Sum rate maximization method for NOMA UAV communication system under user location uncertainty

Abstract

The present invention seeks to protect a method for maximizing the sum rate of a non-orthogonal multiple access (NOMA) drone communication system under uncertain user positions, comprising: initializing the maximum number of iterations and the maximum error factor, user power allocation, drone position, binary decoding order initial value, and user rate; according to the given initial values, calculating the user rate, user allocation power, drone position, and binary decoding order through an inner layer iterative algorithm; if the user rate meets the judgment condition of error accuracy, outputting the user rate and entering the outer layer algorithm; otherwise, iteratively updating the user allocation power, drone position, binary decoding order initial value, and user rate. In the outer layer algorithm, it is determined whether the auxiliary variable meets the error factor; if so, iteratively updating the penalty parameter; otherwise, updating the number of iterations; finally, it is determined whether the number of iterations meets the maximum number of iterations; if so, outputting the system sum rate; otherwise, entering the inner layer algorithm and using the solved value as the initial value for the next iterative update.

Description

Technical Field

[0001] The present invention belongs to the field of NOMA UAV communication resource allocation, and specifically provides a method for maximizing the sum rate of a NOMA UAV communication system under uncertain user positions. Background Art

[0002] As auxiliary communications, drones have mobility and high line-of-sight communications, providing hotspot coverage for users on the ground. Therefore, drones will be an important part of traditional base station communications in the future. By utilizing the mobility of drones and optimizing their deployment positions, the sum rate of the communication system can be improved. The principle of NOMA technology is to use a non-orthogonal superposition method in the power domain on the same time-frequency resource block. The drone uses the NOMA protocol to send signals to the user, and the user end uses the Successive Interference Cancellation (SIC) technology for decoding and elimination, thereby improving the spectrum efficiency of the drone communication network. When the drone faces a scenario where the satellite positioning system fails, the drone cannot accurately obtain the location of the ground user. This patent considers the actual situation of inaccurate ground user locations and studies the NOMA drone network resource allocation problem with a bounded position estimation error model.

[0003] Existing research on the NOMA resource allocation problem for UAVs has been carried out both domestically and internationally, but there is a lack of research on the uncertain location of ground users. X.Liu et al. published an article titled "Placement and Power Allocation for NOMA-UAV Networks" in "Wireless Communications Letters, vol.8, no.3, pp.965-968, June 2019". This article solved the closed-form expressions for UAV location and power allocation to solve the user and rate maximization problem. In the case of perfect estimation of user location, R.Zhang et al. published an article titled "Joint Location and TransmitPower Optimization for NOMA-UAV Networks via Updating Decoding Order" in "Wireless Communications Letters, vol.10, no.1, pp.136-140, Jan 2021". This article solves the user and rate maximization problem by introducing SIC decoding order, power control and location optimization. In the case of traversing different SIC decoding orders, D.Hu et al. published an article titled "Joint Position, Decoding Order, and Power Allocation Optimization in UAV-Based NOMA Downlink Communications" in Systems Journal, vol. 14, no. 2, pp. 2949-2960, June 2020. This article solves the two objectives of minimizing the propagation power and maximizing the achievable rate for specific users by jointly optimizing the position and power allocation of UAVs.

[0004] However, the paper by X. Liu et al. solves the system sum rate maximization problem by deriving a closed-form expression for the optimal UAV position, which is the user's geometric center position and power. This results in a loss in system communication rate. Compared to the paper by X. Liu et al., the SIC decoding order is considered in the papers by R. Zhang et al. and D. Hu et al. To further improve the system sum rate, both papers consider the impact of the SIC decoding order on the system sum rate, which is more complex. Inspired by the above research, the ground user positions in the papers by X. Liu, R. Zhang, and D. Hu are assumed to be perfectly obtained, which is overly optimistic. This paper proposes a method for improving user sum rates by combining UAV position deployment, power allocation, and SIC decoding order in a NOMA-based UAV communication network. A sum rate maximization problem is constructed under a minimum rate threshold constraint. Based on the SIC decoding order principle, a binary variable is introduced to represent the channel gain relationship between the UAV and the user. However, since the proposed optimization problem is mixed integer nonconvex, it is not easy to solve directly. Therefore, the binary conversion variable constraints are converted into continuous inequality constraints. Then, the non-convex optimization problem is converted into a convex one through variable substitution and Successive Convex Approximation (SCA) techniques. Finally, the proposed optimization problem maximizes the number of users and rate while satisfying various constraints, thereby improving the transmission rate of the NOMA-based drone communication network. Summary of the Invention

