Backscatter communication total throughput maximization method based on stacked intelligent metasurface enabling

Abstract

The invention belongs to the technical field of wireless communication, and particularly relates to a backscatter communication total throughput maximization method based on Stacked Intelligent Metasurface (SIM) energization, which specifically comprises the following steps of: constructing a backscatter communication system model based on SIM assistance; establishing a non-convex, multivariable coupling and multi-constraint resource allocation problem taking maximization of the total throughput of the system as a target; the original problem is converted into a transmitting end power distribution optimization sub-problem, a time slot distribution optimization sub-problem and an SIM phase shift optimization sub-problem; and converting the non-convex optimization sub-problem into a convex optimization sub-problem by using a successive convex approximation method, a penalty method and a first-order Taylor expansion, and alternately optimizing to obtain an overall resource allocation scheme. The signal beam forming operation can be realized in the electromagnetic wave domain by introducing the SIM at the transmitting end, compared with the traditional scheme, the total throughput performance of the system is remarkably improved, meanwhile, the dependence of the transmitting end on a complex radio frequency link can be effectively reduced, and good economic benefits are achieved.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and specifically relates to a method for maximizing the total throughput of backscatter communication based on stacked smart metasurfaces. Background Technology

[0002] With the rapid development of wireless communication technology, the evolution from "Internet of Everything" to "Intelligent Interconnection" will be one of the key technologies for the transition from 5G to 6G. Backscatter communication is a wireless communication technology that transmits information by reflecting incident radio frequency signals. It features ultra-low power consumption, low cost, and flexible deployment, providing extensive connectivity for ultra-low power sensors. For example, in scenarios such as logistics warehousing, smart homes, and industrial IoT, backscatter communication technology can achieve low-power or even zero-power device communication, solving the lifecycle problem of sensor nodes and reducing maintenance costs. Traditional backscatter technology is mainly used in Radio Frequency Identification (RFID) systems. A typical RFID system consists of a reader and multiple tags, using backscatter technology for communication. However, traditional backscatter technology has shortcomings such as short communication distance and high path loss. Intelligent metasurface-assisted backscatter communication technology breaks through the transmission distance limitations of traditional backscatter by reconstructing the wireless channel. At the same time, its passive beamforming capability can significantly improve system performance. However, existing solutions use a single-layer metasurface structure with limited freedom of phase control, and achieving efficient collaborative optimization of backscatter signals in complex scenarios still faces significant challenges.

[0003] Recently, inspired by programmable diffractive deep neural networks, researchers have designed a multilayer metasurface structure capable of real-time signal processing directly in the electromagnetic wave domain, naming it Stacked Intelligent Metasurface (SIM). When electromagnetic waves pass through the SIM, each atomic unit of the metasurface becomes a secondary radiation source, influencing and transmitting the electromagnetic waves to the next layer through modulation. Based on this unique interlayer interaction mechanism, SIM can not only directly achieve beamforming in the electromagnetic wave domain, enhancing system performance, but also effectively reduce the dependence of traditional transmitter beamforming on complex RF links, while providing greater controllability and freedom for improving system channel capacity.

[0004] In summary, existing backscattering technologies suffer from drawbacks such as short communication distance, high path loss, low transmission efficiency, and complex hardware structure. Therefore, there is an urgent need for a new technology that can further improve the transmission distance, loss resistance, and overall efficiency of backscattering communication systems while ensuring low cost and low power consumption, thus providing more reliable communication support for the Internet of Things (IoT) and the "intelligent interconnection of everything". Summary of the Invention

[0005] To address the above problems, this invention provides a method for maximizing the total throughput of backscatter communication based on SIM empowerment, comprising the following steps:

[0006] S1. Construct a SIM-assisted backscatter communication system model;

[0007] S2. Establish a non-convex, multivariable coupled, and multi-constraint resource allocation problem with the goal of maximizing the total system throughput;

[0008] S3. Transform the original problem into a transmitter power allocation optimization subproblem, a time slot allocation optimization subproblem, and a SIM phase shift optimization subproblem;

[0009] S4. Using the successive convex approximation method, penalty method and first-order Taylor expansion, the non-convex optimization subproblem is transformed into a convex optimization subproblem, and the overall optimization scheme is obtained by alternating iterations.

