Rate optimization method for IRS-assisted multi-unmanned aerial vehicle NOMA communication system

Abstract

The invention belongs to the technical field of wireless communication, and particularly relates to an IRS-assisted multi-unmanned aerial vehicle NOMA communication system rate optimization method, which comprises the following steps: step 1, constructing an IRS-assisted multi-unmanned aerial vehicle NOMA communication system rate optimization model; 2, initializing an unmanned aerial vehicle position Q, an SIC decoding sequence A, an IRS reflection matrix theta, an unmanned aerial vehicle transmitting power P and a judgment threshold value epsilon; according to the method, under the constraint conditions of the SIC decoding sequence, the two-dimensional position of the UAV, the IRS reflection matrix and the UAV transmitting power, the four variables are jointly optimized, and the sum rate of the IRS-assisted UAV communication system is optimized; binary variables are introduced to participate in channel state sorting, different from a traditional channel condition sorting method, the method adopts a block coordinate descent method, a continuous convex approximation (SCA) method and a penalty-based method to approach a globally optimal solution, and compared with other resource allocation schemes of a network without IRS assistance, the method provided by the invention has the advantages that the system rate is increased, and the system performance is improved. And the method has better practicability and feasibility.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to an IRS-assisted multi-UAV NOMA communication system rate optimization method. Background Art

[0002] Nowadays, the popularity of IoT has triggered a surge in 5G and B5G mobile data traffic. When faced with problems such as overload of ground base stations (BS) caused by a surge in the number of user accesses, or a serious shortage of base stations in emergency relief areas, it is not feasible and too costly to increase ground communication infrastructure in a short period of time. Unmanned aerial vehicles (UAVs) are considered to be a feasible and promising solution to this problem. By carrying base stations on mobile drones to assist ground base station communications, paralyzed communication services can be quickly restored and network coverage can be effectively improved.

[0003] Non-Orthogonal Multiple Access (NOMA) technology is considered to be an effective way to solve problems such as limited network access, high latency, poor reliability and low throughput, and is considered to be one of the most promising wireless access technologies in B5G and 6G. NOMA supports ultra-high density of users and devices to access the network, maintains high-speed network traffic and improves spectrum utilization, and realizes large-scale user and device connections. Its application prospects are far-reaching and it is currently the focus of scientific research by many scholars.

[0004] Intelligent Reflecting Surface (IRS) is a new revolutionary technology that can significantly improve the performance of wireless communication networks by intelligently reconfiguring the wireless propagation environment by integrating a large number of low-cost passive reflective elements on a plane.

[0005] At present, through the study of UAV network resource allocation methods for IRS-assisted communication, it is found that many schemes consider relatively simple scenarios, a small number of users, a relatively single user channel state sorting method of SIC, and fewer variables for joint optimization, resulting in less practicality of the methods and making them difficult to apply to actual scenarios.

[0006] Therefore, in view of the situation where there are many ground users and the channel status order is uncertain, we propose an optimization method that jointly optimizes multiple variables and introduces binary variables to participate in the ordering of user channel states. Since the entire optimization problem is a mixed integer non-convex optimization problem, optimizing this problem is a technical challenge. Summary of the invention

[0007] 1. Technical issues to be solved

[0008] In view of the shortcomings of the prior art, the present invention provides an IRS-assisted multi-UAV NOMA communication system rate optimization method, which solves the problems raised in the above background technology.

[0009] (II) Technical solution

[0010] In order to achieve the above-mentioned purpose, the present invention specifically adopts the following technical solutions:

[0011] An IRS-assisted multi-UAV NOMA communication system rate optimization method comprises the following steps:

[0012] Step 1: Build an IRS-assisted multi-UAV NOMA communication system rate optimization model;

[0013] Step 2: Initialize the UAV position Q, SIC decoding order A, IRS reflection matrix Θ, UAV transmission power P and decision threshold ε;

[0014] Step 3: Given the IRS reflection matrix Θ and the UAV transmit power P, solve the UAV position Q and SIC decoding order A;

[0015] Step 4: Given the UAV position Q, UAV transmit power P, and SIC decoding order A, solve the IRS reflection matrix Θ. At this time, the given UAV position and SIC decoding order are obtained from step 3.