[0005] The present invention aims to solve the above problems of the prior art and proposes a method to improve the sum rate of the NOMA-based drone communication network when the user location is uncertain. The technical solution of the present invention is as follows:

[0006] The method for maximizing the sum rate of the NOMA UAV communication system under user position uncertainty includes the following steps:

[0007] Step 1): Based on the sum rate maximization method of NOMA UAV communication system under user position uncertainty, a NOMA-based UAV communication system is constructed. In this system, user position uncertainty, minimum user rate threshold, and binary decoding order are considered. Under these constraints, a joint optimization of UAV position and UAV power allocation is constructed to maximize user sum rate.

[0008] In the downlink network, drones serve as hotspots to cover ground users. A single drone uses a single antenna to send broadcast signals to K ground users equipped with single antennas. The maximum transmission power of the drone is P uav , the flight altitude of the UAV is represented as H, the deployment position of the UAV is represented as q = [x, y], and the position of the ground user is represented as wm =[x m ,y m ],m=1,...,K, the signals sent by the UAV to the ground user have the same frequency band and are sent using the NOMA protocol that is superimposed in the power domain; when the UAV estimates the ground user position to be uncertain, the user position estimated by the UAV is expressed as w e,m =(x e,m ,y e,m ),m=1,...,K, the relationship between the user's actual location and estimated location is x m =x e,m +Δx e,m ,y m =y e,m +Δy e,m ,m=1,...,K, where Δx e,m and Δy e,m Respectively represent x m and y m The estimation error of where Q m represents the error set of the mth user, ε m Represents the error radius of the mth user; Gaussian white noise has a mean of 0 and a variance of σ 2 The normal distribution of is constructed by the above parameters and the rate maximization optimization problem:

[0009]

[0010] p n ≥0,n=1,...,K, (1.55)

[0011]

[0012] Where P = {p n ,n=1,...,K} represents the power allocated by the drone to the user, Q={q} represents the position of the drone, A={α j,n ,n=1,...,K,j=1,...,K} represents the distance relationship between user j and user n relative to the drone. m=1,...,K represents the channel gain of the mth user, β0 represents the channel power gain per unit distance, P uav Indicates the maximum transmit power of the drone, j=1,...,K represents the distance from the drone to user j, n=1,...,K represents the distance between the drone and user n, m∈{n∪ψ n} means that the signal of user n is decoded not only at user n but also at user ψ n ={k|bk,n =1,k≠n,n=1,...,K,k=1,...,K} can also be decoded.

[0013] Step 2): In order to solve the sum rate maximization problem (1.53)-(1.57), the (1.53)-(1.57) problem is equivalent to the following problem:

[0014]

[0015] (1.55)-(1.57). (1.61)

[0016] Where R = {R n ,n=1,...,K} represents the rate of the ground user, and the rate expression of the nth user is introduced In problems (1.53)-(1.57), the objective function (1.53) is about R n Monotonically increasing, so Translated into Problems (1.58)-(1.61), constraint (1.59) is valid. For Problems (1.58)-(1.61), if m∈{n∪ψ n}, there is b m,n =1 holds, otherwise, b m,n = 0. Therefore, problems (1.58)-(1.61) are equivalently converted into the following equations.

