Method for optimal activation of hybrid intelligent metasurface active elements under total power constraint

Abstract

The application provides a method for optimal activation of hybrid intelligent metasurface active elements under total power constraint, and relates to the technical field of wireless signal communication. Because the hybrid intelligent metasurface is composed of active and passive reflective elements, the advantages of the two are combined flexibly. For realistic considerations, the total power constraint is cited to the hybrid reconfigurable intelligent surface assisted communication, including the transmission power of the base station and the power related to the active and passive reflective elements on the HRIS. In order to better illustrate the influence of the HRIS element distribution, it is first verified in the application that there is a very weak correlation between the power distribution and the number of RIS elements. Subsequently, in the subsequent analysis, we decompose the original problem into two independently solvable sub-optimization problems: the first part can be further transformed to derive an approximate closed-form expression of the amplification factor; the second part solves the unit allocation problem based on the given result by jointly optimizing the power allocation. Finally, numerical results are given.

Description

Technical Field

[0001] This application relates to the field of radio signal communication technology, and in particular to an optimal activation method for hybrid smart metasurface active elements under total power constraints. Background Technology

[0002] Reconfigurable Smart Surfaces (RIS) are considered a revolutionary technology due to their remarkable performance in reconfiguring the propagation characteristics of wireless environments in recent years. By utilizing a large number of low-cost reflective elements to flexibly and dynamically control radio signals in the propagation environment, thereby benefiting wireless communication, RIS significantly improves the spectral and energy efficiency of communications. Therefore, RIS is widely regarded as a key technology for wireless networks beyond 5G and 6G.

[0003] Based on the forwarding protocol, Smart Reflectors (RIS) can be classified into three categories: Passive Smart Reflectors (PRIS), Active Smart Reflectors (ARIS), and Hybrid Smart Reflectors (HRIS). Specifically, PRIS suffers from dual-path loss; ARIS amplifies both signal and noise simultaneously; and HRIS combines passive phase-shifting units with a small number of active units, thus achieving a balance between performance improvement and energy efficiency optimization. By rationally allocating HRIS units, high performance can be achieved with lower power consumption within overall power constraints. Although HRIS has considerable application potential, the optimal allocation scheme for its active units still requires further research.

[0004] To fully explore the application potential of hybrid intelligent reflectors under actual power constraints, recent studies have focused on various aspects of their unit allocation and power management. For example, existing literature [1] focuses on the HRIS architecture and optimizes the allocation scheme of active and passive units under the total deployment cost budget; literature [2] proposes the optimal planning strategy for RIS unit allocation and power budget under the overall power constraint; in addition, literature [3] explores the optimization deployment problem of ARIS auxiliary system under power constraints, focusing on the optimal deployment location and power allocation scheme of ARIS. However, literature [1] does not consider the trade-off between the amplification gain of active units and the beamforming gain of passive units, and only focuses on the cost-based budget scenario; literature [2] only analyzes the threshold condition of the amplification factor under the overall power constraint, and fails to reveal the essential decoupling characteristics between the number of active units and unit allocation; at the same time, literature [3] does not involve the problem of unit collaborative allocation, and its research is only for ARIS, not HRIS.

[0005] Given the constraints of total power and a fixed total number of reflective elements, few studies have explored the optimal number of active reflective elements in HRIS.

[0006] The specific literature in the background technology is as follows:

[0007] References

[0008] Literature [1] Z. Kang, C. You, and R. Zhang, "Active-Passive IRS AidedWireless Communication: New Hybrid Architecture and Elements AllocationOptimization," IEEE Transactions on Wireless Communications, vol. 23, no. 4, pp. 3450-3464, Apr. 2024.

[0009] Literature [2] S. Chen, J. Gu, W. Duan, and PH Ho, "Hybrid RIS AssistedCommunications: Optimal Allocation Under a Total Power Constraint," IEEEInternet of Things Journal, vol. 12, no. 2, pp. 2283-2286, Jan. 2025.

