u ; in order to make the problem convenient to handle, B kc , B kp , B ec , B ep and D kc , D kp , D ec , D ep are replaced by their upper bounds and :

[0089] Substituting the upper bounds of B kc , B kp , B ec , B ep and D kc , D kp , D ec , D ep into the constraint C3'" and the objective function, we can get:

[0090]

[0091] Since is a convex function minus two convex functions, it is still non-convex; using the SCA method, by performing a first-order Taylor expansion at the initial feasible point , we replace by its lower bound :

[0092]

[0093] where denotes the lower bound of after performing a first-order Taylor expansion at the initial feasible point .

[0094] Thus can be rewritten as

[0095]

[0096] For inequality the right side of the inequality is a convex function in variable U, thus the inequality is a non-convex constraint. Using SCA method, a first order Taylor expansion is performed at the initial feasible point to obtain

[0097]

[0098] Thus, inequality can be rewritten as a convex constraint

[0099]

[0100] The constraints C10', C10" and C11', C11" in optimization problem P 4.1 are also non-convex, which need to be handled. Using first order Taylor expansion, the upper bound of the non-convex term in C10', C10" and the lower bound of the non-convex term in C11', C11" are obtained as

[0101] In addition, since is a concave function in variable U, a first order Taylor expansion is performed at the last iteration value and respectively to obtain

[0102]

[0103] Thus, optimization problem P 4.1 can be equivalently rewritten as a convex optimization subproblem

[0104]

[0105] C7,C17

[0106] where τ3 is a slack variable introduced.

[0107] An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor implementing the method of maximizing the minimum safety speed of a RIS-assisted UAV relay system when executing the program.

[0108] ​A non-transitory computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the RIS-assisted UAV relay system minimum safe rate maximization method of any one.

[0109] A computer program product comprising a computer program which, when executed by a processor, implements the RIS-assisted UAV relay system minimum safe rate maximization method of any one.

[0110] The advantages and benefits of the present application are as follows:

[0111] The present application combines RIS, UAV and RSMA, and proposes a joint optimization of base station transmit power, common rate allocation, RIS phase shift and UAV position. Since the system minimum safe rate maximization optimization problem is a non-convex problem, it is difficult to give an optimal solution. The present application introduces a relaxation variable, first-order Taylor expansion and other methods to transform the objective function and constraints into a convex optimization problem under the constraints of base station transmit power, RIS phase shift and UAV position, and then solves the maximum minimum safe rate of the system. The innovation of the present application is to apply the RSMA technology with multiple performance advantages in step one to the RIS-assisted UAV relay system, and to study the physical layer security problem on the basis of considering the fairness among legitimate users, and finally to propose a minimum safe rate maximization method. The present application is ingenious in using the RSMA protocol to enhance the communication security, using the RSMA protocol in the RIS-assisted UAV relay system, and using the common message not only as the useful message needed by the legitimate user, but also as the interference to confuse the eavesdropper. The flexible management of the common message by the RSMA protocol not only enhances the system security, but also greatly reduces the complexity. BRIEF DESCRIPTION OF DRAWINGS

[0112] Figure 1 is a system model schematic diagram of the RIS-assisted UAV relay system established by the preferred embodiment of the present application;

[0113] Figure 2 is a general flowchart of the minimum safe rate maximization method proposed by the present application;

[0114] Figure 3 is a specific implementation flowchart of the alternating iterative optimization algorithm used in the method of the present application. DETAILED DESCRIPTION

[0115] The technical solutions of the embodiments of the present application will be described in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments of the present application.

[0116] The technical solution of the present application to solve the above technical problems is:

[0117] Figure 3 A method for maximizing the minimum safe rate of a RIS-assisted UAV relay system is disclosed. It includes the following steps:

[0118] Step 1: Deploy a RIS-assisted UAV relay system with M reflecting units. The UAV carries RIS as an aerial relay to assist the base station in communicating with legitimate users. Meanwhile, there is an eavesdropper trying to eavesdrop on the data information of legitimate users.