[0017]

[0018] (1.55)-(1.57),(1.65)

[0019]

[0020] In the problem (1.62)-(1.66), the binary variable b is introduced in constraint (1.66). m,n ∈{0,1} represents the decoding decision factor. Due to the uncertainty of the user position, for the constraint (1.63) in the problem (1.62)-(1.66), the left side of the constraint (1.63) has the parameter w m exists in In the expression of The expression is written as

[0021]

[0022] Formula (1.67) is transformed to

[0023]

[0024] Because Equation (1.68) is about (xx m ) 2 +(yy m ) 2 Monotonically decreasing, so we can consider the following questions

[0025]

[0026] By substituting equation (1.69) into equation (1.68), we can obtain

[0027]

[0028] in,

[0029] Then, Equation (1.71) is introduced into constraint (1.63) of problem (1.62)-(1.66) and auxiliary variable T = {t m,n ,m=1,...,K,n=1,...,K}Constraint (1.63) of problems (1.62)-(1.66) can be written as

[0030]

[0031] In addition, {α j,n 、b m,n} as auxiliary variables, and convert the piecewise binary constraints (1.67) of constraints (1.65) in problems (1.62)-(1.66) into piecewise binary constraints (1.66) respectively.

[0032] α n,n =0,n=1,...,K, (1.74)

[0033] α j,n ∈{0,1},j≠n,j=1,...,K,n=1,...,K, (1.75)

[0034] α n,j +α j,n =1,j≠n,j=1,...,K,n=1,...,K, (1.76)

[0035] α j,n (H 2 +||qw j || 2 )≤(H 2 +||qw n || 2 ),j≠n,j=1,...,K,n=1,...,K. (1.77)

[0036] b m,m =1,m=1,...,K, (1.78)

[0037] b m,n ∈{0,1},m≠n,jm=1,...,K,n=1,...,K, (1.79)

[0038] b m,n +b n,m =1,m≠n,m=1,...,K,n=1,...,K, (1.80)

[0039] b m,n (H 2 +||qw m || 2 )≤(H 2 +||qw n || 2 ),m≠n,m=1,...,K,n=1,...,K. (1.81)

[0040] Among them, the integer constraints (1.75) and (1.79) are equivalently converted into continuous inequality constraints

[0041] 0≤α j,n ≤1,j=1,...,K,n=1,...,K,(1.82)

[0042]

[0043] 0≤b m,n ≤1,m=1,...,K,n=1,...,K,(1.84)

[0044]

[0045] By comprehensively processing the constraints (1.63) in problems (1.62)-(1.66), equation (1.67) in constraint (1.65), and constraint (1.66), the mixed integer non-convex optimization problems (1.62)-(1.66) are transformed into continuous non-convex optimization problems (1.86)-(1.88).

[0046]

[0047] st(1.55)-(1.56),(1.64),(1.72)-(1.74),(1.76)-(1.78),(1.80)-(1.85) (1.87)

[0048]

[0049] Step 3): Initialize variables P, Q, A, B and auxiliary variables T, R; initialize the outer iteration number n = 0, and the penalty factor λ>0, μ>0, the maximum error factor ν>0, ν1>0, ν2>0;

[0050] Step 4): For the o+1th outer iteration, starting from the result of the oth outer iteration, fix the penalty factors λ and μ, use variable substitution, and combine the position of the UAV, power allocation, and binary decoding order to solve the rate maximization problem:

[0051]

[0052] st(1.55)-(1.56),(1.64),(1.72)-(1.74),(1.76)-(1.78),(1.80)-(1.85)(1.90)

[0053]

[0054] Step 5): Determine whether the conditions in the outer algorithm meet the error factor. If so, update the penalty factor according to λ=c1λ, μ=c2μ. Otherwise, update the number of iterations o=o+1. Then determine whether the number of iterations meets the maximum number of iterations. If so, exit the outer algorithm and output the final result. Otherwise, enter the inner algorithm again and repeat steps 4) and 5).

