Stacked intelligent metasurface enabled flux-inductance integrated beamforming design method

Abstract

The invention belongs to the technical field of wireless communication sensing integration, and discloses a stacked intelligent metasurface enabled communication sensing integrated beamforming design method, which comprises the following steps: S1, establishing a mathematical model of a stacked intelligent metasurface enabled communication sensing integrated system; s2, constructing a multi-objective optimization problem of the SIM-ISAC system; and S3, designing a double-normalized differential gradient descent algorithm to solve an optimization problem. By the adoption of the stacked intelligent metasurface enabled sensing integrated beam forming design method, downlink communication and radar target detection are achieved, and the sum rate of users is maximized by optimizing a multi-layer phase shift matrix of the stacked intelligent metasurface. Minimizing a mean square error between the normalized sensing beam pattern and the expected beam pattern; on the basis of a double-normalization differential gradient descent algorithm, the problem of non-convex multi-objective optimization is solved, multi-point expected beam forming in a two-dimensional angle domain is achieved, and acceptable balance is achieved in the aspect of communication performance.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless communication perception integration, and in particular to a synaesthesia integrated beamforming design method enabled by stacked intelligent metasurfaces. Background Art

[0002] With the commercial deployment of 5G networks and the research and development of 6G technologies, wireless communication systems are moving towards higher data rates, lower latency, and wider connectivity. At the same time, the demand for high-precision perception and positioning is also growing, especially in application scenarios such as autonomous driving, smart cities, and industrial IoT. In this context, Integrated Sensing and Communication (ISAC) has become one of the key technologies for the next generation of wireless networks. Integrated Sensing and Communication (ISAC) aims to integrate communication and perception systems by sharing hardware platforms, spectrum resources, signal processing algorithms, and waveforms, making full use of increasingly scarce spectrum resources while reducing the hardware cost and energy consumption of the system. Based on the long-term development of Multiple-Input Multiple-Output (MIMO) technology in the fields of communication and radar, existing integrated communication and perception systems widely adopt array antenna architectures, using the spatial degrees of freedom provided by multi-antenna arrays to serve multi-user communication and radar target perception. However, the complex feed network and RF link in the array antenna greatly occupy the cost and power consumption of the system.

[0003] In this regard, some studies have used intelligent metasurfaces deployed in the transceiver of the communication and perception integration system to replace the traditional phased array antenna, which simplifies the system hardware architecture and significantly reduces power consumption. Specifically, the intelligent metasurface is a two-dimensional planar structure composed of a large number of controllable array elements. By adjusting the electromagnetic characteristics of each array element, the phase and amplitude of the incident electromagnetic wave can be precisely controlled, thereby reconstructing the propagation characteristics of the electromagnetic wave at low cost and low power consumption. However, this research is generally limited to a single layer of intelligent metasurfaces, and has not fully explored the potential of intelligent metasurfaces for communication and perception integration. In order to make better use of the ability of intelligent metasurfaces to reconstruct the propagation characteristics of electromagnetic waves, some researchers have proposed the concept of stacked intelligent metasurfaces (SIM), which stacks multiple layers of intelligent metasurfaces in parallel, and uses more metasurface array elements to more effectively reconstruct the propagation characteristics of electromagnetic waves, achieving more complex beamforming.

[0004] Although some studies focus on deploying stacked smart metasurfaces like general smart metasurfaces between base stations and users or targets to enhance the performance of integrated communication and perception systems, there are few discussions on replacing the digital precoding and phased array of transmitters with stacked smart metasurfaces to achieve integrated communication and perception systems. This approach may bring many advantages: first, it can greatly simplify the hardware structure and reduce system cost and power consumption; second, the additional degrees of freedom provided by stacked smart metasurfaces may allow more flexible beamforming, thereby better balancing communication and perception performance. However, the integrated communication and perception system enabled by stacked smart metasurfaces faces many challenges. First, how to optimize the transmission matrix of the stacked smart metasurface under the constant modulus constraint of multi-layer metasurface elements to simultaneously meet the needs of communication and perception is a complex non-convex optimization problem. Second, due to the cascade structure of the stacked smart metasurface, the variables in the optimization problem are highly coupled, which increases the difficulty of solving the problem. In addition, how to achieve high-precision target detection in the 2D angle domain while maintaining acceptable communication performance is also a key issue that needs to be solved urgently. Summary of the invention

