A computational delay optimization method based on URLLC UAV edge computing system

Abstract

The present invention discloses a method for optimizing computational latency based on a URLLC (UAV) unmanned aerial vehicle (UAV) edge computing system. The method comprises the following steps: S1: establishing a three-dimensional Cartesian coordinate system and using the coordinate system to construct a communication model between a computing device and a UAV; S2: determining the conditions of the computational model and constructing a local computational model and an edge computational model based on the conditions of the computational model; S3: minimizing the computational latency of the UAV edge computing system under a finite code length as the optimization objective; S4: using the block coordinate descent method to divide the optimization objective into three alternating iterative subproblems: optimizing the horizontal position of the UAV given resource allocation and hovering height h; optimizing the hovering height of the UAV given resource allocation and horizontal position; and optimizing resource allocation given the UAV position; and S5: solving a method to minimize the computational latency of the URLLC UAV mobile edge computing system. The present invention is more suitable for practical communication environments and can minimize the computational latency of the UAV mobile edge computing system.

Description

Technical Field

[0001] The present invention relates to the field of edge computing, and more specifically, to a computing delay optimization method based on a URLLC (UAV) unmanned aerial vehicle (UAV) edge computing system. Background Art

[0002] Drone communications have garnered widespread attention and research in the wireless communications field due to their flexibility, high maneuverability, and on-demand deployment. Advances in drone manufacturing technology, coupled with the miniaturization of communication and computing devices, have made it possible to combine drone communications with mobile edge computing systems. This can further enhance the system's mission computing performance. This is because drones with computing service capabilities can offload computations to user devices with limited computing power. Furthermore, drones can enhance communication performance with user devices by adjusting their flight position, reducing mission offload latency and transmission errors.

[0003] For example, mission-critical IoT applications such as remote health monitoring, tactile interaction, and factory automation control will be widely used in future wireless networks, enabling ultra-reliable low-latency communications for mission-critical IoT (bit error rate no higher than 10). -7 , end-to-end latency of no more than 1ms, has been listed as one of the primary goals of 5G cellular networks. The main difference between mission-critical IoT and traditional wireless communication systems is the packet length. Most ultra-reliable, low-latency communications carry very small packets, for example, 10-20 bytes. This results in a very small codeword length for physical layer transmission after encoding. Therefore, the traditional design principles for wireless communication systems based on Shannon capacity should be modified accordingly. The Shannon capacity theorem holds true only when the bit error rate is negligible and the transmitted packet length is infinite. However, when analyzing reliability with finite code length, the bit error rate must be non-negligible. Consequently, the law of large numbers and Shannon capacity no longer apply, resulting in underestimated reliability and latency, and the corresponding quality of service cannot be guaranteed. In 2010, Professor Polyanskiy mathematically derived finite code length transmission over an additive white Gaussian noise channel, deriving a complex function that represents the mathematical relationship between short packet communication rate, signal-to-noise ratio, packet length, and bit error rate. This provides guidance and support for data transmission research and wireless communication system design based on finite code lengths.

[0004] The prior art discloses a method for offloading multiple drone tasks and allocating resources in an edge computing system, comprising the following steps: combining the drone's current location, the drone's relative distance, the drone's relative distance to an IoT smart device, and the number of times the IoT smart device has been used to perform tasks into a system state; constructing a deep deterministic policy gradient optimization neural network; inputting the system state into the deep deterministic policy gradient optimization neural network to obtain a system action; the edge computing system executes the system action and obtains a reward for the system action based on an immediate reward function; and continuously training the parameters of the deep deterministic policy gradient optimization neural network based on the obtained reward value until the reward value stabilizes, thereby obtaining an optimal policy. This solution, which uses a deep deterministic policy gradient optimization neural network for task offloading and resource allocation, does not address the problem of minimizing latency in drone edge computing systems with Rician fading under limited code length. Summary of the Invention

[0005] The present invention provides a computing delay optimization method based on the URLLC unmanned aerial vehicle edge computing system, which is more in line with the actual communication environment and can minimize the computing delay of the unmanned aerial vehicle mobile edge computing system.

[0006] The primary purpose of the present invention is to solve the above technical problems, and the technical solutions of the present invention are as follows:

[0007] A method for optimizing computing delay based on a URLLC unmanned aerial vehicle edge computing system, characterized by comprising the following steps:

[0008] S1: Establishing a three-dimensional Cartesian coordinate system and using the coordinate system to construct a communication model between the computing device and the drone;

[0009] S2: Determine the conditions of the computing model, and build a local computing model and an edge computing model based on the conditions of the computing model.

[0010] S3: Minimizing the computational latency of the UAV edge computing system under limited code length is the optimization goal;

[0011] S4: Use the block coordinate descent method to divide the optimization objective into three alternating iterative sub-problems: optimize the horizontal position of the UAV given resource allocation and hovering height, optimize the hovering height of the UAV given resource allocation and horizontal position, and optimize resource allocation given the UAV position;

[0012] S5: Using computing resources and the horizontal position and hovering height of the UAV, solve the problem of minimizing the computational latency of the URLLC UAV mobile edge computing system.

