Smart metasurfaces integrating signal reflection, refraction, amplification and energy harvesting and their applications

Abstract

The present invention discloses an intelligent metasurface integrating signal reflection, refraction, amplification and energy collection and its application. The intelligent metasurface can simultaneously support the reflection, refraction, amplification and energy collection of wireless signals on one surface, so as to achieve the purpose of amplifying the reflected / refracted signals through the collected energy, thereby enhancing the effective coverage of the wireless signal. When the signal model of MF-RIS constructed by the present invention is applied to a multi-user wireless network, with the goal of maximizing the sum rate of multiple users in an orthogonal multiple access network assisted by MF-RIS, a non-convex optimization problem for jointly designing the base station transmit beamforming, the operation modes and parameters of different components of MF-RIS and their deployment locations is constructed, and then an iterative optimization algorithm is designed to effectively solve the aforementioned non-convex optimization problem, thereby maximizing the sum rate of multiple users.

Description

Technical Field

[0001] The present invention relates to the field of wireless resource allocation technology, and in particular to a modeling and optimization method of a reconfigurable multifunctional intelligent metasurface (MF-RIS) integrating signal reflection, refraction, amplification and energy collection. Background Art

[0002] Reconfigurable Intelligence Surface (RIS) or Intelligent Reconfigurable Surface (IRS) has become a potential development direction for future communication networks due to its advantages of improving energy efficiency and spectrum efficiency in a low-cost manner. By modifying the phase shift or amplitude of the incident signal, RISs are able to establish a tunable communication environment and achieve various communication goals, such as improving throughput, enhancing security, and reducing transmission energy consumption. However, due to its hardware limitations, the traditional reflection-based single-function RIS (SF-RIS) can only achieve half-space signal coverage. This greatly limits their deployment flexibility and effectiveness in wireless networks with randomly distributed users.

[0003] To overcome this limitation, dual-functional RIS (DF-RIS) structures have been proposed, such as Simultaneous Transmitting and Reflecting RIS (STAR-RIS) and Intelligent Omni-Surface (IOS). DF-RIS achieves full-space signal coverage by supporting both signal reflection and refraction, thereby creating a ubiquitous intelligent radio environment. However, both SF-RIS and DF-RIS-assisted communication links suffer from double fading, which seriously impairs signal reception.

[0004] In order to solve the double fading phenomenon faced by existing passive RISs, an active RIS structure is proposed. By embedding a power amplifier into the traditional SF-RIS and rationally designing the phase shift and amplification factor, active RISs have achieved significant spectral efficiency gains. In addition, there is another metasurface structure that supports signal amplification: dynamic metasurface antennas (DMAs). DMA overcomes the serious path loss problem of passive RISs by amplifying and phase shifting the incident signal to varying degrees, thereby realizing active large-scale antenna arrays. However, both active RISs and DMAs require additional power consumption to maintain the operation of active components, which makes their performance highly dependent on external power supplies.

[0005] The above RIS structures are all powered by batteries or the grid. For battery-powered RIS, the embedded battery can only provide a limited life and cannot support its long-term operation. Considering environmental hazards and hardware limitations, manually replacing RIS batteries is costly and impractical. In addition, since power line networks are difficult to reach places such as mountainous areas, the grid-powered RIS can be deployed in limited locations. Therefore, the present invention aims to develop a new RIS structure that achieves RIS self-sustainability while maintaining its performance advantages. Summary of the invention

[0006] In view of the fact that the performance of the existing RIS structure is highly dependent on external power supply, the present invention proposes a smart metasurface (Multi-Functional Reconfigurable IntelligenceSurface, MF-RIS) that integrates signal reflection, refraction, amplification and energy collection, which uses the energy collected from the radio frequency (RF) signal to support the simultaneous reflection, transmission and amplification of the incident signal. Therefore, the proposed MF-RIS can not only maintain energy self-sufficiency, but also achieve full spatial coverage of the signal, effectively reducing path loss. By allowing all components to flexibly switch between different operating modes, MF-RIS provides more degrees of freedom for signal processing.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] On the one hand, the present invention provides an intelligent metasurface that integrates signal reflection, refraction, amplification and energy collection, including two working modes: energy collection mode and signal relay mode. In the signal relay mode, surface equivalent electrical impedance and magneto-impedance elements are used to realize reflection and refraction of the incident signal, and the current and magnetic current are controlled by a microcontroller unit chip. The incident signal is divided into two parts, one part is reflected to the reflective half-space, and the other part is refracted to the refractive half-space, and an amplifier circuit is used to realize amplification of the reflected signal and the refracted signal; in the energy collection mode, impedance matching, RF-DC conversion circuit and capacitor are used to obtain RF energy from the incident signal and convert it into DC power, and the energy management module is used to control the energy storage in the energy storage device or supply the phase shift and the operation of the amplifier circuit; by adjusting the circuit connection, each element can flexibly switch between the energy collection mode and the signal relay mode.