[0005] The purpose of the present invention is to provide a synaesthesia integrated beamforming design method enabled by a stacked intelligent metasurface, aiming to simultaneously realize downlink communication and radar target detection, maximize the user's total rate by optimizing the multi-layer phase shift matrix of the stacked intelligent metasurface, and minimize the mean square error between the normalized perception beam pattern and the expected beam pattern; based on a novel double normalized differential gradient descent algorithm, solve the non-convex multi-objective optimization problem, realize target detection in the two-dimensional angular domain, and achieve an acceptable trade-off in communication performance.

[0006] To achieve the above object, the present invention provides a stacked intelligent metasurface-enabled synaesthesia integrated beamforming design method, comprising the following steps:

[0007] S1. Establish a mathematical model of the communication-sensing integrated system enabled by stacked intelligent metasurfaces;

[0008] S2, construct the multi-objective optimization problem of SIM-ISAC system;

[0009] S3. Design a double normalized differential gradient descent algorithm to solve the optimization problem.

[0010] Preferably, in step S1, a base station of a mathematical model of a communication perception integrated system enabled by a stacked intelligent metasurface is composed of a uniform linear array ULA feed antenna with equal power distribution and a stacked intelligent metasurface SIM, serving N C single-antenna communication users and N S sensing targets; where SIM consists of L layers of transmissive metasurfaces, each layer contains M = M r ×Mc metasurface elements, where M r is the number of rows of metasurface elements per layer, M c is the number of columns of metasurface elements in each layer;

[0011] The mathematical model of the received signal at the user is shown in the following formula:

[0012] y=HF SIM x+n

[0013] in, is the channel matrix from SIM to user; n is the additive white Gaussian noise AWGN at the receiving end; F SIM is the transmission matrix of SIM, and its mathematical model is:

[0014] F SIM =Φ L W L Φ L-1 W L-1 …Φ 1 W 1

[0015] in, represents the phase shift matrix of the l-th metasurface, represents the phase shift of the mth metasurface element, W l is the inter-layer path loss matrix from the (l-1)th layer to the lth layer of the super-metasurface, and its element in the mth row and m'th column is From the Rayleigh-Sommerfeld diffraction formula:

[0016]

[0017] in, The physical meaning of is the inter-layer path loss from the mth metasurface element in the (l-1)th layer to the m'th metasurface element in the lth layer; A t is the area of ​​a single metasurface element; is the angle between the direction of the m-th metasurface element in the (l-1)th layer and the m'th metasurface element in the lth layer and the metasurface normal; is the distance between the mth metasurface element in the (l-1)th layer and the m'th metasurface element in the lth layer, and λ is the wavelength corresponding to the system operating frequency.

[0018] Preferably, the signal-to-interference-and-noise ratio at the receiving end of the nth communication user is as follows:

[0019]

[0020] Where, σ is the AWGN power;

[0021] The Shannon formula is used to calculate the sum rate of all communication users as follows:

[0022]

[0023] Among them, R sum It is the communication performance index of SIM-ISAC system.

[0024] Preferably, the normalized beam matching error is used as a performance indicator of radar target perception, and the specific process is as follows:

[0025] S131. First, the SIM-ISAC system is at a pitch angle ψ j and direction φ k The beam gain at the corners is given by:

[0026]

[0027] Where j, k = 1…N D is the index number of the angle space, N D is the sampling number in the angle space; α(·) is the steering vector, which is related to the metasurface array element, azimuth angle and elevation angle. Its mathematical model is as follows:

[0028]

[0029] in, is the Kronecker product, d x and d y is the interval between adjacent metasurface elements, θ is the pitch angle, is the azimuth;

[0030] S132, the mathematical model of the normalized beam gain is as follows:

[0031]

[0032] S133, based on the given desired beam gain P D , the mathematical model of the normalized beam matching error, i.e., the perceptual performance index of the SIM-ISAC system J MSE , as shown below:

[0033]

[0034] Among them, ||·||1 and ||·||2 are the l-1 norm and l-2 norm respectively.