[0013] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0014] The communication model constructed based on computing devices and drones in the present invention takes into account both large-scale and small-scale fading, which is more in line with the actual communication environment, and can give full play to the three-dimensional freedom of drones in the air, improving the communication performance of the offload link; the present invention is based on the offload method of limited code length transmission using ground computing equipment, which fits the time-sensitive application of ultra-reliable and low-latency in the 5G industrial Internet; by dividing the optimization objective into three alternating cyclic iterative sub-problems, and further utilizing the solution results of the sub-problems, the computing delay of the URLLC drone mobile edge computing system is minimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a schematic diagram of a drone edge computing system according to an embodiment of the present invention.

[0016] Figure 2 This is a flow chart of the computational delay optimization method based on the URLLC UAV edge computing system of the present invention.

[0017] Figure 3 Graph showing the convergence of the objective function value in an embodiment of the present invention.

[0018] Figure 4 Schematic diagram of the change of the drone's position during the alternating iteration process of the present invention.

[0019] Figure 5 2 is a performance comparison chart of an embodiment of the present invention and a benchmark solution. DETAILED DESCRIPTION

[0020] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present application and the features therein can be combined with each other.

[0021] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0022] like Figure 1 As shown in the figure, the present invention is based on the URLLC UAV edge computing system. The UAV is equipped with a computing server, which assists K computing devices on the ground (expressed as ) complete their computational tasks.

[0023] Example 1

[0024] like Figure 2As shown in FIG, a method for optimizing computing delay based on a URLLC UAV edge computing system includes the following steps:

[0025] S1: Establishing a three-dimensional Cartesian coordinate system and using the coordinate system to construct a communication model between the computing device and the drone;

[0026] Specifically include:

[0027] Constructing a three-dimensional Cartesian coordinate system, the plane coordinates of K computing devices distributed on a horizontal plane with a height of 0 can be expressed as The coordinates of the drone's hovering position can be expressed as Q = [q T , h] T ,in is the two-dimensional coordinate of the UAV in the horizontal direction, and h is the hovering height of the UAV;

[0028] If affected by the environment and the performance of the drone, the minimum and maximum hovering heights of the drone are h min and h max , then there are the following constraints on the drone's hovering height:

[0029] h min ≤h≤h max

[0030] The present invention considers the short packet communication scenario with low latency. The time for a device to unload a data packet does not exceed the coherence time of the channel. The unloading transmission time of all devices is T. In order to avoid transmission interference between different devices, all devices use orthogonal frequency division multiplexing technology to unload data. Different devices will be allocated to different orthogonal frequency bands, and the bandwidth allocated to device k is expressed as W. k (Hz), and the length of the data packet that device k can transmit in the channel (or the number of times the channel is used) is W k T;

[0031] It should be noted that, because the unloading transmission time T of the device is extremely small, shorter than the channel coherence time, the channel between the device and the UAV can be considered as a quasi-static flat fading channel during the entire transmission process, that is, the corresponding channel parameters remain unchanged. In most of the existing literature on UAV-assisted mobile edge computing, the channel between the UAV and the device simply considers the LoS model that ignores small-scale fading, while the present invention uses a more practical and accurate Rice fading channel model determined by the elevation angle. Due to the lack of closed-form expressions for the key parameters that describe the achievable transmission rate of the fading channel when given an interruption probability constraint, the communication problem using the Rice fading model becomes very difficult to solve. To solve this problem, this patent uses the loss function obtained by the logarithmic probability regression method in the reference literature, which is highly consistent with the calculated data, namely:

[0032]

[0033] where θ k It is a parameter related to the elevation angle (the angle between the UAV-device k channel and the ground). Here, the sine value of the elevation angle is used to represent it. B1<0 reflects the logical midpoint of the positive value, B2>0 is the logical increase rate, and the constants C1>0 and C2>0 need to satisfy C1+C2=1. The transmission power when the device offloads the task to the UAV is set to P k , then the received signal-to-noise ratio of the offloading channel of device k can be expressed as:

[0034]

[0035] where h k is the channel gain, is the large-scale average channel power gain considering signal attenuation including path fading and shadow fading, where β0 is the average channel power gain at the reference distance d0 = 1m, and is the distance between the UAV and the device k, α is the path fading coefficient which is generally between 2 and 6, and N0 represents the noise power spectral density at the receiving end.

[0036] It should be noted that when transmitting short packets, the data packet length of the channel coding is very limited, which makes it impossible to ignore the coding error probability when analyzing its communication performance. Assume that the data packet length of the given channel is N k =W k At time T, when device k unloads data, the error rate of the drone receiving data is ∈ k ∈(0, 1), then the short packet communication rate (bits / s / Hz) when device k offloads tasks in a quasi-static flat channel is:

[0037]

[0038] where Q -1 (·) is the Q function The inverse function of V k is the channel dispersion, which describes the random variability of the channel relative to a deterministic channel with the same capacity. In a single-antenna quasi-static Ricean fading channel, it can be expressed as V k =1-(1+γ k ) -2 .

