Optimization design method based on STAR-RIS auxiliary air computing system and related device

Abstract

The invention discloses an optimization design method based on an STAR-RIS auxiliary air computing system and a related device. According to the invention, under the condition of channel state information error uncertainty, imperfect CSI characteristics of a cascade channel and a direct channel are considered; according to channel data, an initial channel error and a transceiver initial design parameter, a direct channel CSI error, a transmission cascade channel CSI error, a reflection cascade channel CSI error, a transmitter emission coefficient, a receiver receiving beam forming vector and an STAR-RIS phase shift matrix diagonal transmission vector and a reflection vector are alternately optimized. The objective of the invention is to optimize the calculation mean square error precision under the worst CSI condition, and obtain the target design parameters of the transceiver, thereby improving the robust transmission performance of an STAR-RIS auxiliary calculation system under the imperfect CSI condition, and further improving the reliability and efficiency of a wireless communication network.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to an optimized design method and related apparatus for a STAR-RIS-assisted in-flight computing system. Background Technology

[0002] In IoT scenarios, the massive amount of data generated by numerous devices leads to bottlenecks in communication overhead, latency, and energy consumption. Over-the-air computing leverages the waveform superposition characteristics of wireless channels, enabling all IoT devices to transmit in parallel on the same frequency resources, thereby integrating communication and computation processes to alleviate these bottlenecks. However, channel fading introduces aggregation errors, significantly reducing computational accuracy. To address this challenge, Reconfigurable Intelligent Surfaces (RIS) offer an effective solution for compensating for fading through programmable control of the wireless environment. However, traditional RISs can only reflect signals, forcing transceivers to be deployed on the same side, resulting in inherent half-space coverage limitations. To address this, Simultaneous Transmitting and Reflecting Reconfigurable Intelligent Surfaces (STAR-RIS) are introduced, achieving a 360-degree all-space intelligent wireless environment.

[0003] In wireless environments, Channel State Information (CSI) plays a crucial role in optimizing configuration, achieving efficient beam control, interference management, and resource allocation. However, in practical applications, due to factors such as channel estimation and quantization errors, as well as feedback delays, transceivers often struggle to obtain the ideal CSI at the current moment. This leads to non-ideal CSI issues in the optimized design of STAR-RIS systems, impacting the reliability of wireless communication networks. Summary of the Invention

[0004] This invention provides an optimization design method and related apparatus for a STAR-RIS-assisted over-the-air computing system, which addresses the technical problem that existing wireless communication transceivers struggle to obtain the ideal CSI at the current moment, leading to non-ideal CSI issues in the optimization design of STAR-RIS systems and consequently affecting the reliability of wireless communication networks.

[0005] This invention provides an optimization design method for a STAR-RIS-assisted in-flight computing system, the computing system comprising multiple transmitters, a STAR-RIS, and a receiver; the method includes:

[0006] Channel data between each transmitter and receiver is obtained based on large-scale and small-scale fading models. Initial channel errors and transceiver initial design parameters are obtained by initializing the channel errors and design parameters between each transmitter and receiver based on preset constraints. The channel data includes a direct channel matrix, a transmission-cascaded channel matrix, and a reflection-cascaded channel matrix. The initial channel errors include initial direct channel CSI errors, transmission-cascaded channel CSI errors, and reflection-cascaded channel CSI errors. The initial transceiver design parameters include initial transmitter transmit coefficients, receiver receive beamforming vectors, and STAR-RIS phase shift matrix diagonal transmission vectors and reflection vectors.

[0007] Based on the channel data, the initial channel error, and the initial transceiver design parameters, the initial direct channel CSI error, transmission cascaded channel CSI error, reflection cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector are alternately optimized to generate target transceiver design parameters with the goal of minimizing the mean square error of the computing system under the worst CSI error condition.

[0008] Optionally, the step of alternately optimizing the initial direct channel CSI error, transmission-cascaded channel CSI error, reflection-cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector based on the channel data, the initial channel error, and the initial transceiver design parameters, to generate the transceiver target design parameters with the objective of minimizing the mean square error of the computing system under the worst-case CSI error condition, includes:

[0009] With the goal of minimizing the mean square error between the receiver's predicted received signal and the actual received signal under the worst-case CSI error condition, the initial receiver receiving beamforming vector is updated based on the direct channel matrix, the transmission concatenated channel matrix, and the reflection concatenated channel matrix, as well as the initial direct channel CSI error, the transmission concatenated channel CSI error, the reflection concatenated channel CSI error, the transmitter transmit coefficient, and the diagonal transmission vector and reflection vector of the STAR-RIS phase shift matrix, to obtain the optimal receiver receiving beamforming vector.

[0010] Based on the calculation formula for mean square error, according to the initial transmitter transmit coefficient, STAR-RIS phase shift matrix diagonal transmission vector and reflection vector, and the optimal receiver receive beamforming vector, the worst-case CSI error, direct channel CSI error, transmission-cascaded channel CSI error, and reflection-cascaded channel CSI error are determined in the order of the transmitters.

[0011] Based on the direct channel matrix, the transmission concatenated channel matrix, and the reflection concatenated channel matrix, as well as the CSI errors of the direct channel, the transmission concatenated channel, and the reflection concatenated channel under the worst CSI error condition, the direct channel matrix, the transmission concatenated channel matrix, and the reflection concatenated channel matrix under the worst CSI error condition are obtained.

[0012] Based on the Lagrange multiplier method, the initial transmitter transmit coefficients are updated according to the initial STAR-RIS phase shift matrix, diagonal transmission vector, reflection vector, and optimal receiver beamforming vector, as well as the direct channel matrix, transmission concatenated channel matrix, and reflection concatenated channel matrix under the worst CSI error condition, and the optimal transmitter transmit coefficients are obtained.

[0013] By introducing binary vectors, the initial STAR-RIS phase shift matrix diagonal transmission vector and reflection vector are updated based on the worst-case CSI error conditions: direct channel CSI error, transmission-cascaded channel CSI error, reflection-cascaded channel CSI error, direct channel matrix, transmission-cascaded channel matrix, and reflection-cascaded channel matrix, as well as the optimal transmitter transmit coefficient and receiver receive beamforming vector.