[0035] Preferably, in step S2, in order to simultaneously realize downlink communication and target perception, a multi-objective optimization problem is constructed, by optimizing the phase shift of each metasurface array element in the SIM, maximizing the user sum rate and minimizing the beam matching error; wherein the optimization problem is in the form of:

[0036]

[0037] Among them, v represents all optimization variables The collection has R sum represents the communication user and rate, J MSE represents the normalized beam matching error, represents the phase shift of the mth element of the lth metasurface.

[0038] Preferably, in step S3, a double normalized differential gradient descent algorithm is designed to solve the optimization problem, and the specific process is as follows:

[0039] S31. Use the weighted summation method to transform the multi-objective optimization problem into a single-objective problem, as shown below:

[0040]

[0041] S32. Calculate R sum and J MSE right The partial derivative of and As shown below:

[0042]

[0043] Among them, δ p , η p,q and is the intermediate variable in the chain rule, as shown below:

[0044]

[0045]

[0046] S33. Normalize the partial derivatives element-wise and calculate the differential gradient G as follows:

[0047]

[0048] Among them, ∈=10 -8 is a smoothing term to avoid gradient explosion; w1 and w2 are weight factors, which are used to adjust the weights of perception performance and communication performance during the optimization process; w1 is 0, which means that the optimization process does not consider perception performance at all. The higher w1 is, the more the algorithm focuses on perception performance; w2 is 0, which means that the optimization process does not consider communication performance at all. The higher w2 is, the more the algorithm focuses on communication performance.

[0049] S34. Perform global normalization on the differential gradient G as follows:

[0050]

[0051] S35. Update the phase shift based on the double normalized differential gradient and update the step size as shown below:

[0052]

[0053] μ←μβ

[0054] Among them, μ is the learning rate / step size, and β is the decay rate used to reduce the step size;

[0055] S36. Iteratively execute steps S32 to S35 until convergence, and obtain an optimized multi-layer phase shift matrix for stacked intelligent metasurface-enabled communication-aware integrated beamforming.

[0056] Therefore, the present invention adopts the above-mentioned stacked intelligent metasurface-enabled synaesthesia integrated beamforming design method, which greatly reduces the hardware complexity and cost of the base station by optimizing only the phase shift of the SIM, while realizing the integrated function of communication and perception. Based on a novel double normalized differential gradient descent algorithm, the trade-off between communication and perception performance is effectively balanced, and target detection in the two-dimensional angle domain is realized within an acceptable range of communication performance reduction.

[0057] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a flow chart of a synaesthesia integrated beamforming design method enabled by stacked intelligent metasurfaces of the present invention;

[0059] Figure 2 It is a model diagram of the communication perception integrated system enabled by SIM of the present invention;

[0060] Figure 3 It is the beam direction gain diagram of the present invention in two-dimensional angular space;

[0061] Figure 4 Comparison of the beam matching error curves with the number of array elements per SIM layer under different weight factors and SIM layers;

[0062] Figure 5 This is a comparison chart of the communication users and rates with the number of array elements in each SIM layer under different weight factors and SIM layers;

[0063] Figure 6 The present invention is 3 Convergence simulation diagram of the algorithm. DETAILED DESCRIPTION

[0064] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0065] like Figure 1 As shown, the present invention provides a synaesthesia integrated beamforming design method enabled by stacked intelligent metasurfaces, comprising the following steps:

[0066] S1. Establish a mathematical model of the communication-sensing integrated system enabled by stacked intelligent metasurfaces;

[0067] S2, construct the multi-objective optimization problem of SIM-ISAC system;

[0068] S3, design dual-normalized differential gradient descent (Dual-normalized Differential Gradient Descent, D 3 ) algorithm to solve optimization problems.

[0069] Example

[0070] S1. Establish a mathematical model of the communication-perception integrated system enabled by stacked intelligent metasurfaces.