[0016] Step 5: Given the given UAV position Q, SIC decoding order A, and IRS reflection matrix Θ, solve the UAV transmission power P. At this time, the given UAV position, SIC decoding order, and IRS reflection matrix Θ are solved by steps 3 and 4;

[0017] Step 6: Iterate the algorithm until the difference between the two objective function values ​​is less than or equal to the decision threshold ε, and give the maximum sum rate of the system.

[0018] Furthermore, in step 1, an IRS-assisted multi-UAV NOMA communication system rate optimization model is established, and the optimization problem is problem 1, which can be described as:

[0019]

[0020] in represents the expected rate of the system, Θ is the IRS reflection matrix, θ m represents the reflection phase shift of the mth reflection element, represents the expected power gain of the UAV-to-user link superimposed on the reflected link through the IRS, is a function of the drone position q and the reflection matrix Θ, p k,iIt is the transmission power of the k-th UAV sending information to the i-th user in the k-th group, P max is the maximum transmit power of the drone, It is represented as the decoding order of the user's SIC, When , it means that user t decodes user i. The drones and user groups have a corresponding relationship, that is, the kth drone serves the kth group of users, and the number of users is M. k , the set index of each group of users is M k , N represents N reflective elements, q k represents the position of the kth UAV, and represents the t-th user and the i-th user in the k-th group, σ 2 Represents system noise, which obeys Gaussian distribution. The optimization variables of problem one are the two-dimensional position Q of the drone, the decoding order A of SIC, the IRS reflection matrix Θ, and the transmission power P of the drone. The objective function of problem one represents the sum rate of users. The first constraint represents the safety distance constraint of the drone, the second constraint represents the IRS reflection phase shift constraint, the third constraint to the fifth constraint represent the transmission power constraint of the drone, the sixth constraint represents the constraint of the SIC decoding order, and the seventh constraint represents avoiding the situation where two users are at the same distance from the drone and cannot distinguish between strong and weak users. Using the block coordinate descent method, problem one is decomposed into three sub-problems, which are solved by alternating optimization.

[0021] Furthermore, in step 2, the position of the UAV is initialized to q=(x, y, H), the SIC decoding order is A, the IRS reflection matrix is ​​Θ, the UAV transmission power is P, the decision threshold is ε, and the height H of the UAV is a fixed value.

[0022] Furthermore, in step 3, the given IRS reflection matrix Θ and the UAV transmission power P are used to solve the UAV position Q and the NOMA decoding order A. Subproblem 1 (problem 2) can be described as:

[0023]

[0024]

[0025] in, is a set of auxiliary variables, represents the upper bound of the distance between the drone and the service user, represents the lower bound of the distance between the drone and the unserved users, represents the upper bound of the distance between the drone and the IRS, represents the lower bound of the UAV and IRS,

[0026] , where ρ0 is the path loss exponent per unit distance, β 1 is the path fading index between the UAV and the user,

[0027] β 2 is the path fading index between IRS and user, represents the Loss component between IRS and UAV, where is the cosine of the angle of arrival from the UAV to the IRS, K 1 and K 2 represents the Rice factor,

[0028] Problem 2 is a non-convex optimization problem. It is necessary to transform the objective function and constraints, write constraint (11) as a penalty term, and make Problem 2 equivalent to Problem 3. Problem 3 can be described as:

[0029]

[0030] Among them, ζ>0 is the penalty coefficient, penalizing the optimization variable When , the problem is still non-convex, and the continuous convex approximation method is used. To express the objective function of problem 3, assume that the point given after the nth SCA is Using the first-order Taylor formula to expand at this point, we get an upper bound:

[0031]

[0032] in and The first-order Taylor expansion is as follows:

[0033]

[0034] Constraint (1), the upper and lower bounds of the distance, and constraint (9) can all be replaced by the first-order Taylor expansion formula to obtain the global lower bound. Constraints (10) and (11) involve the position of the drone, which causes the arrival angle to change. Assuming that the position change of the drone in each SCA iteration is small, the arrival angle of the nth iteration is approximately unchanged. is also approximately unchanged. On this basis, the right-hand side of constraints (10) and (11) can be regarded as the sum of two convex functions:

[0035] The original formula is The distance constraint for SCA after n times gives the point The first-order Taylor expansion gives the global lower bound as follows:

[0036]

[0037] in:

[0038]

[0039]

[0040] Same reason and The same method is also used to transform problem 3 into a convex optimization problem after problem transformation and constraint transformation. Its optimal solution can be solved by convex optimization tools such as CVX.