[0055] Furthermore, the step 4) specifically includes:

[0056] (4.1) Initialize the variables with the calculation results obtained from the oth outer layer iteration; initialize the number of inner layer iterations i = 0;

[0057] (4.2) According to convex optimization theory, in the i+1th inner iteration, the non-convex constraints (1.72) and (1.73) in the problem (1.86)-(1.88) and the constraint (1.87) are approximated as the following convex constraints using Taylor's formula:

[0058]

[0059] in Represents the variable {t m,n ,b m,n ,R n The calculation results of the i-th inner iteration; the non-convex constraints (1.77) and (1.81) in the problem (1.86)-(1.88) constraint (1.87) are equivalently converted to

[0060]

[0061] in Represents the variable {q,α j,n ,b m,n}Calculation result of the i-th inner iteration; introduce auxiliary variables into the non-convex constraints (1.83) and (1.85) in the problem (1.86)-(1.88) constraint (1.87) and convert them into equivalent

[0062]

[0063] φ j,n ≥0,j=1,...,K,n=1,...,K.(1.99)

[0064]

[0065] in Represents the variable {α j,n ,b m,n The calculation result of the inner algorithm at the i-th time;

[0066] Based on the above analysis, the problem (1.86)-(1.88) and the constraints (1.87) and (1.88) are approximately

[0067]

[0068] st(1.55),(1.56),(1.74),(1.76),(1.78),(1.80),(1.82),(1.103)

[0069] (1.84),(1.89),(1.90),(1.92),(1.94)-(1.98).(1.104)

[0070] (4.3) Determine whether the inner algorithm satisfies the threshold ν. If so, output the calculation result; otherwise, repeat steps (4.2) and (4.3).

[0071] The advantages and beneficial effects of the present invention are as follows:

[0072] Based on the fact that the existing NOMA UAV communication network does not take into account the uncertainty of user positions, the present invention provides a method for maximizing the sum rate of the NOMA UAV communication system under uncertain user positions. The present invention fully considers the problem of changes in the SIC decoding order due to different UAV deployment positions, and introduces binary variables to represent the distance relationship between the UAV and the ground user, thereby constructing a problem of maximizing the sum rate of the joint optimization of the UAV position, power allocation and SIC decoding order, and improving the sum rate of the UAV communication network by solving the mixed integer non-convex optimization problem. This problem is a non-convex optimization problem containing integer variables, so the present invention cleverly converts the integer binary variable constraints into continuous inequality constraints, and converts the complex integer non-convex optimization problem into a continuous non-convex optimization problem. The non-convex problem is converted into a convex problem using SCA technology and variable substitution, and then the convex optimization interior point method is used for iterative optimization to obtain a resource allocation solution that maximizes the system sum rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 This is a schematic diagram of the NOMA UAV communication system under uncertain user location;

[0074] Figure 2 It is a sum rate curve diagram of the present invention when the power increases from 0.01mw to 0.05mw;

[0075] Figure 3 This is a graph of the sum and velocity when the UAV altitude increases from 35m to 55m.

[0076] Figure 4 This is a sum rate curve diagram of the present invention when the error radius increases from 10m to 25m;

[0077] Figure 5 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0078] The following will describe the technical solutions in the embodiments of the present invention in detail with reference to the accompanying drawings. The described embodiments are only a part of the embodiments of the present invention.

[0079] The technical solution of the present invention to solve the above technical problems is:

[0080] In a Figure 1 In the downlink communication network composed of UAVs and ground users shown in the figure, a UAV equipped with a single antenna sends a broadcast signal to a user equipped with a single antenna using the NOMA protocol. The number of ground users K = 4, the unit channel power gain β0 = 10 -3 , ε m =15m,σ 2 =10 -14For such a UAV communication network, the present invention proposes a joint optimization method for UAV position, power allocation and SIC decoding order, such as Figure 5 As shown, the specific steps include:

[0081] Step 1): Based on the NOMA UAV communication system sum rate maximization method under user position uncertainty, a NOMA-based UAV communication system is constructed. In this system, user position uncertainty, minimum user rate threshold, and binary decoding order are considered. Under these constraints, a joint optimization of UAV position and UAV power allocation is constructed to maximize user sum rate. Using the above parameters, the optimization problem is constructed:

[0082]

[0083] p n ≥0,n=1,...,K,(1.107)

[0084]