[0010] Literature [3] W. Jiao et al., "Active RIS Deployment Design and Its DetailedOptimal Solution under Overall Power Constraint," IEEE Transactions onVehicular Technology, pp. 1-6, 2025. Summary of the Invention

[0011] The purpose of this application is to address the technical problem of the lack of research on the optimal number of active reflective elements in HRIS in the prior art.

[0012] To achieve the above objectives, this application provides the following technical solution:

[0013] An optimal activation method for hybrid smart metasurface active devices under total power constraints includes:

[0014] S1: Construct a wireless communication system model assisted by a hybrid intelligent metasurface (HRIS). The wireless communication system model consists of a single-antenna base station (BS), a single-antenna user, and the HRIS. The direct link between the single-antenna base station (BS) and the single-antenna user is blocked. The HRIS contains a fixed total number of passive and active reflective elements, with a total power of... Base station transmit power With HRIS amplification power sum;

[0015] S2: Establish the optimization problem of maximizing signal-to-interference-plus-noise ratio (SINR) under total power constraints and location constraints;

[0016] S3: Verify the optimal power allocation and the number of active reflective elements. The correlation is weak.

[0017] S4: Solve the closed-form expression for the optimal amplification factor based on the weak correlation decomposition optimization problem;

[0018] S5: The alternating optimization algorithm is used to iteratively optimize the power allocation, amplification factor and active / passive reflective element allocation to obtain the optimal active reflective element activation strategy.

[0019] Preferably, in the system model of S1:

[0020] The horizontal distance between the single-antenna base station BS and the single-antenna user is: The HRIS deployment height is The horizontal distance from the single-antenna base station BS to the HRIS Horizontal distance from HRIS to the single-antenna user satisfy ;

[0021] The distance from the single-antenna base station BS to HRIS Distance from HRIS to the single-antenna user .

[0022] Preferably, in the HRIS of S1:

[0023] The passive subsurface reflection matrix is ​​a diagonal phase-shift matrix with a constant amplitude of 1;

[0024] The active subsurface reflection matrix is ​​the product of the amplification matrix and the phase shift matrix, and all active reflective elements use the same amplification factor. ,and .

[0025] Preferably, the total power constraint and the amplification power constraint in S2 are respectively:

[0026] ;

[0027] ,

[0028] in For the optimal phase shift matrix, This is the base station to HRIS channel. For HRIS noise power, It is an identity matrix.

[0029] Preferably, the weak correlation in S4 is:

[0030] The number of active reflective elements When it changes, the base station transmit power With HRIS amplification power The optimal allocation remains essentially unchanged; the achievable rate performance achieved by the fixed power allocation ratio is very close to that achieved by the free optimization power allocation.

[0031] Preferably, the closed-form solution for the optimal amplification factor in S4 is:

[0032] ;

[0033] in This refers to the number of passive reflective elements. This represents the Gaussian white noise power at the user end.

[0034] Preferably, the alternating optimization algorithm in S5 includes:

[0035] Initialize the number of active reflective elements Number of passive reflective elements Base station transmission power and HRIS amplification power ;

[0036] Fixed component allocation, using closed-form formula to update amplification factor , and ;

[0037] With a fixed power allocation, a one-dimensional search is performed within the interval [0, N] to find the optimal solution. and ;

[0038] Calculate the achievable rate and determine convergence. If the convergence threshold is met, output the optimal activation strategy.

[0039] Preferably, the overall computational complexity of the alternating optimization algorithm in S5 is O(TN), where T is the number of iterations and N is the total number of HRIS reflective elements.

[0040] Compared with the prior art, this application has at least the following beneficial effects:

[0041] 1. This invention clarifies the optimal allocation of base station transmit power and HRIS amplification power under total power constraints, which is weakly correlated with the number of active components. Even if the number of active components changes, the optimal performance can be approximated by using a fixed power allocation ratio. There is no need to frequently adjust the power allocation parameters based on the number of components, which greatly simplifies the system parameter configuration and real-time scheduling process, and facilitates actual deployment and hardware implementation.