[0014] The target design parameters of the transceiver are determined by using the direct channel matrix, transmission-cascaded channel matrix, and reflection-cascaded channel matrix under the worst-case CSI error condition, as well as the optimal transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector.

[0015] Optionally, the step of determining the transceiver target design parameters using the direct channel matrix, transmission-cascaded channel matrix, and reflection-cascaded channel matrix under the worst-case CSI error condition, as well as the optimal transmitter transmit coefficients, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector, includes:

[0016] According to the formula for calculating the mean square error, the mean square error is calculated by using the direct channel matrix, transmission concatenated channel matrix, and reflection concatenated channel matrix under the worst CSI error condition, as well as the optimal transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector.

[0017] Determine whether the calculated mean square error meets the preset calculation accuracy conditions;

[0018] If not satisfied, the worst-case CSI error conditions for direct channel CSI, transmission-cascaded channel CSI, and reflection-cascaded channel CSI, along with the optimal transmitter transmit coefficient, receiver receive beamforming vector, STAR-RIS phase shift matrix diagonal transmission vector, and reflection vector, are used as the initial direct channel CSI error, transmission-cascaded channel CSI error, reflection-cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector.

[0019] The process jumps to the step of minimizing the mean square error between the estimated and actual received signals of the receiver. Under the first-order optimality condition of the mean square error, the initial receiver beamforming vector is updated based on the direct channel matrix, the transmission concatenated channel matrix, the reflection concatenated channel matrix, the initial direct channel CSI error, the transmission concatenated channel CSI error, the reflection concatenated channel CSI error, the transmitter transmit coefficient, and the diagonal transmission vector and reflection vector of the STAR-RIS phase shift matrix, to obtain the optimal receiver beamforming vector.

[0020] If satisfied, the optimal transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector are used as the target design parameters for the transceiver.

[0021] Optionally, the formula for calculating the mean square error is expressed as follows:

[0022]

[0023] In the formula: The received signal predicted by the receiver The actual signal received by the receiver The mean square error of the calculation; A set of labels for transmitters in the transmission space; This is the set of labels for transmitters in the reflected space; The total number of transmitter labels; To receive the beamforming vector, For receiving beamforming vector The conjugate transpose of; This is the estimated direct channel matrix vector from transmitter to receiver for the kth transmitter. The CSI error of the k-th direct channel; and These are the cascaded channel matrices from the transmitter to the receiver via STAR-RIS, respectively, when the k-th transmitter is estimated to be located in the transmission and reflection spaces. and These represent the CSI error of the cascaded channel where the k-th transmitter is located in the transmission or reflection space; and These are the diagonal transmission and reflection vectors of STAR-RIS, respectively; For the first Transmitter emission coefficient of each transmitter; The energy is additive white Gaussian noise.

[0024] Optionally, the preset constraints include:

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] In the formula: At maximum transmission power, This is the set of transmitter labels; and The m-th element of the diagonal transmission vector and reflection vector of STAR-RIS, respectively. and These are the transmission and reflection phase coefficients, respectively. The set of labels for STAR-RIS elements; It is a 2-norm. It is the F-norm; and These are the bounded error limits for the direct channel and the cascaded channel, respectively.

[0034] Optionally, the step of determining the worst-case CSI error, the direct channel CSI error, the transmission-cascaded channel CSI error, and the reflection-cascaded channel CSI error based on the calculation formula for the mean square error, according to the initial transmitter transmit coefficients, the STAR-RIS phase shift matrix diagonal transmission vector and reflection vector, and the optimal receiver receive beamforming vector, in the order of the transmitters, includes:

[0035] Based on the formula for calculating the mean square error, the maximum direct channel CSI error is calculated according to the transmitter sequence, the initial transmitter transmit coefficients, and the optimal receiver receive beamforming vector. It is then determined whether the maximum direct channel CSI error meets the preset constraints. If it does, the maximum direct channel CSI error is used as the direct channel CSI error under the worst-case CSI error condition. If it does not meet the constraints, the maximum direct channel CSI error is normalized to obtain the direct channel CSI error under the worst-case CSI error condition.

[0036] Based on the formula for calculating the mean square error, the maximum transmission cascaded channel CSI error is calculated according to the transmitter sequence, the initial transmitter transmission coefficients, the STAR-RIS phase shift matrix diagonal transmission vector, and the optimal receiver beamforming vector. It is then determined whether the maximum transmission cascaded channel CSI error meets preset constraints. If it does, the maximum transmission cascaded channel CSI error is used as the transmission cascaded channel CSI error under the worst-case CSI error condition. If it does not meet the constraints, the maximum transmission cascaded channel CSI error is normalized to obtain the transmission cascaded channel CSI error under the worst-case CSI error condition.

[0037] Based on the formula for calculating the mean square error, the maximum reflection cascaded channel CSI error is calculated according to the transmitter sequence, the initial transmitter transmit coefficients, the STAR-RIS phase shift matrix diagonal reflection vector, and the optimal receiver receive beamforming vector. It is then determined whether the maximum reflection cascaded channel CSI error meets preset constraints. If it does, the maximum reflection cascaded channel CSI error is used as the worst-case CSI error. If it does not meet the constraints, the maximum reflection cascaded channel CSI error is normalized to obtain the worst-case CSI error.

[0038] This invention also provides a robust design system based on a STAR-RIS-assisted in-flight computing system, the computing system comprising multiple transmitters, a STAR-RIS, and a receiver; the design system includes:

[0039] The parameter initialization unit is used to obtain channel data between each transmitter and receiver based on large-scale and small-scale fading models, and to initialize the channel errors and design parameters between each transmitter and receiver based on preset constraints to obtain initial channel errors and initial transceiver design parameters. The channel data includes a direct channel matrix, a transmission-cascaded channel matrix, and a reflection-cascaded channel matrix. The initial channel errors include initial direct channel CSI errors, transmission-cascaded channel CSI errors, and reflection-cascaded channel CSI errors. The initial transceiver design parameters include initial transmitter transmit coefficients, receiver receive beamforming vectors, and STAR-RIS phase shift matrix diagonal transmission vectors and reflection vectors.