[0071] S11, a base station composed of a uniform linear array (ULA) feed antenna with equal power distribution and a stacked intelligent metasurface (SIM) to enable a mathematical model of a communication perception integrated system, serving N C single-antenna communication users and N S A perception target, such as Figure 2 As shown in the figure, SIM consists of L layers of transmission metasurfaces, each of which contains M = M r ×M c metasurface elements. r is the number of rows of metasurface elements per layer, M c is the number of columns of each layer of metasurface elements

[0072] The mathematical model of the received signal at the user is shown in the following formula:

[0073] y=HF SIM x+n

[0074] in, is the channel matrix from SIM to user; n is the additive white Gaussian noise (AWGN) at the receiving end. SIM is the transmission matrix of SIM, and its mathematical model is:

[0075] F SIM =Φ L W L ΦL-1 W L-1 …Φ 1 W 1

[0076] in, represents the phase shift matrix of the l-th metasurface, represents the phase shift of the mth metasurface element, W l is the inter-layer path loss matrix from the (l-1)th layer to the lth layer of the super-metasurface, and its element in the mth row and m'th column is From the Rayleigh-Sommerfeld diffraction formula:

[0077]

[0078] in, The physical meaning of is the inter-layer path loss from the mth metasurface element in the (l-1)th layer to the m'th metasurface element in the lth layer; A t is the area of ​​a single metasurface element; is the angle between the direction of the m-th metasurface element in the (l-1)th layer and the m'th metasurface element in the lth layer and the metasurface normal; is the distance between the mth metasurface element in the (l-1)th layer and the m'th metasurface element in the lth layer, and λ is the wavelength corresponding to the system operating frequency.

[0079] S12. Based on the above steps, the receiving end signal to interference and noise ratio (SINR) of the nth communication user is as follows:

[0080]

[0081] Where σ is the AWGN power.

[0082] The Shannon formula is used to calculate the sum rate of all communication users as follows:

[0083]

[0084] Among them, R sum It is the communication performance index of SIM-ISAC system.

[0085] S13. The normalized beam matching error is used as the performance indicator of radar target perception.

[0086] S131. First, the SIM-ISAC system is at a pitch angle ψ j and direction φ k The beam gain at the corners is given by:

[0087]

[0088] Where j, k = 1…N Dis the index number of the angle space, N D is the sampling number in the angle space; α(·) is the steering vector, which is related to the metasurface array element, azimuth angle and elevation angle. Its mathematical model is as follows:

[0089]

[0090] in, is the Kronecker product, d x and d y is the interval between adjacent metasurface elements, θ is the pitch angle, is the azimuth.

[0091] S132, the mathematical model of the normalized beam gain is as follows:

[0092]

[0093] S133, based on the given desired beam gain P D , the mathematical model of the normalized beam matching error, i.e., the perceptual performance index of the SIM-ISAC system J MSE , as shown below:

[0094]

[0095] Among them, ∥·∥1 and ∥·∥2 are the l-1 norm and l-2 norm respectively.

[0096] S2. Construct the multi-objective optimization problem of SIM-ISAC system.

[0097] In order to achieve downlink communication and target perception simultaneously, a multi-objective optimization problem is constructed to maximize the user sum rate and minimize the beam matching error by optimizing the phase shift of each metasurface array element in SIM.

[0098] The optimization problem form is as follows:

[0099]

[0100] Among them, v represents all optimization variables The collection has R sum represents the communication user and rate, J MSE represents the normalized beam matching error, represents the phase shift of the mth element of the lth metasurface.

[0101] S3, design double normalized differential gradient descent (D 3 ) algorithm to solve optimization problems.

[0102] S31. Use the weighted summation method to transform the multi-objective optimization problem into a single objective problem (SOP), as shown below:

[0103]

[0104] S32. Calculate R sum and J MSE right The partial derivative of and As shown below:

[0105]

[0106] Among them, δ p , η p,q and is the intermediate variable in the chain rule, as shown below:

[0107]

[0108] S33. Normalize the partial derivatives element-wise and calculate the differential gradient G as follows:

[0109]

[0110] Among them, ∈=10 -8 is a smoothing term to avoid gradient explosion; w1 and w2 are weight factors, which are used to adjust the weights of perception performance and communication performance during the optimization process respectively; w1 is 0, which means that the optimization process does not consider perception performance at all. The higher w1 is, the more the algorithm focuses on perception performance; w2 is 0, which means that the optimization process does not consider communication performance at all. The higher w2 is, the more the algorithm focuses on communication performance.

[0111] S34. Perform global normalization on the differential gradient G as follows:

[0112]

[0113] S35. Update the phase shift based on the double normalized differential gradient and update the step size as shown below:

[0114]

[0115] μ←μβ

[0116] Among them, μ is the learning rate / step size, and β is the decay rate used to reduce the step size.

