Optimization method of air computing heterogeneous network facing imperfect channel

Abstract

The invention belongs to the field of Internet of Things, and relates to an optimization method of an air computing heterogeneous network facing an imperfect channel, which comprises the following steps of: constructing an RIS-assisted air computing heterogeneous network model MD facing the imperfect channel; the mean square error of the model MD is calculated, and a target optimization problem P based on a channel error matrix delta, an equipment transmitting power vector b, a base station receiving beam forming vector v and an intelligent reflecting surface shift vector theta is constructed with the minimum and maximum mean square error as the target; solving P to obtain an optimal equipment transmitting power vector b *, a base station receiving beam forming vector v * and an intelligent reflecting surface shift vector theta *; b, v and theta of the air computing heterogeneous network are set as b *, v * and theta * respectively, and the optimized air computing heterogeneous network is obtained; according to the method, the target optimization problem based on delta, b, v and theta is constructed with the mean square error of the minimum and maximum network model MD as the target, and the performance of the air computing heterogeneous network is remarkably improved.

Description

Technical Field

[0001] The invention belongs to the field of Internet of Things and relates to an optimization method for an air computing heterogeneous network facing an imperfect channel. Background Art

[0002] In recent years, with the development of wireless communication technology, the Internet of Things (IoT) has gradually become an important part of modern society. Through sensors, software and network technology, various physical devices are interconnected and networked to realize real-time transmission and processing of information, so that these devices can perceive environmental changes and exchange data, thereby providing various intelligent services such as smart homes, smart cities, and industrial automation. However, after the rapid development of the past few decades, the number of nodes in the Internet of Things has increased dramatically. Due to the dramatic increase in the number of node devices, the Internet of Things also faces huge challenges in data aggregation and communication, such as high latency, high energy consumption and limited bandwidth. One of the existing solutions is wireless data aggregation (WDA), which aims to simplify transmission, reduce data volume, and improve overall system performance by integrating, aggregating and processing data obtained from multiple sensors and devices. However, in the face of large-scale WDA with massive nodes, the low-band efficiency and high latency brought about by the traditional method of communicating first and then calculating are inevitable.

[0003] To address these challenges in the Internet of Things, Over-the-Air Computation (AirComp) as an emerging technology is believed to effectively overcome the limitations of wireless data fusion. By exploiting the waveform superposition characteristics of multiple access channels, AirComp combines concurrent data from multiple IoT devices with nomographic function (e.g., average and geometric mean) calculations. Through concurrent transmission, AirComp achieves low transmission delay that is independent of the number of IoT devices, thereby achieving fast WDA. In this way, parallel processing of computing tasks can be achieved on the wireless link, thereby greatly reducing the delay and bandwidth pressure of data transmission. Due to the above advantages, AirComp has received widespread attention in the fields of federated learning, signal processing, and drones. However, AirComp also faces some challenges. As the number of wireless devices connected increases, the poor communication environment will significantly affect the performance of AirComp. To solve this problem, researchers have proposed a number of methods for AirComp cells, such as power control, massive multi-input multi-output (MIMO), etc. However, these technologies are not suitable for multi-cellular scenarios, because in multi-cellular scenarios, the performance of AirComp is seriously affected by inter-cellular interference. Some research works have proposed cooperative interference management for multi-cellular scenarios and interference management mechanisms for AirComp coexistence networks. However, the above methods have limited improvement on the performance of AirComp by adjusting the transmit and receive coefficients of the transceiver. How to further suppress interference and thus reduce the mean square error of the system to improve the performance of AirComp is an urgent problem to be solved.

[0004] As a new technology, Reconfigurable Intelligent Surface (RIS) can effectively and cost-effectively assist AirComp in suppressing interference. RIS is a plane composed of multiple passive reflective elements that can adjust the phase and amplitude of the reflected signal. By controlling the reflective elements above, this technology can reconfigure the phase and amplitude of the signal to optimize the propagation path of the wireless signal, improve signal quality, increase coverage and reduce interference. At the same time, RIS also has the characteristics of low cost, low energy consumption and flexible deployment. Based on the above excellent characteristics, in 5G and future 6G communication systems, RIS is considered to be an important technology to improve network capacity, coverage and energy efficiency. Similarly, applying RIS to heterogeneous networks of aerial computing can also achieve interference suppression and thus improve the performance of AirComp.