[0010] Preferably, the SIM-assisted backscatter communication system model specifically includes: a system with a deployed SIM and possessing... The radio frequency source of the antenna, a single antenna receiver, and A single-antenna backscatter device (BD), wherein the SIM is composed of It consists of layers of metasurfaces, each metasurface being composed of Composed of individual atoms;

[0011] To avoid mutual interference between different backscattered signals during transmission, the system employs the Time Division Multiple Access (TDMA) protocol to provide the first... The time slots allocated to each BD are The duration of one frame is And the first The BD only exists in time slots In work mode, at the rest of the time In sleep mode, where in working mode, the radio frequency source uses the SIM to transmit signals to the first... Each BD transmits a signal, and the BD receives the signal and reflects the tag signal to the single antenna receiver by adjusting the impedance. At the same time, the BD uses a nonlinear energy harvesting mode to collect the remaining energy.

[0012] Preferably, the original problem is transformed into a transmitter power allocation optimization sub-problem, a time slot allocation optimization sub-problem, and a SIM phase shift optimization sub-problem. Step S3 specifically includes:

[0013] S31. Fixed time slot and SIM phase shift vector The original problem is transformed into a subproblem of optimizing transmitter power allocation, thereby optimizing the backscattering coefficient. and power distribution ;

[0014] S32. Fixed backscattering coefficient Power distribution and SIM phase shift vector The original problem is transformed into a time slot optimization subproblem, and the time slots are optimized. ;

[0015] S33. Fixed backscattering coefficient Power distribution and time slots The original problem is transformed into a SIM phase shift optimization subproblem, which optimizes the phase shift vector. .

[0016] Preferably, the non-convex optimization subproblem is transformed into a convex optimization subproblem using a successive convex approximation method, a penalty method, and a first-order Taylor expansion, and the overall optimization scheme is obtained through alternating iterations. Step S4 specifically includes:

[0017] S41. The non-convex transmitter power allocation problem is transformed into a convex optimization problem by using the successive convex approximation method and the first-order Taylor expansion.

[0018] S42. By replacing variables, the original non-convex phase shift optimization subproblem is transformed into a positive semidefinite relaxation problem. The penalty method is used to iteratively process the rank 1 constraint. The successive convex approximation method and the first-order Taylor expansion are used to transform the original non-convex phase shift optimization subproblem into a positive semidefinite programming problem.

[0019] S43. Using a hierarchical optimization strategy, optimize the total phase shift vector of the highly coupled SIM layer by layer. ;

[0020] S44. Using the CVX convex optimization toolbox, the three transformed convex optimization subproblems are solved iteratively and alternately to obtain the optimal transmitter power allocation vector. Backscattering coefficient vector Time slot vector and SIM total phase shift vector That is, the overall optimization plan.

[0021] The beneficial effects of this invention are:

[0022] This invention reduces the dependence of traditional transmitter beamforming on complex radio frequency links by introducing a SIM at the transmitter, enabling signal beamforming operation in the electromagnetic wave domain. This maximizes the total system throughput, effectively enhances system performance, and improves economic efficiency. Compared with traditional backscatter communication systems without SIM assistance, this system has stronger performance advantages. Attached Figure Description

[0023] Figure 1 This is a flowchart of a method for maximizing the total throughput of backscatter communication based on SIM empowerment according to the present invention;

[0024] Figure 2 This is a schematic diagram of the system model of the present invention;

[0025] Figure 3 The figure shows the simulation results relating the total system throughput to the number of SIM layers. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Furthermore, the accompanying drawings are for illustrative purposes only and represent schematic diagrams, not actual physical images, and should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some components in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0028] In this invention, the following notation is used: , , These represent the conjugation, transpose, and conjugate transpose operations on a vector or matrix, respectively. express Exponentiation; It represents the mean of a random variable; The bottom is The logarithmic function; express function; This represents the floor function; express Divide by The remainder after; Indicates gradient operation; express The maximum value operation is performed. Represents the modulus of a complex number; The 2-norm of a vector; Denotes the Frobenius norm of a matrix; express A complex matrix of dimension 1; express A 3D real matrix; Indicates vector diagonalization; Represents the trace of a matrix; Represents matrix vectorization; express An identity matrix of 3D; Representation matrix Semi-positive definite; Mean and variance The distribution of a circularly symmetric complex Gaussian random variable.