[0039] S2: Determine the conditions of the computing model, and build a local computing model and an edge computing model based on the conditions of the computing model.

[0040] It should be noted that the conditions for the calculation model include:

[0041] The computing task data input to each computing device is set to be bit-independent and can be arbitrarily divided into two parts, one for local computing on the computing device and the other for edge computing on the drone, so that the two can be calculated in parallel without affecting the validity of the task data;

[0042] The mobile edge computing server installed on the drone is configured with multiple independent computing units with powerful computing capabilities, so that tasks from different devices can be calculated simultaneously without interfering with each other and without queuing or congestion;

[0043] Set the computing resources required for each bit of task data of device k, that is, the number of operating cycles of the central processing unit (CPU) to c k Because the size of the task calculation result is much smaller than the size of the unloaded data, and the power of the return transmission is relatively large, the delay of the UAV's feedback of the calculation result is ignored. Local calculation model:

[0044] All computing devices can perform local computing in parallel with task offloading and edge computing without stopping during the entire process. Therefore, the local computing time is equal to the computing delay of the system. The minimum computing delay of the system under the optimal computing solution is expressed as t min , the CPU operating frequency of device k is f k , the unit is cycle / s, and the effective capacitance coefficient determined by the processor chip architecture is The corresponding local computing task volume and energy consumption Expressed as:

[0045]

[0046]

[0047] Edge computing model:

[0048] Edge computing consists of two parts: uplinking the task data to be offloaded to the drone's server using short packet communication, and computing the data after the drone's server receives the offloaded task.

[0049] According to the previous settings, the device will encode the data to be unloaded into data packets and transmit them to the drone. That is, the unloading delay of the device is T. When the transmission rate is less than the channel capacity, the device k will unload the task to the drone within the transmission time T. And the communication energy consumption It can be expressed as:

[0050]

[0051]

[0052] Because the computing power of the drone server is relatively strong, the drone can be set to perform calculations immediately after receiving the complete data packet unloaded by the device, so the time for edge computing is Set the CPU frequency used by the drone to calculate the offloaded tasks from device k to f U，k (cycles / s), the effective capacitance coefficient determined by the processor chip architecture is Then the edge computing task volume of device k is and energy consumption They are:

[0053]

[0054]

[0055] Because the bit error rate cannot be ignored in short packet communication, and there is also an interruption probability in the Rice fading model, that is, the effective task volume received by the drone must be less than the task volume unloaded by the device. If the bit error rate is ∈ k When the effective task volume actually received by the UAV is Because the amount of edge computing tasks cannot be greater than the amount of tasks that the drone has already received from the device offload, the following computational causal constraints apply:

[0056]

[0057] Set device k to effectively complete L k In order to ensure that the task volume requirements are met, the following task volume constraints are imposed on the task calculation of bits:

[0058]

[0059] S3: Minimizing the computational latency of the UAV edge computing system under limited code length is the optimization goal;

[0060] It should be noted that in order to give full play to the advantages of the flexibility of the position deployment of UAVs in wireless communication systems and combine the characteristics of Ricean channels that are closely related to elevation angles, the goal of this invention is to optimize the bandwidth allocation W k 、User equipment calculates frequency f k and the drone server calculates the frequency f U，k , and the three-dimensional spatial position of the UAV (horizontal coordinate q and height h), adjust the distance and elevation angle between the UAV and the ground equipment to balance the path loss and small-scale fading, so as to minimize the computing delay of the UAV edge computing system in the case of short packet communication, that is, limited code length.

[0061] Only consider the process of the device unloading and transmitting a data packet. The optimization objective expression is:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068] h min ≤h≤h max (10g)

[0069] The constraint (10a) is to avoid the error rate ∈ k When the communication rate R is relatively small k For negative values, because the function Q -1 The value of (x) near x = 0 tends to infinity, while (10d) is the constraint on the communication and computing energy consumption budget of the device during the computing process, and (10e) and (10f) are the resource allocation constraints on computing frequency and transmission power, respectively.

[0070] S4: Use the block coordinate descent method to divide the optimization objective into three alternating iterative sub-problems: namely, optimize the horizontal position of the UAV given the resource allocation and hovering height h, optimize the hovering height of the UAV given the resource allocation and horizontal position, and optimize the resource allocation given the UAV position;

[0071] It should be noted that due to the complexity of the expressions of Ricean channel signal-to-noise ratio and short packet communication rate, as well as the non-convexity of constraints (10a) and (10c) and the coupling of variables, formula (10) is a non-convex optimization problem that is difficult to solve. In order to facilitate the solution of the problem, the block coordinate descent method is used to divide the problem into three sub-problems that can be alternately iterated, namely: given resource allocation and hovering height h to optimize the horizontal position q of the UAV, given resource allocation Optimize the hovering height h of the drone and the horizontal position q, and optimize the resource allocation given the position {q, h} of the drone

[0072] Given resource allocation The optimized horizontal position q of the UAV with the hovering height h is:

[0073] First, we derive the monotonicity of the short packet rate and simplify the expression of the short packet rate. k (γ k ) relative to the signal-to-noise ratio γ k The first and second derivatives of are:

[0074]

[0075]

[0076] If R′ k ( c k )=0, we can get the following relationship:

[0077]

[0078] After solving, we can get R′ k ( c k )=0 k for:

[0079]

[0080] It is worth noting that This shows is the function R k (γ k ) is a minimum point. Because Yes k is a monotonically increasing function, so R′ k ( c k ) is also about γ k is a monotonically increasing function, so the short packet communication rate R in (6) k (γ k ) is a k is a convex function. Since And R k (0)=0, so we can get R k (γ k ) is monotonic:

[0081] 1) When When R′ k (γ k )<0, function R k (γ k ) is a monotonically decreasing function, and R k (γ k )≤0.

[0082] 2) When When R′ k (γ k)>0, function R k (γ k ) is a monotonically increasing function.

[0083] Therefore, when R k (γ k )≥0, there must be So the short packet communication rate is a function of the signal-to-noise ratio γ k A monotonically increasing function, we can know Short packet communication rate R k (γ k )exist It is a monotonically increasing function, so we can and a suitably large signal-to-noise ratio by dichotomy to find the equation R k (γ k )=0, let it be Right now Then the constraint (10a) in the problem can be equivalent to

[0084] Because the signal-to-noise ratio γ k The value of is usually relatively large (γ k >>1), so in order to facilitate the problem handling, many literatures have replaced the dispersion V in the short packet communication rate expression (4) with k Approximately 1, that is, V k ≈1 (usually when the signal-to-noise ratio is greater than 20dB, the dispersion V k The value of will exceed 0.99 and can be approximated to 1). k After being approximately equal to 1, we can find that Became the original Although this approximation is reasonable in most cases, it is not much different from the traditional Shannon capacity in the research of UAV deployment location or flight trajectory optimization, and there is a large error. Next, we use the logarithmic function to nonlinear approximation. and ln(1+x), and further process the problem.

[0085] For any given The following inequality holds:

[0086]

[0087] The parameters ρ and η are defined as: when When , the approximate function F(x) is tight, that is

[0088] Similarly, for any given The following inequality holds:

[0089]

[0090] The parameters and Defined as: Likewise when When , the lower bound of the function ln(1+x) is tight.

[0091] Since the signal-to-noise ratio in wireless communication systems is relatively large, let x = γ k When , the inequality in (14) and (15) will hold, which can be used to analyze the impact of the signal-to-noise ratio on the short packet communication rate. It can be known that for a given initial value of the signal-to-noise ratio Short packet communication rate R k The nonlinear lower bound of is:

[0092]

[0093] The coefficient This nonlinear approximation of the log function form is much more accurate than the linear approximation obtained by methods such as first-order Taylor expansion if and only if When , the rate lower bound is tight, that is,

[0094] Based on the monotonicity of the short packet communication rate expression discussed above and the obtained nonlinear lower bound, problem (10) is transformed and approximated into the following form:

[0095]

[0096]

[0097] It is not difficult to find that the feasible solution set of problem (17) is actually a subset of the feasible solution set of problem (10), so the optimal objective function value of problem (17) is the upper bound of the optimal objective function value of problem (10). Because the logarithmic function log2(x) is monotonically increasing, and substituting (16) into (17b), constraints (17a) and (17b) can be combined into:

[0098]

[0099] If we define a constant Combining (2) and (3) we can get the signal-to-noise ratio γ at this time k Specifically expressed as:

[0100]

[0101] Now the problem is convex except for the constraint (18). If we want to reduce the signal-to-noise ratio γ k The complexity of the introduction of auxiliary variables Then the sub-problem of optimizing the horizontal position q of the UAV with a fixed hovering height h can be expressed as:

[0102]

[0103]

[0104]

[0105] Although the form of the problem is simplified a lot and the right-hand side of constraint (20b) is also convex, the expression of the signal-to-noise ratio on the left-hand side is still neither convex nor concave for the optimization variable q.

[0106] For ω>0, C1>0 and C2>0, the function The first-order partial derivatives with respect to x and y are:

[0107]

[0108]

[0109] Then we can get the Hessian matrix of ξ(x, y) as:

[0110]

[0111] The second-order derivatives are:

[0112]

[0113]

[0114]

[0115] For any vector t = [t1, t2] T , for α≥2, x≥0, y≥0, we have:

[0116]

[0117] By the definition of convex function, the function ξ(x, y) is jointly convex with respect to x and y, and the signal-to-noise ratio expression γ on the left hand side of the constraint (20b) is k about and is jointly convex. Although the constraint (20b) is still non-convex, since the first-order Taylor expansion approximation of a convex function is its global lower bound, we then use the continuous convex approximation (SCA) method to derive a convex approximation.