[0005] However, the existing RIS-assisted aerial computing heterogeneous networks fail to take channel errors into account, resulting in high latency and insufficient mean square error (MSE) of the intelligent reflector-assisted aerial computing heterogeneous networks for imperfect channels, which in turn leads to poor performance. Summary of the invention

[0006] In order to solve the above-mentioned prior art problems, the present invention adopts an optimization method for an air computing heterogeneous network for imperfect channels, comprising:

[0007] S1. Constructing a RIS-assisted air computing heterogeneous network model MD for imperfect channels; the model MD includes: air computing cells, traditional cells and RIS, the air computing cells include: base stations and air computing devices, the traditional cells include: base stations and traditional devices; wherein RIS is a smart reflection surface;

[0008] S2. Calculate the mean square error of the model MD, and construct a target optimization problem based on the channel error matrix, the device transmit power vector, the base station receive beamforming vector, and the smart reflector phase shift vector with the goal of minimizing the mean square error;

[0009] S3. According to the target optimization problem, a first-level target optimization problem based on the channel error matrix is ​​constructed, and the first-level target optimization problem is solved by an analytical method to obtain a closed-form solution of the optimal channel error matrix;

[0010] S4. According to the closed-form solution of the target optimization problem and the optimal channel error matrix, a secondary target optimization problem based on the device transmit power vector, the base station receive beamforming vector and the smart reflector phase shift vector is constructed; the secondary target optimization problem is solved by using an alternating optimization algorithm to obtain the optimal device transmit power vector, the optimal base station receive beamforming vector and the optimal smart reflector phase shift vector;

[0011] S5. The device transmission vector, base station receive beamforming vector and RIS phase shift vector of the RIS-assisted air computing heterogeneous network for imperfect channels are respectively set to the optimal device transmission power vector, the optimal base station receive beamforming vector and the optimal smart reflection surface phase shift vector to obtain an optimized RIS-assisted air computing heterogeneous network for imperfect channels.

[0012] The air computing cell consists of a base station and K single-antenna air computing devices; the traditional cell consists of a base station and a single-antenna traditional device; in the air computing heterogeneous network model, one cell is the target cell and the rest are interference cells To calculate the set of cells l in the air, is the set of traditional cells n, the equipment of the target cell is the set of devices in the target cell, and the devices in the air computing cell l The set of devices in the air computing cell l and the devices in the traditional cell n It is a collection of devices in a traditional cellular n; the smart reflective surface has M reflective elements.

[0013] Objective Optimization Problem for:

[0014]

[0015] Among them, C1 is the constraint of the phase shift matrix of the smart reflection surface, and C2 is the transmission power b of the device of the target cell. k C3 and C4 are the constraints of the channel error matrix of the direct link path between the device and the target base station and the path through the smart reflector, respectively. b is the device transmit power vector of the target cell, v is the receive beamforming vector of the base station of the target cell, θ is the phase shift vector of the smart reflector, θ m is the phase shift of the reflective element m of the smart reflective surface, P max is the maximum value of the device’s transmit power, MSE is the mean square error of the intelligent reflector-assisted aerial computing heterogeneous network model for imperfect channels, Δ p is the channel error matrix of the direct link path between device p and the base station of the target cell, is the channel error matrix of the path between device p and the base station of the target cell through the smart reflector, and ρ is the maximum error of the channel error matrix.