[0119] Step 2: Consider fairness and communication reliability among legitimate users, and construct the minimum safe rate maximization problem of the RIS-assisted UAV relay system. The optimization variables are base station transmit power P, common rate allocation C, RIS phase shift Θ, and UAV position w u ;

[0120] Step 3: Initialize base station transmit power P, common rate allocation C, RIS phase shift Θ, and UAV position w u , set the maximum number of iterations n max , and the convergence precision ε;

[0121] Step 4: Fix RIS phase shift Θ and UAV position w u , and solve for base station transmit power P and common rate allocation C.

[0122] Step 5: Fix base station transmit power P, common rate allocation C, and UAV position w u , and solve for RIS phase shift Θ.

[0123] Step 6: Fix base station transmit power P, common rate allocation C, and RIS phase shift Θ, and solve for UAV position w u ;

[0124] Step 7: Alternately optimize base station transmit power P, common rate allocation C, RIS phase shift Θ, and UAV position w u until the minimum safe rate error value is less than the threshold value or the maximum number of iterations is reached.

[0125] Further, in the first step, the system model is as follows:

[0126] Consider a RIS-assisted UAV relay secure communication system. The system model consists of a base station, a UAV carrying RIS, K legitimate users, and an eavesdropper. The base station, legitimate users, and eavesdropper are all equipped with a single antenna. The base station communicates with legitimate users using the RSMA protocol.

[0127] The transmitted signal at the base station can be represented as:

[0128]

[0129] s c and s k denote the common message and the k-th legitimate user's private message transmitted at the base station, respectively, p c and p k are the transmit powers of s c and s k , respectively. Thus, the received signals at the legitimate user k and the eavesdropper can be expressed as:

[0130]

[0131] where h k , h e , and h r denote the channel gains between the RIS to the legitimate user k, the RIS to the eavesdropper, and the base station to the RIS, respectively, denote the additive white Gaussian noise at the legitimate user k and the eavesdropper, respectively.

[0132] According to the RSMA principle, the instantaneous signal-to-interference-and-noise ratio (SINR) for decoding the common message and the private message at the legitimate user k can be expressed as:

[0133]

[0134] where is the noise variance at the legitimate user k. Thus, the instantaneous achievable rates for decoding the common message and the private message at the legitimate user k in unit bandwidth can be expressed as:

[0135] R kc = log2(l + Γ c,k )

[0136] R kp = log2(l + Γ p,k )

[0137] It is noted that to ensure that the common message can be successfully decoded by all users, the actual transmission rate R c of the common message should not exceed the minimum value of the achievable rates of the common message at all legitimate users, i.e., R c satisfies R c ≤ min k∈K R kc . In addition, R c should be shared by all legitimate users, and each legitimate user k is allocated a portion C c of R k . The common rate allocation vector C1, C2,..., C K should satisfy ∑ k∈K C k= R c Thus, the total achievable rate for the legitimate user k can be expressed as:

[0138] R k,tot = C k + R kp

[0139] The achievable wiretapping rate for the eavesdropper to decode the common message and the private message of the legitimate user k can be expressed as:

[0140] R ec = log2(1 + Γ ec )

[0141]

[0142] where and denote the signal-to-noise-and-interference ratio (SINR) for the eavesdropper to decode the common message and the private message of the legitimate user k, respectively, which can be expressed as:

[0143]

[0144] where is the noise variance at the eavesdropper. Without loss of generality, assuming that the achievable wiretapping rate of the common message at the eavesdropper is evenly distributed to each legitimate user, the total achievable wiretapping rate for the eavesdropper to wiretap the legitimate user k can be expressed as:

[0145]

[0146] Finally, the security rate for the legitimate user k is defined as follows:

[0147]

[0148] where [x] + = max{x, 0}.[·] + can be omitted, the reason being that at the optimal solution, the security rate R s,k for each legitimate user corresponding to it is at least 0.

