IRS-aided air computing multi-time scale transmission method and IRS-aided air computing multi-time scale transmission system

Abstract

The invention discloses an IRS-aided air computing multi-time scale transmission method and system. The method comprises the following steps: constructing an IRS-aided large-scale AirComp system; on the basis of an IRS-assisted large-scale AirComp system, data is generated according to multiple single-antenna Internet of Things devices, access point parameters are obtained, array flow patterns of the access points and the IRS are calculated, receiving signals of the access points are obtained on the basis of channel parameters of all direct links in the system and a reflection matrix theta of the IRS, and then access point parameter estimation values are obtained. The distortion between the access point parameters and the parameter estimation values is measured by using the MSE; receiving beam forming at the access point is determined in advance based on the static angle information, IRS phase shift is optimized according to long-term statistical CSI, and an optimization problem corresponding to a multi-time scale transmission scheme is given; and solving the optimization problem. The method is low in calculation complexity and has more advantages for a large-scale system with a large amount of N and K.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication assisted by intelligent reflecting surfaces, and in particular relates to an IRS-assisted aerial computing multi-time scale transmission method and system. Background Art

[0002] Air Computing (AirComp) is regarded as an innovative technology that can achieve fast wireless data aggregation on distributed IoT devices to solve the latency problem of large-scale access in the IoT era. The basic idea of ​​AirComp is to use the waveform superposition characteristics of multiple access channels to enable access points to directly receive data transmitted simultaneously from a large number of devices. By seamlessly integrating computing and communication, AirComp is particularly suitable for various latency-critical applications that require data aggregation, such as wireless control, distributed sensing, and wireless federated learning.

[0003] Unlike traditional rate-oriented communications, mean square error (MSE) is widely used as a performance metric to quantify the error in AirComp calculations. To achieve reliable AirComp, relevant scholars have devoted themselves to the design of transceivers based on AirComp calculations, which involves the control of transmit power and the shaping of receive beams. These schemes are designed around the principle of minimizing the MSE caused by wireless fading and receiver noise. Despite theoretical progress, due to random wireless fading, the computational performance may not be guaranteed by transceiver design alone. To address this issue, Zhai et al. (SCI article "Simultaneously transmitting and reflecting (STAR)RIS assisted over-the-aircomputation systems") used the high passive beamforming gain of smart reflective surfaces (IRS) to suppress the MSE caused by AirComp. However, the schemes involved mainly rely on full instantaneous channel state information (I-CSI), which will result in high channel estimation overhead, especially for large-scale AirComp systems with a large number of devices and IRS elements. Therefore, in order to meet the needs of large-scale AirComp systems, it is necessary to develop a high-reliability transmission protocol and system that does not rely on full I-CSI operation. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a multi-time scale transmission method for IRS-assisted airborne computing. By utilizing large-scale IRS-assisted AirComp, a new multi-time scale protocol is developed to provide a prerequisite for the construction of subsequent energy-saving architecture.

[0005] Another object of the present invention is to provide a transmission system for the method.

[0006] Technical solution: The invention provides an IRS-assisted airborne computing multi-time scale transmission method, comprising the following steps:

[0007] S1. Deploy the intelligent reflective surface IRS around the access point and build an IRS-assisted AirComp system. In the system, there are direct links between the IRS and the access point, between the single-antenna IoT device and the access point, and between the single-antenna IoT device and the IRS.

[0008] S2. Based on the IRS-assisted AirComp system, the set s of electromagnetic wave data emitted by all single-antenna IoT devices is calculated, the array flow pattern of the access point and IRS is calculated, and the electromagnetic wave data y received by the access point is obtained based on the channel parameters of each direct link in the system and the reflection matrix Θ of the IRS, and then the estimated value of the set of electromagnetic wave data emitted by all single-antenna IoT devices at the access point is obtained. And use MSE to measure s and Distortion between

[0009] S3, predetermine the receive beamforming at the access point based on the static angle information, optimize the IRS phase shift according to the long-term statistical CSI, and give the corresponding optimization problem of the multi-time scale transmission scheme;

[0010] S4, the optimization problem in step S3 is solved using a two-step algorithm, first solving the optimization problem of the reflection matrix Θ of the IRS, and then solving {b k ,η} optimization problem, b k is the emission scalar of the single-antenna IoT device k, and η is the noise factor at the access point.