[0040] The target optimization unit is used to alternately optimize the initial direct channel CSI error, transmission cascaded channel CSI error, reflection cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector based on the channel data, the initial channel error, and the initial transceiver design parameters, in order to generate transceiver target design parameters with the goal of minimizing the mean square error of the computing system under the worst CSI error condition.

[0041] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of any of the optimization design methods described above.

[0042] The present invention also provides a computer-readable storage medium having a computer program or instructions stored thereon, wherein the computer program or instructions, when executed by a processor, implement the steps of any of the above-described optimization design methods.

[0043] The present invention also provides a computer program product, including a computer program or instructions, characterized in that, when the computer program or instructions are executed by a processor, they implement the steps of any of the above-described optimization design methods.

[0044] As can be seen from the above technical solutions, the present invention has the following advantages:

[0045] This invention provides an optimization design method and related apparatus for a STAR-RIS-assisted in-flight computing system, wherein the method includes:

[0046] Channel data between each transmitter and receiver is obtained based on large-scale and small-scale fading models. Initial channel errors and transceiver initial design parameters are obtained by initializing the channel errors and design parameters between each transmitter and receiver based on preset constraints. The channel data includes the direct channel matrix, the transmission-cascaded channel matrix, and the reflection-cascaded channel matrix. The initial channel errors include the initial direct channel CSI error, the transmission-cascaded channel CSI error, and the reflection-cascaded channel CSI error. The initial transceiver design parameters include the initial transmitter transmit coefficients, the receiver receive beamforming vector, and the STAR-RIS phase shift matrix diagonal transmission vector and reflection vector.

[0047] Based on channel data, initial channel error, and initial transceiver design parameters, the initial direct channel CSI error, transmission cascaded channel CSI error, reflection cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector are alternately optimized to generate target transceiver design parameters with the goal of minimizing the mean square error of the computational system under the worst CSI error condition.

[0048] This invention, under the condition of uncertainty in Channel State Information (CSI) error, simultaneously considers the imperfect CSI characteristics of cascaded and direct channels. Based on channel data, initial channel error, and initial transceiver design parameters, it alternately optimizes the CSI error of direct channel, CSI error of transmission cascaded channel, CSI error of reflection cascaded channel, transmitter transmit coefficient, receiver receive beamforming vector, and diagonal transmission and reflection vectors of the STAR-RIS phase shift matrix. The aim is to optimize the mean square error accuracy under the worst-case CSI condition, obtain the target design parameters of the transceiver, thereby improving the robust transmission performance of the STAR-RIS-assisted computing system under imperfect CSI conditions, and thus enhancing the reliability and efficiency of wireless communication networks. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 A flowchart illustrating the steps of an optimization design method for a STAR-RIS-assisted in-flight computing system provided in this embodiment of the invention;

[0051] Figure 2A schematic diagram of the structure of a STAR-RIS-assisted in-flight computing system provided in an optional embodiment of the present invention;

[0052] Figure 3 The system performance simulation diagram of the STAR-RIS assisted in-flight computing system based on different numbers of elements is provided for the embodiments of the present invention.

[0053] Figure 4 This is a structural block diagram of an optimized design system based on the STAR-RIS-assisted in-flight computing system provided for an embodiment of the present invention. Detailed Implementation

[0054] This invention provides an optimization design method and related apparatus for a STAR-RIS-assisted over-the-air computing system, which addresses the technical problem that existing wireless communication transceivers struggle to obtain the ideal CSI at the current moment, leading to non-ideal CSI issues in the optimization design of the STAR-RIS system and consequently affecting the reliability of the wireless communication network.

[0055] To make the objectives, features, and advantages of this invention more apparent and understandable, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0056] Please see Figure 1 This invention provides an optimization design method for a STAR-RIS-assisted in-flight computing system, the method comprising:

[0057] Step 101: Obtain channel data between each transmitter and receiver based on large-scale and small-scale fading models, and initialize the channel error and design parameters between each transmitter and receiver based on preset constraints to obtain the initial channel error and the initial design parameters of the transceiver.

[0058] It should be noted that this invention relates to a STAR-RIS-assisted in-flight computing system, such as... Figure 2As shown, the computing system includes k transmitters, one STAR-RIS, and one receiver. In this computing system, the transmitters can transmit signals to the receiver via a direct channel or reflect signals to the receiver via a cascaded channel through the STAR-RIS. The direct channel refers to the wireless transmission path between the transmitter and the receiver, and its channel response is determined by path loss, shadowing fading, and multipath effects. The cascaded channel refers to the combined path of the signal transmitted by the transmitter, transmitted through the STAR-RIS, reflected, and then arriving at the receiver.

[0059] In this embodiment, channel modeling of the STAR-RIS computing system and its transceiver is performed based on large-scale and small-scale fading models to obtain estimated channel data. Pre-defined constraints are set according to actual requirements, and channel errors and design parameters are randomly initialized within the constraints. It is understood that the channel data containing channel errors provides data support consistent with real channel characteristics for subsequent alternating optimization of the system's robustness, significantly enhancing the reliability of the computing system in uncertain channel environments.

[0060] The channel data includes the direct channel matrix estimated from the k-th transmitter to the receiver. The cascaded channel matrix estimated from k transmitters to the receiver via STAR-RIS (including transmission concatenated channel matrix) and reflection concatenated channel matrix The initial channel error includes the initial direct channel CSI error from the k-th transmitter to the receiver. CSI error of the cascaded channel from k transmitters through STAR-RIS to the receiver (including transmission concatenation channel CSI error) CSI error of reflection-cascaded channel The initial design parameters for the transceiver include the k-th initial transmitter transmission coefficient. The initial receiver receives the beamforming vector. and the initial STAR-RIS phase shift matrix diagonal transfer vector and reflection vector .

[0061] The large-scale and small-scale fading models involved in this embodiment are given below.