[0085] Where P = {p n ,n=1,...,K} represents the power allocated by the drone to the user, Q={q} represents the position of the drone, A={α j,n ,n=1,...,K,j=1,...,K} represents the distance relationship between user j and user n relative to the drone. m=1,...,K represents the channel gain of the mth user, β0 represents the channel power gain per unit distance, P uav Indicates the maximum transmit power of the drone, j=1,...,K represents the distance from the drone to user j, n=1,...,K represents the distance between the drone and user n, m∈{n∪ψ n} means that the signal of user n is decoded not only at user n but also at user ψ n ={k|b k,n =1, k≠n, n=1,...,K, k=1,...,K} can also be decoded. Constraint (1.106) represents the user's communication service quality constraint, constraints (1.107) and (1.108) represent the transmission power constraints, and constraint (1.109) represents the decoding order constraint.

[0086] Step 2): In order to solve the sum rate maximization problem (1.105)-(1.109), the (1.105)-(1.109) problem is equivalent to the following problem:

[0087]

[0088] (1.107)-(1.109). (1.113)

[0089] Where R = {R n ,n=1,...,K} represents the rate of the ground user, and the rate expression of the nth user is introduced

[0090] In problems (1.105)-(1.109), the objective function (1.105) is about R n Monotonically increasing, so Translated into Problems (1.110)-(1.113), constraint (1.111) is established. For Problems (1.110)-(1.113), if m∈{n∪ψ n}, there is b m,n =1 holds, otherwise, b m,n = 0. Therefore, problems (1.110)-(1.113) are equivalently converted into the following equations.

[0091]

[0092] (1.107)-(1.109),(1.117)

[0093]

[0094] In the problem (1.114)-(1.118), the binary variable b is introduced in constraint (1.118) m,n ∈{0,1} represents the decoding decision factor. Due to the uncertainty of the user position, for the constraint (1.115) in the problem (1.114)-(1.118), the left side of the constraint (1.115) has the parameter w m exists in In the expression of The expression is written as

[0095]

[0096] Formula (1.119) is transformed to

[0097]

[0098] Because Equation (1.120) is about (xx m ) 2 +(yy m ) 2 Monotonically decreasing, so we can consider the following questions

[0099]

[0100] By substituting equation (1.121) into equation (1.120), we can obtain

[0101]

[0102] in,

[0103] Then, Equation (1.123) is introduced into the constraint (1.115) of Problems (1.114)-(1.118) and the auxiliary variable T = {t m,n ,m=1,...,K,n=1,...,K}Constraint (1.115) of problems (1.114)-(1.118) can be written as

[0104] (log2(t m,n +p n )-log2(t m,n ))≥b m,n R n (1.124)

[0105]

[0106] In addition, {α j,n 、b m,n} as auxiliary variables, and convert the piecewise binary constraints (1.109) of constraints (1.117) in problems (1.114)-(1.118) into piecewise binary constraints (1.118) respectively.

[0107] α n,n =0,n=1,...,K, (1.126)

[0108] α j,n ∈{0,1},j≠n,j=1,...,K,n=1,...,K, (1.127)

[0109] α n,j +α j,n =1,j≠n,j=1,...,K,n=1,...,K, (1.128)

[0110] α j,n (H 2 +||qw j || 2 )≤(H 2 +||qw n || 2),j≠n,j=1,...,K,n=1,...,K. (1.129)

[0111] b m,m =1,m=1,...,K, (1.130)

[0112] b m,n ∈{0,1},m≠n,m=1,...,K,n=1,...,K, (1.131)

[0113] b m,n +b n,m =1,m≠n,m=1,...,K,n=1,...,K, (1.132)

[0114] b m,n (H 2 +||qw m || 2 )≤(H 2 +||qw n || 2 ),m≠n,m=1,...,K,n=1,...,K. (1.133)

[0115] Among them, the integer constraints (1.127) and (1.131) are equivalently converted into continuous inequality constraints

[0116] 0≤α j,n ≤1,j=1,...,K,n=1,...,K, (1.134)

[0117]

[0118] 0≤b m,n ≤1,m=1,...,K,n=1,...,K,(1.136)

[0119]

[0120] Constraint (1.115) in problems (1.114)-(1.118), equation (1.109) in constraint (1.117), and constraint (1.118) are processed comprehensively to transform the mixed integer non-convex optimization problems (1.114)-(1.118) into continuous non-convex optimization problems.