[0042] 2. This invention derives an approximate closed-form expression for the optimal amplification factor, which can quickly determine the amplification factor without complex iteration and global search. The calculation process is simple and efficient, and can meet the low latency and real-time operation requirements of communication systems. It is especially suitable for rapid parameter configuration in large-scale component scenarios.

[0043] 3. This invention employs an alternating optimization algorithm to decompose the high-dimensional non-convex joint optimization problem into low-dimensional sub-problems. Each iteration only requires power and amplification factor optimization through a closed-form formula, and then component allocation is completed through a one-dimensional search. The overall computational complexity increases linearly with the total number of components. While maintaining near-optimal performance, it can efficiently support the deployment and application of large-scale hybrid intelligent metasurfaces.

[0044] 4. Under the constraint of fixed total power, by optimizing the activation and allocation of active and passive reflective elements, the advantages of active element signal amplification and passive element low power consumption and low noise are fully combined, effectively balancing signal gain and noise amplification, achieving higher achievable speed and signal-to-interference-plus-noise ratio under lower power consumption conditions, and significantly improving system energy efficiency and spectral efficiency.

[0045] 5. This invention is based on SISO system modeling of single-antenna base stations and users. The constraints and optimization methods are applicable to most HRIS-assisted communication scenarios. The component allocation, power allocation and deployment strategies can be directly migrated to next-generation wireless networks such as 5G and 6G, and have good technical versatility and expansion potential. Attached Figure Description

[0046] Figure 1 The simulation graph shows the correlation between power distribution and the number of active components, where a) shows the HRIS amplification power as a function of the number of active components under different total power conditions. a) The curve showing the change in power distribution; b) The curve comparing the achievable rate of the system under fixed power distribution ratio and free optimized power distribution.

[0047] Figure 2 shows the results under local optimal performance: the optimal number of active units and amplification factor under different deployment scenarios, including (a) deployment height, (b) overall power constraint, (c) total number of units, (d) power allocation between the base station and HRIS, and (e) comparison results of alternating optimization algorithm and exhaustive search in terms of achievable rate and rate fluctuation with the number of iterations.

[0048] Figure 3 shows the results under the global optimal scenario: (a) the optimal number of active units at different deployment locations; (b) ARIS power allocation at different heights; (c) the distribution of the number of ARIS under different power constraints; (d) the distribution of the number of ARIS under different total number of units; and (e) the distribution of the number of ARIS under different power allocation ratios. Detailed Implementation

[0049] The above content will be explained in conjunction with specific verification experiments:

[0050] I. System Model

[0051] This application considers a wireless communication system assisted by a Hybrid Smart Reflector (HRIS), consisting of a base station (BS) and a user, both equipped with a single antenna. For simplicity, it is assumed that the HRIS is deployed at a height H, and its active and passive reflective elements are appropriately allocated to serve the user within its half-space region. It should be noted that due to the presence of dense obstacles, the direct link between the base station and its served user is blocked; the horizontal distance between the base station and the user is denoted as D. Let... and These represent the horizontal distances from the base station to the hybrid smart reflector and from the hybrid smart reflector to the user, respectively. + =D.

[0052] Therefore, the distances from the base station to the hybrid smart reflector and from the hybrid smart reflector to the user can be expressed as follows: and For ease of implementation, assume the hybrid intelligent reflective surface consists of two sub-surfaces, each containing... One passive reflective element and One active reflective element.

[0053] Specifically, the reflection matrix of the passive sub-surface is denoted as... iag( ,..., )in Let n represent the phase shift of the nth passive element, and satisfy n Furthermore, the reflection amplitude of each passive element is set to 1.

[0054] On the other hand, since the active sub-surface can simultaneously amplify the signal and adjust its phase shift, the reflection matrix of the active sub-surface is denoted as follows in this application. ,in iag( ,..., )and iag( ,..., ) represent its reflection amplification matrix and phase shift matrix, respectively. and Each active element n represents a different active element. The amplification factor and phase shift.