[0009] On the other hand, the present invention also provides an application method of the above-mentioned smart metasurface integrating signal reflection, refraction, amplification and energy collection in a multi-user wireless network, comprising the following steps:

[0010] S1. Design the operation modes and parameters of base station transmit beamforming, different components of MF-RIS and their deployment locations, with the goal of maximizing the achievable and rate of all users, and construct a mixed integer nonlinear programming non-convex optimization problem and constraints;

[0011] S2. Decompose the non-convex problem constructed in step S1 into three sub-problems: base station transmit beamforming optimization problem, MF-RIS coefficient design problem and MF-RIS deployment optimization problem;

[0012] S3. Alternately optimize the sub-problems converted in step S2 to ensure that each sub-algorithm converges to the local optimum. Among them, for the base station transmit beamforming optimization problem, after introducing auxiliary variables, the sequential rank-one constraint relaxation method is used to solve the transmit beamforming optimization. For the MF-RIS coefficient design problem, after introducing auxiliary variables, the non-convex objective function is replaced by its convex upper bound, and then the penalty function method is used to handle the equality constraints, and then the MF-RIS coefficients are designed. For the MF-RIS deployment optimization problem, the local area optimization method is used to design the MF-RIS position, and the successive convex approximation is used to handle the non-convex terms, so that the MF-RIS deployment optimization problem is converted into a solvable convex problem.

[0013] Furthermore, the optimization problem and constraints of step S1 are:

[0014]

[0015] w∈P={[x,y,z] T |x min ≤x≤x max ,ymin ≤y≤y max ,z min ≤z≤z max},

[0016]

[0017] Assume that the number of MF-RIS elements is M, and the set of MF-RIS elements is indexed as M = {1, ..., M}, where m is the mth element in the element set; the number of antennas is J, the space set is K = {r, t}, and the user set is J = {1, 2, ..., J}, where j is the jth element in the user set, J k ={1,2,…,J k} is represented as a set of users in space K, and J r ∪J t = J, if k = t, then And if k = r, then Index user j in space K as U kj ; Represents the distance from BS to user U kj The combined channel vector, Θ k is the coefficient of MF-RIS, R MF is the feasible set of MF-RIS coefficients; For user U kj The achievable rate of the expected signal, Represents user U kj The minimum service quality requirement, f k is the transmit beamforming vector in space k, represents the maximum transmit power of the base station, P represents the predefined area for MF-RIS deployment, and a three-dimensional Cartesian coordinate system is considered, where BS, MF-RIS and user U kj The locations are

[0018] w b =[x b ,y b ,z b ] T ,w=[x,y,z] T , and w kj =[x kj ,y kj ,0] T ,[x min ,x max ],[y min ,y max ] and [z min ,z max ] represent the candidate ranges along the X-axis, Y-axis, and Z-axis respectively; represents the amplified noise introduced at the MF-RIS, with noise power per unit Indicates that user U kj Additive Gaussian white noise at , with power Constant a m Indicates the influence of the circuit sensitivity limitation on the mth element, P b ,P DC ,P C They represent the amount of power consumed by each phase shifter, the DC bias power consumed by the amplifier circuit, and the power consumed by the RF-DC power conversion circuit; ξ is the inverse of the energy conversion coefficient, Indicates the output power of MF-RIS.

[0019] Furthermore, the process of decomposing the non-convex problem into three sub-problems in step S2 is:

[0020] Constrain can be removed from the original question;

[0021] Introduce the slack variable set Δ0={A kj ,B kj ,Γ kj ,C m ,ζ m},satisfy:

[0022]

[0023] Then rewrite the original constraint as:

[0024]

[0025] Where W = 2(P b +P DC )∑ m α m +(M-∑ m α m ) C ;

[0026] The continuous convex approximation (SCA) method is used to deal with the non-convex constraints in the second equation above. According to the first-order Taylor expansion, and In the In the iteration, at the feasible point The lower bound of the right-hand side term is:

[0027]

[0028] At this point, the original problem is decomposed into three sub-problems: base station transmit beamforming optimization problem, MF-RIS coefficient design problem and MF-RIS deployment optimization problem.