[0016] The mean square error (MSE) of the intelligent reflector-assisted aerial computing heterogeneous network model for imperfect channels is:

[0017]

[0018] Among them, b i denote the transmission power of device i, (·) H represents the conjugate transpose, and They represent the measured channel vectors of the direct link path between the target cell device k, the air computing cell device i, the traditional cell device j and the base station of the target cell, respectively. and They represent the cascade channel error matrices of the target cell device k, the air computing cell device i, the traditional cell device j and the base station of the target cell through the intelligent reflection surface path, Δ k , Δ i and Δ jThey represent the channel error matrices of the direct link path between the target cell device k, the air computing cell device i, the traditional cell device j and the base station of the target cell, σ 2 represents the power of additive white Gaussian noise, and They respectively represent the cascade measurement channel matrices between the device k of the target cell, the air computing cell device i, the traditional cell device j and the base station of the target cell through the intelligent reflection surface path.

[0019] The first-level objective optimization problem is:

[0020]

[0021] The analytical method for solving the first-level optimization problem includes:

[0022] S31, using complex triangular inequalities to calculate the inequality of the primary objective optimization problem;

[0023] S32, according to the equality of the inequality of the primary objective optimization problem, an equation containing an optimal channel error matrix is ​​obtained;

[0024] S33, solving the equation containing the optimal channel error matrix according to the constraints C1 and C2 of the channel error matrix, and obtaining the closed-form solution Δ of the optimal channel error matrix * .

[0025] The closed-form solution of the optimal channel error matrix Δ * for:

[0026]

[0027] Among them, Δ k * , Δ i * , Δ j * They are Δ k , Δ i and Δ j The closed-form solution of They are and The closed form solution of .

[0028] The secondary objective optimization problem is:

[0029]

[0030] Using the alternating optimization method to optimize the secondary objective optimization problems includes:

[0031] S41. Fix v and θ of the secondary objective optimization problem to obtain the subproblem Optimizing subproblems by Lagrange multiplier method Get b k The optimal value b k * ; According to the b of all devices k k * Get the optimal device transmission coefficient b * ;

[0032] S42, b k * Substitute into the secondary objective optimization problem and get the subproblem based on v and θ Set the initial value θ0 of θ and the iteration stop condition threshold ∈;

[0033] S43, the sub-problem The θ of the previous iteration is fixed to θ t-1 , we get the subproblem based on v Use gradient descent to solve subproblems Optimize and get the optimized v t ;

[0034] S44, the problem of sub- The v is fixed to the optimized v t , we get the subproblem based on θ Use semidefinite relaxation and Taylor series expansion to solve subproblems After processing, the sub-problem Use convex optimization tools to solve subproblems Optimize and get the optimized θ t ;

[0035] S45, according to the optimized v t and θ t Calculate the ratio q t , if q t is less than the iteration stop condition threshold ∈, then v t and θ t are respectively used as the optimal base station receive beamforming vector v * and the optimal smart reflector phase shift vector θ * ; Otherwise, return to step S43.

[0036] According to the optimized v t and θ t Calculate the ratio q t Including: According to the optimized v t and θ t Calculate the mean square error (MSE) of the current iteration round t, calculate the absolute value of the difference between the MSE of the current iteration round t and the MSE of the previous iteration, divide the absolute value by the MSE of the previous iteration, and get the ratio qt .

[0037] Beneficial effects:

[0038] 1. The present invention constructs a RIS-assisted aerial computing heterogeneous network model MD for imperfect channels. Taking into account the channel error, the present invention constructs a target optimization problem based on the channel error matrix, the device transmit power vector, the base station receive beamforming vector and the intelligent reflector phase shift vector with the goal of minimizing the mean square error of the network model MD, and solves the optimization problem to obtain the optimal device transmit power vector, the optimal base station receive beamforming vector and the optimal intelligent reflector phase shift vector, which significantly improves the performance of the aerial computing heterogeneous network for imperfect channels; 2. The present invention adopts an alternating optimization method to solve the target optimization function, which significantly reduces the complexity of the method of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A flowchart of an optimization method for an in-flight computing heterogeneous network for imperfect channels provided by an embodiment of the present invention;

[0040] Figure 2 A schematic diagram of a system model of an in-flight computing heterogeneous network for imperfect channels provided by an embodiment of the present invention;

[0041] Figure 3 A flow chart of optimizing a target optimization problem using an alternating optimization algorithm provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0042] 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.