[0149] Further, in the second step, the constructed minimum security rate maximization optimization problem is:

[0150]

[0151] C7: 0≤ x u ≤ X, 0≤ y u ≤ Y

[0152] where the constraint C1 is the minimum rate requirement constraint for each legitimate user, denotes the minimum rate requirement of each legitimate user. Constraint C2 is the maximum transmit power constraint at the base station, p max is the maximum transmit power at the base station. Constraint C3 ensures that each legitimate user can decode the common stream. Constraint C4 ensures that the common stream cannot be completely decoded by the eavesdropper. Constraint C5 denotes that the common rate allocated to each legitimate user is non-negative; constraint C6 denotes the phase shift constraint of each reflecting element of the RIS, Θ m denotes the reflection phase of each reflecting element of the RIS; constraint C7 denotes that the UAV is deployed within a certain area range, x u denotes the horizontal abscissa of the UAV location, y u denotes the horizontal ordinate of the UAV location, X denotes the maximum value of the horizontal abscissa of the UAV location, and Y denotes the maximum value of the horizontal ordinate of the UAV location.

[0153] Further, in the third step, the base station transmit power P, the common rate allocation C, the RIS phase shift Θ, and the UAV location w u are initialized, the maximum number of iterations n max is set, and the convergence precision ε is set.

[0154] Further, in the fourth step, the method for obtaining the joint optimization subproblem of the base station transmit power P and the common rate allocation C and converting it into an equivalent convex optimization problem is as follows:

[0155] First, the RIS phase shift Θ and the UAV location w u are fixed, and the joint optimization subproblem of the base station transmit power P and the common rate allocation C is obtained:

[0156]

[0157] s.t.C1~C5

[0158]

[0159] where τ1 is a relaxation variable introduced. It is noted that, given the RIS phase shift Θ and the UAV location w u , C2 and C5 are affine with respect to the optimization variables P and C, while C1, C3, C4, and C8 are all non-convex, and thus the subproblem is a non-convex optimization problem.

[0160] Let R s,k =C k +(f kp -g kp )-(f ec -g ec ) / K-(f ep -g ep ), R kc =f kc -gkc . where f kc , g kc , f kp , g kp , f ec , g ec , f ep , g ep are respectively:

[0161]

[0162] f kc , g kc are respectively R kc , g kp , f kp , g kp , f ec , g ec , f ec , g ep , f ep , g ep are respectively R kp , g kc , f ec , g ep are respectively R (n) .

[0163] Then, the optimization problem P2 can be rewritten as:

[0164]

[0165] s.t.C2, C5

[0166]

[0167] Using the SCA method, first-order Taylor expansion of g kp , g kc , f ec and f ep at the initial feasible point P (n) is performed to obtain the upper bounds and Replacing g 2.1 , g kp , f kc and f ec in the optimization problem P ep with their upper bounds, the equivalent convex optimization problem is obtained as:

[0168]

[0169] s.t.C2, C5

[0170]

[0171] Further, in the fifth step, the method for obtaining the RIS phase shift Θ optimization sub-problem and converting it into an equivalent convex optimization problem is:

[0172] First, fix the base station transmit power P, the common rate allocation C and the UAV position w u , let the channel gain η k = |v H H k | 2 , η e = |v H H e | 2 , where is an auxiliary variable introduced. The RIS phase shift Θ optimization sub-problem is obtained:

[0173]

[0174] s.t.C1, C3, C4, C6

[0175] Note that the objective function and constraints C1, C3 and C4 of the optimization problem P3 are all non-convex with respect to the variable v, which needs to be processed. Replace R kc , R kp and R ec , R ep with the lower bound and the upper bound respectively.

[0176] Therefore, the objective function can be rewritten as:

[0177]

[0178] The optimization problem P3 can be equivalently converted into a convex optimization sub-problem:

[0179]

[0180] s.t.C6

[0181]

[0182] where τ2 is a relaxation variable introduced.