[0029] Furthermore, in step S3, the base station transmit beamforming optimization problem is given by {Θ k ,w}, introduce the satisfaction and Auxiliary variable Q kj and C kj For the objective function Transform and use SCA technology to handle non-convex constraints In the lth iteration, find the lower bound of the right-hand side of the non-convex constraint, and define and Satisfy F k ±0 and rank(F k )=1, introducing the auxiliary variable set Δ1={A kj ,B kj ,C kj ,Q kj ,Γ kj ,C m ,ζ m}and So that: The rank-one constraint is relaxed gradually (SROCR) using the method Replace it with the following linear constraint: in For the In the iteration F k The trace ratio parameter, is corresponding to The eigenvector of the largest eigenvalue, is given The solution in the (l-1)-th iteration of , the original problem is transformed into a convex semidefinite programming problem.

[0030] Furthermore, the solution algorithm for the convex semidefinite programming problem transformed from the base station transmit beamforming optimization problem is as follows: First, initialize the feasible point and step length Set the iteration index Repeat the following steps until the stopping criterion is met: If the above convex semidefinite programming problem is solvable, then update renew Otherwise update renew renew Then end this round.

[0031] Furthermore, in step S3, the MF-RIS coefficient design problem is given by {f k ,w}, definition and u k =[v k ; 1]; Definition Meet U k ±0,rank(U k )=1, and [U k ] M+1,M+1 =1, we get the following equation:

[0032]

[0033] The same can be said and P O =∑ k Tr(HU k )

[0034] About A kj ,B kj ,C kj , The constraints are rewritten as:

[0035]

[0036] Rank-one constraint Approximately Binary Constraint Equivalently converts to For constraints Use SCA technology to handle; for non-convex constraints Introducing auxiliary variables It can be expressed equivalently as: Then apply the penalty function to handle the equality constraint The original problem is transformed into a problem based on the penalty function method.

[0037] Furthermore, the solution algorithm based on the penalty function method is: Initialize the feasible point Step Length Set the iteration index and penalty factor ρ max The maximum value of; repeat the following steps: if If the original problem is solvable, then by solving the problem update renew Otherwise update renew If the updated renew Then end; otherwise, reinitialize with a new Let ε>1, until the stopping criterion is met.

[0038] Furthermore, in step S3, the MF-RIS deployment optimization problem is solved by using a local area optimization method to design the MF-RIS location w, defining w(i-1) is the MF-RIS position obtained in the (i-1)th iteration, then the position variable satisfies the constraint ||ww (i-1) ||≤ò; Assume that in the (i-1)th iteration and in and From the base station to the MF-RIS and from the MF-RIS to the user U kj The array response and small-scale fading after the (i-1)th iteration of A are expressed as kj ,B kj ,C kj , A set of auxiliary variables are introduced to replace the complex terms of the constraints, and then SCA is used to approximate its non-convex part; for non-convex constraints The right side is about According to the first-order Taylor expansion, the constraint is rewritten as the following convex constraint: in For the The feasible point in the iteration.

[0039] Furthermore, the steps of the problem solving algorithm based on the local area are as follows: First, initialize the feasible points Set the iteration index Then repeat the steps: Update by resolving the issue renew until the stopping criterion is met.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] The intelligent metasurface with integrated signal reflection, refraction, amplification and energy collection proposed in the present invention has multiple signal processing functions and can simultaneously support the reflection, transmission / refraction, amplification and energy collection of wireless signals on one surface, so as to achieve the purpose of amplifying the reflected / refracted signals through the collected energy, thereby enhancing the effective coverage of the wireless signal. The MF-RIS proposed in the present invention can not only maintain energy self-sufficiency, but also achieve full spatial coverage of the signal, effectively reducing path loss. By allowing all components to flexibly switch between different operating modes, MF-RIS provides more degrees of freedom for signal processing. Compared with traditional passive RIS and self-sufficient RIS, by integrating multiple signal processing functions on one surface, the proposed MF-RIS can achieve performance gains of up to 23.4% and 98.8%, respectively.