[0043] like Figure 1 As shown, the present invention adopts an optimization method for an air computing heterogeneous network for imperfect channels, including:

[0044] S1. Construct a RIS-assisted air computing heterogeneous network model MD for imperfect channels;

[0045] like Figure 2As shown in the figure, a RIS-assisted heterogeneous cellular network consisting of multiple AirComp cells and multiple traditional cells is considered. In this network, the target cell is surrounded by multiple other cells, so it will receive interference (Interference) generated by the uplink transmission of other cells during uplink transmission; each AirComp cell in the network consists of a base station with Nr antennas and K single-antenna devices (device), while each traditional cell consists of a single-antenna base station and a single-antenna device, and the network is equipped with a RIS with M reflective elements; for the universality of the model, the location of the base station adopts the Matern hard core point process (MHCPP); where the AirComp cell density is λ a , while the traditional cellular density is λ b , the coverage radius of each cell is R, and the locations of devices within the coverage area are uniformly distributed.

[0046] In one embodiment, the target cell is the AirComp cell; Represents the set of devices in the target cell, let represents the set of L interfering AirComp cells, let represents a collection of N traditional cells that generate interference, represents the set of K devices in AirComp cell l that cause interference, Represents a collection of devices in a traditional cellular n, Represents the collection of all devices in the system, that is

[0047] Let x p Representative equipment The measured data, where x is assumed p are independent and identically distributed. In order to facilitate power control, let Represents the data sent by device p, where represents the normalization function, and s p The mean is 0 and the variance is 1, that is, Then, the base station receiving signal of the target cell is expressed as follows:

[0048]

[0049] Where n represents additive Gaussian white noise;

[0050] The post-processed signal recovered by the target base station can be expressed as:

[0051]

[0052] It is assumed that the interfering AirComp cell adopts the optimal wireless power control strategy, that is, the transmission power Among them, f i Indicates the device and base station The channel vector between Representative base station The receive beamforming vector of .

[0053] The channel model of the embodiment of the present invention is a Rician model (Rician fading channel model). The channel vector between device k and the base station T of the target cell, the channel vector between device k and RIS, and the channel matrix between RIS and the base station T of the target cell are defined as follows:

[0054]

[0055] in, The path losses of the links between device k and the base station T of the target cell, device k and RIS, and RIS and the base station of the target cell are represented by represents the reference path loss and path loss exponent at d0 = 1 m, d k,T d k,R and R,T They represent the distances between device k and the base station T of the target cell, device k and RIS, and RIS and the base station of the target cell respectively; β represents the Rician factor, represents the field of real numbers, represents a complex domain; Represents the non-line of sight (NLoS) component, whose elements are independent and identically distributed and obey the complex Gaussian distribution represents the Line of Sight (LoS) component, represented by a Uniform Linear Array (ULA), whose array response is in, denote the antenna spacing and wavelength respectively, ω denotes the angle of departure (AoD) or the angle of arrival (AoA), then where ω AOA ,ω AOD Represent AOA and AOD respectively.

[0056] S2. Calculate the mean square error of the RIS-assisted over-the-air computing heterogeneous network model of the imperfect channel, and construct a target optimization problem based on the channel error matrix, device transmit power vector, base station receive beamforming vector and smart reflector phase shift matrix with the goal of minimizing the mean square error;

[0057] The mean square error (MSE) of the heterogeneous network model can be calculated in the air by combining the function g with the corresponding estimation function express:

[0058]

[0059] represents the diagonal phase shift matrix of RIS, where represents the phase shift of the reflective element, and function g represents the ideal received signal, that is, the signal sent by the device.