[0029] A method for maximizing the total throughput of SIM-enabled backscatter communication, such as Figure 1 As shown, it includes:

[0030] S1. Construct a SIM-assisted backscatter communication system model;

[0031] S2. Establish a non-convex, multivariable coupled, and multi-constraint resource allocation problem with the goal of maximizing the total system throughput;

[0032] S3. Transform the original problem into a transmitter power allocation optimization subproblem, a time slot allocation optimization subproblem, and a SIM phase shift optimization subproblem;

[0033] S4. Using the successive convex approximation method, penalty method and first-order Taylor expansion, the non-convex optimization subproblem is transformed into a convex optimization subproblem, and the overall optimization scheme is obtained by alternating iterations.

[0034] Preferably, a SIM-assisted backscatter communication system model is constructed, such as... Figure 2 As shown:

[0035] A SIM deployed and possessing The radio frequency source of the root antenna, service A single antenna BD, wherein the SIM is composed of It consists of layers of metasurfaces, each metasurface being composed of It is composed of individual atoms. To avoid mutual interference between different backscattered signals during transmission, the system adopts the TDMA protocol to provide the first... The time slots allocated to each BD are The duration of one frame is And the first The BD only exists in time slots In work mode, at the rest of the time In sleep mode, where in working mode, the radio frequency source transmits to the SIM via the SIM. Each BD transmits a signal, and the BD receives the signal and reflects the tag signal to the single antenna receiver by adjusting the impedance. At the same time, the BD uses nonlinear energy harvesting technology to recover the remaining energy.

[0036] Because SIM can perform precise beamforming in the electromagnetic wave domain, the RF source only needs to be in Selecting from root antennas root antenna to serve Each BD only needs to serve one BD.

[0037] definition Represents the SIM layer index set; Represents the set of atomic indices for each level; Represents the BD index set. Definition This represents the vector of radio frequency signals emitted by the radio frequency source. It is for the first The signal sent by each BD satisfies Therefore, the signal after SIM processing Represented as:

[0038]

[0039] in It is for Distributed power, , It is the total transmission power of the transmitting end; It is the beamforming matrix of SIM. Indicates SIM number The phase shift matrix of the layer, Indicates the first The first layer Phase shift of individual atoms, Indicates the internal SIM number layer to the first Interlayer propagation matrix of metasurface yes The first in Elements at position, Indicates the distance between adjacent layers. This represents the area of ​​each elementary atom. Indicates the first The first layer From the first atom to the second The first layer The Euclidean distance between individual atoms ,and Indicates the first in the same layer The first atom and the first The center distance between individual atoms; Indicates the center-to-center distance between adjacent atoms. Indicates wavelength. It is the carrier frequency. It's the speed of light; express The atomic index of the direction is calculated as follows: ,in Indicates the maximum number of row and column atoms, and has ; Indicates the selected first The propagation vector from the root transmit antenna to the first-layer SIM, where The Each element represents ,in .

[0040] Therefore, the first received by the receiving end BD signal as follows:

[0041]

[0042] in Indicates SIM to the Channel vectors of BD; Indicates the first Channel coefficients between the BD and the receiver; Indicates the first BD reflectance coefficient; The first one that needs to be transmitted The signal of each BD satisfies ; It is Gaussian white noise, which obeys... .

[0043] Preferably, in step S2, a non-convex, multi-variable coupled, multi-constraint resource allocation problem is established with the goal of maximizing the total system throughput, specifically including:

[0044] S21. Introduce a non-linear energy storage mode that conforms to real-world scenarios, specifically including:

[0045] Define function Indicates input power The relevant nonlinear energy harvesting function. Indicates the first Maximum collection power of each BD; , and These are parameters related to specific circuit specifications, such as circuit sensitivity or leakage current; therefore, the first The remaining energy collected by each BD Represented as:

[0046]

[0047] The receiver received the first Signal-to-noise ratio of each BD signal as follows:

[0048]

[0049] S22. Establish a non-convex objective problem that maximizes the total system throughput. Specifically, it includes:

[0050]

[0051] Where the SIM total phase shift vector represents , Indicates the first Phase shift vector of layer SIM; They represent the first The circuit losses and energy collected by a BD; Indicates the first The transmission rate of each BD; This represents the lowest rate for all BDs; This indicates the total energy constraint of the radio frequency source. This indicates a hardware phase modulo-1 constraint; This indicates the reflection coefficient constraint of BD; This indicates the total time slot constraint under the TDMA protocol; This represents the energy constraint for each BD; This indicates a minimum rate constraint.