[0042] The signal model of MF-RIS constructed by the present invention aims to maximize the sum rate of multiple users in the non-orthogonal multiple access network assisted by MF-RIS, constructs a non-convex optimization problem for jointly designing the base station transmit beamforming, the operation mode and parameters of different components of MF-RIS and their deployment locations, and then designs an iterative optimization algorithm to effectively solve the aforementioned non-convex optimization problem, thereby maximizing the sum rate of multiple users. In addition, deploying MF-RIS closer to the transmitter is conducive to energy collection and can bring higher performance gains. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0044] Figure 1 A schematic diagram of the implementation of MF-RIS provided in an embodiment of the present invention.

[0045] Figure 2 This is a flow chart of the AO algorithm provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0046] In order to better understand the technical solution, the method of the present invention is described in detail below with reference to the accompanying drawings.

[0047] See also Figure 1 The present invention first proposes an intelligent metasurface (MF-RIS) integrating signal reflection, refraction, amplification and energy collection, including two working modes: energy collection mode (H mode) and signal relay mode (S mode). In the signal relay mode, the surface equivalent electrical impedance and magneto-impedance elements are used to realize the reflection and refraction of the incident signal, and the current and magnetic current are controlled by the microcontroller unit chip. The incident signal is divided into two parts, one part is reflected to the reflection half space, and the other part is refracted to the refraction half space, and the amplifier circuit is used to realize the amplification of the reflected signal and the refracted signal; in the energy collection mode, impedance matching, RF-DC conversion circuit and capacitor are used to obtain RF energy from the incident signal and convert it into DC power, and the energy management module is used to control the energy storage in the energy storage device or the supply phase shift and the operation of the amplifier circuit; by adjusting the circuit connection, each element can flexibly switch between the energy collection mode and the signal relay mode. Since the switching frequency of the positive and negative intrinsic diodes can reach up to 5MHz, the mode switching time of MF-RIS is negligible compared with the typical wireless channel coherence time (e.g., 4.2ms).

[0048] Energy harvesting circuits rely primarily on the following components:

[0049] An impedance matching network consisting of high-quality resonators ensures maximum power transfer from the components to the rectifier block. The RF-DC conversion circuit rectifies the available RF power into a DC voltage. Capacitors are used to ensure that the current is smoothly delivered to the energy storage device or as a short-term reserve when RF energy is not available. The power management module decides whether to store the converted electrical energy or use it directly for signal reflection, transmission, and amplification. Energy storage devices (e.g., rechargeable batteries and supercapacitors) are used to store energy. When the energy collected exceeds the energy consumed, the excess energy is stored for future use, thereby achieving continuous self-sufficiency.

[0050] For other elements operating in S mode, the incident signal is split into two parts by controlling the current and magnetic flow. One part is reflected into the reflective half-space and the other part is refracted into the refractive half-space. With the help of a microcontroller unit, these elements can use the harvested energy to maintain the operation of the phase shift and amplifier circuits. Therefore, the proposed MF-RIS does not require any external power supply in principle. Note that Figure 1 Also shown is the implementation of the reflection and transmit amplifiers, where operational amplifier-based current converters are used to generate amplified reflection and transmit signals.

[0051] The intelligent metasurface structure with integrated energy collection and signal reflection, refraction and amplification functions proposed in the present invention can realize signal reflection, transmission or refraction, amplification and energy collection. At the same time, the implementation method of MF-RIS is provided, and an operation protocol is designed for it to work in an actual wireless network.

[0052] Specifically, the steps of applying the MF-RIS proposed in the present invention in a multi-user wireless network are as follows:

[0053] S1. A mixed integer nonlinear programming nonconvex problem is constructed to jointly design the base station transmit beamforming, the operation modes and parameters of different elements of MF-RIS and their deployment locations to maximize the sum rate of multiple users.

[0054] To characterize the signal model of MF-RIS, we consider a MF-RIS with M elements, where the set of MF-RIS elements is indexed as M = {1, ..., M}. Let s m represents the signal received by the mth element. Due to hardware limitations, we believe that each element cannot work in H and S modes at the same time. Therefore, the signals collected, reflected, and refracted by the mth element are modeled as:

[0055]

[0056] where α m ∈{0,1}, Respectively represent the energy collection coefficient, reflection and refraction phase shift and their corresponding amplitudes. Here α m =1 means the mth element works in S mode, α m =0 means working in H mode, β max ≥1 indicates the amplification factor. According to the law of conservation of energy, the energy consumed by the amplifier should not exceed the maximum available energy that the MF-RIS can provide, that is, The reflection and refraction coefficients of MF-RIS are modeled as:

[0057]

[0058] where α m ∈{0,1},

[0059] We consider a MF-RIS-assisted downlink Non-Orthogonal Multiple Access (NOMA) network, where an N-antenna base station serves J single-antenna users with the help of an MF-RIS consisting of M units. We denote the reflection (refraction) space by r(t). The space set and user set are denoted by K = {r, t} and J = {1, 2, …, J}, respectively. In addition, we denote J k ={1,2,…,J k} is represented as a set of users in space K, and J r ∪J t = J. For simplicity of notation, we index user J in space K as U kj .