[0118] Similarly, we can know the function It is also a convex function about x≥-X and y≥-Y. Its first-order Taylor expansion at given x=x0 and y=y0 is:

[0119]

[0120] in

[0121]

[0122]

[0123] If we set x0=0 and y0=0, we can get

[0124]

[0125] If the initial horizontal position of the UAV is given make where ω = ω k , as well as Then for γ k The SCA methods used are:

[0126]

[0127] in Yes k The lower bound of , which can be shown to be concave, is if and only if hour Established.

[0128] Substituting the concave lower bound of the signal-to-noise ratio (28) into the constraint (20b), and relaxing the non-affine equality constraint (20a) into an inequality constraint, the problem (20) can be transformed into:

[0129]

[0130]

[0131] It can be shown that when the optimal solution is obtained for problem (29), the inequality constraint (29a) will become an equality. Otherwise, if there is a strict inequality constraint in (29a) when the optimal solution is obtained, then the slack variable E can always be increased. kUntil the equation is established, no constraints will be violated or the objective function value will be changed, so there will always be an optimal solution that makes the left and right constraints (29a) equal.

[0132] Next, define a function It is not difficult to prove that θ(x) is a convex function about x ≥ -X, so the constraint (29a) is non-convex. Also using the SCA method, when a feasible x0 is given and a first-order Taylor expansion is performed, we have:

[0133]

[0134] If x0=0, then Let D = h, as well as Can get The lower bound of is:

[0135]

[0136] It can be proved is concave, the equality sign in the above formula is true if and only if Established when.

[0137] Substituting the concave lower bound (31) into the constraint (29a), problem (29) can be approximated as:

[0138]

[0139] At this point, Problem (32) is a standard convex optimization problem that can be efficiently solved using the existing solver CVX. It is worth noting that in constraints (29b) and (32), the concave lower bounds of the non-convex constraints are used to approximate them. This makes the feasible solution set of Problem (32) a subset of the feasible solution set of Problem (20). Therefore, solving Problem (32) actually yields an upper bound on the objective function value of Problem (20).

[0140] If a feasible UAV horizontal position q is given, the subproblem of optimizing the UAV hovering height h can be expressed as:

[0141]

[0142]

[0143] It can be found that problem (33) is quite similar to problem (20), so in this sub-problem, we still use the process and method similar to (20) → (29) (using the SCA method to obtain the convex approximation form of constraint condition (20b)) to transform problem (33) into the following approximate problem:

[0144]

[0145]

[0146] Similarly, for a given initial drone hovering height And ω=ω k , It is not difficult to prove Since the optimization variable h is a concave function, constraint (34a) is already convex in the hover height subproblem, eliminating the need for a convex approximation as in the horizontal trajectory subproblem. Problem (34) has been transformed into a convex optimization problem and can be solved efficiently using either the CVX solver or an interior point method.

[0147] It should be noted that after the above two sub-problems are optimized and solved, constraint (10b) will become an equation, and when the position of the UAV is fixed, the system's computational delay will be equal to the target task computation amount L of the user equipment. k So the calculation delay of the system is t min Fix the objective function value obtained by optimizing the previous subproblem, then the subproblem of optimizing resource allocation can be converted to:

[0148]

[0149] In this way, the problem can be optimized more by relaxing the constraint (10b), and the computational delay t can be minimized in the above two sub-problems of optimizing the position of the drone. min Since constraints (10a) and (10c) are not convex, this makes the subproblem still difficult to solve. If we define Then the short packet communication rate can be expressed as:

[0150]

[0151] Because N k =W k T is non-negative, so it is natural to have the constraint (10a) equivalent to W k TR k ≥0, that is, S k (W k )-Z k (W k )≥0. Since the function It is a perspective function. It is not difficult to know that S k (W k ) is a kConcave function. k (W k ) before the convexity of U k About W k The first and second derivatives of are:

[0152]

[0153]

[0154] Then we can deduce that Z k (W k )The first-order derivative and the second-order derivative are:

[0155]

[0156]

[0157] So the function Z k (W k ) is a k So the left hand side of constraint (10c) is the difference of two concave functions. If the initial To Z k (W k ) is expanded by the first order Taylor:

[0158]

[0159] If and only if Sometimes Substituting (39) into constraint (10c), problem (35) can be approximated as:

[0160]

[0161] Because the right-hand side of constraint (40) is greater than zero, the rate positivity constraint (10a) can be omitted. Problem (40) is now a convex function and can be efficiently solved using the CVX solver. Similarly, the set of feasible solutions to problem (40) is a subset of the set of feasible solutions to problem (35). Therefore, solving problem (40) actually yields a lower bound on the objective function value of problem (35).

[0162] S5: Using computing resources and the UAV’s horizontal position q and hovering height h, solve the problem of minimizing the computational delay of the URLLC UAV mobile edge computing system.