[0011] Furthermore, the set s of electromagnetic wave data emitted by all single-antenna IoT devices in step S2 is expressed as:

[0012]

[0013] Where K is the number of single-antenna IoT devices, s k is the data generated at k of a single-antenna IoT device, and its properties are: k}=0,Ε{s k 2}=1, E{i} and |i| 2 are the mathematical expectation operator and the modulus identifier respectively; the data of different single-antenna IoT devices are orthogonal to each other, that is, For j The conjugate of j is the data generated at single-antenna IoT device j;

[0014] Array flow pattern of access points and IRS a M (φr )and They are:

[0015]

[0016] Among them, a M (φ r ) is the array flow type of the access point, is the array flow type of IRS, () T It is represented as the transpose operator, d is the spacing of the IRS reflection unit or antenna unit, λ is the wavelength of the electromagnetic wave emitted by the single-antenna IoT device, φ r and are the arrival angle and departure angle of the electromagnetic wave from the IRS to the access point, respectively.

[0017] Further, in step S2, based on the channel parameters of each direct link in the system and the reflection matrix θ of the IRS, a received signal of the access point is obtained, including:

[0018] The expression of the baseband channel G from IRS to the access point is:

[0019]

[0020] Where ρ1 is the path loss of the direct link from IRS to access point, a M (φ r ) is the array flow type of the access point, for The conjugate transpose of is the array flow pattern of IRS;

[0021] Baseband channel h from single-antenna IoT device to access point d,k The expression is:

[0022]

[0023] Among them, ρ d is the path loss of the direct link from single-antenna IoT device k to the access point, is the channel from a single-antenna IoT device to an access point without considering fading, For a single antenna IoT device set;

[0024] Baseband channel h from single-antenna IoT device to IRS r,k The expression is:

[0025]

[0026] Among them, δ is the Rice factor, ρ r,k is the path loss of the direct link from single-antenna IoT device k to IRS; and are the channel components of the direct link and indirect link from the single-antenna IoT device k to the IRS, respectively, where the IRS-assisted steering vector The arrival angle υ of the single-antenna IoT device k to the IRS k related;

[0027] The reflection matrix Θ of IRS is:

[0028]

[0029] Where diag{} represents the diagonal matrix operator, θ1 and θ N denote the phase shifts of the 1st and Nth IRS reflection units, respectively;

[0030] The electromagnetic wave data y received by the access point is expressed as:

[0031]

[0032] Among them, h k (θ) = h d,k +GΘh r,k is the equivalent channel vector from single-antenna IoT device k to the access point, b k is the transmission scalar of the single-antenna IoT device k, and the square of the transmission scalar is less than or equal to the maximum transmission power P of each single-antenna IoT device max ,s k is the data generated at k of a single-antenna IoT device, and n represents the additive white Gaussian noise at the access point;

[0033] An estimate of the aggregate electromagnetic wave data emitted by all single-antenna IoT devices at the access point for:

[0034]

[0035] Where η and v represent the noise factor and receiving beam vector at the access point, respectively. H is the conjugate transpose of v.

[0036] Further, in step S2, MSE is used to measure s and The distortion between is expressed as:

[0037]

[0038] Among them, MSE(v,Θ,b k ,η) is related to the parameter v,Θ,b k ,η, v is the receiving beam vector at the access point, v H is the conjugate transpose of v, Θ is the reflection matrix of IRS, bk is the emission scalar of the single-antenna IoT device k, η is the noise factor at the access point, and h k (Θ) is the equivalent channel vector from single-antenna IoT device k to the access point, K is the number of single-antenna IoT devices, σ 2 is the noise power of the additive white Gaussian noise at the access point.

[0039] Furthermore, in step S3, the receiving beamforming at the access point is predetermined based on the static angle information, that is:

[0040]

[0041] Among them, v * is the optimal solution for v, v is the receiving beam vector at the access point, a M (φ r ) is the array flow type of the access point, and M is the number of antenna units equipped with the access point;

[0042] According to the long-term statistical CSI, the IRS phase shift is optimized, and the corresponding optimization problem of the multi-time scale transmission scheme is given as:

[0043]

[0044] Among them, MSE(v * ,Θ,b k ,η) is the same as the parameter v * ,Θ,b k ,η is the mean square error, Θ is the reflection matrix of IRS, b k is the emission scalar of single-antenna IoT device k, η is the noise factor at the access point, P max is the maximum transmit power of each single-antenna IoT device, θ n is the phase shift of the nth IRS reflection unit, L represents the IRS quantization level, For a single-antenna IoT device set, is the IRS reflection unit set; the internal MSE minimization problem uses the variables {b k ,η}, while the external MSE minimization problem is solved with the help of variable Θ.

