A design method for synaesthesia-integrated beamforming enabled by stacked intelligent metasurfaces

Abstract

The present invention belongs to the field of wireless communication perception integration technology, and discloses a stacked intelligent metasurface-enabled synaesthesia integrated beamforming design method, comprising the following steps: S1, establishing a mathematical model of the stacked intelligent metasurface-enabled communication perception integrated system; S2, constructing a multi-objective optimization problem of the SIM-ISAC system; S3, designing a double normalized differential gradient descent algorithm to solve the optimization problem. The present invention adopts the above-mentioned stacked intelligent metasurface-enabled synaesthesia integrated beamforming design method to achieve downlink communication and radar target detection, maximizes the user's total rate by optimizing the multi-layer phase shift matrix of the stacked intelligent metasurface, and minimizes the mean square error between the normalized perception beam pattern and the desired beam pattern; based on the double normalized differential gradient descent algorithm, solves the non-convex multi-objective optimization problem, realizes multi-point desired beamforming in a two-dimensional angular domain, and achieves an acceptable trade-off in 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 ongoing research into 6G technologies, wireless communication systems are evolving towards higher data rates, lower latency, and wider connectivity. Simultaneously, the demand for high-precision perception and positioning is growing, particularly in application scenarios such as autonomous driving, smart cities, and the Industrial Internet of Things. Against this backdrop, Integrated Sensing and Communication (ISAC) has become a key technology for next-generation wireless networks. ISAC aims to integrate communication and perception systems by sharing hardware platforms, spectrum resources, signal processing algorithms, and waveforms, fully utilizing increasingly scarce spectrum resources while reducing system hardware costs and energy consumption. Building on the long-term development of Multiple-Input Multiple-Output (MIMO) technology in the communications and radar fields, existing ISAC systems widely employ array antenna architectures, leveraging the spatial degrees of freedom provided by multi-antenna arrays for multi-user communications and radar target perception. However, the complex feed networks and RF links in array antennas significantly increase system cost and power consumption.

[0003] In this regard, some studies have used intelligent metasurfaces deployed in transceivers of integrated communication and perception systems to replace traditional phased array antennas, simplifying the system hardware architecture while significantly reducing power consumption. Specifically, an 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, it can achieve precise control of the phase and amplitude of the incident electromagnetic wave, thereby reconstructing the propagation characteristics of the electromagnetic wave at low cost and low power consumption. However, this research is generally limited to single-layer intelligent metasurfaces and has not fully explored the potential of intelligent metasurfaces for integrated communication and perception. In order to make full 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, thereby achieving more complex beamforming.

[0004] While some research has focused on deploying stacked smart metasurfaces between base stations and users or targets, similar to conventional smart metasurfaces, to enhance the performance of integrated communication and perception systems, there has been limited discussion of using stacked smart metasurfaces to replace the digital precoding and phased arrays in transmitters to achieve integrated communication and perception systems. This approach could offer several advantages: first, it could significantly simplify the hardware architecture, reducing system cost and power consumption; second, the additional degrees of freedom provided by stacked smart metasurfaces could allow for more flexible beamforming, thereby better balancing communication and perception performance. However, stacked smart metasurface-enabled integrated communication and perception systems face numerous challenges. First, optimizing the transmission matrix of the stacked smart metasurface under the constant modulus constraints of the multilayer metasurface elements to simultaneously meet the requirements of communication and perception is a complex non-convex optimization problem. Second, due to the cascaded structure of the stacked smart metasurfaces, the variables in the optimization problem are highly coupled, which increases the difficulty of solving the problem. Furthermore, achieving high-precision target detection in the 2D angular domain while maintaining acceptable communication performance is a key issue that needs to be addressed. Summary of the Invention

[0005] The purpose of the present invention is to provide a synaesthesia integrated beamforming design method enabled by stacked intelligent metasurfaces, aiming to simultaneously achieve 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 objectives, the present invention provides a stacked intelligent metasurface-enabled synaesthesia integrated beamforming design method, comprising the following steps:

[0007] S1. Establish a mathematical model for the communication and perception 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 as follows:

[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 m-th 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 m-th 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 communicating 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. 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 as follows:

[0026]

[0027] Where j, k = 1…N D is the index number of the angle space, N D is the number of samples 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, that is, the perceptual performance index J of the SIM-ISAC system 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 achieve downlink communication and target perception, 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. The optimization problem is formulated as follows:

[0036]

[0037] Among them, v represents all optimization variables The collection of R sum represents the communication user sum 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. 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. Perform element-wise normalization on the partial derivatives and calculate the differential gradient G as follows:

[0047]

[0048] Where ∈ = 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 respectively 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 follows:

[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 stacking intelligent metasurface-enabled communication-aware integrated beamforming.

[0056] Therefore, the present invention adopts the aforementioned stacked intelligent metasurface-enabled synaesthesia-integrated beamforming design method. By optimizing only the SIM phase shift, this significantly reduces base station hardware complexity and cost, while simultaneously achieving integrated communication and perception functionality. Based on a novel dual-normalized differential gradient descent algorithm, this method effectively balances communication and perception performance, achieving target detection in the two-dimensional angular domain within an acceptable range of communication performance degradation.

[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 stacked intelligent metasurface-enabled synaesthesia integrated beamforming design method of the present invention;

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

[0060] Figure 3 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 layer numbers;

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

[0063] Figure 6 This invention proposes D 3 Convergence simulation diagram of the algorithm. DETAILED DESCRIPTION

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

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

[0066] S1. Establish a mathematical model for the communication and perception 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)-enabled communication and perception integrated system mathematical model, serving N C single-antenna communication users and N S Perception targets, such as Figure 2 As shown. SIM consists of L layers of transmission metasurfaces, each layer 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 metasurface elements in each layer

[0072] The mathematical model of the received signal at the user is shown as follows:

[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 m-th 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 m-th 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 signal-to-interference-and-noise ratio (SINR) of the receiving end 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 communicating 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 as follows:

[0087]

[0088] Where j, k = 1…N Dis the index number of the angle space, N D is the number of samples 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, that is, the perceptual performance index J of the SIM-ISAC system 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 of R sum represents the communication user sum 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. Perform element-wise normalization on the partial derivatives and calculate the differential gradient G as follows:

[0109]

[0110] Where ∈ = 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 respectively during the optimization process; w1 being 0 means that the optimization process does not consider perception performance at all, and the higher w1 is, the more the algorithm focuses on perception performance; w2 being 0 means that the optimization process does not consider communication performance at all, and 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 follows:

[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 stacking intelligent metasurface-enabled communication-aware integrated beamforming.

[0118] like Figure 3 As shown, the beam direction gain of the present invention in the 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-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 of 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 2, 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 layer number (L) configurations. It can be observed from the figure that as M increases, the J of all configurations increases. 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, the communication users and rates (R sum ) changes with the number of elements per SIM layer M. The horizontal axis represents the number of elements per metasurface layer M, and the vertical axis represents the number of 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 the cases of w1=1 and w1=0, which completely ignore the communication performance and only optimize the perception performance, the R sum The overall trend is upward, indicating that increasing the number of array elements in each layer can improve communication performance. Secondly, changing the weight factor can freely adjust the optimization process's emphasis on communication and perception performance.