[0062] The large-scale fading model is specifically modeled as follows:

[0063] ,

[0064] in, For distance-related path loss; For reference distance = Path loss at 1 meter (m); The distance between them; The path loss index;

[0065] Small-scale fading uses a Rician fading channel, which consists of line-of-sight and non-line-of-sight components. The specific fading channel is modeled as follows:

[0066]

[0067]

[0068] in, For the STAR-RIS to receiver cascade channel, For user k, this is the direct channel to the receiver; The path loss is calculated with a reference distance of 1 meter. and These represent the distances between the receiver and STAR-RIS, and between STAR-RIS and transmitter k, respectively. and Both represent path loss exponents; and All are Rice's K-factors, defined as the ratio of line-of-sight path power to non-line-of-sight path power; and All are deterministic line-of-sight components. and All are stochastic nonlinear line-of-sight components modeled by Rayleigh fading.

[0069] The preset constraints include:

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] In the formula: At maximum transmission power, This is the set of transmitter labels; and Let the m-th element of the diagonal transmission vector and reflection vector of STAR-RIS be respectively, where , The set of labels for STAR-RIS elements; It is a 2-norm. It is the F-norm; and These are the bounded error limits for the direct channel and the cascaded channel, respectively.

[0079] Among the aforementioned preset constraints, the transmission power of the transmitter's transmission coefficient must be less than or equal to the maximum transmission power. Constraints; and The m-th element of the transmission vector and reflection vector, respectively, is defined as... ,in Due to the characteristics of STAR-RIS, the transmission and reflection phase coefficients need to be coupled as follows: Direct channel CIS error Cascaded channel CIS error when the transmitter is located in the transmission and reflection space and It needs to be limited to the upper bound of the bounded error. and Inside.

[0080] Step 102: Based on the channel data, initial channel error, and initial transceiver design parameters, alternately optimize the initial direct channel CSI error, transmission cascaded channel CSI error, reflection cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector to generate target transceiver design parameters with the goal of minimizing the mean square error of the computing system under the worst CSI error condition.

[0081] It should be noted that the mean square error of the calculation system is used to measure the accuracy of the received signal. Specifically, it refers to the mean square error between the receiver's estimated received signal and the actual received signal.

[0082] In this embodiment, under the worst-case CSI error condition, the goal is to minimize the mean square error of the calculated received signal versus the actual received signal. The direct channel CSI error, cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and the diagonal transmission and reflection vectors of the STAR-RIS phase shift matrix are alternately optimized to generate the transceiver target design parameters. This ensures that the mean square error of the computing system remains minimized (i.e., effectively suppressed) under the worst-case CSI condition, thereby improving the robust transmission performance of the computing system under CSI error conditions, and ultimately enhancing the reliability and efficiency of the wireless communication network.

[0083] In a specific implementation method, step 102 specifically includes the following steps:

[0084] S11. With the goal of minimizing the mean square error between the receiver's predicted received signal and the actual received signal under the worst CSI error condition, the initial receiver receiving beamforming vector is updated based on the direct channel matrix, the transmission concatenated channel matrix, the reflection concatenated channel matrix, the initial direct channel CSI error, the transmission concatenated channel CSI error, the reflection concatenated channel CSI error, the transmitter transmit coefficient, and the diagonal transmission vector and reflection vector of the STAR-RIS phase shift matrix, in order to obtain the optimal receiver receiving beamforming vector.

[0085] S12. Based on the calculation formula for mean square error, according to the initial transmitter transmit coefficient, STAR-RIS phase shift matrix diagonal transmission vector and reflection vector, and the optimal receiver receive beamforming vector, determine the worst-case CSI error for direct channel CSI error, transmission-cascaded channel CSI error and reflection-cascaded channel CSI error in the order of transmitters.

[0086] S13. Based on the direct channel matrix, the transmission concatenated channel matrix, and the reflection concatenated channel matrix, as well as the direct channel CSI error, the transmission concatenated channel CSI error, and the reflection concatenated channel CSI error under the worst CSI error condition, the direct channel matrix, the transmission concatenated channel matrix, and the reflection concatenated channel matrix under the worst CSI error condition are obtained.

[0087] S14. Based on the Lagrange multiplier method, according to the initial STAR-RIS phase shift matrix, diagonal transmission vector, reflection vector, and optimal receiver beamforming vector, as well as the direct channel matrix, transmission concatenated channel matrix, and reflection concatenated channel matrix under the worst CSI error condition, the initial transmitter transmit coefficients are updated to obtain the optimal transmitter transmit coefficients.

[0088] S15. Introduce binary vectors. Based on the direct channel matrix, transmission concatenated channel matrix, and reflection concatenated channel matrix under the worst CSI error condition, as well as the optimal transmitter transmit coefficient and receiver receive beamforming vector, update the initial STAR-RIS phase shift matrix diagonal transmission vector and reflection vector to obtain the optimal STAR-RIS phase shift matrix diagonal transmission vector and reflection vector.

[0089] S16. Determine the target design parameters of the transceiver by using the direct channel matrix, transmission-cascaded channel matrix, and reflection-cascaded channel matrix under the worst-case CSI error condition, as well as the optimal transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector.

[0090] In this specific embodiment, the formula for calculating the mean square error (MSE) between the estimated received signal and the actual received signal (i.e., the MSE calculation function) is expressed as follows:

[0091]

[0092] In the formula: The received signal predicted by the receiver The actual signal received by the receiver The mean square error of the calculation; A set of labels for transmitters in the transmission space; This is the set of labels for transmitters in the reflected space; The total number of transmitter labels; To receive the beamforming vector, For receiving beamforming vector The conjugate transpose of; Let be the direct channel vector estimated for the k-th transmitter-to-receiver pair; The CSI error of the k-th direct channel; and These are the cascaded channel matrices from the transmitter to the receiver via STAR-RIS, respectively, when the k-th transmitter is estimated to be located in the transmission and reflection spaces. and These represent the cascaded channel CSI errors of the k-th transmitter located in the transmission space and reflection space, respectively. and These are the diagonal transmission vector and reflection vector of the STAR-RIS phase shift matrix, respectively; For the first Transmitter emission coefficient of each transmitter; The energy is additive white Gaussian noise.

[0093] The optimization function, which aims to minimize the mean square error between the receiver's predicted received signal and the actual received signal under the worst-case CSI error condition, can be expressed as:

[0094]

[0095] In the formula: .