[0060] However, there are errors in the measurement of channel state information, so the mean square error under imperfect channels is:

[0061]

[0062] Among them, b k represents the transmission coefficient of device k in the target cell, v is the receive beamforming vector of the base station in the target cell, (·) H represents the conjugate transpose, Represents the measurement channel matrix between the smart reflector and the base station of the target cell, and They represent the measurement channel matrices between the target cellular device k, the air computing cellular device i, the traditional cellular device j and the smart reflective surface, respectively. and They represent the measured channel vectors of the direct link path between the target cell device k, the air computing cell device i, the traditional cell device j and the base station of the target cell, respectively. and They represent the channel error matrices of the target cell device k, the air computing cell device i, the traditional cell device j and the base station of the target cell through the intelligent reflection surface path, Δ k , Δ i and Δ j They represent the channel error vectors of the direct link path between the target cell device k, the air computing cell device i, the traditional cell device j and the base station of the target cell, θ represents the phase shift vector of the smart reflection surface, and σ 2 represents the power of additive white Gaussian noise, and They respectively represent the cascade measurement channel matrices between the device k of the target cell, the air computing cell device i, the traditional cell device j and the base station of the target cell through the intelligent reflection surface path.

[0063] To minimize the MSE under the constraints of the channel error matrix, the device power and the unit mode constraints of the RIS reflector phase shift, the optimization problem is: as follows:

[0064]

[0065] Among them, C1 is the constraint of the phase shift matrix of the smart reflection surface, and C2 is the transmission power b of the device of the target cell. k C3 and C4 are the constraints of the channel error matrix of the direct link path between the device and the target base station and the path through the smart reflector, respectively. b is the device transmit power vector of the target cell, θ m is the phase shift of the reflective element m of the smart reflective surface, P max is the maximum value of the device’s transmit power, Δ p is the channel error matrix of the direct link path between device p and the base station of the target cell, is the channel error matrix of the path between device p and the base station of the target cell through the smart reflector, and ρ is the maximum error of the channel error matrix.

[0066] S3. According to the target optimization problem, a first-level target optimization problem based on the channel error matrix is ​​constructed, and the first-level target optimization problem is solved by an analytical method to obtain a closed-form solution of the optimal channel error matrix;

[0067] First-order optimization problem based on channel error matrix Δ for:

[0068]

[0069] Solve the first-order optimization problem using analytical methods include:

[0070] S31. Optimize the primary objective Expand each term in the second normal form and use the complex triangle inequality to obtain the inequality for the target optimization problem;

[0071]

[0072] S322, according to the equality of the inequality of the primary objective optimization problem, an equation containing an optimal channel error matrix is ​​obtained;

[0073] Specifically, the first-level optimization problem is solved if and only if the following equation is satisfied. Get the maximum value:

[0074]

[0075] Among them, λ1, λ2, λ3, λ4, λ5, and λ6 are real numbers.

[0076] S33, solving the equation containing the optimal channel error matrix according to the constraints C1 and C2 of the channel error matrix to obtain the optimal channel error matrix Δ * The closed-form solution of is:

[0077]

[0078] S4. According to the closed-form solution of the target optimization problem and the optimal channel error matrix, a secondary target optimization problem based on the device transmit power vector, the base station receive beamforming vector and the smart reflector phase shift vector is constructed; the secondary target optimization problem is solved by the alternating optimization algorithm to obtain the optimal device transmit power vector b * , the optimal base station receive beamforming vector v * and the optimal smart reflector phase shift vector θ * ;

[0079] The secondary objective optimization problem based on the device transmit power vector, base station receive beamforming vector and smart reflector phase shift vector is:

[0080]

[0081] S5. Use the alternating optimization algorithm to solve the secondary target optimization problem and obtain the optimal device transmission power vector b of the target cell. * , base station receive beamforming vector v * and the smart reflector phase shift vector θ * ;

[0082] like Figure 3 As shown in Figure 2, using the alternating optimization algorithm to solve the secondary objective optimization problem includes:

[0083] S41. Fix v and θ of the secondary objective optimization problem to obtain the subproblem Optimizing subproblems by Lagrange multiplier method Get b k The closed-form solution of k * ; Set all devices k's b k * As the optimal device sends coefficient b * ;

[0084] S42, the device transmission power vector b of the secondary target optimization problem k Fixed to b k *, we get a subproblem that only contains v and θ Set the initial values ​​v0 and θ0 of v and θ and the iteration stop condition threshold ∈;