[0055] For an active sub-surface, it is assumed that all reflecting elements use the same magnification factor, i.e. And impose constraints on the amplification factor of each active element: ,in and .

[0056] Furthermore, in this application, the channel between the base station and the nth element of the smart reflector is denoted as... Let n be the channel between the nth reflective element of the smart reflective surface and the user. ,n, where n 1,2,...,N ; and = Here, is the distance-related path loss factor, where This is the path loss index.

[0057] According to the line-of-sight channel model, the channel from the base station to the active subplane is denoted as... It can be modeled as ,in Indicates the complex channel gain. For carrier wavelength, This is the reference channel power gain. Furthermore... This represents the azimuth (elevation) angle (AoA) at the active sub-plane.

[0058] Specifically, Represents the received response vector, where Represents the guiding vector function. Indicates the distance between adjacent reflective elements. and These represent the number of reflecting elements along the x-axis and y-axis, respectively. Similarly, the line-of-sight channel from the active subsurface to the user is denoted as... Similar modeling can also be performed. Furthermore, the channel from the base station to the passive subsurface... and passive subsurface-to-user channel For reference and The definition is presented in a specific way; for the sake of brevity, the details are omitted here.

[0059] Assume the total power Q includes the base station's transmit power ( ) and the amplification power of the hybrid smart reflective surface ( ),Right now And satisfy The first term represents the power consumed in amplifying the desired signal, and the second term corresponds to the power consumed in amplifying the input noise across all components. This implies that there are maximum values ​​for the amplification power of both the signal and noise to optimize system performance. Similarly, by using an optimal continuous phase shift design of the intelligent reflector to eliminate interference from residual phase errors, the received signal at the user can be expressed as...

[0060] (1)

[0061] Where s represents the transmitted signal, and its power is ,and Furthermore, the active subsurface generates amplified noise at all reflecting elements, denoted as . It follows an independent circularly symmetric complex Gaussian distribution, i.e. ~ ),and ~ Add Gaussian white noise (AWGN) at the user's location.

[0062] II. Problem Modeling:

[0063] This application considers a wireless communication system assisted by a hybrid smart reflector (HRIS), studies the optimal power allocation under total power constraints, and the allocation problem of active smart reflector (ARIS) components between the base station (BS) and the hybrid smart reflector (HRIS).

[0064] As can be seen from equation (1), the achievable speed of the proposed Hybrid Intelligent Reflector (HRIS) assisted system can be obtained from the following equation:

[0065] (2)

[0066] Under the total power constraint, it is necessary to determine the optimal power allocation between PB and PF. The power constraint is as follows:

[0067] ( ) (3)

[0068] For ease of analysis and research, this application equates the signal reflected by the active element to the signal reflected by the passive element. Therefore, under the constraints of total power and distance, the signal-to-interference-plus-noise ratio (SINR) optimization problem at the user location can be expressed as:

[0069]

[0070] (4a)

[0071] (4b)

[0072] (4c)

[0073] (4d)

[0074] This application fixes the total number of cells under a total power constraint and reveals a very weak correlation between power allocation and the number of RIS cells. This is because... The impact on the equalization of signal and noise components, coupled with potential normalization operations in the system design.

[0075] Specifically, in the Active Intelligent Reflector (ARIS) scenario, increasing the number of cells proportionally enhances signal amplification, but also introduces additional noise. Total power constraints require amplification power... satisfy: ( ) Mathematically, the signal power in the numerator and the ARIS amplification noise in the denominator usually increase with each other. It increases with increasing size. Furthermore, since the magnification factor is often normalized according to the number of units, this makes... The effects were largely offset or significantly reduced.