[0045] Furthermore, the solution method for optimizing θ in the optimization problem in step S4 is:

[0046] First, the expected value of the effective channel power gain Γ is derived k for:

[0047]

[0048] Among them, Ε{i} and |i| 2are the mathematical expectation operator and modulus identifier respectively, (v * ) H v * The conjugate transpose of * is the optimal solution for v, v is the receiving beam vector at the access point, h k (Θ) is the equivalent channel vector from the single-antenna IoT device k to the access point, ρ d is the path loss of the direct link from single-antenna IoT device k to the access point, M is the number of antenna units equipped on the access point, ρ1 is the path loss of the direct link from IRS to the access point, ρ r,k is the path loss of the direct link from single-antenna IoT device k to IRS, δ is the Rice factor, is the array flow pattern of IRS, for The conjugate transpose of N ( k ) is the IRS-assisted steering vector, and N is the number of IRS reflection units;

[0049] Then maximize The solution for Θ is obtained by projecting the optimized phase shifts of successive IRS reflection units onto The closest discrete value is obtained by:

[0050]

[0051] in, is the optimal solution for the phase shift of the nth IRS reflector unit of the kth device, θ k,n is the phase shift of the nth IRS reflection unit of the kth device, d is the spacing of the IRS reflection units or antenna units, λ is the wavelength of the electromagnetic wave emitted by the single-antenna IoT device, is the departure angle of the electromagnetic wave from the IRS to the access point, υ k is the arrival angle from single-antenna IoT device k to IRS, and L represents the IRS quantization level;

[0052] According to the obtained The optimal solution of IRS reflection matrix Θ is constructed by majority voting technique. The optimal solution for the phase shift of each IRS reflection unit in is:

[0053]

[0054] in, and are the optimal solutions for the phase shifts of the 1st, nth and Nth IRS reflection units respectively.

[0055] Further, in step S4, the optimization problem is optimized.k ,η} is solved as follows:

[0056] Let the kth intermediate temporary variable be γ k =(v * ) H h k (Θ * ), (v * ) H v * The conjugate transpose of * is the optimal solution for v, v is the receiving beam vector at the access point, Θ * is the optimal solution of the IRS reflection matrix Θ, h k (Θ * ) is the same as Θ * The relevant equivalent channel vector; b k is the emission scalar of single-antenna IoT device k, p k is the transmission power of the kth single-antenna IoT device, For γ k First, we measure s and The distortion formula between is rewritten as:

[0057]

[0058] Among them, MSE(p k ,η) is the same as the parameter p k ,η is the mean square error related to the access point, η is the noise factor at the access point, σ 2 is the noise power of additive white Gaussian noise at the access point, K is the number of single-antenna IoT devices;

[0059] Therefore, optimizing {b k ,η} is simplified to {p k ,η} optimization, that is:

[0060]

[0061] Among them, P max is the maximum transmit power of each single-antenna IoT device;

[0062] Secondly, assuming that γ1 2 ≤...≤γ K | 2 , where γ1| 2 and γ K | 2 Respectively represent the square of the modulus of the 1st and Kth intermediate temporary variables. The solution to the above optimization problem is as follows:

[0063]

[0064] Among them, η * is the optimal solution for η, is the intermediate variable, γ j 2 represents the square of the modulus value of the jth intermediate temporary variable, For a single antenna IoT device set; combined with η * Get the optimal power control:

[0065]

[0066] in, Yes k The optimal solution of

[0067] The system corresponding to the method of the present invention includes:

[0068] A system building unit is used to deploy the intelligent reflective surface IRS around the access point to build an IRS-assisted AirComp system, in which there are direct links between the IRS and the access point, between the single-antenna IoT device and the access point, and between the single-antenna IoT device and the IRS;

[0069] The parameter calculation unit is used to calculate the set s of electromagnetic wave data emitted by all single-antenna IoT devices based on the IRS-assisted AirComp system, calculate the array flow type of the access point and the IRS, and obtain the electromagnetic wave data y received by the access point based on the channel parameters of each direct link in the system and the reflection matrix Θ of the IRS, and then obtain the estimated value of the set of electromagnetic wave data emitted by all single-antenna IoT devices at the access point. And use MSE to measure s and Distortion between

[0070] An optimization problem determination unit, configured to predetermine the receive beamforming at the access point based on the static angle information, optimize the IRS phase shift according to the long-term statistical CSI, and provide an optimization problem corresponding to the multi-time scale transmission scheme;

[0071] The optimization problem solving unit is used to solve the optimization problem using a two-step algorithm. First, the reflection matrix Θ optimization problem of IRS is solved, and then {b k ,η} optimization problem, b k is the emission scalar of the single-antenna IoT device k, and η is the noise factor at the access point.