[0085] S43, the sub-problem θ is fixed to θ0, and the subproblem based on v is obtained Use gradient descent to solve subproblems Perform optimization to obtain optimized v1;

[0086] S44, the problem of sub- The v is fixed to the optimized v1, and the subproblem based on θ is obtained Use semidefinite relaxation and Taylor series expansion to solve subproblems After processing, the sub-problem Use convex optimization tools CVX for subproblems Perform optimization to obtain the optimized θ1;

[0087] S45, calculate the ratio q1 according to the optimized v1 and θ1, if q1 is less than the iteration stop condition threshold ∈, then stop the iteration, and use v1 and θ1 as the optimal base station receive beamforming vector v * and the smart reflector phase shift vector θ * ; Otherwise, execute step S46;

[0088] S46, the problem of sub- The θ of the previous iteration is fixed to θ t-1 , we get the subproblem based on v Use gradient descent to solve subproblems Optimize and get the optimized v t ;

[0089] S47, the problem of sub- The v is fixed to the optimized v t , we get the subproblem based on θ Use semidefinite relaxation and Taylor series expansion to solve subproblems After processing, the sub-problem Use convex optimization tools to solve subproblems Optimize and get the optimized θ t ;

[0090] S48, according to the optimized v t and θ t Calculate the ratio q t , if q t If it is less than the iteration stop condition threshold ∈, the iteration is stopped and v t and θ t As the optimal base station receive beamforming vector v* and the smart reflector phase shift vector θ * ; Otherwise, return to step S46.

[0091] Sub-questions for:

[0092]

[0093] in,

[0094]

[0095] Among them, A k , B and C are intermediate parameters, and represents the cascade equivalent channel vectors from the target cellular device, the air computing cellular device, the traditional cellular device to the base station of the target cellular device, b k represents the transmission coefficient of device k, v represents the receiving beamforming vector of the base station of the target cell, (·) H represents the conjugate transpose, P max is the maximum transmission power of device k, θ represents the phase shift vector of RIS, σ 2 represents the power of additive white Gaussian noise, and They represent the cascade measurement channel matrix between the target cell device k, the air computing cell device i, the traditional cell device j and the base station of the target cell through the intelligent reflection surface path, and represents the measurement channel matrix of the direct link path between the target cell device k, the air computing cell device i, the traditional cell device j and the base station of the target cell, respectively, i represents the emission coefficient of cellular device i calculated in the air, The complex domain.

[0096] Optimize subproblems using Lagrange multiplier method include:

[0097] Construct the Lagrangian function: Among them, λ k is the Lagrange multiplier.

[0098] For each variable x k Find the first-order derivative and take the point where the derivative is zero:

[0099]

[0100] Arranged:

[0101]

[0102] in, denotes conjugation;

[0103] When k = 0, that is When λ k >0, that is , consider the module constraints:

[0104]

[0105] After sorting, we get k The quadratic equation is:

[0106]

[0107] Due to λ k ≥0, we can get:

[0108]

[0109] Will Substitute into b k The expression of , we can get:

[0110]

[0111] Solve the Lagrangian function to get the optimal device transmission power

[0112]

[0113] Substitute b k * , sub-problem As shown below:

[0114]

[0115] Let θ be a fixed value, we can get the subproblem as follows:

[0116]

[0117] Where θ = θ t-1 , They respectively represent the cascade equivalent measurement channel matrices between device k in the target cell, device i in the AirComp cell in the interference cell, device j in the traditional cell in the interference cell and the BS of the target cell.

[0118] This is an unconstrained quadratic programming (QP) problem. Since the gradient of the objective function is obtainable, its first-order derivative function with respect to v can be obtained as follows:

[0119]

[0120] let The optimal solution is as follows:

[0121]

[0122] in, I is the identity matrix.

[0123] Let v be a fixed value v t , we can get the sub-problem as follows:

[0124]

[0125] in,

[0126]

[0127] v=v t , D, E, F are intermediate parameters, Tr is the trace of the matrix, rank is the rank of the matrix, For the matrix The elements of m rows and m columns in , ≥ are semi-positive definite.