[0076] The aforementioned weak correlation can be visually verified through simulation results. Figure 1 (a) illustrates the different total power constraints. Follow The changing trend of Q can be observed. It can be seen that regardless of the value of Q, the power of the passive intelligent reflector (HRIS) changes with... The number of cells increases while remaining essentially constant, and the average value of each curve is close to the horizontal line, indicating that the number of cells has no significant impact on power distribution. Figure 1 (b) The achievable rates of the system under a fixed power allocation ratio and under free optimized power allocation were further compared. The results show that the two curves highly overlap, even... Increasing the number of ARIS cells from 100 to 1000 did not result in a significant performance difference. This confirms that, under total power constraints, changes in the number of ARIS cells have a negligible impact on the optimal power allocation strategy, thus verifying the weak correlation between power allocation and cell count.

[0077] Mathematically prove that the total power Q is in and The optimal allocation between them, and the number of active units It exhibits weak correlation. Even if the number of cells in the Active Smart Reflector (ARIS) changes, it can approach optimal performance with a fixed power allocation ratio without the need for frequent adjustments to the power allocation parameters.

[0078] Secondly, based on the aforementioned analysis, it is known that there is a weak correlation between power allocation and the number of cells. Accordingly, this application decomposes the original problem into two sub-optimization problems, which are solved separately in the subsequent analysis: the first part can be further transformed to obtain an approximate closed-form expression for the amplification factor; the second part, based on the determined power allocation results, completes the solution of the cell allocation problem.

[0079] 1) Optimal amplification factor of Hybrid Intelligent Reflector (HRIS): For a single-input single-output (SISO) system assisted by a hybrid intelligent reflector, the optimal amplification factor is determined by focusing on joint optimization while keeping the number of active components Na constant. and .

[0080] First, we can verify that the necessary and sufficient condition for equation (3) to be feasible is: ≥ / ( )+ It can then be proven that for any {ρ, , The optimal phase shift matrix Θ should align the cascaded base station – active intelligent reflector – user channel, i.e. = Based on the above conditions, substituting the phase shift of the optimal active intelligent reflector (ARIS) into equation (2), the system model can be simplified to:

[0081]

[0082]

[0083] Since both the objective function and the constraints are convex, this application uses the Lagrange multiplier method to solve the problem. After simplification, the expression for the optimal magnification factor is obtained as follows:

[0084]

[0085] Optimal component configuration for Smart Reflectors (RIS): Analyzing the signal-to-interference-plus-noise ratio (SINR) and providing the optimal allocation strategy for RIS units.

[0086] Assume independent and identically distributed (iid) Rayleigh fading, where n and The average power of n are respectively and By Substituting back into equation (2), the signal-to-interference-plus-noise ratio (SINR) expression can be approximately transformed into...

[0087] = ,

[0088] St + (9a)

[0089] In total power Total number of RIS units Assuming the communication distance is fixed, the constraints on the amplification factor can be further derived: Clearly, the above problem can be transformed into dealing with active units in RIS. With passive unit Optimization of the proportions.

[0090] exist and When fixed, optimal This can be achieved by differentiating the fraction and letting We obtain the following from equation (9): Differentiation yields: From the above results, we can see that: when That is, when all are PRIS. ;when That is, when all are ARIS, Therefore, in the interval There exists at least one The root of the problem is found in the objective function. Since the objective function contains highly nonlinearly coupled terms with respect to Na and the power allocation variables, a direct analytical solution is difficult to implement. Therefore, a one-dimensional search for component allocation is performed within the interval [0, N]. In this case, the joint optimization problem can be transformed into... This problem can be effectively solved by an alternating optimization algorithm as shown in Algorithm 1.

[0091] C. Computational complexity

[0092] Suppose that component allocation requires a one-dimensional search across N+1 possible values. Performing a global exhaustive search for all combinations of component allocation and continuous power variables would result in unacceptable computational complexity. In contrast, the alternating optimization strategy proposed in this application optimizes power allocation and component allocation iteratively. In each iteration, power allocation and amplification coefficients can be optimized using a closed-form expression with a complexity of O(1), while component allocation via a one-dimensional search has a complexity of O(N). Let the total number of iterations before convergence be T, then the overall complexity is O(TN). Therefore, compared to the global exhaustive strategy, the alternating optimization method significantly reduces complexity while maintaining near-optimal performance.