[0072] An electronic device for storing and executing the method, the device comprising:

[0073] A memory storing executable program code;

[0074] a processor coupled to the memory;

[0075] The processor calls the executable program code stored in the memory to execute the steps of the IRS-assisted air-computation multi-time-scale transmission method.

[0076] A computer-readable storage medium for storing and executing the method, wherein the computer-readable storage medium stores computer instructions, and when the computer instructions are called, they are used to execute the steps of the IRS-assisted airborne computational multi-time scale transmission method.

[0077] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are: the proposed solution is derived using a closed-form expression, does not require an iterative algorithm, and thus has low computational complexity, which makes it more advantageous for large-scale IRS-assisted AirComp systems with a large number of N and K. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 It is a flow chart of the present invention;

[0079] Figure 2 This is an IoT application scenario diagram of IRS-assisted AirComp proposed in the present invention;

[0080] Figure 3 It is a diagram of the multi-time scale transmission scheme of IRS-assisted AirComp proposed in the present invention;

[0081] Figure 4 This is a rendering of the multi-time-scale transmission scheme of IRS-assisted AirComp proposed in the present invention. DETAILED DESCRIPTION

[0082] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0083] like Figure 1 As shown, the IRS-assisted airborne computing multi-time scale transmission method described in the present invention comprises the following steps:

[0084] Step 1. Considering the IoT application scenario, deploy an intelligent reflective surface IRS around an access point to assist in aggregating data from multiple single-antenna IoT devices. Assuming that there are direct links between the IRS and the access point, between the single-antenna IoT device and the access point, and between the single-antenna IoT device and the IRS, build an IRS-assisted AirComp system, which includes an access point, an IRS, and K single-antenna IoT devices; the access point is equipped with M antenna units, and the IRS is equipped with N IRS reflective units. Without loss of generality, assume that the antennas and reflective units are uniformly linearly arranged. Let and They are represented as a single-antenna IoT device set and an IRS reflection unit set respectively. Figure 2 The application of this system in the Internet of Things scenario.

[0085] Step 2: When the IRS-assisted AirComp system is applied to the IoT scenario, consider s k is the electromagnetic wave data emitted by the single-antenna IoT device k(k∈), and assuming that s k It has the following properties:

[0086] Ε{s k}=0,Ε{s k 2}=1 (1)

[0087] Among them, Ε{i} and |i| 2 are the mathematical expectation operator and modulus identifier, respectively, Ε{s k} is s k In addition, the electromagnetic wave data emitted by different single-antenna IoT devices are orthogonal to each other, that is, where s i is the electromagnetic wave data emitted by a single-antenna IoT device i, (i) * represents the conjugate operator, For j The conjugate of j is the electromagnetic wave data emitted by the single-antenna IoT device j, and the set of electromagnetic wave data emitted by all single-antenna IoT devices is recorded as Let the array flow type of access point and IRS be a M (φ r )and They are respectively expressed as follows:

[0088]

[0089] Among them, a M (φ r ) is the array flow type of the access point, is the array flow type of IRS, () T It is represented as the transpose operator, d is the spacing of the IRS reflection unit or antenna unit, λ is the wavelength of the electromagnetic wave emitted by the single-antenna IoT device, φ r and are the arrival angle and departure angle of the electromagnetic wave from the IRS to the access point, respectively.

[0090] When the IRS-assisted AirComp system is applied to IoT scenarios, the channel parameters are calculated as follows:

[0091] (1) The baseband channel from IRS to access point is expressed as And give the mathematical expression:

[0092]

[0093] Where ρ1 is the path loss of the direct link from IRS to access point, () H is represented as the conjugate transpose operator, for The conjugate transpose of .

[0094] (2) Considering that the direct links from K single-antenna IoT devices to the access point may be easily blocked, the Rayleigh fading model is used to characterize these direct links. The baseband channel from the single-antenna IoT device k to the access point is expressed as And give the mathematical expression:

[0095]

[0096] Among them, ρ d is the path loss of the direct link from single-antenna IoT device k to the access point, is the channel from a single-antenna IoT device to an access point without considering fading, The mean is 0 and the covariance matrix is ​​I M The complex Gaussian distribution, I M It is an M-order unit matrix.