[0128] Relax using semidefinite relaxation (SDR) The constraints and the Taylor series expansion result in the subproblem for:

[0129]

[0130] in, for The first-order Taylor expansion of c0, t E ,t F 、c E 、c F These are all intermediate parameters. Represents The value of the Taylor expansion point, Represents The value of the Taylor expansion point, the first-order Taylor expansion of f(x) is The corresponding value is f(x0).

[0131] By alternating optimization and This question turns into a The semidefinite programming (SDP) can be solved by existing convex optimization tools (such as CVX or MOSEK).

[0132] According to the optimized v t and θ t Calculate the ratio q t Including: According to the optimized v t and θ t Calculate the mean square error (MSE) of the current iteration round t, calculate the absolute value of the difference between the MSE of the current iteration round t and the MSE of the previous iteration, divide the absolute value by the MSE of the previous iteration, and get the ratio q t .

[0133] S5. Set the device transmit vector, base station receive beamforming vector and RIS phase shift vector of model MD to b respectively. * 、v * and θ * , and obtain the optimized RIS-assisted air computing heterogeneous network for imperfect channels.

[0134] The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation modes of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An optimization method for heterogeneous networks of air computing for imperfect channels, characterized in that: include: S1. Construct a RIS-assisted air computing heterogeneous network model MD for imperfect channels; The model MD includes: an air computing cell, a traditional cell and a RIS, wherein the air computing cell includes: a base station and an air computing device, and the traditional cell includes: a base station and a traditional device; wherein the RIS is an intelligent reflective surface; S2. Calculate the mean square error of the model MD, and construct a target optimization problem based on the channel error matrix, the device transmit power vector, the base station receive beamforming vector, and the smart reflector phase shift vector with the goal of minimizing the mean square error; S3. According to the target optimization problem, a first-level target optimization problem based on the channel error matrix is ​​constructed, and the first-level target optimization problem is solved by an analytical method to obtain a closed-form solution of the optimal channel error matrix; S4. According to the closed-form solution of the target optimization problem and the optimal channel error matrix, a secondary target optimization problem based on the device transmit power vector, the base station receive beamforming vector and the smart reflector phase shift vector is constructed; the secondary target optimization problem is solved by using an alternating optimization algorithm to obtain the optimal device transmit power vector, the optimal base station receive beamforming vector and the optimal smart reflector phase shift vector; S5. The device transmission vector, base station receive beamforming vector and RIS phase shift vector of the RIS-assisted air computing heterogeneous network for imperfect channels are respectively set to the optimal device transmission power vector, the optimal base station receive beamforming vector and the optimal smart reflection surface phase shift vector to obtain an optimized RIS-assisted air computing heterogeneous network for imperfect channels.

2. The optimization method for an in-flight computing heterogeneous network for imperfect channels according to claim 1, characterized in that: The air computing cell consists of a base station and K single-antenna air computing devices; the traditional cell consists of a base station and a single-antenna traditional device; in the air computing heterogeneous network model, one cell is the target cell and the rest are interference cells To calculate the set of cells l in the air, is the set of traditional cells n, the equipment of the target cell is the set of devices in the target cell, and the devices in the air computing cell l The set of devices in the air computing cell l, the devices in the traditional cell n is the set of devices in the traditional cellular n; The smart reflective surface has M reflective elements.

3. The optimization method for an in-flight computing heterogeneous network for imperfect channels according to claim 2, characterized in that: Objective Optimization Problem for: Among them, C1 is the constraint of the phase shift matrix of the smart reflection surface, and C2 is the transmission power b of the device of the target cell. k C3 and C4 are the constraints of the channel error matrix of the direct link path between the device and the target base station and the path through the smart reflector, respectively. b is the device transmit power vector of the target cell, v is the receive beamforming vector of the base station of the target cell, θ is the phase shift vector of the smart reflector, θ m is the phase shift of the reflective element m of the smart reflective surface, P max is the maximum value of the device’s transmit power, MSE is the mean square error of the intelligent reflector-assisted aerial computing heterogeneous network model for imperfect channels, Δ p is the channel error matrix of the direct link path between device p and the base station of the target cell, is the channel error matrix of the path between device p and the base station of the target cell through the smart reflection surface, and ρ is the maximum error of the channel error matrix.