[0041] Furthermore, in step 4, given Q, A, and P, the IRS reflection matrix Θ is optimized, and sub-problem 2 (problem 4) can be described as:

[0042]

[0043] The above problem is a non-convex problem, so rewrite it as The first item is:

[0044]

[0045] The rewritten formula is:

[0046]

[0047] in, V satisfies the constraints: V is a semi-positive definite matrix, the rank of V is 1 and all the elements on the diagonal of V are 1. Rewrite for:

[0048]

[0049] in

[0050]

[0051]

[0052] Therefore, Question 4 can be equivalent to Question 5, which can be described as:

[0053]

[0054] st[V] nn =1,n=1,2,...,N+1

[0055] V ≥ 0

[0056] rank(V)=1

[0057] According to the semidefinite relaxation method, ignoring the third constraint, the original formula can be solved by solving the lower bound approximation problem. Through the SCA technology, at the point V after the nth iteration of SCA, (n) Place, right Performing a first-order Taylor expansion gives the upper bound Problem 5 becomes a convex optimization problem, but the solution obtained may not satisfy rank(V)=1, so it is necessary to construct a solution with rank(V)=1. Use the maximum eigenvalue method to construct a solution with rank 1 from the optimal solution of Problem 5.

[0058] The specific steps of the method for constructing a solution with rank 1 by the maximum eigenvalue method are as follows: Perform eigenvalue decomposition so that where U∈ (N+1)×(N+1) is the eigenvector matrix, Λ=diag∈{λ 1 ,λ 2 ,...,λ n+1}∈ (N+1)×(N+1) is the eigenvalue diagonal matrix; then find the largest eigenvalue λ max And the corresponding eigenvector u max , the solution of rank 1 is constructed as

[0059] Furthermore, in step 5, given Q, A, θ, the transmission power P of the UAV is optimized, and sub-problem 3 (problem 6) can be described as:

[0060]

[0061] in, and The expression is as follows:

[0062]

[0063] g k.i is a concave function about p, At point P (n) In the first-order Taylor expansion, we get The upper bound of The original problem is rewritten as Question 7, which is described as follows:

[0064]

[0065] The first-order Taylor expansion is a linear approximate expression, and the negative logarithmic function is a convex function, so the problem becomes a linear function plus a convex function. At this time, the problem is a convex optimization problem, which can be solved using CVX or the convex optimization interior point method.

[0066] Further, in step 6, when When , the algorithm converges and obtains the maximum sum rate of the communication system. If the above situation is not met, the algorithm continues to iterate until the algorithm converges.

[0067] (III) Beneficial effects

[0068] Compared with the prior art, the present invention provides an IRS-assisted multi-UAV NOMA communication system rate optimization method, which has the following beneficial effects:

[0069] 1. The present invention jointly optimizes four variables under the constraints of SIC decoding order, two-dimensional position of UAV, IRS reflection matrix, and UAV transmission power, and optimizes the sum rate of the IRS-assisted UAV communication system.