[0163] It should be noted that the present invention jointly optimizes communication and computing resources The distribution of the UAV, as well as the horizontal position q and hovering height h, is used to minimize the computational delay t of the URLLC UAV mobile edge computing system. min Based on the previous theoretical analysis and the processing of the three sub-problems, the specific algorithm steps for solving problem (10) to obtain the optimal deployment position of the UAV through alternating optimization and cyclic iteration are as follows:

[0164] (1) Set the short packet transmission delay T, bit error rate ∈ k , the target task computation amount L k , equipment energy consumption budget and other parameters;

[0165] (2) Let the cycle number i = 0, the initial delay Accuracy threshold ε=10 -8 , initialize bandwidth allocation Calculation frequency Horizontal position q (i) and hovering height h (i) ;

[0166] (3) Substitute the relevant parameters into (13) to calculate and in the interval In the binary search R k (γ k )=0

[0167] (4) Substitution And solve problem (32) to get the local optimal solution

[0168] (5) Substitution And solve problem (34) to get the local optimal solution

[0169] (6) Substitution And solve problem (40) to get the optimal solution

[0170] (7) Let the minimum delay obtained by the i+1th step loop Update the ordinal number i = i + 1;

[0171] (8) If That is, the algorithm converges to the preset threshold range and obtains the optimal solution Otherwise, repeat steps (3)-(7).

[0172] It should be noted that the method for optimizing the deployment position of drones in short packet communication proposed in the present invention fully considers the influence of channel spread in short packet communication capacity, and reasonably reduces the complexity of the optimization solution through methods such as log function approximation and first-order Taylor expansion approximation, thereby effectively improving the convergence rate of the proposed alternating optimization algorithm.

[0173] Example 2

[0174] Based on the above process, this embodiment conducts a convergence analysis of the method, assuming represents the objective function value of the problem (10) obtained in the i-th iteration of the loop. For the optimization of the horizontal position of the UAV, the following relationship holds:

[0175]

[0176] where t log It represents the objective function value of problem (17). The equality relation (a) holds because the nonlinear lower bound of the log form in (16) is at a given local point, i.e., q = q (i) The place is tight. It represents the objective function value of problem (32). Similarly, the equality relation (b) holds because the first-order Taylor expansion is tight at the expansion point. The inequality relation (c) exists because problem (32) has been optimally solved. Finally, the inequality relation (d) exists because the optimal objective function value of problem (32) is the upper bound of the optimal objective function value of problem (20), and the optimal objective function value of problem (20) is the upper bound of the optimal objective function value of problem (10). Therefore, solving problem (32) can ensure that the objective function value of problem (20) is non-increasing. Similarly, for the optimization of the drone's hovering position, we have:

[0177]

[0178] Combining the two relations (41) and (42), we can get

[0179]

[0180] As for the optimization of resource allocation, there are:

[0181]

[0182] However, when problem (40) obtains a larger objective function value, problems (32) and (34) can obtain smaller objective function values ​​in the next iteration. The algorithm uses the optimal value of problem (34) as the convergence judgment condition. It can be proved that the objective function value of problem (10) is non-increasing in the alternating iterations. Because it is restricted by the computational constraint condition (10b) of the target task, the computational delay of the system is a finite value with a lower bound. Therefore, the proposed algorithm can converge to a local optimal solution of problem (10) by solving it.

[0183] Example 3

[0184] This example conducts experimental verification and analysis, setting the target task calculation amount L k =2.15kbit, computing device energy budget Accuracy threshold ε=10 -8 When , the computer simulation results of the proposed algorithm's convergence in the alternating iteration process can be presented. Figure 3 It can be seen that after the fourth iteration, the objective function value of the optimization problem has converged and stabilized. At the 13th iteration, the algorithm converges, meeting the judgment criteria and ending the iteration. Similar convergence behavior is observed when the relevant parameters are changed to other values, demonstrating that the algorithm proposed in this invention has the advantage of fast convergence.

[0185] Figure 4 The “×” and “☆” in the figure represent the initial three-dimensional position of the UAV and the optimal three-dimensional position obtained when the algorithm converges, respectively. It can be observed that the position of the UAV gradually approaches the optimal position along an arc from the initial position during the four cycles. In the following nine cycles, the position of the UAV is basically at the optimal position. This phenomenon once again illustrates the fast convergence speed and stability of the proposed algorithm. It also illustrates that due to the use of the SCA method, the optimal solution of Problem (32) and Problem (34) is actually the upper bound of the original problem, but this upper bound will gradually become tighter as the number of iterations increases. At the same time, it can be found that the optimal position of the UAV under the Rician fading channel needs to take into account both path loss and small-scale fading, and adjust the distance from the device and the elevation angle to the ground. Therefore, unlike the LoS channel, it does not simply reduce the path loss in order to reduce the distance between the UAV and the ground device, so that the optimized UAV flight altitude is maintained at the preset minimum flight altitude.

[0186] Next, the performance of the method for optimizing the three-dimensional position of the drone is compared with two baseline schemes. The proposed algorithm for jointly optimizing the horizontal position and hovering height of the drone is denoted as "JQH". "NQ" means that the horizontal position of the drone is not optimized, only the hovering height is optimized. In this case, the horizontal position of the drone is fixed to the center position of the four ground computing devices. "NH" means that only the horizontal position is optimized, and the hovering height of the drone is fixed to the preset minimum flight altitude. Figure 5 Shows the system calculation delay and the device target task calculation amount L k The comparison of the curves shows that as L k With the increase of , the minimum computational delay of the system also increases, and the system computational delay obtained by the JQH algorithm is smaller than that of the other two benchmark schemes, which proves the necessity of jointly optimizing the horizontal position and hovering height of the UAV considering the Ricean fading channel.