[0121] like Figure 6 As shown, the proposed D 3 The convergence performance of the algorithm. 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 sets 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 aforementioned stacked intelligent metasurface-enabled synaesthesia-integrated beamforming design method. By optimizing only the SIM phase shift, this significantly reduces base station hardware complexity and cost, while simultaneously achieving integrated communication and perception functionality. Based on a novel dual-normalized differential gradient descent algorithm, this method effectively balances communication and perception performance, achieving target detection in the two-dimensional angular domain within an acceptable range of communication performance degradation.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. 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 solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions 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 for the communication and perception integrated system enabled by stacked intelligent metasurfaces; The base station is composed of a uniform linear array ULA feed antenna with equal power distribution and a stacked intelligent metasurface SIM, which is a mathematical model of a communication and perception integrated system enabled by a stacked intelligent metasurface, serving Single antenna communication users and perception targets; among them, SIM consists of Layer-transmitting metasurface, each layer contains metasurface elements, where is the number of rows of metasurface elements per layer, is the number of columns of metasurface elements in each layer; The mathematical model of the received signal at the user is shown as follows: ； in, It is the channel matrix from SIM to user; is the additive white Gaussian noise AWGN at the receiving end; is the transmission matrix of SIM, and its mathematical model is: ； in, Indicates the The phase shift matrix of the layer metasurface, Indicates the The phase shift of the metasurface elements, For the Layer to inter-layer path loss matrix of the layer-super surface; S2, construct the multi-objective optimization problem of SIM-ISAC system; The normalized beam matching error is used as the performance indicator of radar target perception, where the mathematical model of the normalized beam gain is as follows: ； Based on the desired beam gain , the mathematical model of the normalized beam matching error, i.e. the perceptual performance index of the SIM-ISAC system , as shown below: ； in, They are Norm and norm; To achieve both downlink communication and target perception, a multi-objective optimization problem is constructed. By optimizing the phase shift of each metasurface element in the SIM, the user sum rate is maximized and the beam matching error is minimized. The optimization problem is formulated as follows: ； in, Represents all optimization variables The collection of , ; represents the communication users and rate, represents the normalized beam matching error, Indicates the Layer metasurface Phase shift of each array element; S3. Design a double normalized differential gradient descent algorithm to solve the optimization problem; S31. Use the weighted summation method to transform the multi-objective optimization problem into a single-objective problem; S32, calculation and right The partial derivative of and ; S33, perform element-wise normalization on the partial derivatives and calculate the differential gradient ; S34, differential gradient Perform global normalization; S35. Update the phase shift based on the double-normalized differential gradient and update the step size; S36. Iteratively execute steps S32 to S35 until convergence, and obtain an optimized multi-layer phase shift matrix for stacking intelligent metasurface-enabled communication-aware integrated beamforming.

2. The method for designing synaesthesia-integrated beamforming enabled by stacked intelligent metasurfaces according to claim 1, characterized in that: In step S1, the inter-layer path loss matrix No. OK Elements of a column From the Rayleigh-Sommerfeld diffraction formula: ； in, The physical meaning is Tier metasurface elements to the Tier The inter-layer path loss of each metasurface element; is the area of ​​a single metasurface element; For the Tier The metasurface element and the Tier The angle between the direction of each metasurface element and the metasurface normal; For the Tier The metasurface element and the Tier The distance between the metasurface elements, 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: No. The signal-to-interference-and-noise ratio of the receiving end of a communication user is as follows: ； in, is the AWGN power; The Shannon formula is used to calculate the sum rate of all communicating users as follows: ； in, 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 index of radar target perception. First, the SIM-ISAC system is used to calculate the pitch angle. and direction The beam gain at the corners is as follows: ； in, is the index number of the angle space, is the number of samples in the angle space; is the steering vector, which is related to the metasurface array element, azimuth angle and pitch angle. Its mathematical model is as follows: ； ； in, is the Kronecker product, and is the spacing between adjacent metasurface elements, is the pitch angle, is the azimuth.

5. The method for designing synaesthesia-integrated beamforming enabled by stacked intelligent metasurfaces according to claim 1, wherein: 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, calculation and right The partial derivative of and , as shown below: ； ； in, 、 and is the intermediate variable in the chain rule, as shown below: ； ； ； ； S33, perform element-wise normalization on the partial derivatives and calculate the differential gradient , as shown below: ； in, is a smoothing term to avoid gradient explosion; and are weight factors, which are used to adjust the weights of perception performance and communication performance during the optimization process; A value of 0 means that the optimization process does not consider perceptual performance at all. The higher the value, the more the algorithm focuses on perceptual performance; A value of 0 means that the optimization process does not consider communication performance at all. The higher the value, the more emphasis the algorithm places on communication performance; S34, differential gradient Perform global normalization as follows: ； S35. Update the phase shift based on the double-normalized differential gradient and update the step size as follows: ； ； in, is the learning rate / step size, 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 stacking intelligent metasurface-enabled communication-aware integrated beamforming.

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