4. The optimization method for an in-flight computing heterogeneous network for imperfect channels according to claim 3, characterized in that: The mean square error (MSE) of the intelligent reflector-assisted aerial computing heterogeneous network model for imperfect channels is: Among them, b i denote the transmission power of device i, (·) H represents the conjugate transpose, and They represent the measured channel vectors of the direct link path between the target cell device k, the air computing cell device i, the traditional cell device j and the base station of the target cell, respectively. and They represent the cascade channel error matrices of the target cell device k, the air computing cell device i, the traditional cell device j and the base station of the target cell through the intelligent reflection surface path, Δ k , Δ i and Δ j They represent the channel error matrices of the direct link path between the target cell device k, the air computing cell device i, the traditional cell device j and the base station of the target cell, σ 2 represents the power of additive white Gaussian noise, and They respectively represent the cascade measurement channel matrices between the device k of the target cell, the air computing cell device i, the traditional cell device j and the base station of the target cell through the intelligent reflection surface path.

5. The optimization method for an in-flight computing heterogeneous network for imperfect channels according to claim 4, characterized in that: The first-level objective optimization problem is:

6. The optimization method for an in-flight computing heterogeneous network for imperfect channels according to claim 5, characterized in that: The analytical method for solving the first-level optimization problem includes: S31, using complex triangular inequalities to calculate the inequality of the primary objective optimization problem; S32, according to the equality of the inequality of the primary objective optimization problem, an equation containing an optimal channel error matrix is ​​obtained; S33, solving the equation containing the optimal channel error matrix according to the constraints C1 and C2 of the channel error matrix, and obtaining the closed-form solution Δ of the optimal channel error matrix * .

7. The optimization method for an in-flight computing heterogeneous network for imperfect channels according to claim 6, characterized in that: The closed-form solution of the optimal channel error matrix Δ * for: Among them, Δ k * , Δ i * , Δ j * They are Δ k , Δ i and Δ j The closed-form solution of They are and The closed form solution of .

8. The optimization method for an in-flight computing heterogeneous network for imperfect channels according to claim 3, characterized in that: The secondary objective optimization problem is:

9. The optimization method for an in-flight computing heterogeneous network for imperfect channels according to claim 8, characterized in that: Using the alternating optimization method to optimize the secondary objective optimization problems includes: S41. Fix v and θ of the secondary objective optimization problem to obtain the subproblem Optimizing subproblems by Lagrange multiplier method Get b k The optimal value b k * ; According to the b of all devices k k * Get the optimal device transmission coefficient b * ; S42, b k * Substitute into the secondary objective optimization problem and get the subproblem based on v and θ Set the initial value θ0 of θ and the iteration stop condition threshold ∈; S43, the sub-problem The θ of the previous iteration is fixed to θ t-1 , we get the subproblem based on v Use gradient descent to solve the subproblem Optimize and get the optimized v t ; S44, the problem of sub- The v is fixed to the optimized v t , we get the subproblem based on θ Use semidefinite relaxation and Taylor series expansion to solve subproblems After processing, the sub-problem Use convex optimization tools to solve subproblems Optimize and get the optimized θ t ; S45, according to the optimized v t and θ t Calculate the ratio q t , if q t is less than the iteration stop condition threshold ∈, then v t and θ t are respectively used as the optimal base station receive beamforming vector v * and the optimal smart reflector phase shift vector θ * ; Otherwise, return to step S43.

10. The optimization method for an in-flight computing heterogeneous network for imperfect channels according to claim 9, characterized in that: According to the optimized v t and θ t Calculate the ratio q t Including: According to the optimized v t and θ t Calculate the mean square error (MSE) of the current iteration round t, calculate the absolute value of the difference between the MSE of the current iteration round t and the MSE of the previous iteration, divide the absolute value by the MSE of the previous iteration, and get the ratio q t .

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