[0052] Preferably, the original problem is transformed into a transmitter power allocation optimization sub-problem, a time slot allocation optimization sub-problem, and a SIM phase shift optimization sub-problem. Step S3 specifically includes:

[0053] Introducing auxiliary variables Represents a nonlinear energy harvesting function Input power The maximum lower bound is in processing step S22. Multivariate coupling of the problem Constraints, therefore The constraint transformation is as follows:

[0054]

[0055] Will , Substituting constraints into the original problem In the middle, the original problem It is divided into 3 sub-problems, specifically including:

[0056] S31. Fixed time slot and SIM phase shift vector Define variables The original problem Transformed into a transmitter power allocation optimization subproblem Optimize the backscattering coefficient and power distribution :

[0057]

[0058] S32. Fixed backscattering coefficient Power distribution and SIM phase shift vector The original problem Transform into a time-slot optimization subproblem Optimize time slots :

[0059]

[0060] S33. Fixed backscattering coefficient Power distribution and time slots The original problem Transformed into a SIM phase shift optimization subproblem Optimize phase shift vector :

[0061]

[0062] Preferably, the non-convex optimization subproblem is transformed into a convex optimization subproblem using a successive convex approximation method, a penalty method, and a first-order Taylor expansion, and the overall optimization scheme is obtained through alternating iterations. Step S4 specifically includes:

[0063] S41. Handling the transmitter power allocation optimization subproblem The nonconvexity of the constraint. In this process, a successive convex approximation method is used. Complex fractional structures, for exist First-order Taylor expansion: ,in , where n represents the current iteration number. Subproblem This can be transformed into a convex problem:

[0064]

[0065] S42. Due to the complex multi-layered structure of the SIM, a hierarchical optimization strategy is adopted to optimize the phase shift layer by layer. The following describes the optimization of any one of the... Taking layer phase shift as an example, define variables , :

[0066]

[0067] Therefore, the SIM beamforming matrix can be represented as: .

[0068] Define variables Therefore, subproblems In , After constraint integration, it can be represented as: .

[0069] Define variables , , , ,therefore Therefore, the subproblem Semideterministic relaxation can be transformed into :

[0070]

[0071] Using equivalent transformation deal with Rank 1 constraint in the problem To address the nonconvexity of the objective function, a penalty-based iterative solution method is proposed. This method treats the equivalent rank-1 constraint as a penalty term and introduces it into the objective function. The problem can be transformed into :

[0072]

[0073] Among the variables This represents the penalty factor, used for penalty. Cases where the rank-1 constraint is not satisfied.

[0074] The successive convex approximation method is used to process the matrix spectral norm. as follows: ,in express The eigenvector corresponding to the largest eigenvalue. Therefore... The problem can be transformed into a standard positive semidefinite programming problem. :

[0075]

[0076] S43. Use a hierarchical optimization strategy to optimize the total phase shift of the highly coupled SIM layer by layer. Specifically, this includes: fixing the phase shift of the remaining layers, and first optimizing the first... Phase shift of layer SIM. The layer SIM phase shift problem can be solved iteratively by nested inner and outer loops. In the inner loop, for a given penalty factor... subproblems This is a standard positive semidefinite programming problem; in the outer layer, the penalty factor gradually increases with each iteration, as the optimization problem... The penalty term of the objective function satisfies The iteration terminates. The precision of the violation of the rank-1 constraint varies with the penalty factor. With the increase, the penalty term will meet the accuracy requirement. Require.

[0077] Next, optimize the first The phase shift of the SIM layer is optimized alternately, and so on, until all phase shifts are optimized, resulting in a temporary solution for the total phase shift vector of the SIM. , Indicates the number of iterations.