[0070] 2. Binary variables are introduced to participate in channel state sorting. Different from the traditional channel condition sorting method, the present invention adopts block coordinate descent method, successive convex approximation (SCA) and penalty-based method to approximate the global optimal solution. Compared with other resource allocation schemes of networks without IRS assistance, the method provided by the present invention improves the system rate and has better practicality and feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 This is a flow chart of a rate optimization method for an IRS-assisted multi-UAV NOMA communication system of the present invention;

[0072] Figure 2 This is a model diagram of the IRS-assisted multi-UAV NOMA communication system of the present invention;

[0073] Figure 3 The system and rate convergence diagrams obtained under different conditions of the maximum transmission power and the number of IRS reflective elements of the UAV of the present invention. DETAILED DESCRIPTION

[0074] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0075] Example

[0076] like Figure 1-3 As shown, an IRS-assisted multi-UAV NOMA communication system rate optimization method proposed in one embodiment of the present invention includes the following steps:

[0077] Step 1: Build an IRS-assisted multi-UAV NOMA communication system rate optimization model;

[0078] Step 2: Initialize the UAV position Q, SIC decoding order A, IRS reflection matrix Θ, UAV transmission power P and decision threshold ε;

[0079] Step 3: Given the IRS reflection matrix Θ and the UAV transmit power P, solve the UAV position Q and SIC decoding order A;

[0080] Step 4: Given the UAV position Q, UAV transmit power P, and SIC decoding order A, solve the IRS reflection matrix Θ. At this time, the given UAV position and SIC decoding order are obtained from step 3.

[0081] Step 5: Given the given UAV position Q, SIC decoding order A, and IRS reflection matrix Θ, solve the UAV transmission power P. At this time, the given UAV position, SIC decoding order, and IRS reflection matrix Θ are solved by steps 3 and 4;

[0082] Step 6: Iterate the algorithm until the difference between the two objective function values ​​is less than or equal to the decision threshold ε, and give the maximum sum rate of the system.

[0083] In this embodiment, in step 1, an IRS-assisted multi-UAV NOMA communication system rate optimization model is established, and the optimization problem is problem 1, which can be described as:

[0084]

[0085] in represents the expected rate of the system, Θ is the IRS reflection matrix, θ m represents the reflection phase shift of the mth reflection element, represents the expected power gain of the UAV-to-user link superimposed on the reflected link through the IRS, is a function of the drone position q and the reflection matrix Θ, p k,i It is the transmission power of the k-th UAV sending information to the i-th user in the k-th group, P max is the maximum transmit power of the drone, It is represented as the decoding order of the user's SIC, When , it means that user t decodes user i. The drones and user groups have a corresponding relationship, that is, the kth drone serves the kth group of users, and the number of users is M. k , the set index of each group of users is M k , N represents N reflective elements, q k represents the position of the kth UAV, and represents the t-th user and the i-th user in the k-th group, σ 2 Represents system noise, which obeys Gaussian distribution. The optimization variables of problem one are the two-dimensional position Q of the drone, the decoding order A of SIC, the IRS reflection matrix Θ, and the transmission power P of the drone. The objective function of problem one represents the sum rate of users. The first constraint represents the safety distance constraint of the drone, the second constraint represents the IRS reflection phase shift constraint, the third constraint to the fifth constraint represent the transmission power constraint of the drone, the sixth constraint represents the constraint of the SIC decoding order, and the seventh constraint represents avoiding the situation where two users are at the same distance from the drone and cannot distinguish between strong and weak users. Using the block coordinate descent method, problem one is decomposed into three sub-problems, which are solved by alternating optimization.

[0086] In this embodiment, in step 2, the position of the UAV is initialized to q = (x, y, H), the SIC decoding order is A, the IRS reflection matrix is ​​Θ, the UAV transmission power is P, the decision threshold is ε, and the height H of the UAV is a fixed value.

[0087] In this embodiment, in step 3, the given IRS reflection matrix Θ and the drone transmission power P are used to solve the drone position Q and the NOMA decoding order A. Subproblem 1 (problem 2) can be described as:

[0088]

[0089]

[0090] in, is a set of auxiliary variables, represents the upper bound of the distance between the drone and the service user, represents the lower bound of the distance between the drone and the unserved users, represents the upper bound of the distance between the drone and the IRS, represents the lower bound of the UAV and IRS,

[0091] , where ρ 0 is the path loss exponent per unit distance, β 1 is the path fading index between the UAV and the user,

[0092] β 2 is the path fading index between IRS and user, represents the Loss component between IRS and UAV, where is the cosine of the angle of arrival from the UAV to the IRS, K 1 and K 2 represents the Rice factor,