[0060] In addition, we consider a three-dimensional (3D) Cartesian coordinate system, where the base station (BS), MF-RIS and user U kj The positions are w b =[x b ,y b ,z b ] T ,w=[x,y,z] T , and w kj =[x kj ,y kj ,0] T Due to the limited coverage of MF-RIS, its deployable area is also limited. Let P be the predefined area for MF-RIS deployment, which should satisfy the following constraints:

[0061] w∈P={[x,y,z] T |x min ≤x≤xmax ,y min ≤y≤y max ,z min ≤z≤z max},

[0062] where [x min ,x max ],[y min ,y max ] and [z min ,z max ] represent the candidate ranges along the X-axis, Y-axis, and Z-axis respectively.

[0063] To characterize the upper limit of the performance that MF-RIS can achieve, we assume that perfect channel state information is available for all channels. We use Rician fading modeling for all channels. For example, the channel matrix between BS and MF-RIS is Given by:

[0064]

[0065] Where L bs is the distance-dependent path loss, Specifically, h0 is the path loss at a reference distance of 1 meter, d bs is the link distance between the base station and MF-RIS, and κ bs is the corresponding path loss exponent. For small-scale fading, β bs is the Rice factor, H NLoS is the non-LoS component that follows independent and identically distributed Rayleigh fading. Assume that MF-RIS is placed parallel to the YZ plane, and its M elements form an M y ×M z = M uniform rectangular array, LoS component H LoS It is expressed as:

[0066]

[0067] Among them, the operator represents the Kronecker product, λ is the carrier wavelength, and d is the antenna spacing. In addition, θ r , and θ t denote the vertical and horizontal angles of arrival, and the vertical and horizontal angles of departure, respectively. In addition, and Represents the distance from BS to user U kj and from MF-RIS to user U kj The channel vector of can be obtained by a process similar to that of obtaining H and is given by:

[0068]

[0069] To facilitate NOMA transmission, the BS transmits superimposed signals by utilizing multiple beamforming vectors, i.e., where f k is the transmit beamforming vector in space k. In addition, p kj Is user U kj The power allocation factor, s kj ∈CN(0,1) represents the corresponding modulated data symbol, which is independent of k. kj The signal received at is given as follows:

[0070]

[0071] If k = t, If k = r, also, represents the amplified noise introduced at MF-RIS, and the noise power per unit is Represents user U kj The AWGN at the position is also, Represents the distance from BS to user U kj The combined channel vector of .

[0072] According to the NOMA protocol, all users adopt SIC to eliminate interference. We assume that the users in space k are arranged in ascending order according to their equivalent combined channel gains, expressed as:

[0073]

[0074] Where L k ={j,j+1,...,J k}. Therefore, for any user U satisfying j≤l kj and U kl , user U kl Decode user U kj The achievable rate of the expected signal is given by:

[0075]

[0076] in To ensure the success of SIC, for all j≤l, at user U kl Decode user U kj The achievable SINR for the signal should be no less than that of user U kj The achievable SINR when decoding its own signal. Therefore, we have the following SIC decoding rate constraint:

[0077]

[0078] The energy harvesting coefficient matrix of the mth element is defined as

[0079] Next, the RF power received at the mth element is expressed as:

[0080]

[0081] In order to capture the dynamic changes of RF energy conversion efficiency under different input power levels, the present invention adopts a nonlinear energy harvesting model. Therefore, the total power collected by the mth element is given by:

[0082]

[0083] Among them, Y m is the received RF power The logic function of , Z ≥ 0 is a constant that determines the maximum harvested power. The constant Ω is used to ensure the zero input / zero output response in H mode, and the constants a>0 and q>0 represent the combined effects of circuit sensitivity limitations and current leakage. In order to achieve self-sustainability of MF-RIS, the following energy constraints should be met:

[0084]

[0085] Where P b ,P DC ,P C They represent the amount of power consumed by each phase shifter, the DC bias power consumed by the amplifier circuit, and the power consumed by the RF-DC power conversion circuit. Here ξ is the inverse of the energy conversion coefficient, Represents the output power of MF-RIS.