[0096] In this specific embodiment, we use first-order linear conditions to update the receiver beamforming vector, use the Lagrange multiplier method to update the transmitter transmit coefficients, and obtain the worst-case channel error and the STAR-RIS receiver beamforming vector by element-wise solution. Based on this, we can obtain the local optimum by fixing the other variables in the mean square error function.

[0097] Specifically, the solution process employs an alternating optimization algorithm. First, based on the initial channel information and other design parameters, the optimal receive beamforming vector is derived. Then, in the optimal receiving beamforming vector Based on this, the worst-case channel state error ( ) is found. , and Next, the transmitter emission coefficients are updated using the Lagrange multiplier method. Finally, the diagonal beamforming vector is optimized by utilizing constant mode constraints and binary characteristics. and ), and finally the target design parameters of the transceiver were obtained ( , , and When CSI has errors, the performance of the computing system optimized by the alternating optimization algorithm proposed in this embodiment can approach the lower bound of the performance under the assumption of perfect CSI.

[0098] Specifically, in step S11, based on the first-order optimality condition, the estimated direct channel matrix is ​​used. Transmission cascaded channel matrix and reflection concatenated channel matrix Initial direct channel CSI error CSI error of transmission concatenation channel CSI error of reflection cascaded channel Transmitter emission coefficient And the STAR-RIS phase shift matrix, diagonal transmission vector, and reflection vector. and / For the receiver's received beamforming vector The update will be performed as follows:

[0099]

[0100]

[0101]

[0102] In the formula: and These are the intermediate channel variables from transmitter to receiver in the transmission space and reflection space, respectively.

[0103] In step S12, the derived optimal receiving beamforming vector is... Substituting these parameters into the function for calculating the mean square error, using the initial emission parameters... Optimal receiver reception vector Diagonal transmission with the initial STAR-RIS phase shift matrix and reflection vector The direct channel error and cascaded channel error under the worst-case CSI scenario are calculated according to the transmitter sequence.

[0104] In one specific implementation method, step S12 includes the following steps:

[0105] S121. Based on the calculation formula for mean square error, the maximum direct channel CSI error is calculated according to the transmitter sequence, the initial transmitter transmission coefficient, and the optimal receiver beamforming vector. It is then determined whether the maximum direct channel CSI error meets the preset constraint conditions. If it does, the maximum direct channel CSI error is used as the direct channel CSI error under the worst CSI error condition. If it does not meet the constraint conditions, the maximum direct channel CSI error is normalized to obtain the direct channel CSI error under the worst CSI error condition.

[0106] Specifically, the update process in step S121 is represented as follows:

[0107]

[0108] if Therefore, the maximum direct channel CSI error is taken as the direct channel CSI error under the worst-case CSI error condition, that is:

[0109]

[0110] Conversely, the maximum direct channel CSI error is normalized, i.e.:

[0111]

[0112] In the formula: This is the maximum direct channel CSI error calculated when the direct channel CSI error vector does not exceed the upper limit of the error. It is the conjugate vector of the transmitter's transmission coefficients.

[0113] S122. Based on the formula for calculating the mean square error, the maximum transmission cascaded channel CSI error is calculated according to the transmitter sequence, the initial transmitter transmission coefficients, the STAR-RIS phase shift matrix diagonal transmission vector, and the optimal receiver beamforming vector. It is then determined whether the maximum transmission cascaded channel CSI error meets the preset constraints. If it does, the maximum transmission cascaded channel CSI error is used as the transmission cascaded channel CSI error under the worst-case CSI error condition. If it does not meet the constraints, the maximum transmission cascaded channel CSI error is normalized to obtain the transmission cascaded channel CSI error under the worst-case CSI error condition.

[0114] Specifically, the update process in step S122 is represented as follows:

[0115]

[0116] if Therefore, the maximum transmission cascade channel CSI error is taken as the transmission cascade channel CSI error under the worst-case CSI error condition, that is:

[0117]

[0118] Conversely, the maximum transmission cascade channel CSI error is normalized, i.e.:

[0119]

[0120] In the formula: This is the maximum transmission cascaded channel CSI error matrix calculated in the transmission space when the cascaded channel CSI error matrix does not exceed the upper error limit. The element in the i-th row and j-th column; The j-th element is the conjugate vector of the diagonal transmission vector of the STAR-RIS phase shift matrix. This is the i-th element of the beamforming vector received by the receiver.

[0121] S123. Based on the calculation formula for mean square error, the maximum reflection cascaded channel CSI error is calculated according to the transmitter sequence, the initial transmitter transmission coefficient, the STAR-RIS phase shift matrix diagonal reflection vector, and the optimal receiver beamforming vector. It is then determined whether the maximum reflection cascaded channel CSI error meets the preset constraint conditions. If it does, the maximum reflection cascaded channel CSI error is used as the reflection cascaded channel CSI error under the worst CSI error condition. If it does not meet the constraint conditions, the maximum reflection cascaded channel CSI error is normalized to obtain the reflection cascaded channel CSI error under the worst CSI error condition.

[0122] Specifically, the update process in step S123 is represented as follows:

[0123]

[0124] if Therefore, the maximum reflection cascaded channel CSI error is taken as the worst-case CSI error, i.e.:

[0125]

[0126] Conversely, the maximum reflection cascaded channel CSI error is normalized, i.e.:

[0127]

[0128] In the formula: This is the maximum reflection-based cascaded channel CSI error matrix obtained when the cascaded channel CSI error matrix in the reflection space does not exceed the upper error limit. The element in the i-th row and j-th column; It is the j-th element of the conjugate vector of the diagonal reflection vector of the STAR-RIS phase shift matrix.

[0129] In step S13, based on the direct channel matrix, the transmission concatenated channel matrix, and the reflection concatenated channel matrix, as well as the direct channel CSI error, transmission concatenated channel CSI error, and reflection concatenated channel CSI error under the worst-case CSI error condition, the direct channel matrix under the worst-case CSI error condition is obtained. Transmission cascaded channel matrix and reflection concatenated channel matrix .