[0093] Problem 2 is a non-convex optimization problem. It is necessary to transform the objective function and constraints, write constraint (11) as a penalty term, and make Problem 2 equivalent to Problem 3. Problem 3 can be described as:

[0094]

[0095]

[0096] Among them, ζ>0 is the penalty coefficient, penalizing the optimization variable When , the problem is still non-convex, and the continuous convex approximation method is used. To express the objective function of problem 3, assume that the point given after the nth SCA is Using the first-order Taylor formula to expand at this point, we get an upper bound:

[0097]

[0098] in and The first-order Taylor expansion is as follows:

[0099]

[0100] Constraint (1), the upper and lower bounds of the distance, and constraint (9) can all be replaced by the first-order Taylor expansion formula to obtain the global lower bound. Constraints (10) and (11) involve the position of the drone, which causes the arrival angle to change. Assuming that the position change of the drone in each SCA iteration is small, the arrival angle of the nth iteration is approximately unchanged. is also approximately unchanged. On this basis, the right-hand side of constraints (10) and (11) can be regarded as the sum of two convex functions:

[0101] The original formula is The distance constraint for SCA after n times gives the point The first-order Taylor expansion gives the global lower bound as follows:

[0102]

[0103] in:

[0104]

[0105] Same reason and The same method is also used to transform problem 3 into a convex optimization problem after problem transformation and constraint transformation. Its optimal solution can be solved by convex optimization tools such as CVX.

[0106] In this embodiment, in step 4, given Q, A, and P, the IRS reflection matrix Θ is optimized, and sub-problem 2 (problem 4) can be described as:

[0107]

[0108] The above problem is a non-convex problem, so rewrite it as The first item is:

[0109]

[0110] The rewritten formula is:

[0111]

[0112] in, V=vv H , v=[θ T 1] T , V satisfies the constraints: V is a semi-positive definite matrix, the rank of V is 1 and all the elements on the diagonal of V are 1. Rewrite R k,i for:

[0113]

[0114] in

[0115]

[0116] make

[0117]

[0118] Therefore, Question 4 can be equivalent to Question 5, which can be described as:

[0119]

[0120] According to the semidefinite relaxation method, ignoring the third constraint, the original formula can be solved by solving the lower bound approximation problem. Through the SCA technology, at the point V after the nth iteration of SCA, (n) Place, right Performing a first-order Taylor expansion gives the upper bound Problem 5 becomes a convex optimization problem, but the solution obtained may not satisfy rank(V)=1, so it is necessary to construct a solution with rank(V)=1. Use the maximum eigenvalue method to construct a solution with rank 1 from the optimal solution of Problem 5.

[0121] The specific steps of the method for constructing a solution with rank 1 by the maximum eigenvalue method are as follows: Perform eigenvalue decomposition so that where U∈ (N+1)×(N+1) is the eigenvector matrix, Λ=diag∈{λ 1 ,λ 2 ,...,λ n+1}∈ (N+1)×(N+1) is the eigenvalue diagonal matrix; then find the largest eigenvalue λ max And the corresponding eigenvector u max , the solution of rank 1 is constructed as

[0122] In this embodiment, in step 5, given Q, A, Θ, the transmission power P of the drone is optimized, and sub-problem three (problem six) can be described as:

[0123]

[0124] in, and The expression is as follows:

[0125]

[0126] g k.i is a concave function about p, At point P (n) In the first-order Taylor expansion, we get The upper bound of The original problem is rewritten as Question 7, which is described as follows:

[0127]

[0128] The first-order Taylor expansion is a linear approximate expression, and the negative logarithmic function is a convex function, so the problem becomes a linear function plus a convex function. At this time, the problem is a convex optimization problem, which can be solved using CVX or the convex optimization interior point method.

[0129] In this embodiment, in step 6, when When , the algorithm converges and obtains the maximum sum rate of the communication system. If the above situation is not met, the algorithm continues to iterate until the algorithm converges.