[0121]

[0122] st(1.107)-(1.108),(1.116),(1.124)-(1.126),(1.128)-(1.130),(1.132)-(1.137) (1.139)

[0123]

[0124] Step 3): Initialize variables P, Q, A, B and auxiliary variables T, R; initialize the outer iteration number n = 0, and the penalty factor λ>0, μ>0, the maximum error factor ν>0, ν1>0, ν2>0;

[0125] Step 4): For the o+1th outer iteration, starting from the result of the oth outer iteration, fix the penalty factors λ and μ, use variable substitution, and combine the position of the UAV, power allocation, and binary decoding order to solve the rate maximization problem:

[0126]

[0127] st(1.107)-(1.108),(1.116),(1.124)-(1.126),(1.128)-(1.130),(1.132)-(1.137)(1.142)

[0128]

[0129] Step 5): Determine whether the conditions in the outer algorithm meet the error factor. If so, update the penalty factor according to λ=c1λ, μ=c2μ. Otherwise, update the number of iterations o=o+1. Then determine whether the number of iterations meets the maximum number of iterations. If so, exit the outer algorithm and output the final result. Otherwise, enter the inner algorithm again and repeat steps 4) and 5).

[0130] 2. The method for maximizing the sum rate of a NOMA UAV communication system under user position uncertainty according to claim 1, wherein step 4) specifically comprises:

[0131] (4.1) Initialize the variables with the calculation results obtained from the oth outer layer iteration; initialize the number of inner layer iterations i = 0;

[0132] (4.2) According to convex optimization theory, in the i+1th inner iteration, the non-convex constraints (1.124) and (1.125) in the problem (1.138)-(1.140) and the constraint (1.139) are approximated as the following convex constraints using Taylor's formula:

[0133]

[0134] in Represents the variable {t m,n ,b m,n ,R n The calculation result of the i-th inner iteration; the non-convex constraints (1.129) and (1.133) in the constraints (1.139) of problems (1.138)-(1.140) are equivalently converted to

[0135]

[0136] in Represents the variable {q,α j,n ,b m,n}Calculation result of the i-th inner iteration; Introduce auxiliary variables into the non-convex constraints (1.135) and (1.137) in the problem (1.138)-(1.140) constraint (1.139) and convert them into equivalent

[0137]

[0138] φ j,n ≥0,j=1,...,K,n=1,...,K(1.151)

[0139]

[0140] in Represents the variable {α j,n ,b m,n The calculation result of the inner algorithm at the i-th time;

[0141] Based on the above analysis, the problems (1.138)-(1.140) and the constraints (1.139) and (1.140) are approximately

[0142]

[0143] st(1.107),(1.108),(1.126),(1.128),(1.130),(1.132),(1.134),(1.155)

[0144] (1.136),(1.141),(1.142),(1.144),(1.146)-(1.150).(1.156)

[0145] (4.3) Determine whether the inner algorithm satisfies the threshold ν. If so, output the calculation result; otherwise, repeat steps (4.2) and (4.3).

[0146] For different user position errors, Figure 2It shows the change of user and rate relative to the maximum transmission power of the UAV under the constraint of minimum rate threshold. Figure 2 It can be found that as the transmission power increases, the user sum rate also increases. In order to maximize the user sum rate, the drone will allocate more power to each user. Among them, when the maximum transmission power of the drone is 20mw, the sum rate of the non-orthogonal multiple access scheme exceeds that of the orthogonal multiple access scheme. At the same time, Figure 2 In the example above, when the error radius of the user's location is 15m, we can see that the optimized drone position performs better than the random drone position. Therefore, the drone deployment location plays an increasingly important role in performance improvement.