[0130] In step S14, the transmission and reflection coefficients of the transmitter are independent in the transmission and reflection spaces. Therefore, this specific embodiment uses the Lagrange multiplier method to independently update the transmitter transmission coefficients; the direct channel matrix under the worst-case CSI condition is used. and cascaded channel matrix Optimal receiver reception vector Diagonal transmission with the initial STAR-RIS phase shift matrix and reflection vector To obtain the optimal transmitter transmission coefficient (transmission space) emission parameters of the reflection space Specifically:

[0131]

[0132]

[0133] In the formula: and The optimal Lagrange multipliers related to the transmit power constraint in the transmission space and reflection space, respectively, can be derived by the bisection method.

[0134] In step S15, a binary vector is introduced to address the constant mode constraint and the coupled phase shift constraint. , making ,in , Let m be the m-th element of the introduced binary vector. Here, the constant mode constraint means that when each element (unit) of STAR-RIS modulates a signal, it can only change the phase of the signal, not its amplitude; the coupling phase shift constraint means that the diagonal transmission vector of the STAR-RIS phase shift matrix of the same element in STAR-RIS... and STAR-RIS phase shift matrix diagonal reflection vector The phases are not independent; they must maintain a fixed difference.

[0135] Since the binary vector and reflection coefficient are separate in the constant mode constraint and coupled phase shift constraint, and the elements of the reflection coefficient are independent of each other, in this specific embodiment, the vector can be updated first according to the element order. Then, using the updated STAR-RIS phase shift matrix to diagonally reflect the vector Update the STAR-RIS phase shift matrix diagonal transfer vector Direct channel matrix under worst-case CSI scenario. and cascaded channel matrix Optimal launch parameters and the optimal beamforming vector The formulas for calculating the diagonal beamforming vectors in the reflection and transmission spaces are obtained, specifically expressed as follows:

[0136]

[0137]

[0138] In the formula: The diagonal reflection vector of the STAR-RIS phase shift matrix The m-th element; When the constant constraint is ignored, The negative of the optimal solution is used to reflect the contribution of the transmission and reflection space transmitters; For the Hadamard product (element-by-element multiplication) operation;

[0139] in,

[0140]

[0141]

[0142]

[0143]

[0144] ,

[0145]

[0146] In the formula, , , and All Intermediate calculation variable parameters; For vectors, and As a scalar, The m-th element in the vector The imaginary unit; For symbolic functions, To perform the operation of taking the real part; This is a conjugate operation.

[0147] In step S16, the target design parameters of the transceiver are determined by the direct channel matrix, transmission concatenated channel matrix, and reflection concatenated channel matrix under the worst CSI error condition, as well as the optimal transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector.

[0148] In a specific implementation method, step S16 specifically includes the following steps:

[0149] S161. Based on the formula for calculating the mean square error, the mean square error is calculated by using the direct channel matrix, transmission concatenated channel matrix, and reflection concatenated channel matrix under the worst CSI error condition, as well as the optimal transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector.

[0150] S162. Determine whether the calculated mean square error meets the preset calculation accuracy conditions.

[0151] S163. If not satisfied, the worst-case CSI error conditions for the direct channel CSI error, the transmission-cascaded channel CSI error, and the reflection-cascaded channel CSI error, along with the optimal transmitter transmit coefficient, receiver receive beamforming vector, STAR-RIS phase shift matrix diagonal transmission vector, and reflection vector, are taken as the initial direct channel CSI error, transmission-cascaded channel CSI error, reflection-cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector.

[0152] S164. Jump to execute the step of minimizing the mean square error of the calculated received signal and the actual received signal of the receiver. Under the condition of first-order optimality of the calculated mean square error, update the initial receiver receiving beamforming vector based on the direct channel matrix, the transmission concatenated channel matrix, the reflection concatenated channel matrix, the initial direct channel CSI error, the transmission concatenated channel CSI error, the reflection concatenated channel CSI error, the transmitter transmit coefficient, and the diagonal transmission vector and reflection vector of the STAR-RIS phase shift matrix to obtain the optimal receiver receiving beamforming vector.

[0153] S165. If satisfied, the optimal transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector shall be used as the target design parameters for the transceiver.

[0154] It should be noted that this specific embodiment ultimately needs to find a set of optimal transceiver target design parameters to minimize the mean square error of the computing system under the worst CSI channel error. To this end, in the actual calculation process, the initial channel error and the initial transceiver design parameters (direct channel CSI error, transmission cascaded channel CSI error, reflection cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector) of the current iteration update need to be substituted into the formula for calculating the mean square error. If the calculated mean square error is greater than or equal to the preset calculation accuracy threshold, it indicates that the preset calculation accuracy condition has not been met. At this time, all parameters of the current iteration update need to be set to new initial values, and the alternating optimization update calculation needs to be restarted. Until the calculated mean square error is less than the preset calculation accuracy threshold, it indicates that the preset calculation accuracy condition has been met, that is, the convergence condition has been met. At this time, the optimal transceiver target design parameters can be output, so that the mean square error is effectively minimized under the worst channel error, thereby providing a reliable and high-performance robust design scheme for the computing system in uncertain channel environments.

[0155] Please see Figure 3 This invention also provides system performance simulation diagrams of STAR-RIS-assisted airborne computing systems based on different numbers of elements. Figure 3 In the figure, the horizontal axis represents the number of STAR-RIS elements, and the vertical axis represents the mean square error of the computation system. It can be observed that as the number of STAR-RIS elements increases, the mean square error of the computation system optimized using this invention gradually decreases, indicating a continuous improvement in system performance. It is evident that, under the worst-case channel conditions, the system performance curve of the computation system optimized using this invention almost coincides with the baseline curve under ideal channel conditions, demonstrating that this invention can achieve near-ideal communication performance in practical applications, possessing good engineering feasibility and superiority.

[0156] The robust design system based on the STAR-RIS assisted in-flight computing system provided in the embodiments of this application is described below. The robust design system based on the STAR-RIS assisted in-flight computing system described below and the optimization design method based on the STAR-RIS assisted in-flight computing system described above can be referred to in correspondence with each other.