[0078] S44. Use the CVX Convex Optimization Toolbox to iteratively solve the three transformed convex optimization subproblems described above, using the temporary solution from the previous iteration for each iteration. , , , As the current number The input of each iteration is used to alternately optimize the subproblems until the total system throughput converges, yielding the optimal transmitter power allocation vector. Backscattering coefficient vector Time slot vector and SIM total phase shift vector .

[0079] The application effects of this invention will be described in detail below with reference to simulation.

[0080] 1) Simulation conditions

[0081] This section verifies the convergence and effectiveness of the method of this invention through simulation results. Assume that there is a system with a deployed SIM and possesses... The RF source for the antenna has a gain of 5dBi, and a single-antenna receiver. A single-antenna BD. A large-scale path loss model is used. , The path loss exponent is represented by a superimposed small-scale fading model, where the link from the transmitter to the receiver uses a Ricean small-scale fading model, and the link from the receiver to the receiver uses a Rayleigh small-scale fading model. The parameters of the nonlinear energy harvesting circuit are also included. =150, =0.014, and maximum received power =0.024W. Other simulation parameters are shown in Table 1.

[0082] Table 1 Other simulation parameters

[0083] parameter value parameter value carrier frequency 28GHz speed of light Interlayer spacing Metaatomic size Frame length 1s BD quantity 3 Transmitter to BD path loss index 2.1 BD to receiver path loss index 2.8 3 BD distances from SIM straight line distance 5m, 6m, 7m Path loss reference distance 1m Total transmission power 34dBm noise power -90dBm minimum rate 1.5bps / Hz Each BD circuit consumes energy.

[0084] 2) Simulation results

[0085] Figure 3 The system's total throughput and number of SIM layers were displayed. The relationship between them, considering the case where the number of atoms in each layer is different. =25, 49, and 100. From Figure 3 As can be seen, when the SIM layer When the number of layers is small, the overall system speed increases with increasing layer count. However, more layers are not always better. The number of elements in each layer continues to rise, when the number of elements in each layer is When the system throughput reaches 25, the total throughput begins to decline, and when... The rate still increases at 64 and 100, but the trend slows down. This is because the penetration loss of electromagnetic waves between SIM layers increases with the number of layers. When the number of atomic atoms in each layer is relatively small, electromagnetic beamforming cannot offset this penetration loss, leading to performance degradation. Meanwhile, compared to traditional backscatter communication scenarios without SIM assistance, the overall rate of the SIM-enabled backscatter communication system is significantly improved. This verifies the clear advantages of the SIM multilayer structure and demonstrates good economic benefits.

[0086] This invention belongs to the field of wireless communication technology, and specifically relates to a method for maximizing the total throughput of backscatter communication based on stacked smart metasurfaces. By introducing a SIM at the transmitter, this invention reduces the dependence of traditional transmitter beamforming on complex RF links, enabling signal beamforming operations in the electromagnetic domain. This maximizes the total system throughput, effectively enhances system performance, and improves economic efficiency. Compared with traditional backscatter communication systems without SIM assistance, this system has stronger performance advantages.

[0087] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, which may include ROM, RAM, disk, or optical disk, etc.

[0088] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for maximizing the total throughput of backscatter communication based on stacked intelligent metasurface (SIM), characterized in that, Includes the following steps: S1. Construct a SIM-assisted backscatter communication system model; S2. Establish a non-convex, multivariable coupled, and multi-constraint resource allocation problem with the goal of maximizing the total system throughput; S3. The original problem is transformed into a transmitter power allocation optimization subproblem, a time slot allocation optimization subproblem, and a SIM phase shift optimization subproblem, respectively; S4. Using the successive convex approximation method, penalty method and first-order Taylor expansion, the non-convex optimization subproblem is transformed into a convex optimization subproblem, and the overall optimization scheme is obtained by alternating iterations.