[0147] Figure 3 and Figure 4 The relationship between the sum rate and the height of the drone and the error radius of the user's position is shown respectively. When other parameters are fixed, as the height of the drone increases or the error radius of the user's position increases, the transmission rate from the drone to the ground user decreases. This is because the distance from the drone to the user increases, and the channel gain between the drone and the user becomes worse and worse.

[0148] This paper provides a method for maximizing the sum rate of a NOMA (Normally Unmanned Aerial Vehicle) communication system under user location uncertainty. A joint optimization method for the drone's location, power allocation, and SIC decoding order is used for NOMA-based drone communication networks.

[0149] The above embodiments should be understood as merely illustrating the present invention and not as limiting the scope of protection of the present invention. After reading the contents of the present invention, technicians may make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A method for maximizing the sum rate of a NOMA UAV communication system under user position uncertainty, characterized in that: The following steps are involved: Step 1): Based on a method for maximizing the sum rate of NOMA UAV communication systems under user position uncertainty, a NOMA-based UAV communication system is constructed. In this system, user position uncertainty, minimum user rate threshold, and binary decoding order are considered. Using these constraints, a joint optimization of UAV position and UAV power allocation is constructed to maximize the system sum rate. In the downlink network, drones serve as hotspots to cover users on the ground. A single drone uses a single antenna to send broadcast signals to K ground users equipped with single antennas. The maximum transmission power of the drone is P uav , the flight altitude of the UAV is represented as H, the deployment position of the UAV is represented as q = [x, y], and the position of the ground user is represented as w m =[x m ,y m ] T ,m=1,...,K,For the signals sent by the UAV to the ground user, they have the same frequency band and are sent using the NOMA protocol that is superimposed in the power domain. When the UAV estimates the ground user position to be uncertain, the user position estimated by the UAV is expressed as w e,m =(x e,m ,y e,m ),m=1,...,K, the relationship between the user's actual location and estimated location is x m =x e,m +Δx e,m ,y m =y e,m +Δy e,m ,m=1,...,K, where Δx e,m and Δy e,m Respectively represent x m and y m The estimation error of where Q m represents the error set of the mth user, ε m Represents the error radius of the mth user; Gaussian white noise has a mean of 0 and a variance of σ 2 The normal distribution of is constructed by the above parameters and the rate maximization optimization problem: Where P = {p n ,n=1,...,K} represents the power allocated by the drone to the user, Q={q} represents the position of the drone, A={α j,n ,n=1,...,K,j=1,...,K} represents the distance relationship between user j and user n relative to the drone. represents the channel gain of the mth user, β0 represents the channel power gain per unit distance, P uav Indicates the maximum transmit power of the drone, represents the distance from the drone to user j, represents the distance from the drone to user n, m∈{n∪ψ n } means that the signal of user n is decoded not only at user n but also at user ψ n ={k|b k,n =1,k≠n,n=1,...,K,k=1,...,K} can also be decoded; Step 2): In order to solve the sum rate maximization problem (1.1)-(1.5), the following equivalent treatment is performed on the (1.1)-(1.5) problem. The sum rate maximization problem (1.1)-(1.5) is equivalent to the following problem Where R = {R n ,n=1,...,K} represents the rate of the ground user, and the rate expression of the nth user is introduced In problems (1.1)-(1.5), the objective function (1.1) is about R n Monotonically increasing, so Translated into Problems (1.6)-(1.9), Constraint (1.7) is established. For Problems (1.6)-(1.9), if m∈{n∪ψ n }, there is b m,n =1 holds, otherwise, b m,n =0; Therefore, problems (1.6)-(1.9) are equivalently