[0093] IV. Numerical Results:

[0094] Numerical results are presented in this application to evaluate the system performance related to optimal activation of active cells. Simulation parameters are set as follows: communication distance. Path loss constant noise power Amplify noise power

[0095] In Figures 2(a)–2(d), we present the optimal number of active cells and amplification factor under different deployment locations, assuming local optima and setting different conditions as variables. Figure 2(a) shows the impact of deployment height on optimal cell configuration: the results show that lower deployment heights are more suitable for configuring more active cells due to stronger incident signal power; while higher deployment heights require a "passive-dominated" design to mitigate the adverse effects of amplification noise. Figure 2(b) illustrates that under overall power constraints, the system needs more active cells to obtain sufficient signal energy; while when power resources are abundant, the system will configure fewer active cells and operate them at higher amplification gain to avoid noise accumulation. Figures 2(c) and 2(d) further explore the system behavior when the total number of cells and the power allocation ratio change: in Figure 2(c), the achievable rate of the system increases with the increase of the total number of RIS cells, but the optimal proportion of active cells remains highly stable, which verifies our theoretical analysis conclusion that "power allocation is weakly correlated with the number of cells". Figure 2(d) shows that the system performance is highly sensitive to the power allocation between the base station and HRIS. Figure 2(e) compares the convergence characteristics of the proposed alternative optimization algorithm and exhaustive search: within 10 iterations, the alternative optimization strategy can gradually approach the maximum achievable rate, and the rate fluctuation is close to zero, demonstrating fast convergence and efficient computational performance.

[0096] Figures 3(a)–3(e) illustrate the simulation results under global optimization. In Figure 3(a), we fixed the overall power constraint and the total number of units, and analyzed the impact of the optimal number of active units Na on the HRIS deployment. We found that the global perspective can accurately reveal the nonlinear interaction between the HRIS location and the active units. Figure 3(b), with other parameters fixed, explored the impact of height on ARIS power allocation by setting the ARIS height to 20 m and 40 m respectively. The simulation results clearly show that increasing the height introduces additional path loss and weakens the cascaded channel gain, thereby reducing the gain advantage of the active units. In Figure 3(c), we fixed the total number of units and the power allocation ratio, and set the total power... and As the total power increases, the optimal number of active cells, Na, shifts significantly: because the amplified signal outweighs the noise amplification, higher transmit power allows for more efficient utilization of active cells; conversely, at low power, excessive Na becomes inefficient due to noise amplification, resulting in a smaller optimal active cell set. Figure 3(d) visually illustrates the impact of the total number of cells on HRIS deployment (at a fixed height). Total power (The total number of units was set to 300 and 800 respectively). Although increasing the total number of units N can improve the overall system speed, the optimal Na does not increase proportionally with N. This indicates that when the total number of units exceeds a certain threshold, the newly added units are mainly used to enhance the passive beamforming performance, rather than to simultaneously increase the active components. In Figure 3(e), we fixed the height, total power, and total number of units, and changing the power allocation ratio significantly affected the optimal configuration: the results show that stronger amplification capability is a reasonable basis for deploying more active units.

[0097] Based on the above description, this application studies a hybrid smart reflector (HRIS)-assisted wireless communication system under total power constraints, focusing on optimizing the deployment of active smart reflector (ARIS) components to maximize achievable data rates. Through numerical simulations, we evaluate the system performance under different channel types and power levels, and derive the optimal power allocation between the base station and the ARIS, as well as the optimal amplification factor.