[0086] Our goal is to maximize the achievable SR for all users while maintaining the self-sustainability of MF-RIS by jointly optimizing the power allocation, transmit beamforming at the BS, the coefficient matrix, and the 3D location of the MF-RIS. The following optimization problem is formulated:

[0087]

[0088] w∈P={[x,y,z] T |x min ≤x≤x max ,y min ≤y≤y max ,z min ≤z≤z max},

[0089]

[0090] in, Indicates the maximum transmit power of the base station. Represents user U kj Minimum quality of service requirements, is the feasible set of MF-RIS coefficients. Constraint Limit the total transmit power at the BS.

[0091] S2. For the non-convex problem constructed in step S1, it is first converted into a more tractable form, and then an algorithm based on alternating optimization is proposed to effectively find high-performance suboptimal solutions. The original problem is decomposed into three sub-problems: base station transmit beamforming optimization problem, MF-RIS coefficient design problem, and MF-RIS deployment optimization problem;

[0092] Before solving the original problem, we transform it into a more tractable form. First, we observe that the constraint is a necessary condition for the following inequality:

[0093]

[0094] Specifically, according to the above inequality, for the user U whose decoding order satisfies j≤l kj and U kl , their equivalent combined channel gains satisfy the following conditions:

[0095]

[0096] By multiplying both sides of the inequality by p kj , and add on both sides Performing equivalent transformations, we obtain the following inequality:

[0097]

[0098] Obviously, the above inequality ensures that the constraint The establishment of.

[0099] Therefore, when there is a constraint

[0100] When removing the constraint It does not affect the optimality of the original problem. Therefore, the constraint can be removed from the original question.

[0101] Next, to handle highly coupled constraints

[0102]

[0103] We introduce the slack variable set Δ0 = {A kj ,B kj ,Γ kj ,C m ,ζ m}, so that:

[0104]

[0105] Using these variable definitions, the above two constraints can be rewritten as:

[0106]

[0107] Where W = 2(P b +P DC )Σ m α m +(M-Σ m α m ) C The constraints in the second equation above are non-convex because their right-hand sides are convex terms. Here, we use the SCA technique to solve them. Using the fact that the first-order Taylor expansion of a convex function is a global underestimate, they are Feasible points in iteration The lower bounds of the right-hand side terms at are given by:

[0108]

[0109] As a result, the original problem is equivalently transformed into the following problem:

[0110]

[0111] (W+ξP O )(1-Ω)Z -1 +MΩ≤C lb ,

[0112] w∈P={[x,y,z] T |x min ≤x≤x max ,y min ≤y≤y max ,z min ≤z≤z max},

[0113]

[0114] Next, we start to solve the three sub-problems one by one:

[0115] S4. For the base station transmit beamforming problem in step S3, a sequential rank-one constraint relaxation method is used to solve the transmit beamforming optimization after introducing auxiliary variables;

[0116] First, for the optimization problem of base station transmit beamforming, given {Θ k ,w}, our goal is to solve the transmit beamforming vector f k Since the non-concave objective function and non-convex constraints The original problem is still difficult to solve directly. To this end, we introduce an auxiliary variable Q kj and C kj ,satisfy and Objective Function is converted to:

[0117]

[0118] In addition, we obtain the following new constraints:

[0119] C kj ≥|h kj f k | 2 P kj +B kj ,

[0120]

[0121] SCA technique is used to handle non-convex constraints:

[0122]

[0123] Specifically, in During iteration, the lower bound of its right side is expressed as:

[0124]

[0125] Next we define and Satisfy F k ±0,rank(F k )=1. The transmit beamforming vector is then optimized by solving the following problem:

[0126]

[0127] With the auxiliary variable set Δ1={A kj ,B kj ,C kj ,Q kj ,Γ kj ,C m ,ζ m}and The main difficulty in solving the above problem lies in the rank-one constraint We use the SROCR method to deal with this constraint. The basic idea of ​​the SROCR method is to gradually relax the rank-one constraint in order to find a feasible rank-one solution.