[0097] (3) Similarly, the baseband channel from a single-antenna IoT device to the IRS is expressed as And give the mathematical expression:

[0098]

[0099] Among them, δ is the Rice factor, ρ r,k is the path loss of the direct link from single-antenna IoT device k to IRS, and are the channel components of the direct link and indirect link from the single-antenna IoT device k to the IRS, respectively, where the IRS-assisted steering vector The arrival angle υ of the single-antenna IoT device k to the IRS k related, The mean is 0 and the covariance matrix is ​​I N The complex Gaussian distribution, I N is an N-order unit matrix.

[0100] (4) The reflection matrix Θ of IRS is defined as the following diagonal matrix:

[0101]

[0102] Where diag{} represents the diagonal matrix operator, θ1 and θ NThey represent the phase shifts of the 1st and Nth IRS reflection units, respectively. In order to reduce the actual hardware cost, only discrete phase shifts are considered, and the phase shift of the nth IRS reflection unit is L represents the IRS quantization level.

[0103] In combination with the above, it can be seen that under a given IRS reflection matrix, the electromagnetic wave data y received by the access point of the present invention can be expressed as:

[0104]

[0105] Among them, h k (θ) = h d,k +GΘh r,k is the equivalent channel vector from the single-antenna IoT device k to the access point. k is the transmission scalar of the single-antenna IoT device k, and the square of the transmission scalar is less than or equal to the maximum transmission power P of each single-antenna IoT device max n represents the additive Gaussian white noise at the access point, which has a mean of 0 and a covariance matrix of σ 2 I M The complex Gaussian distribution, σ 2 is the noise power, I M is an M-order unit matrix. Then, at the access point Estimated value of It can be expressed as:

[0106]

[0107] Among them, η and satisfy ||v|| 2 = 1, respectively, v represents the noise factor and the receiving beam vector at the access point, v H is the conjugate transpose of v. According to formula (9), the present invention uses the mean square error MSE to measure s and The distortion between

[0108]

[0109] Among them, MSE(v,Θ,b k ,η) is related to the parameter v,Θ,b k ,η is the mean square error related to .

[0110] And use formula (10) to optimize {v, Θ, b k ,η}, in order to suppress the MSE.

[0111] Step 3: Combined with formula (10), we can see that in large-scale networks where K and N are large enough, the optimization algorithm based on semi-positive definite programming is highly dependent on the complete CSI, that is, {v, Θ, b k,η}, resulting in a heavy channel estimation overhead. To this end, the present invention proposes a multi-time scale protocol scheme in the IRS-assisted spatial computing system to reduce the channel estimation overhead caused by a large number of IRS reflection units and single-antenna IoT devices. The multi-time scale transmission scheme is as follows Figure 3 As shown, by utilizing a specific channel structure, the receive beamforming of the access point is predetermined based on static angle information, while the phase shift of the IRS reflection unit is optimized based on long-term statistical channel state information (S-CSI); using the obtained receive beamforming and IRS reflection unit phase shift, the effective I-CSI of each device can be reduced to a scalar, which greatly reduces the amount of CSI that needs to be acquired. And in each channel coherent block, the effective I-CSI is used to determine power control. The following is a detailed description of the multi-time scale transmission scheme:

[0112] First, the present invention utilizes a specific channel structure, and the receiving beamforming at the access point is predetermined based on static angle information, that is:

[0113]

[0114] Among them, v * is the optimal solution for v.

[0115] Secondly, the phase shift of the IRS reflection unit is optimized according to the S-CSI, and the corresponding optimization problem of the multi-time scale transmission scheme is given:

[0116]

[0117] Among them, MSE(v * ,Θ,b k ,η) is the same as the parameter v * ,Θ,b k ,η is the mean square error related to .

[0118] For the optimization problem (12), the internal MSE minimization problem is solved by using the variables {b k ,η}, and the external MSE minimization problem is solved with the help of variable Θ. Meanwhile, the expectation in formula (12) is taken from all random realizations of I-CSI.

[0119] Step 4: Since the optimal {b k ,η} is difficult to derive, so it is difficult to get the optimal solution for the optimization problem (12). To this end, the present invention provides a two-step algorithm to obtain a highly stable and low-complexity solution.

[0120] (1) Optimizing Θ:

[0121] According to the optimization problem (12), the present invention first derives the expected value of the effective channel power gain Γk for:

[0122]

[0123] Among them, (v * ) H v * The conjugate transpose of .

[0124] Then maximize The solution for Θ is obtained by projecting the phase shifts of the optimized successive IRS reflection units onto The closest discrete value is obtained by:

[0125]

[0126] in, is the optimal solution for the phase shift of the nth IRS reflector unit of the kth device, θ k,n is the phase shift of the nth IRS reflection unit of the kth device.