converted into the following formula; In the problem (1.10)-(1.14), the binary variable b is introduced in constraint (1.14) m,n ∈{0,1} represents the decoding decision factor; due to the uncertainty of the user position, for the constraint (1.11) in the problem (1.10)-(1.14), the left side of the constraint (1.11) has the parameter w m exists in In the expression of The expression is written as Formula (1.15) is transformed to Because Equation (1.16) is about (xx m ) 2 +(yy m ) 2 Monotonically decreasing, so we can consider the following questions By substituting equation (1.17) into equation (1.16), we can obtain in, Then, Equation (1.19) is introduced into the constraint (1.11) of Problems (1.10)-(1.14) and the auxiliary variable set T = {t m,n ,m=1,...,K,n=1,...,K}Constraint (1.11) of problems (1.10)-(1.14) can be written as (log2(t m,n +p n )-log2(t m,n ))≥b m,n R n ,m=1,...,K,n=1,...,K (1.20) In addition, {α j,n 、b m,n } as auxiliary variables, and convert the piecewise binary constraints (1.5) and piecewise binary constraints (1.14) of constraints (1.13) in problems (1.10)-(1.14) into equivalent a n,n =0,n=1,...,K,(1.22) α j,n ∈{0,1},j≠n,j=1,...,K,n=1,...,K,(1.23) a n,j +a j,n =1,j≠n,j=1,...,K,n=1,...,K,(1.24) α j,n (H 2 +||qw j || 2 )≤(H 2 +||qw n || 2 ),j≠n,j=1,...,K,n=1,...,K.(1.25) b m,m =1,m=1,...,K,(1.26) b m,n ∈{0,1},m≠n,m=1,...,K,n=1,...,K,(1.27) b m,n +b n,m =1,m≠n,m=1,...,K,n=1,...,K,(1.28) b m,n (H 2 +||q-w m || 2 )≤(H 2 +||q-w n || 2 ),m≠n,m=1,...,K,n=1,...,K.(1.29) Among them, the integer constraints (1.23) and (1.27) are equivalently converted into continuous inequality constraints 0≤α j,n ≤1,j=1,...,K,n=1,...,K,(1.30) 0≤b m,n ≤1,m=1,...,K,n=1,...,K,(1.32) By combining constraints (1.11) in problems (1.10)-(1.14), equation (1.5) in constraint (1.13), and constraint (1.14), we can transform the mixed integer non-convex optimization problems (1.10)-(1.14) into continuous non-convex optimization problems. Step 3): Initialize variables P, Q, A, B and auxiliary variables T, R; initialize the outer iteration number o = 0, and the penalty factor λ>0, μ>0, the maximum error factor ν>0, ν1>0, ν2>0; Step 4): For the o+1th outer iteration, starting from the result of the oth outer iteration, fix the penalty factors λ and μ, use variable substitution, and combine the position of the UAV, power allocation, and binary decoding order to solve the rate maximization problem: Step 5): Determine whether the conditions in the outer algorithm meet the error factor. If so, update the penalty factor according to λ=c1λ, μ=c2μ. Otherwise, update the number of iterations o=o+1. Then determine whether the number of iterations meets the maximum number of iterations. If so, exit the outer algorithm and output the final result. Otherwise, enter the inner algorithm again and repeat steps 4) and 5). The step 4) specifically includes: (4.1) Initialize the variables with the calculation results obtained from the oth outer layer iteration; initialize the number of inner layer iterations i = 0; (4.2) According to convex optimization theory, in the i+1th inner iteration, the non-convex constraints (1.20) and (1.21) in the problem (1.37)-(1.39) and constraint (1.38) are approximated as the following convex constraints using Taylor's formula: in Represents the variable {t m,n ,b m,n ,R n The result of the calculation of the inner layer iteration in the i-th order; the non-convex constraints (1.25) and (1.29) in the constraint (1.38) of the problem (1.37)-(1.39) are equivalently converted to in Represents the variable {q,α j,n ,b m,n }Calculation result of the i-th inner iteration; introduce auxiliary variables into the non-convex constraints (1.31) and (1.33) in the problem (1.37)-(1.39) constraint (1.38) and convert them into equivalent Where Φ={φ j,n ,j=1,..,K,n=1,...,K}, are the sets of slack variables, Represents the variable {α j,n ,b m,n The calculation result of the inner algorithm at the i-th time; Based on the above analysis, problems (1.37)-(1.39) and constraints (1.38) and (1.39) are approximately (4.3) Determine whether the inner algorithm meets the threshold ν. If so, output the calculation result; otherwise, repeat steps (4.2) and (4.3).

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