[0157] Please see Figure 4 The present invention also provides a robust design system based on a STAR-RIS-assisted in-flight computing system. The computing system includes multiple transmitters, a STAR-RIS, and a receiver; the design system includes:

[0158] The parameter initialization unit 201 is used to obtain channel data between each transmitter and receiver based on large-scale and small-scale fading models, and to initialize the channel errors and design parameters between each transmitter and receiver based on preset constraints to obtain initial channel errors and initial transceiver design parameters. The channel data includes the direct channel matrix, the transmission-cascaded channel matrix, and the reflection-cascaded channel matrix; the initial channel errors include the initial direct channel CSI error, the transmission-cascaded channel CSI error, and the reflection-cascaded channel CSI error; the initial transceiver design parameters include the initial transmitter transmit coefficients, the initial receiver receive beamforming vector, and the initial STAR-RIS phase shift matrix diagonal transmission vector and reflection vector.

[0159] The target optimization unit 202 is used to alternately optimize the direct channel CSI error, the transmission cascaded channel CSI error, the reflection cascaded channel CSI error, the initial transmitter transmit coefficient, the initial receiver receive beamforming vector, and the initial STAR-RIS phase shift matrix diagonal transmission vector and reflection vector based on channel data, initial channel error, and initial transceiver design parameters, in order to generate transceiver target design parameters with the goal of minimizing the mean square error of the computing system under the worst CSI error condition.

[0160] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of any of the above-mentioned optimization design methods.

[0161] The present invention also provides a computer-readable storage medium having a computer program or instructions stored thereon, wherein the computer program or instructions, when executed by a processor, implement the steps of any of the above-mentioned optimization design methods.

[0162] The present invention also provides a computer program product, including a computer program or instructions, characterized in that the computer program or instructions, when executed by a processor, implement the steps of any of the above-mentioned optimization design methods.

[0163] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0164] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between apparatuses or units through some interfaces, and may be electrical, mechanical, or other forms.

[0165] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0166] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0167] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0168] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An optimization design method for a STAR-RIS-assisted in-flight computing system, characterized in that, The computing system includes multiple transmitters, a STAR-RIS, and a receiver; the method includes: Channel data between each transmitter and receiver is obtained based on large-scale and small-scale fading models. Initial channel errors and transceiver initial design parameters are obtained by initializing the channel errors and design parameters between each transmitter and receiver based on preset constraints. The channel data includes a direct channel matrix, a transmission-cascaded channel matrix, and a reflection-cascaded channel matrix. The initial channel errors include initial direct channel CSI errors, transmission-cascaded channel CSI errors, and reflection-cascaded channel CSI errors. The initial transceiver design parameters include initial transmitter transmit coefficients, receiver receive beamforming vectors, and STAR-RIS phase shift matrix diagonal transmission vectors and reflection vectors. Based on the channel data, the initial channel error, and the initial transceiver design parameters, the initial direct channel CSI error, transmission cascaded channel CSI error, reflection cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector are alternately optimized to generate target transceiver design parameters with the goal of minimizing the mean square error of the computing system under the worst CSI error condition.

2. The optimization design method according to claim 1, characterized in that, The step of generating target transceiver design parameters by alternately optimizing the initial direct channel CSI error, transmission-cascaded channel CSI error, reflection-cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector based on the channel data, the initial channel error, and the initial transceiver design parameters, with the goal of minimizing the mean square error of the computing system under the worst-case CSI error condition, includes: In the worst-case CSI error scenario, with the objective of minimizing the mean square error between the receiver's predicted received signal and the actual received signal, under the first-order optimality condition of the calculated mean square error, the initial receiver receiving beamforming vector is updated based on the direct channel matrix, the transmission concatenated channel matrix, and the reflection concatenated channel matrix, as well as the initial direct channel CSI error, the transmission concatenated channel CSI error, the reflection concatenated channel CSI error, the transmitter transmit coefficient, and the diagonal transmission vector and reflection vector of the STAR-RIS phase shift matrix, to obtain the optimal receiver receiving beamforming vector. Based on the calculation formula for mean square error, according to the initial transmitter transmit coefficient, STAR-RIS phase shift matrix diagonal transmission vector and reflection vector, and the optimal receiver receive beamforming vector, the worst-case CSI error, direct channel CSI error, transmission-cascaded channel CSI error, and reflection-cascaded channel CSI error are determined in the order of the transmitters. Based on the direct channel matrix, the transmission concatenated channel matrix, and the reflection concatenated channel matrix, as well as the CSI errors of the direct channel, the transmission concatenated channel, and the reflection concatenated channel under the worst CSI error condition, the direct channel matrix, the transmission concatenated channel matrix, and the reflection concatenated channel matrix under the worst CSI error condition are obtained. Based on the Lagrange multiplier method, the initial transmitter transmit coefficients are updated according to the initial STAR-RIS phase shift matrix, diagonal transmission vector, reflection vector, and optimal receiver beamforming vector, as well as the direct channel matrix, transmission concatenated channel matrix, and reflection concatenated channel matrix under the worst CSI error condition, and the optimal transmitter transmit coefficients are obtained. By introducing binary vectors, the initial STAR-RIS phase shift matrix diagonal transmission vector and reflection vector are updated based on the direct channel matrix, transmission concatenated channel matrix, and reflection concatenated channel matrix under the worst CSI error condition, as well as the optimal transmitter transmit coefficient and receiver receive beamforming vector, to obtain the optimal STAR-RIS phase shift matrix diagonal transmission vector and reflection vector. The target design parameters of the transceiver are determined by using the direct channel matrix, transmission-cascaded channel matrix, and reflection-cascaded channel matrix under the worst-case CSI error condition, as well as the optimal transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector.