Claims

1. An optimal activation method for a hybrid smart metasurface active element under total power constraint, characterized in that, include: S1: Construct a wireless communication system model assisted by a hybrid intelligent metasurface (HRIS). The wireless communication system model consists of a single-antenna base station (BS), a single-antenna user, and the HRIS. The direct link between the single-antenna base station (BS) and the single-antenna user is blocked. The HRIS contains a fixed total number of passive and active reflective elements, with a total power of... Base station transmit power With HRIS amplification power sum; S2: Establish the optimization problem of maximizing signal-to-interference-plus-noise ratio (SINR) under total power constraints and location constraints; S3: Verify the optimal power allocation and the number of active reflective elements. The correlation is weak. S4: Solve the closed-form expression for the optimal amplification factor based on the weak correlation decomposition optimization problem; S5: The alternating optimization algorithm is used to iteratively optimize the power allocation, amplification factor and active / passive reflective element allocation to obtain the optimal active reflective element activation strategy.

2. The optimal activation method for a hybrid smart metasurface active element under total power constraint according to claim 1, characterized in that, In the system model of S1: The horizontal distance between the single-antenna base station BS and the single-antenna user is: The HRIS deployment height is The horizontal distance from the single-antenna base station BS to the HRIS Horizontal distance from HRIS to the single-antenna user satisfy ; The distance from the single-antenna base station BS to HRIS The distance from HRIS to the single-antenna user .

3. The optimal activation method for a hybrid intelligent metasurface active reflective element under total power constraint according to claim 1, characterized in that, In the HRIS of S1: The passive subsurface reflection matrix is ​​a diagonal phase-shift matrix with a constant amplitude of 1; The active subsurface reflection matrix is ​​the product of the amplification matrix and the phase shift matrix, and all active reflective elements use the same amplification factor. ,and .

4. The optimal activation method for a hybrid smart metasurface active element under total power constraint according to claim 1, characterized in that, The total power constraint and amplification power constraint in S2 are as follows: ； ， in For the optimal phase shift matrix, This is the base station to HRIS channel. For HRIS noise power, It is an identity matrix.

5. The optimal activation method for a hybrid smart metasurface active element under total power constraint according to claim 1, characterized in that, The weak correlation in S4 is: The number of active reflective elements When it changes, the base station transmit power With HRIS amplification power The optimal allocation remains essentially unchanged; the achievable rate performance achieved by the fixed power allocation ratio is very close to that achieved by the free optimization power allocation.

6. The optimal activation method for a hybrid smart metasurface active element under total power constraint according to claim 1, characterized in that, The closed-form solution for the optimal amplification factor in S4 is: ; in The number of passive reflective elements, This represents the Gaussian white noise power at the user end.

7. The optimal activation method for a hybrid smart metasurface active element under total power constraint according to claim 1, characterized in that, The alternating optimization algorithm in S5 includes: Initialize the number of active reflective elements Number of passive reflective elements Base station transmission power and HRIS amplification power ; Fixed component allocation, using closed-form formula to update amplification factor , and ; With a fixed power allocation, a one-dimensional search is performed within the interval [0, N] to find the optimal solution. and ; Calculate the achievable rate and determine convergence. If the convergence threshold is met, output the optimal activation strategy.

8. The optimal activation method for a hybrid smart metasurface active element under total power constraint according to claim 1, characterized in that, The overall computational complexity of the alternating optimization algorithm in S5 is O(TN), where T is the number of iterations and N is the total number of HRIS reflective elements.

9. The method according to claim 1, characterized in that, The HRIS deployment location in S1 satisfies: In line-of-sight channels, HRISs are deployed closer to the base station when the total power is high, and deployed further away from the base station when the total power is low. For HRISs deployed closer to the base station, the optimal number of active components activated first increases and then tends to stabilize as the total power increases. For HRISs deployed closer to the user, the optimal number of active components activated remains at a fixed low level.

10. The optimal activation method for a hybrid smart metasurface active element under total power constraint according to claim 1, characterized in that, The HRIS deployment in S1 highly satisfies the following: In low-height HRIS deployments, the number of activated active reflective elements increases slowly and linearly with total power. For HRIS deployed at high altitudes, the number of active components activated increases more sharply at medium to high power, activating more active reflective components at the same power.

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