[0117] S36. Iteratively execute steps S32 to S35 until convergence, and obtain an optimized multi-layer phase shift matrix for stacked intelligent metasurface-enabled communication-aware integrated beamforming.

[0118] like Figure 3 As shown, the beam direction gain of the present invention in two-dimensional angular space (pitch angle and azimuth angle) is demonstrated, where the x-axis is the pitch angle, the y-axis is the azimuth angle, and the z-axis is the beam gain size. Two sensing targets are set, located in the pitch angle-azimuth plane: (42.5°, -42.5°) and (-42.5°, 42.5°), with a beam width of 5°. Two obvious main lobes can be observed from the figure, and their positions are consistent with the expected beam pattern. The gain in the area outside the main lobe is relatively low, indicating that the present invention can effectively concentrate energy in the target direction and achieve precise spatial selectivity.

[0119] like Figure 4 As shown in Figure 1, the normalized beam matching error under different weight factors and SIM layers varies with the number of metasurface elements per layer M. The figure contains 6 curves, representing different weight factors (w1, w2) and SIM layers (L) configurations. It can be observed from the figure that as M increases, the J MSE The overall trend is downward, indicating that increasing the number of array elements in each layer can improve the beam matching accuracy. Secondly, changing the weight factor can freely adjust the optimization process's emphasis on communication and perception performance.

[0120] like Figure 5 As shown, it shows the communication users and rates (R sum ) changes with the number of array elements M per layer of SIM. The horizontal axis represents the number of array elements M per layer of the metasurface, and the vertical axis represents the communication users and rate R sum (bit / s / Hz). The figure also contains 6 curves, representing different weight factors (w1, w2) and SIM layer number (L) configurations. It can be observed from the figure that as M increases, except for w1=1 and w1=0, which completely ignores communication performance and only optimizes perception performance, the R sum The overall trend is upward, indicating that increasing the number of array elements in each layer can improve the communication performance. Secondly, changing the weight factor can freely adjust the optimization process's emphasis between communication and perception performance.

[0121] like Figure 6 As shown, the proposed D 3 The horizontal axis represents the number of iterations, and the left vertical axis represents the normalized beam matching error (J MSE ), the right vertical axis represents the communication users and rate (R sum , bit / s / Hz). The figure contains multiple groups of curves, where 5 different colored lines correspond to 5 different channels (Saleh-Valenzuela channel model). All solid lines represent J MSE , and all dotted lines represent R sumIn most cases, the algorithm converges after about 15 iterations, indicating that D 3 The algorithm has a good convergence speed. Under different channel implementations, the algorithm can converge to a similar performance level, indicating that D 3 The algorithm has good stability and robustness.

[0122] Therefore, the present invention adopts the above-mentioned stacked intelligent metasurface-enabled synaesthesia integrated beamforming design method, which greatly reduces the hardware complexity and cost of the base station by optimizing only the phase shift of the SIM, while realizing the integrated function of communication and perception. Based on a novel double normalized differential gradient descent algorithm, the trade-off between communication and perception performance is effectively balanced, and target detection in the two-dimensional angle domain is realized within an acceptable range of communication performance reduction.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A design method for synaesthesia integrated beamforming enabled by stacked intelligent metasurfaces, characterized in that: The following steps are involved: S1. Establish a mathematical model of the communication-sensing integrated system enabled by stacked intelligent metasurfaces; S2, construct the multi-objective optimization problem of SIM-ISAC system; S3. Design a double normalized differential gradient descent algorithm to solve the optimization problem.