[0183] Further, in the sixth step, the method for obtaining the UAV position w u optimization sub-problem and converting it into an equivalent convex optimization problem is:

[0184] First, fix the base station transmit power P, the common rate allocation C and the RIS phase shift Θ, and obtain the UAV position w u optimization sub-problem:

[0185]

[0186] s.t.C1, C3, C4, C7

[0187] Since the objective function and the constraints C1, C3 and C4 in the optimization problem P4 are all non-convex with respect to the optimization variable w u , the optimization problem P4 is a non-convex optimization problem and cannot be solved directly, which needs to be processed.

[0188] In order to facilitate processing, R kc , R kp and R ec , R ep are simplified respectively, and have:

[0189]

[0190]

[0191] where d r , d k , d e represent the distance between the base station and the RIS, the distance between the RIS and the legitimate user k and the distance between the RIS and the eavesdropper respectively; β0 represents the path loss exponent; B kc , D kc are the second terms of the numerator and the denominator in the fraction after simplification and transformation of R kc ; B kp , D kp are the second terms of the numerator and the denominator in the fraction after simplification and transformation of R kp ; B ec , D ec are the second terms of the numerator and the denominator in the fraction after simplification and transformation of R ec ; B ep , D ep are the second terms of the numerator and the denominator in the fraction after simplification and transformation of R ep ; B kc , B kp , B ec , B ep and D kc , D kp , D ec , D ep represent respectively:

[0192]

[0193] Due to the non-convexity of and , the relaxation variable The optimization problem P4 can be converted into:

[0194]

[0195] s.t.C7

[0196]

[0197] where the optimization problem P 4.1 The objective function can be written as:

[0198]

[0199] Since the change of the optimization variable w u will also affect the values of φ r , φ k and φ e , the B kc , B kp , B ec , B ep and D kc , D kp , D ec , D ep are complex functions of the optimization variable w u . In order to make the problem easy to handle, the B kc , B kp , B ec , B ep and D kc , D kp , D ec , D ep are replaced by their upper bounds and :

[0200] Substituting the upper bounds of B kc , B kp , B ec , B ep and D kc , D kp , D ec , D ep into the constraint C3″′ and the objective function, we can get:

[0201]

[0202] Since is a convex function minus two convex functions, it is still non-convex. Using the SCA method, by first-order Taylor expansion at the initial feasible point , we replace by its lower bound :

[0203]

[0204] where, represents the lower bound obtained after first order Taylor expansion at the initial feasible point .

[0205] Thus the inequality can be rewritten as:

[0206]

[0207] For the inequality the right hand side is a convex function in variable U, thus the inequality is a non-convex constraint. Using SCA method, first order Taylor expansion is performed at the initial feasible point to obtain:

[0208]

[0209] Thus, the inequality can be rewritten as a convex constraint:

[0210]

[0211] The constraints C10', C10" and C11', C11" in the optimization problem P 4.1 are also non-convex, which need to be handled. Using first order Taylor expansion, the upper bound of the non-convex term in C10', C10" and the lower bound of the non-convex term in C11', C11" are obtained.

[0212] In addition, since and in the constraints C11', C11" are concave functions, first order Taylor expansion is performed at the last iteration values and respectively:

[0213]

[0214] Thus, the optimization problem P 4.1 can be equivalently rewritten as a convex optimization subproblem:

[0215]

[0216] C7, C17

[0217] where, τ3 is the introduced slack variable.

[0218] Further, in the seventh step, the base station transmit power P, the common rate allocation C, the RIS phase shift Θ and the UAV position w are alternately iterated and optimized u until the minimum safety rate error value is less than a threshold value or a maximum iteration number is reached.

[0219] The systems, apparatuses, modules or units illustrated in the above embodiments can be specifically implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, the computer can be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

[0220] The computer readable medium includes permanent and non-permanent, removable and non-removable media, which can be implemented by any method or technology to store information. The information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read only memory (ROM), electrically erasable programmable read only memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information accessible by a computing device. According to the definition herein, computer readable medium does not include transitory computer readable media, such as modulated data signals and carriers.