[0130] The present invention optimizes the sum rate of the entire system under the constraints of SIC decoding order, two-dimensional position of UAV, IRS reflection matrix, and UAV transmission power. The innovation of the present invention lies in that the two-dimensional position of the UAV is highly coupled with the SIC decoding order, and binary variables are introduced to participate in the channel state sorting. Different from the traditional channel condition sorting method, the present invention adopts block coordinate descent method, successive convex approximation (SCA) and penalty-based method to approximate the global optimal solution. Compared with other resource allocation schemes of networks without IRS assistance, the method provided by the present invention improves the system rate and has better practicality and feasibility.

[0131] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An IRS-assisted multi-UAV NOMA communication system rate optimization method, characterized by: The following steps are involved: Step 1: Build an IRS-assisted multi-UAV NOMA communication system rate optimization model; Step 2: Initialize the UAV position Q, SIC decoding order A, IRS reflection matrix Θ, UAV transmission power P and decision threshold ε; Step 3: Given the IRS reflection matrix Θ and the UAV transmit power P, solve the UAV position Q and SIC decoding order A; Step 4: Given the UAV position Q, UAV transmit power P, and SIC decoding order A, solve the IRS reflection matrix Θ. At this time, the given UAV position and SIC decoding order are obtained from step 3. Step 5: Given the given UAV position Q, SIC decoding order A, and IRS reflection matrix Θ, solve the UAV transmission power P. At this time, the given UAV position, SIC decoding order, and IRS reflection matrix Θ are solved by steps 3 and 4; Step 6: Iterate the algorithm until the difference between the two objective function values ​​is less than or equal to the decision threshold ε, and give the maximum sum rate of the system.

2. According to claim 1, an IRS-assisted multi-UAV NOMA communication system rate optimization method is characterized by: In step 1, an IRS-assisted multi-UAV NOMA communication system rate optimization model is established. The optimization problem is problem 1, which can be described as: p k,i ≥0,k∈{1,2},i∈M k , (3) in represents the expected rate of the system, Θ is the IRS reflection matrix, θ m represents the reflection phase shift of the mth reflection element, represents the expected power gain of the UAV-to-user link superimposed on the reflected link through the IRS, is a function of the drone position q and the reflection matrix Θ, p k,i It is the transmission power of the k-th UAV sending information to the i-th user in the k-th group, P max is the maximum transmit power of the drone, It is represented as the decoding order of the user's SIC, When , it means that user t decodes user i. The drones and user groups have a corresponding relationship, that is, the kth drone serves the kth group of users, and the number of users is M. k , the set index of each group of users is M k , N represents N reflective elements, q k represents the position of the kth UAV, and represents the t-th user and the i-th user in the k-th group, σ 2 Represents system noise, which obeys Gaussian distribution. The optimization variables of problem one are the two-dimensional position Q of the drone, the decoding order A of SIC, the IRS reflection matrix Θ, and the transmission power P of the drone. The objective function of problem one represents the sum rate of users. The first constraint represents the safety distance constraint of the drone, the second constraint represents the IRS reflection phase shift constraint, the third constraint to the fifth constraint represent the transmission power constraint of the drone, the sixth constraint represents the constraint of the SIC decoding order, and the seventh constraint represents avoiding the situation where two users are at the same distance from the drone and cannot distinguish between strong and weak users. Using the block coordinate descent method, problem one is decomposed into three sub-problems, which are solved by alternating optimization.

3. According to claim 2, an IRS-assisted multi-UAV NOMA communication system rate optimization method is characterized by: In step 2, the position of the drone is initialized to q=(x, y, H), the SIC decoding order is A, the IRS reflection matrix is ​​Θ, the drone transmission power is P, the decision threshold is ε, and the drone height H is a fixed value.