[0128] Specifically, we define For the In the iteration F k Then, Rank-one constraint in iteration can be replaced by the following linear constraint:

[0129]

[0130] in is corresponding to The eigenvector of the largest eigenvalue is is given No. The solution in iterations. Therefore, the problem is transformed into:

[0131]

[0132] This problem is a SDP problem and can be solved efficiently using CVX. As we increase from 0 to 1, we gradually approach a rank 1 solution. The following algorithm summarizes the iterative algorithm for solving this problem. k Perform Cholesky decomposition to obtain f k The solution is

[0133] Problem solving algorithm based on SROCR: First initialize the feasible point and step length Set the iteration index Repeat the following steps until the stopping criterion is met: If the above SDP problem is solvable, then update renew Otherwise update renew renew Then end this round.

[0134] S4. Next, for the MF-RIS coefficient design problem in step S2, after introducing auxiliary variables, the non-convex objective function is replaced by its convex upper bound, and then the penalty function method is used to process the equality constraints, and then the MF-RIS coefficients are designed.

[0135] For any given {f k ,w}, we use express and u k =[vk ; 1]. We further define satisfy [U k ] M+1,M+1 =1. Then, the following equation holds:

[0136]

[0137] Likewise, we get:

[0138] and

[0139] in

[0140]

[0141] Then, the constraint

[0142]

[0143] are rewritten as:

[0144]

[0145] Therefore, the MF-RIS coefficient design problem is simplified to:

[0146]

[0147] The non-convexity of the problem arises from the non-convex constraints Rank-one constraint and binary constraints In the previous section, we showed how to use SROCR to handle rank-one constraints. Similarly, by defining Corresponding to the constraints In Rank-one constraint Approximately:

[0148]

[0149] For α m We equivalently transform the binary constraints on into the following two continuous constraints:

[0150]

[0151] However, due to the non-convex constraint is still non-convex. SCA technique is used to solve this problem. Specifically, for Any feasible point in the iteration The upper bound is as follows:

[0152]

[0153] To address the highly coupled constraints Introducing auxiliary variables Thus we can obtain The equivalent form is:

[0154]

[0155] Next, we apply a penalty function-based approach to handle the constraints Note that if we directly add it as a penalty term to the objective function In this case, the objective function becomes Where ρ>0 represents the penalty factor. Due to the existence of non-convex terms The resulting objective function is non-concave. For this reason, we use its CUB alternative. Define the function For yes And, when When and Established, of which express Finally, the original problem is reformulated as:

[0156]

[0157] in When ρ→∞, the solution obtained by solving the above problem satisfies This problem is a SDP problem and can be solved efficiently using CVX. A given point in the iteration according to Update. The details of the proposed penalty-based algorithm are given in the following algorithm:

[0158] The algorithm solves the problem based on the penalty function and initializes the feasible point ε>1, step length Set the iteration index and penalty factor ρ max Repeat the following steps: If If the original problem is solvable, then by solving the problem update renew Otherwise update renew If the updated renew Then end. Otherwise, reinitialize with a new Let ε>1, until the stopping criterion is met.

[0159] S5. Finally, for the MF-RIS deployment optimization problem in step S2, since the sight distance component containing the MF-RIS position variable is nonlinear, the local area optimization method is used to design the MF-RIS position, and the successive convex approximation is used to process the non-convex terms, so as to transform the MF-RIS deployment optimization problem into a solvable convex problem. Finally, it can be ensured that each sub-algorithm converges to the local optimum.

[0160] Finally, this paper focuses on the location optimization problem of MF-RIS. We observe from the expression of the original problem that the distance-independent variable L bs and L skj and the LoS component H LoS and are all related to the MF-RIS position w. However

[0161]

[0162] It is revealed that these LoS components are nonlinear with respect to w and difficult to handle directly. To this end, we adopt a local area optimization method to design w. Specifically, w (i-1) Denoted as the feasible MF-RIS position obtained in the (i-1)th iteration, the position variable should satisfy the following constraints:

[0163]

[0164] The constant is relatively small, so that the MF-RIS position in the (i-1)th iteration can be used to approximately obtain the H in the i-th iteration. LoS and Assume that in the (i-1)th iteration and Then, the constraints can be rewritten as:

[0165]

[0166] in

[0167]

[0168] Therefore, given {f k ,Θ k}, the original problem is simplified to:

[0169]

[0170] stw∈P={[x,y,z] T |x min ≤x≤x max,y min ≤y≤y max ,z min ≤z≤z max},

[0171]

[0172] constraint

[0173]

[0174] It is still nonlinear and nonconvex with respect to w. To solve this problem, we first introduce a set of auxiliary variables to replace its complex terms, and then use SCA to approximate the nonconvex part. Specifically, by introducing the slack variable set And define The constraint linear approximation is:

[0175]

[0176] in For the The feasible points obtained in the iteration.