[0221] It should also be noted that the terms "comprising", "including", or any other variant thereof are intended to cover non-exclusive inclusion, so that processes, methods, articles or devices including a series of elements not only include those elements, but also include other elements not explicitly listed, or other elements inherent in such processes, methods, articles or devices. Without more limitations, the element defined by the statement "including a" does not exclude the presence of additional identical elements in the process, method, article or device including the element.

[0222] The above embodiments should be understood as only illustrating the present application and not limiting the protection scope of the present application. After reading the description of the present application, those skilled in the art can make various changes or modifications to the present application, and these equivalent changes and modifications also fall within the scope defined by the claims of the present application.

Claims

1. A method for maximizing the minimum safe rate in a RIS-assisted unmanned aerial vehicle relay system, characterized in that, Includes the following steps: Step 1: Deploy a RIS-assisted UAV relay system with M reflector units. The UAV carries the RIS as an airborne relay to assist the base station in communicating with the legitimate user using the RSMA protocol. At the same time, there is an eavesdropper attempting to eavesdrop on the legitimate user's data information. Step 2: Considering fairness and communication reliability among legitimate users, construct the minimum safe rate maximization problem for the RIS-assisted UAV relay system. The optimization variables are the base station transmit power P, the common rate allocation C, the RIS phase shift Θ, and the UAV position w. u The public rate allocation C represents a portion of the transmission rate of public messages that is allocated and shared by legitimate users. Step 3: Initialize base station transmit power P, common rate allocation C, RIS phase shift Θ, and UAV position w. u Set the maximum number of iterations n max Convergence accuracy ε; Step 4: Fix RIS phase shift Θ and UAV position w u Solve for the base station transmit power P and the common rate allocation C; Step 5: Fixed base station transmit power P, common rate allocation C, and UAV location w u Solve for the RIS phase shift Θ; Step 6: Fix the base station transmit power P, common rate allocation C, and RIS phase shift Θ, and solve for the UAV position w. u ; Step 7: Iteratively optimize base station transmit power P, common rate allocation C, RIS phase shift Θ, and UAV position w. u This continues until the minimum safe rate error value is less than the threshold or the maximum number of iterations is reached.

2. The method for maximizing the minimum safe rate of a RIS-assisted UAV relay system according to claim 1, characterized in that, In step one, the UAV relay system model is as follows: Consider a RIS-assisted drone relay secure communication system. The model consists of a base station, a drone equipped with a RIS, K legitimate users, and an eavesdropper, where the base station, legitimate users, and eavesdropper are all equipped with a single antenna. The transmitted signal at the base station is represented as follows: s c and s k Let p represent the public message transmitted at the base station and the private message of the kth legitimate user, respectively. c and p k They are s c and s k Given the transmission power, the signals received at the legitimate user k and the eavesdropper are respectively expressed as: Among them, h k h e and h r These represent the channel gains from RIS to legitimate user k, from RIS to the eavesdropper, and from the base station to RIS, respectively. Let k represent the additive white Gaussian noise at the legitimate user's location and the eavesdropper's location, respectively. According to the RSMA principle, the instantaneous signal-to-interference-plus-noise ratio (SIRR) for decoding public and private messages at legitimate user k is expressed as follows: in, Let be the noise variance at the legitimate user k. Therefore, the instantaneous reach rate of legitimate user k decoding public and private messages per unit bandwidth is expressed as follows: R kc =log2(1+Γ c,k ) R kp =log2(1+Γ p,k ) To ensure that public messages can be successfully decoded by all users, the actual transmission rate R of public messages is... c The rate does not exceed the minimum reachability of public messages among all legitimate users, i.e., R. c Satisfy R c ≤min k∈K R kc Additionally, R c Shared by all legitimate users, each legitimate user k is assigned to R. c Part of C k Common rate allocation vectors C1, C2, ..., C K It should satisfy ∑ k∈K C k =R c Therefore, the total reachability rate of a legitimate user k is expressed as: R k,tot =C k +R kp The achievable eavesdropping rates for an eavesdropper to decode public messages and private messages from a legitimate user (k) are expressed as follows: R ec =log2(1+Γ ec ) in, and Let the signal-to-interference-plus-noise ratios (SIRs) at the eavesdropper's location for decoding public messages and at the location of legitimate user k for decoding private messages be expressed as follows: in, Let be the noise variance at the eavesdropper's location; assuming that the eavesdropping rate of public messages at the eavesdropper's location is evenly distributed to each legitimate user, then the total eavesdropping rate of legitimate user k can be expressed as: Finally, the safe rate for a legitimate user k is defined as follows: Where, [x] + =max{x,0},[·] + This can be omitted because, in the optimal solution, the security rate R corresponding to each legitimate user is... s,k At least 0.