[0127] According to formula (14), Constructing the optimal solution of IRS reflection matrix using majority voting technique The optimal solution for the phase shift of each IRS reflection unit in is as follows:

[0128]

[0129] in, is the optimal solution for the phase shift of the nth IRS reflection unit.

[0130] (2) Optimize {b k ,η}:

[0131] Let the kth intermediate temporary variable be γ k =(v * ) H h k (Θ * )and h k (Θ * ) is the same as Θ * The equivalent channel vector, p k is the transmission power of the kth single-antenna IoT device. First, formula (10) can be rewritten as:

[0132]

[0133] Among them, MSE(p k ,η) is the same as the parameter p k ,η is the mean square error related to .

[0134] Therefore, optimizing {b k ,η} is simplified to {p k ,η} optimization, that is:

[0135]

[0136] Secondly, assuming that γ1 2 ≤...≤γ K | 2 , where γ1| 2 and γ K | 2 They represent the square of the modulus of the 1st and Kth intermediate temporary variables respectively. The solution of the optimization problem (17) is as follows:

[0137]

[0138] Among them, η * is the optimal solution for η, is the intermediate variable, γ j 2 They represent the square of the modulus of the jth intermediate temporary variable. Combined with formula (18), the optimal power control can be obtained:

[0139]

[0140] in, Yes k The optimal solution of Using the obtained receive beamforming and phase shifting of the IRS reflection unit, the effective I-CSI of each device is reduced to a scalar, which greatly reduces the amount of CSI that needs to be obtained. The effective I-CSI is used in each channel coherence block to determine power control.

[0141] In the embodiment of the present invention, the specific parameters are set as follows: the access point and IRS are located at (0,0,0) meters and (0,0,10) meters respectively. The devices are evenly distributed in a circle with a radius of 20 meters and a center of (200,0,0) meters. The path loss of the direct link from the IRS to the access point and the single-antenna IoT device to the IRS is set to 2.2, and the path loss of the direct link from the single-antenna IoT device to the access point is set to 3.8. The Rice factor and the signal attenuation at a reference distance of 1 meter are set to 10 dB and 30 dB. Let M = 10, P max =20dBm and σ 2 =-80dBm. The effect diagram of the multi-time scale transmission scheme of IRS-assisted AirComp proposed in the present invention is as follows Figure 4As shown in the figure, it can be seen that the scheme using optimized IRS phase shift significantly outperforms other benchmark schemes, and the performance improvement is more obvious as N increases. In addition, without IRS, optimal power control is significantly better than channel inversion power control, and with the deployment of IRS, the corresponding performance loss becomes negligible, especially when the channel state information is assumed to be known.

Claims

1. An IRS-assisted airborne computing multi-time scale transmission method, characterized in that: The following steps are involved: S1. Deploy the intelligent reflective surface IRS around the access point and build an IRS-assisted AirComp system. In the system, there are direct links between the IRS and the access point, between the single-antenna IoT device and the access point, and between the single-antenna IoT device and the IRS. S2. Based on the IRS-assisted AirComp system, the set s of electromagnetic wave data emitted by all single-antenna IoT devices is calculated, the array flow pattern of the access point and IRS is calculated, and the electromagnetic wave data y received by the access point is obtained based on the channel parameters of each direct link in the system and the reflection matrix Θ of the IRS, and then the estimated value of the set of electromagnetic wave data emitted by all single-antenna IoT devices at the access point is obtained. And use MSE to measure s and Distortion between S3, predetermine the receive beamforming at the access point based on the static angle information, optimize the IRS phase shift according to the long-term statistical CSI, and give the corresponding optimization problem of the multi-time scale transmission scheme; S4, the optimization problem in step S3 is solved using a two-step algorithm, first solving the optimization problem of the reflection matrix Θ of the IRS, and then solving {b k ,η} optimization problem, b k is the emission scalar of the single-antenna IoT device k, and η is the noise factor at the access point.

2. The IRS-assisted airborne computing multi-time scale transmission method according to claim 1, characterized in that: The set s of electromagnetic wave data emitted by all single-antenna IoT devices in step S2 is expressed as: Where K is the number of single-antenna IoT devices, s k is the data generated at k of a single-antenna IoT device, and its properties are: k }=0,Ε{s k 2 }=1, E{i} and |i| 2 are the mathematical expectation operator and the modulus identifier respectively; the data of different single-antenna IoT devices are orthogonal to each other, that is, For j The conjugate of j is the data generated at single-antenna IoT device j; Array flow pattern of access points and IRS a M (φ r )and They are: Among them, a M (φ r ) is the array flow type of the access point, is the array flow type of IRS, () T It is represented as the transpose operator, d is the spacing of the IRS reflection unit or antenna unit, λ is the wavelength of the electromagnetic wave emitted by the single-antenna IoT device, φ r and are the arrival angle and departure angle of the electromagnetic wave from the IRS to the access point, respectively.