2. The method for maximizing the total throughput of SIM-enabled backscatter communication according to claim 1, characterized in that, The aforementioned SIM-assisted backscatter communication system model specifically includes: a system with a deployed SIM and possessing... The radio frequency source of the antenna, a single antenna receiver, and A single-antenna backscatter device (BD), wherein the SIM is composed of It consists of layers of metasurfaces, each metasurface being composed of Composed of individual atoms; To avoid mutual interference between different backscattered signals during transmission, the system employs the Time Division Multiple Access (TDMA) protocol to provide the first... The time slots allocated to each BD are The duration of one frame is And the first The BD only exists in time slots In work mode, at the rest of the time In sleep mode, where in working mode, the radio frequency source transmits to the SIM via the SIM. Each BD transmits a signal, and the BD receives the signal and reflects the tag signal to the single antenna receiver by adjusting the impedance. At the same time, the BD uses nonlinear energy harvesting technology to absorb the remaining energy.

3. The method for maximizing the total throughput of SIM-enabled backscatter communication according to claim 1, characterized in that, Establish a non-convex, multivariable coupled, and multi-constraint resource allocation problem with the objective of maximizing the total system throughput, specifically including: S21. Introduce a non-linear energy storage mode that conforms to real-world scenarios; S22. Establish a non-convex objective problem that maximizes the total system throughput. Specifically, it includes:

4. Among them, Represents the SIM layer index set; Represents the set of atomic indices for each level; Represents the BD index set; Indicates assignment to the first One BD time slot; Indicates the duration of one frame; This represents the reflection coefficient of the k-th BD; This indicates the total transmit power of the radio frequency source; Indicates the power allocated by the radio frequency source; Represents the total phase shift vector of the SIM. Indicates the first Phase shift vector of layer SIM; Indicates SIM to the BD channel vector; Indicates the first Channel coefficients between the BD and the receiver; Indicates the first The propagation vector from the root transmit antenna to the first-layer SIM; This represents the beamforming matrix based on SIM; Indicates the first Noise variance between the BD and the receiver; Indicates SIM number The first layer Phase shift of individual atoms, Indicates phase; They represent the first The circuit losses and energy collected by a BD; Indicates the first The transmission rate of each BD; This represents the lowest rate for all BDs; This indicates the total energy constraint of the radio frequency source. This indicates a hardware phase modulo-1 constraint; This indicates the reflection coefficient constraint of BD; This indicates the total time slot constraint under the TDMA protocol; This represents the energy constraint for each BD; This indicates a minimum rate constraint.

5. The method for maximizing the total throughput of SIM-enabled backscatter communication according to claim 1, characterized in that, The original problem is transformed into a transmitter power allocation optimization sub-problem, a time slot allocation optimization sub-problem, and a SIM phase shift optimization sub-problem, respectively. Step S3 specifically includes: S31. Fixed time slot and SIM phase shift vector The original problem is transformed into a subproblem of optimizing transmitter power allocation, thereby optimizing the backscattering coefficient. and power distribution ; S32. Fixed backscattering coefficient Power distribution and SIM phase shift vector The original problem is transformed into a time slot optimization subproblem, and the time slots are optimized. ; S33. Fixed backscattering coefficient Power distribution and time slots The original problem is transformed into a SIM phase shift optimization subproblem, which optimizes the phase shift vector. .

6. The method for maximizing the total throughput of SIM-enabled backscatter communication according to claim 1, characterized in that, The non-convex optimization subproblem is transformed into a convex optimization subproblem using a successive convex approximation method, a penalty method, and a first-order Taylor expansion. The overall optimization scheme is obtained through alternating iterations. Step S4 specifically includes: S41. The non-convex transmitter power allocation problem is transformed into a convex optimization problem by using the successive convex approximation method and the first-order Taylor expansion. S42. By replacing variables, the original non-convex phase shift optimization subproblem is transformed into a positive semidefinite relaxation problem. The penalty method is used to iteratively process the rank 1 constraint. The successive convex approximation method and the first-order Taylor expansion are used to transform the original non-convex phase shift optimization subproblem into a positive semidefinite programming problem. S43. Using a hierarchical optimization strategy, optimize the total phase shift vector of the highly coupled SIM layer by layer. ; S44. Using the CVX convex optimization toolbox, the three transformed convex optimization subproblems are solved iteratively and alternately to obtain the optimal transmitter power allocation vector. Backscattering coefficient vector Time slot vector and SIM total phase shift vector That is, the overall optimization plan.

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