3. The method for maximizing the minimum safe rate of a RIS-assisted UAV relay system according to claim 2, characterized in that, In step two, the minimum safe rate maximization optimization problem is: Among them, constraint C1 is the minimum rate requirement constraint for each legitimate user. Represents the minimum rate requirement for each legitimate user, constraint C2 is the maximum transmit power constraint at the base station, p max θ represents the maximum transmit power at the base station. Constraint C3 ensures that every legitimate user can decode the common stream; constraint C4 ensures that the common stream cannot be fully decoded by an eavesdropper; constraint C5 indicates that the common rate allocated to each legitimate user is non-negative; constraint C6 represents the phase shift constraint for each reflection unit of the RIS. m This represents the reflection phase of each reflection unit in the RIS; constraint C7 indicates that the UAV is deployed within a certain area, x u The horizontal coordinate of the drone's position, y u The horizontal coordinate of the drone's position is represented by X, where X represents the maximum value of the horizontal coordinate of the drone's position, and Y represents the maximum value of the horizontal coordinate of the drone's position.

4. The method for maximizing the minimum safe rate of a RIS-assisted UAV relay system according to claim 3, characterized in that, In step four, the joint optimization subproblem of base station transmit power P and common rate allocation C is obtained, and then transformed into an equivalent convex optimization problem. First, fix the RIS phase shift Θ and the UAV position w. u This yields a joint optimization subproblem of base station transmit power P and common rate allocation C: Where τ1 is an introduced relaxation variable, given the RIS phase shift Θ and the UAV position w u In this case, C2 and C5 are affine with respect to the optimization variables P and C, while C1, C3, C4 and C8 are nonconvex. Therefore, this subproblem is a nonconvex optimization problem. Let R s,k =C k +(f kp -g kp )-(f ec -g ec ) / K-(f ep -g ep ), R kc =f kc -g kc ; where f kc g kc f kp g kp f ec g ec f ep g ep They are respectively: f kc g kc They are R kc The first and second terms after transforming into the form of the subtraction of two functions, f kp g kp They are R kp The first and second terms after transforming into the form of the subtraction of two functions, f ec g ec They are R ec The first and second terms after transforming into the form of the subtraction of two functions, f ep g ep They are R ep The first and second terms after transforming into the form of subtracting two functions; Then, the optimization problem P2 can be rewritten as: Using the SCA method, respectively for g kp g kc f ec and f ep At the initial feasible point P (n) Performing a first-order Taylor expansion at the given point yields the upper bound. and The optimization problem P 2.1 g kp g kc f ec and f ep Replacing them with their upper bounds respectively, we can obtain an equivalent convex optimization problem: 。 5. The method for maximizing the minimum safe rate of a RIS-assisted UAV relay system according to claim 4, characterized in that, In step five, the method for obtaining the RIS phase shift Θ optimization subproblem and converting it into an equivalent convex optimization problem is as follows: First, fix the base station transmit power P, the common rate allocation C, and the drone location w. u Increase channel gain in The RIS phase shift Θ optimization subproblem is obtained by introducing auxiliary variables: The objective function and constraints C1, C3, and C4 of optimization problem P3 are all non-convex with respect to the variable v, and need to be addressed; R kc R kp and R ec R ep Using the lower bound respectively and the Upper Realm Substitute; Therefore, the objective function can be rewritten as: The optimization problem P3 can be equivalently transformed into a convex optimization subproblem: Here, τ2 is the introduced slack variable.