[0187] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing computing delay based on URLLC UAV edge computing system, characterized in that: The following steps are involved: S1: Establishing a three-dimensional Cartesian coordinate system and using the coordinate system to construct a communication model between the computing device and the drone; S2: Determine the conditions of the computing model, and build a local computing model and an edge computing model based on the conditions of the computing model. S3: Minimizing the computational latency of the UAV edge computing system under limited code length is the optimization goal; S4: Use the block coordinate descent method to divide the optimization objective into three alternating iterative sub-problems: optimize the horizontal position of the UAV given resource allocation and hovering height, optimize the hovering height of the UAV given resource allocation and horizontal position, and optimize resource allocation given the UAV position; S5: Using computing resources and the horizontal position and hovering height of the UAV, solve the problem of minimizing the computational latency of the URLLC UAV mobile edge computing system.

2. A method for optimizing computing delay based on a URLLC UAV edge computing system according to claim 1, characterized in that: Establishing a three-dimensional Cartesian coordinate system and using the coordinate system to construct a communication model between the computing device and the drone specifically includes: Constructing a three-dimensional Cartesian coordinate system, the plane coordinates of K computing devices distributed on a horizontal plane with a height of 0 can be expressed as The coordinates of the drone's hovering position can be expressed as Q = [q T ,h] T ,in is the two-dimensional coordinate of the UAV in the horizontal direction, and h is the hovering height of the UAV; If affected by the environment and the performance of the drone, the minimum and maximum hovering heights of the drone are h min and h max , then there are the following constraints on the drone's hovering height: h min ≤h≤h max (1) In a low-latency short-packet communication scenario, the time it takes for a device to unload a data packet does not exceed the coherence time of the channel. The unloading transmission time for all devices is T. In order to avoid transmission interference between different devices, all devices use orthogonal frequency division multiplexing technology to unload data. Different devices will be assigned to different orthogonal frequency bands, and the bandwidth allocated to device k is expressed as W. k (Hz), and the length of the data packet that device k can transmit in the channel is W k T; Selecting the Rice fading channel model as the channel model, the loss function obtained by the logarithmic probability regression method that is highly consistent with the calculated data is: where θ k is the sine value of the elevation angle, which is the angle between the drone-device k channel and the ground, and B1<0 reflects the logical midpoint of the positive value, B2>0 is the logical increase rate, and the constants C1>0 and C2>0 need to satisfy C1+C2=1; set the transmission power when the device offloads the task to the drone to P k , then the received signal-to-noise ratio of the offloading channel of device k can be expressed as: where h k is the channel gain, is the large-scale average channel power gain considering signal attenuation including path fading and shadow fading, where β0 is the average channel power gain at the reference distance d0 = 1m, and is the distance between the UAV and device k, α is the path fading coefficient, and N0 represents the noise power spectral density at the receiving end; Determine the short packet communication rate: Set the packet length on a given channel to N k =W k At time T, when device k unloads data, the error rate of the drone receiving data is ∈ k ∈(0,1), then the short packet communication rate (bits / s / Hz) when device k offloads tasks in a quasi-static flat channel is: where Q -1 (·) is the Q function The inverse function of V k is the channel dispersion, which describes the random variability of the channel relative to a deterministic channel with the same capacity. In a single-antenna quasi-static Ricean fading channel, it can be expressed as V k =1-(1+γ k ) -2 .

3. A method for optimizing computing delay based on a URLLC UAV edge computing system according to claim 1, characterized in that: The conditions of the calculation model described in step S2 include: The computing task data input to each computing device is set to be bit-independent and can be arbitrarily divided into two parts, one for local computing on the computing device and the other for edge computing on the drone, so that the two can be calculated in parallel without affecting the validity of the task data; The mobile edge computing server installed on the drone is configured with multiple independent computing units with powerful computing capabilities, so that tasks from different devices can be calculated simultaneously without interfering with each other and without queuing or congestion; Set the computing resources required for each bit of task data of device k, that is, the number of operating cycles of the central processing unit to c k .

4. A method for optimizing computing delay based on a URLLC UAV edge computing system according to claim 3, characterized in that: The local calculation model is: All computing devices can perform local computing in parallel with task offloading and edge computing without stopping during the entire process. Therefore, the local computing time is equal to the computing delay of the system. The minimum computing delay of the system under the optimal computing solution is expressed as t min , the CPU operating frequency of device k is f k , the unit is cycle / s, and the effective capacitance coefficient determined by the processor chip architecture is The corresponding local computing task volume and energy consumption Expressed as:

5. A method for optimizing computing delay based on URLLC UAV edge computing system according to claim 3, characterized in that: The edge computing model is: Edge computing model: Edge computing is divided into two parts: uplinking the task data to be offloaded to the drone's server using short packet communication, and the drone's server performing calculations after receiving the offloaded task; The time it takes for the device to encode the data to be unloaded into a data packet and transmit it to the drone is T. When the transmission rate is less than the channel capacity, the device k will unload the task to the drone within the transmission time T. And the communication energy consumption It can be expressed as: Because the computing power of the drone server is relatively strong, the drone is set to perform calculations immediately after receiving the complete data packet unloaded by the device, so the time for edge computing is Set the CPU frequency used by the drone to calculate the offloaded tasks from device k to f U,k (cycles / s), the effective capacitance coefficient determined by the processor chip architecture is Then the edge computing task volume of device k is and energy consumption They are: Because the bit error rate cannot be ignored in short packet communication, and there is also an interruption probability in the Rice fading model, that is, the effective task volume received by the drone must be less than the task volume unloaded by the device. If the bit error rate is ∈ k When the effective task volume actually received by the UAV is Because the amount of edge computing tasks cannot be greater than the amount of tasks that the drone has already received from the device offload, the following computational causal constraints apply: Set device k to effectively complete L k In order to ensure that the task volume requirements are met, the following task volume constraints are imposed on the task calculation of bits:

6. A method for optimizing computing delay based on a URLLC UAV edge computing system according to claim 5, characterized in that: Under the condition of limited code length, minimizing the computational delay of the UAV edge computing system is the optimization goal. Specifically: Only consider the process of the device unloading and transmitting a data packet. The optimization objective expression is: h min ≤h≤h max (10g) The constraint (10a) is to avoid the error rate ∈ k When the communication rate R is relatively small k For negative values, because the function Q -1 The value of (x) near x=0 tends to infinity, and formula (10d) is the constraint condition on the communication and computing energy consumption budget of the device during the calculation process. Formula (10e) and formula (10f) are the resource allocation constraints on the computing frequency and transmission power, respectively.

7. A method for optimizing computing delay based on a URLLC UAV edge computing system according to claim 6, characterized in that: Given resource allocation The optimized horizontal position q of the UAV with the hovering height h is: Determine the monotonicity and nonlinear lower bounds of the short packet communication rate expression, where For a given initial value of the signal-to-noise ratio Short packet communication rate R k The nonlinear lower bound of is: The coefficient If and only if When , the rate lower bound is tight, that is, Then the optimization objective expression is transformed and approximated as: Constraints (17a) and (17b) are combined into: If we define a constant Combining formula (2) and formula (3), we can get the signal-to-noise ratio γ at this time k Specifically expressed as: If we want to reduce the signal-to-noise ratio γ k The complexity of the introduction of auxiliary variables Then the sub-problem of optimizing the horizontal position q of the UAV with a fixed hovering height h is expressed as: The signal-to-noise ratio γ k The SCA methods used are: in Yes k The lower bound, is concave if and only if hour Established; Substituting the concave lower bound of the signal-to-noise ratio (28) into the constraint (20b), and relaxing the non-affine equality constraint (20a) into an inequality constraint, equation (20) can be transformed into: When the optimal solution is obtained for formula (29), the inequality constraint (29a) will become an equality; otherwise, if there is a strict inequality constraint in (29a) when the optimal solution is obtained, then the slack variable E can always be increased. k Until the equation is established, no constraints will be violated or the objective function value will be changed, so there will always be an optimal solution that makes the left and right constraints (29a) equal; Using the concave lower bound, (29) can be approximated as: Among them, formula (32) is a standard convex optimization problem, which is solved using the existing solver CVX.

8. A method for optimizing computing delay based on a URLLC UAV edge computing system according to claim 6, characterized in that: If a feasible UAV horizontal position q is given, the subproblem of optimizing the UAV hovering height h can be expressed as: Formula (33) is further transformed into: Among them, for a given initial drone hovering height And ω=ω k , 9. A method for optimizing computing delay based on a URLLC UAV edge computing system according to claim 6, characterized in that: The expression for optimizing resource allocation given the position of the UAV is: Formula (35) can be further approximated as: Wherein, formula (40) is a convex function and is solved using the CVX solver.

10. A method for optimizing computing delay based on URLLC UAV edge computing system according to claim 9, characterized in that: The specific process of step S5 is: (1) Set the short packet transmission delay T, bit error rate ∈ k , the target task computation amount L k ,Equipment Energy Consumption Budget (2) Let the cycle number i = 0, the initial delay Accuracy threshold ε=10 -8 , initialize bandwidth allocation Calculation frequency Horizontal position q (i) and hovering height h (i) ; (3) Calculate the minimum signal-to-noise ratio and in the interval In the binary search R k (γ k )=0 (4) Substitution And solve formula (32) to get the local optimal solution (5) Substitution And solve formula (34) to get the local optimal solution (6) Substitution And solve formula (40) to get the optimal solution (7) Let the minimum delay obtained by the i+1th step loop Update the ordinal number i = i + 1; (8) If That is, the algorithm converges to the preset threshold range and obtains the optimal solution q opt =q (i+1) , h opt =h (i+1) , Otherwise, repeat steps (3)-(7).

Images