3. The IRS-assisted airborne computing multi-time scale transmission method according to claim 1, characterized in that: In step S2, based on the channel parameters of each direct link in the system and the reflection matrix θ of the IRS, a received signal of the access point is obtained, including: The expression of the baseband channel G from IRS to the access point is: Where ρ1 is the path loss of the direct link from IRS to access point, a M (φ r ) is the array flow type of the access point, for The conjugate transpose of is the array flow pattern of IRS; Baseband channel h from single-antenna IoT device to access point d,k The expression is: Among them, ρ d is the path loss of the direct link from single-antenna IoT device k to the access point, is the channel from a single-antenna IoT device to an access point without considering fading, For a single antenna IoT device set; Baseband channel h from single-antenna IoT device to IRS r,k The expression is: Among them, δ is the Rice factor, ρ r,k is the path loss of the direct link from single-antenna IoT device k to IRS; and are the channel components of the direct link and indirect link from the single-antenna IoT device k to the IRS, respectively, where the IRS-assisted steering vector The arrival angle υ of the single-antenna IoT device k to the IRS k related; The reflection matrix Θ of IRS is: Where diag{} represents the diagonal matrix operator, θ1 and θ N denote the phase shifts of the 1st and Nth IRS reflection units, respectively; The electromagnetic wave data y received by the access point is expressed as: Among them, h k (θ) = h d,k +GΘh r,k is the equivalent channel vector from single-antenna IoT device k to the access point, b k is the transmission scalar of the single-antenna IoT device k, and the square of the transmission scalar is less than or equal to the maximum transmission power P of each single-antenna IoT device max ,s k is the data generated at k of a single-antenna IoT device, and n represents the additive white Gaussian noise at the access point; An estimate of the aggregate electromagnetic wave data emitted by all single-antenna IoT devices at the access point for: Where η and v represent the noise factor and receiving beam vector at the access point, respectively, and v H is the conjugate transpose of v.

4. The IRS-assisted airborne computing multi-time scale transmission method according to claim 1, characterized in that: In step S2, MSE is used to measure s and The distortion between is expressed as: Among them, MSE(v,Θ,b k ,η) is related to the parameters v,Θ,b k ,η, v is the receiving beam vector at the access point, v H is the conjugate transpose of v, Θ is the reflection matrix of IRS, b k is the emission scalar of the single-antenna IoT device k, η is the noise factor at the access point, and h k (Θ) is the equivalent channel vector from single-antenna IoT device k to the access point, K is the number of single-antenna IoT devices, σ 2 is the noise power of the additive white Gaussian noise at the access point.

5. The IRS-assisted airborne computing multi-time scale transmission method according to claim 1, characterized in that: In step S3, the receiving beamforming at the access point is predetermined based on the static angle information, that is: Among them, v * is the optimal solution for v, v is the receiving beam vector at the access point, a M (φ r ) is the array flow type of the access point, and M is the number of antenna units equipped with the access point; According to the long-term statistical CSI, the IRS phase shift is optimized, and the corresponding optimization problem of the multi-time scale transmission scheme is given as: η≥0, Among them, MSE(v * ,Θ,b k ,η) is the same as the parameter v * ,Θ,b k ,η is the mean square error, Θ is the reflection matrix of IRS, b k is the emission scalar of single-antenna IoT device k, η is the noise factor at the access point, P max is the maximum transmit power of each single-antenna IoT device, θ n is the phase shift of the nth IRS reflection unit, L represents the IRS quantization level, For a single-antenna IoT device set, is the IRS reflection unit set; the internal MSE minimization problem uses the variables {b k ,η}, while the external MSE minimization problem is solved with the help of variable Θ.