6. The method for maximizing the minimum safe rate of a RIS-assisted UAV relay system according to claim 5, characterized in that, In step six, the location w of the UAV is obtained. u The steps to optimize a subproblem and transform it into an equivalent convex optimization problem are as follows: First, fix the base station transmit power P, common rate allocation C, and RIS phase shift Θ to obtain the UAV position w. u Optimization subproblems: Because the objective function and constraints C1, C3, and C4 in optimization problem P4 have certainty regarding the optimization variable w u Since all of them are non-convex, optimization problem P4 is a non-convex optimization problem that cannot be solved directly and needs to be processed. For ease of processing, R is processed separately. kc R kp and R ec R ep After simplification, we have: Where, d r d k d e These represent the distances from the base station to the RIS, the distance from the RIS to the legitimate user k, and the distance from the RIS to the eavesdropper, respectively; β0 represents the path loss exponent; B kc D kc R respectively kc The second term in the numerator and denominator of the simplified fraction; B kp D kp R respectively kp The second term in the numerator and denominator of the simplified fraction; B ec D ec R respectively ec The second term in the numerator and denominator of the simplified fraction; B ep D ep R respectively ep The second term in the numerator and denominator of the simplified fraction; B kc B kp B ec B ep and D kc D kp D ec D ep They are represented as follows: because and Nonconvexity, introducing slack variables The optimization problem P4 can be transformed into: Among them, the optimization problem P 4.1 The objective function can be written as: Because during the iteration process, the optimization variable w u Changes will also affect φ r φ k and φ e The value of B, therefore, kc B kp B ec B ep and D kc D kp D ec D ep It's about the optimization variable w. u Complex functions; to make the problem easier to handle, B... kc B kp B ec B ep and D kc D kp D ec D ep Use their upper bounds and Replace: B kc B kp B ec B ep and D kc D kp D ec D ep Substituting the upper bound into constraint C3″′ and the objective function, we can obtain: because It is a convex function minus two convex functions, therefore it is still nonconvex; applying the SCA method to it, through the initial feasible point... Perform a first-order Taylor expansion at the point Use its lower bound replace: in, Indicates to At the initial feasible point The lower bound obtained by performing a first-order Taylor expansion at that point; therefore It can be rewritten as: For inequalities The right-hand side of the inequality is a convex function with respect to variable U; therefore, the inequality is a non-convex constraint. Applying the SCA method to it, at the initial feasible point... Performing a first-order Taylor expansion at this point, we obtain: Therefore, the inequality This can be rewritten as a convex constraint: Optimization problem P 4.1 The constraints C10′, C10″ and C11′, C11″ are also nonconvex and need to be processed. A first-order Taylor expansion is used to obtain the nonconvex terms in C10′ and C10″. The upper realm and the non-convex terms in C11′ and C11″ lower bound Furthermore, due to constraints C11′ and C11″ and For a concave function, it is necessary to consider the values ​​from the previous iteration. and Perform a first-order Taylor expansion at this point: Therefore, the optimization problem P 4.1 It can be equivalently rewritten as a convex optimization subproblem: Here, τ3 is the introduced slack variable.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the minimum safe rate maximization method for a RIS-assisted unmanned aerial vehicle relay system as described in any one of claims 1 to 6.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the minimum safe rate maximization method for the RIS-assisted unmanned aerial vehicle relay system as described in any one of claims 1 to 6.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the minimum safe rate maximization method for the RIS-assisted unmanned aerial vehicle relay system as described in any one of claims 1 to 6.

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