[0177] The proof of the above formula is as follows:

[0178] We will relax the variable set Defined as:

[0179]

[0180] Then, the constraint

[0181]

[0182] are rewritten as:

[0183]

[0184] Due to constraints It is still non-convex, so we apply the SCA method to deal with it. The right side term is relative to is convex. Using the first-order Taylor expansion, it is The lower bound of the right-hand side of is obtained as follows:

[0185]

[0186] Therefore, the constraint is rewritten as a convex constraint

[0187]

[0188] To facilitate the subsequent derivation of other constraints, we rewrite them as follows:

[0189]

[0190] Non-convex term -x 2 ,-y 2 ,-z 2 The existence of makes these constraints non-convex. To solve this problem, we first introduce a set of auxiliary variables to replace the SCA method, which can be obtained -x 2 ,-y 2 ,-z 2 At feasible point The upper bound of:

[0191]

[0192] Finally, by replacing the non-convex terms with their respective convex approximations, we obtain the convex constraints as follows:

[0193]

[0194] Proof of completion.

[0195] Next, by using the convex constraint

[0196]

[0197] Replace the following nonconvex constraints:

[0198]

[0199] Re-stating the original problem yields the following optimization problem:

[0200]

[0201] stw∈P={[x,y,z] T |x min ≤x≤x max ,y min ≤y≤y max ,z min ≤z≤z max},

[0202]

[0203] This problem is convex and can be solved efficiently using CVX. The details of the proposed local region based algorithm are given in the following algorithm.

[0204] The steps of the local area-based problem solving algorithm are:

[0205] First, initialize the feasible points Set the iteration index Then repeat the steps: Update by resolving the issue renew until the stopping criterion is met.

[0206] Based on the above algorithm, Figure 2 The flowchart of the AO algorithm for solving this optimization problem is given in . Since each sub-algorithm converges to its own local optimum, the entire AO algorithm is guaranteed to converge.

[0207] 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 aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An application method of an intelligent metasurface integrating signal reflection, refraction, amplification and energy collection in a multi-user wireless network, characterized in that: The intelligent metasurface with integrated signal reflection, refraction, amplification and energy collection (MF-RIS) includes two working modes: energy collection mode and signal relay mode. In the signal relay mode, the surface equivalent electrical impedance and magneto-impedance elements are used to realize the reflection and refraction of the incident signal. The current and magnetic current are controlled by the microcontroller unit chip. The incident signal is divided into two parts, one part is reflected to the reflective half-space, and the other part is refracted to the refractive half-space. The amplifier circuit is used to realize the amplification of the reflected signal and the refracted signal. In the energy harvesting mode, impedance matching, RF-DC conversion circuit and capacitor are used to obtain RF energy from the incident signal and convert it into DC power, and the energy management module is used to control the energy storage in the energy storage device or the operation of the phase shift and amplifier circuit; by adjusting the circuit connection, each component can be flexibly switched between the energy harvesting mode and the signal relay mode; the application method includes the following steps: S1. Design the operation modes and parameters of base station transmit beamforming, different components of MF-RIS and their deployment locations, with the goal of maximizing the achievable and rate of all users, and construct a mixed integer nonlinear programming non-convex optimization problem and constraints; S2. Decompose the non-convex problem constructed in step S1 into three sub-problems: base station transmit beamforming optimization problem, MF-RIS coefficient design problem and MF-RIS deployment optimization problem; S3. Alternately optimize the sub-problems converted in step S2 to ensure that each sub-algorithm converges to the local optimum. Among them, for the base station transmit beamforming optimization problem, after introducing auxiliary variables, the sequential rank-one constraint relaxation method is used to solve the transmit beamforming optimization. For the MF-RIS coefficient design problem, after introducing auxiliary variables, the non-convex objective function is replaced by its convex upper bound, and then the penalty function method is used to handle the equality constraints, and then the MF-RIS coefficients are designed. For the MF-RIS deployment optimization problem, the local area optimization method is used to design the MF-RIS position, and the successive convex approximation is used to handle the non-convex terms, so as to transform the MF-RIS deployment optimization problem into a solvable convex problem.

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