3. The optimization design method according to claim 2, characterized in that, The steps of determining the transceiver target design parameters using the direct channel matrix, transmission-cascaded channel matrix, and reflection-cascaded channel matrix under the worst-case CSI error condition, as well as the optimal transmitter transmit coefficients, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector, include: According to the formula for calculating the mean square error, the mean square error is calculated by using the direct channel matrix, transmission concatenated channel matrix, and reflection concatenated channel matrix under the worst CSI error condition, as well as the optimal transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector. Determine whether the calculated mean square error meets the preset calculation accuracy conditions; If not satisfied, the worst-case CSI error conditions for the direct channel CSI error, the transmission-cascaded channel CSI error, the reflection-cascaded channel CSI error, and the optimal transmitter transmit coefficient, receiver receive beamforming vector, STAR-RIS phase shift matrix diagonal transmission vector, and reflection vector are used as the initial direct channel CSI error, transmission-cascaded channel CSI error, reflection-cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector. The process jumps to the step of minimizing the mean square error between the estimated and actual received signals of the receiver. Under the first-order optimality condition of the mean square error, the initial receiver beamforming vector is updated based on the direct channel matrix, the transmission concatenated channel matrix, the reflection concatenated channel matrix, the initial direct channel CSI error, the transmission concatenated channel CSI error, the reflection concatenated channel CSI error, the transmitter transmit coefficient, and the diagonal transmission vector and reflection vector of the STAR-RIS phase shift matrix, to obtain the optimal receiver beamforming vector. If satisfied, the optimal transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector are used as the target design parameters for the transceiver.

4. The optimization design method according to claim 2, characterized in that, The formula for calculating the mean square error is expressed as follows: In the formula: The received signal predicted by the receiver The actual signal received by the receiver The mean square error of the calculation; A set of labels for transmitters in the transmission space; This is the set of labels for transmitters in the reflected space; The total number of transmitter labels; To receive the beamforming vector, For receiving beamforming vector The conjugate transpose of; Let be the direct channel matrix vector estimated for the k-th transmitter-to-receiver pair; The CSI error of the k-th direct channel; and These are the cascaded channel matrices from the transmitter to the receiver via STAR-RIS, respectively, when the k-th transmitter is estimated to be located in the transmission and reflection spaces. and These represent the CSI error of the cascaded channel where the k-th transmitter is located in the transmission or reflection space; and These are the diagonal transmission and reflection vectors of STAR-RIS, respectively; For the first Transmitter emission coefficient of each transmitter; The energy is additive white Gaussian noise.

5. The optimization design method according to claim 1, characterized in that, The preset constraints include: In the formula: At maximum transmission power, This is the set of transmitter labels; and The m-th element of the diagonal transmission vector and reflection vector of STAR-RIS, respectively. and These are the transmission and reflection phase coefficients, respectively. The set of labels for STAR-RIS elements; It is a 2-norm. It is the F-norm; and These are the bounded error limits for the direct channel and the cascaded channel, respectively.

6. The optimization design method according to claim 2, characterized in that, The steps for determining the worst-case CSI error, including the direct channel CSI error, transmission-cascaded channel CSI error, and reflection-cascaded channel CSI error, based on the calculation formula for the mean square error and according to the initial transmitter transmit coefficients, STAR-RIS phase shift matrix diagonal transmission vector and reflection vector, and the optimal receiver receive beamforming vector, in the order of the transmitters, are as follows: Based on the formula for calculating the mean square error, the maximum direct channel CSI error is calculated according to the transmitter sequence, the initial transmitter transmit coefficients, and the optimal receiver receive beamforming vector. It is then determined whether the maximum direct channel CSI error meets the preset constraints. If it does, the maximum direct channel CSI error is used as the direct channel CSI error under the worst-case CSI error condition. If it does not meet the constraints, the maximum direct channel CSI error is normalized to obtain the direct channel CSI error under the worst-case CSI error condition. Based on the formula for calculating the mean square error, the maximum transmission cascaded channel CSI error is calculated according to the transmitter sequence, based on the initial transmitter transmission coefficients, the STAR-RIS phase shift matrix diagonal transmission vector, and the optimal receiver beamforming vector. It is then determined whether the maximum transmission cascaded channel CSI error meets preset constraints. If it does, the maximum transmission cascaded channel CSI error is used as the transmission cascaded channel CSI error under the worst-case CSI error condition. If it does not meet the constraints, the maximum transmission cascaded channel CSI error is normalized to obtain the transmission cascaded channel CSI error under the worst-case CSI error condition. Based on the formula for calculating the mean square error, the maximum reflection cascaded channel CSI error is calculated according to the transmitter sequence, the initial transmitter transmit coefficients, the STAR-RIS phase shift matrix diagonal reflection vector, and the optimal receiver receive beamforming vector. It is then determined whether the maximum reflection cascaded channel CSI error meets preset constraints. If it does, the maximum reflection cascaded channel CSI error is used as the worst-case CSI error. If it does not meet the constraints, the maximum reflection cascaded channel CSI error is normalized to obtain the worst-case CSI error.

7. A robust design system based on the STAR-RIS-assisted in-flight computing system, characterized in that, The computing system includes multiple transmitters, one STAR-RIS, and one receiver; the design system includes: The parameter initialization unit is used to obtain channel data between each transmitter and receiver based on large-scale and small-scale fading models, and to initialize the channel errors and design parameters between each transmitter and receiver based on preset constraints to obtain initial channel errors and initial transceiver design parameters. The channel data includes a direct channel matrix, a transmission-cascaded channel matrix, and a reflection-cascaded channel matrix. The initial channel errors include initial direct channel CSI errors, transmission-cascaded channel CSI errors, and reflection-cascaded channel CSI errors. The initial transceiver design parameters include initial transmitter transmit coefficients, receiver receive beamforming vectors, and STAR-RIS phase shift matrix diagonal transmission vectors and reflection vectors. The target optimization unit is used to alternately optimize the initial direct channel CSI error, transmission cascaded channel CSI error, reflection cascaded channel CSI error, transmitter transmit coefficient, receiver receive beamforming vector, and STAR-RIS phase shift matrix diagonal transmission vector and reflection vector based on the channel data, the initial channel error, and the initial transceiver design parameters, in order to generate transceiver target design parameters with the goal of minimizing the mean square error of the computing system under the worst CSI error condition.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the optimization design method as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by the processor, they implement the steps of the optimization design method as described in any one of claims 1-6.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by the processor, they implement the steps of the optimization design method as described in any one of claims 1-6.

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