6. The IRS-assisted airborne computing multi-time scale transmission method according to claim 1, characterized in that: The solution method for optimizing Θ in the optimization problem in step S4 is: First, the expected value of the effective channel power gain Γ is derived k for: Among them, Ε{i} and |i| 2 are the mathematical expectation operator and modulus identifier respectively, (v * ) H v * The conjugate transpose of * is the optimal solution for v, v is the receiving beam vector at the access point, h k (Θ) is the equivalent channel vector from the single-antenna IoT device k to the access point, ρ d is the path loss of the direct link from single-antenna IoT device k to the access point, M is the number of antenna units equipped on the access point, ρ1 is the path loss of the direct link from IRS to the access point, ρ r,k is the path loss of the direct link from single-antenna IoT device k to IRS, δ is the Rice factor, is the array flow pattern of IRS, for The conjugate transpose of N ( k ) is the IRS-assisted steering vector, and N is the number of IRS reflection units; Then maximize The solution for Θ is obtained by projecting the optimized phase shifts of successive IRS reflection units onto The closest discrete value is obtained by: in, is the optimal solution for the phase shift of the nth IRS reflector unit of the kth device, θ k,n is the phase shift of the nth IRS reflection unit of the kth device, d is the spacing of the IRS reflection units or antenna units, λ is the wavelength of the electromagnetic wave emitted by the single-antenna IoT device, is the departure angle of the electromagnetic wave from the IRS to the access point, υ k is the arrival angle from single-antenna IoT device k to IRS, and L represents the IRS quantization level; According to the obtained The optimal solution of IRS reflection matrix Θ is constructed by majority voting technique. The optimal solution for the phase shift of each IRS reflection unit in is: in, and are the optimal solutions for the phase shifts of the 1st, nth and Nth IRS reflection units respectively.

7. The IRS-assisted airborne computing multi-time scale transmission method according to claim 1, characterized in that: In step S4, the optimization problem is optimized. k ,η} is solved as follows: Let the kth intermediate temporary variable be γ k =(v * ) H h k (Θ * ), (v * ) H v * The conjugate transpose of * is the optimal solution for v, v is the receiving beam vector at the access point, Θ * is the optimal solution of the IRS reflection matrix Θ, h k (Θ * ) is the same as Θ * The relevant equivalent channel vector; b k is the emission scalar of single-antenna IoT device k, p k is the transmission power of the kth single-antenna IoT device, For γ k First, we measure s and The distortion formula between is rewritten as: Among them, MSE(p k ,η) is the same as the parameter p k ,η is the mean square error related to the access point, η is the noise factor at the access point, σ 2 is the noise power of additive white Gaussian noise at the access point, K is the number of single-antenna IoT devices; Therefore, optimizing {b k ,η} is simplified to {p k ,η} optimization, that is: Among them, P max is the maximum transmit power of each single-antenna IoT device; Secondly, assuming that γ1 2 ≤...≤γ K | 2 , where γ1| 2 and γ K | 2 Respectively represent the square of the modulus of the 1st and Kth intermediate temporary variables. The solution to the above optimization problem is as follows: Among them, η * is the optimal solution for η, is the intermediate variable, γ j 2 represents the square of the modulus value of the jth intermediate temporary variable, For a single antenna IoT device set; combined with η * Get the optimal power control: in, Yes k The optimal solution of 8. An IRS-assisted airborne computing multi-time scale transmission system, characterized in that: include: A system building unit is used to deploy the intelligent reflective surface IRS around the access point to build an IRS-assisted AirComp system, in which there are direct links between the IRS and the access point, between the single-antenna IoT device and the access point, and between the single-antenna IoT device and the IRS; The parameter calculation unit is used to calculate the set s of electromagnetic wave data emitted by all single-antenna IoT devices based on the IRS-assisted AirComp system, calculate the array flow type of the access point and the IRS, and obtain the electromagnetic wave data y received by the access point based on the channel parameters of each direct link in the system and the reflection matrix Θ of the IRS, and then obtain the estimated value of the set of electromagnetic wave data emitted by all single-antenna IoT devices at the access point. And use MSE to measure s and Distortion between An optimization problem determination unit, configured to predetermine the receive beamforming at the access point based on the static angle information, optimize the IRS phase shift according to the long-term statistical CSI, and provide an optimization problem corresponding to the multi-time scale transmission scheme; The optimization problem solving unit is used to solve the optimization problem using a two-step algorithm. First, the reflection matrix Θ optimization problem of IRS is solved, and then {b k ,η} optimization problem, b k is the emission scalar of the single-antenna IoT device k, and η is the noise factor at the access point.

9. An electronic device, characterized in that: The device comprises: A memory storing executable program code; a processor coupled to the memory; The processor calls the executable program code stored in the memory to execute the steps of the IRS-assisted airborne computing multi-time scale transmission method described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, which, when called, are used to execute the steps of the IRS-assisted airborne computing multi-time scale transmission method described in any one of claims 1 to 7.

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