4. The IRS-assisted multi-UAV NOMA communication system rate optimization method according to claim 3 is characterized by: In step 3, the given IRS reflection matrix Θ and the UAV transmission power P are used to solve the UAV position Q and the NOMA decoding order A. Subproblem 1 (problem 2) can be described as: (1)(5)(6)(7) in, is a set of auxiliary variables, represents the upper bound of the distance between the drone and the service user, represents the lower bound of the distance between the drone and the unserved users, represents the upper bound of the distance between the drone and the IRS, represents the lower bound of the UAV and IRS, , where ρ0 is the path loss index per unit distance, β1 is the path fading index between the drone and the user, β2 is the path fading index between IRS and user, represents the Loss component between IRS and UAV, where is the cosine of the arrival angle from the drone to the IRS, K1 and K2 represent the Rice factors, Problem 2 is a non-convex optimization problem. It is necessary to transform the objective function and constraints, write constraint (11) as a penalty term, and make Problem 2 equivalent to Problem 3. Problem 3 can be described as: st(1)(5)-(15) Among them, ζ>0 is the penalty coefficient, penalizing the optimization variable When , the problem is still non-convex, and the continuous convex approximation method is used. To express the objective function of problem 3, assume that the point given after the nth SCA is Using the first-order Taylor formula to expand at this point, we get an upper bound: in and The first-order Taylor expansion is as follows: Constraint (1), the upper and lower bounds of the distance, and constraint (9) can all be replaced by the first-order Taylor expansion formula to obtain the global lower bound. Constraints (10) and (11) involve the position of the drone, which causes the arrival angle to change. Assuming that the position change of the drone in each SCA iteration is small, the arrival angle of the nth iteration is approximately unchanged. is also approximately unchanged. On this basis, the right-hand side of constraints (10) and (11) can be regarded as the sum of two convex functions: The original formula is The distance constraint for SCA after n times gives the point The first-order Taylor expansion gives the global lower bound as follows: in: Same reason and The same method is also used to transform problem 3 into a convex optimization problem after problem transformation and constraint transformation. Its optimal solution can be solved by convex optimization tools such as CVX.

5. The IRS-assisted multi-UAV NOMA communication system rate optimization method according to claim 4 is characterized by: In step 4, given Q, A, and P, the IRS reflection matrix Θ is optimized, and sub-problem 2 (problem 4) can be described as: st(2) The above problem is a non-convex problem, so rewrite it as The first item is: The rewritten formula is: in, V=vv H , V satisfies the constraints: V is a semi-positive definite matrix, the rank of V is 1 and all the elements on the diagonal of V are 1. Rewrite for: in make Therefore, Question 4 can be equivalent to Question 5, which can be described as: s.t.[V] nn =1,n=1,2,...,N+1 V≥0 rank(V)=1 According to the semidefinite relaxation method, ignoring the third constraint, the original formula can be solved by solving the lower bound approximation problem. Through the SCA technology, at the point V after the nth iteration of SCA, (n) Place, right Performing a first-order Taylor expansion gives the upper bound Problem 5 becomes a convex optimization problem, but the solution obtained may not satisfy rank(V)=1, so it is necessary to construct a solution with rank(V)=1. Use the maximum eigenvalue method to construct a solution with rank 1 from the optimal solution of Problem 5. The specific steps of the method for constructing a solution with rank 1 by the maximum eigenvalue method are as follows: Perform eigenvalue decomposition so that where U∈ (N+1)×(N+1) is the eigenvector matrix, Λ=diag∈{λ1,λ2,...,λ n+1 }∈ (N+1)×(N+1) is the eigenvalue diagonal matrix; then find the largest eigenvalue λ max And the corresponding eigenvector u max , the solution of rank 1 is constructed as 6. The IRS-assisted multi-UAV NOMA communication system rate optimization method according to claim 5 is characterized in that: In step 5, given Q, A, θ, the transmission power P of the UAV is optimized, and sub-problem 3 (problem 6) can be described as: st(3)(4)(5) in, and The expression is as follows: is a concave function about p, At point P (n) In the first-order Taylor expansion, we get The upper bound of The original problem is rewritten as Question 7, which is described as follows: st(3)(4)(5) At this time, the problem is a convex optimization problem, which can be solved using CVX or using the convex optimization interior point method.

7. The IRS-assisted multi-UAV NOMA communication system rate optimization method according to claim 6 is characterized by: In step 6, when When , the algorithm converges and obtains the maximum sum rate of the communication system. If the above situation is not met, the algorithm continues to iterate until the algorithm converges.

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