2. The method for designing synaesthesia integrated beamforming enabled by stacked intelligent metasurfaces according to claim 1, characterized in that: In step S1, a base station of a mathematical model of a communication and perception integrated system enabled by a stacked intelligent metasurface is composed of a uniform linear array ULA feed antenna with equal power distribution and a stacked intelligent metasurface SIM, serving N C single-antenna communication users and N S sensing targets; where SIM consists of L layers of transmissive metasurfaces, each layer contains M = M r ×M c metasurface elements, where M r is the number of rows of metasurface elements per layer, M c is the number of columns of metasurface elements in each layer; The mathematical model of the received signal at the user is shown in the following formula: y=HF SIM x+n in, is the channel matrix from SIM to user; n is the additive white Gaussian noise AWGN at the receiving end; F SIM is the transmission matrix of SIM, and its mathematical model is: F SIM =Φ L W L F L-1 W L-1 …F 1 W 1 in, represents the phase shift matrix of the l-th metasurface, represents the phase shift of the mth metasurface element, W l is the inter-layer path loss matrix from the (l-1)th layer to the lth layer of the super-metasurface, and its element in the mth row and m'th column is From the Rayleigh-Sommerfeld diffraction formula: in, The physical meaning of is the inter-layer path loss from the mth metasurface element in the (l-1)th layer to the m'th metasurface element in the lth layer; A t is the area of ​​a single metasurface element; is the angle between the direction of the m-th metasurface element in the (l-1)th layer and the m'th metasurface element in the lth layer and the metasurface normal; is the distance between the mth metasurface element in the (l-1)th layer and the m'th metasurface element in the lth layer, and λ is the wavelength corresponding to the system operating frequency.

3. The method for designing synaesthesia integrated beamforming enabled by stacked intelligent metasurfaces according to claim 2, characterized in that: The signal-to-interference-to-noise ratio of the receiving end of the nth communication user is as follows: Where, σ is the AWGN power; The Shannon formula is used to calculate the sum rate of all communication users as follows: Among them, R sum It is the communication performance index of SIM-ISAC system.

4. The method for designing synaesthesia integrated beamforming enabled by stacked intelligent metasurfaces according to claim 3, characterized in that: The normalized beam matching error is used as the performance indicator of radar target perception. The specific process is as follows: S131. First, the SIM-ISAC system is at a pitch angle ψ j and direction φ k The beam gain at the corners is given by: Where j, k = 1…N D is the index number of the angle space, N D is the sampling number in the angle space; α(·) is the steering vector, which is related to the metasurface array element, azimuth angle and elevation angle. Its mathematical model is as follows: in, is the Kronecker product, d x and d y is the interval between adjacent metasurface elements, θ is the pitch angle, is the azimuth; S132. The mathematical model of the normalized beam gain is as follows: S133, based on the given desired beam gain P D , the mathematical model of the normalized beam matching error, i.e., the perceptual performance index of the SIM-ISAC system J MSE , as shown below: Among them, ∥·∥1 and ∥·∥2 are the l-1 norm and l-2 norm respectively.

5. The method for designing synaesthesia integrated beamforming enabled by stacked intelligent metasurfaces according to claim 1, characterized in that: In step S2, in order to achieve downlink communication and target perception at the same time, a multi-objective optimization problem is constructed to maximize the user sum rate and minimize the beam matching error by optimizing the phase shift of each metasurface array element in the SIM; wherein the optimization problem is in the form of: Among them, v represents all optimization variables The collection has R sum represents the communication user and rate, J MSE represents the normalized beam matching error, represents the phase shift of the mth element of the lth metasurface.

6. The method for designing synaesthesia integrated beamforming enabled by stacked intelligent metasurfaces according to claim 1, characterized in that: In step S3, a double normalized differential gradient descent algorithm is designed to solve the optimization problem. The specific process is as follows: S31. Use the weighted summation method to transform the multi-objective optimization problem into a single-objective problem, as shown below: S32. Calculate R sum and J MSE right The partial derivative of and As shown below: Among them, δ p , η p,q and is the intermediate variable in the chain rule, as shown below: S33. Normalize the partial derivatives element-wise and calculate the differential gradient G as follows: Among them, ∈=10 -8 is a smoothing term to avoid gradient explosion; w1 and w2 are weight factors, which are used to adjust the weights of perception performance and communication performance during the optimization process; w1 is 0, which means that the optimization process does not consider perception performance at all. The higher w1 is, the more the algorithm focuses on perception performance; w2 is 0, which means that the optimization process does not consider communication performance at all. The higher w2 is, the more the algorithm focuses on communication performance. S34. Perform global normalization on the differential gradient G as follows: S35. Update the phase shift based on the double-normalized differential gradient and update the step size as shown below: μ←μβ Among them, μ is the learning rate / step size, and β is the decay rate used to reduce the step size; S36. Iteratively execute steps S32 to S35 until convergence, and obtain an optimized multi-layer phase shift matrix for stacked intelligent metasurface-enabled communication-aware integrated beamforming.

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