A robust beamforming method for reconfigurable multifunctional smart metasurface

Abstract

The application discloses a kind of robust beamforming methods for reconfigurable multifunctional intelligent metasurface, improve the performance of wireless network by intelligently reconfiguring wireless environment.For the problem of double fading attenuation and strong dependence on power grid / battery existing in existing passive intelligent metasurface, an MF-RIS architecture integrating signal reflection, amplification and energy collection is proposed, energy self-sustainability is realized, and the asymptotic capacity of the communication network assisted by MF-RIS architecture is analyzed.Then, with the goal of realizing a self-sustaining communication system, a resource allocation problem under imperfect channel state information is constructed.By using S-process and generalized symbolic deterministic approximation semi-infinite constraint, a high-robustness beamforming scheme is proposed, which overcomes the inevitable channel estimation error and solves the double fading problem.Compared with existing self-sustaining RIS, MF-RIS can better balance the relationship between energy collection and throughput improvement.

Description

Technical Field

[0001] This invention relates to the field of wireless resource allocation technology, and in particular to a robust beamforming method for a multi-functional reconfigurable intelligence surface (MF-RIS). Background Technology

[0002] With the development of metasurface technology, reconfigurable intelligence surfaces (RIS) have emerged as a promising paradigm for creating intelligent radio environments for various emerging applications, such as smart factories and mobile holography. A RIS is a plane composed of numerous energy-efficient passive cells, each of which generates an independent phase shift of the incident signal via an embedded microcontroller chip. By rationally adjusting the phase of the incident signal, it can improve the expected reception for the intended user or mitigate information leakage by malicious eavesdroppers. This programmability makes RIS a key technology for improving throughput, enhancing security, and reducing energy consumption.

[0003] However, deploying RIS in practical communication systems still faces significant challenges. For example, the signal relayed by the RIS suffers two large-scale fadings, leading to substantial power loss when the direct link is blocked, severely limiting the achievable performance of the RIS. While this problem can be addressed by increasing the number of cells, the maximum number of cells is limited by the RIS's power budget. Furthermore, large-size RISs typically increase production costs and deployment complexity. Therefore, it is necessary to design a cost-effective and easily deployable RIS architecture to overcome the double-fading dilemma faced by existing RIS structures. In addition, RIS operation requires advanced signal processing, intelligent computing, and active electronic units such as diodes, RF switches, and phase shifters. These components consume significant amounts of energy, introducing non-negligible power consumption into the RIS cells, necessitating the development of effective power supply strategies to support their long-term operation. However, existing RISs are typically non-rechargeable, making it difficult to achieve energy self-sufficiency by eliminating dependence on batteries or the power grid. Given the growing service demands in wireless networks and the limitations of existing RISs, there is an urgent need to develop a novel RIS architecture that can mitigate the double-fading effect while simultaneously achieving sustainability.

[0004] To effectively overcome the double fading problem, existing work has proposed a novel RIS architecture called Hybrid Relay-RIS (HR-RIS). Unlike passive RIS, HR-RIS activates RIS cells by connecting them to an RF chain and a power amplifier. These cells thus become amplification and relay units, allowing HR-RIS to amplify the power of the incident signal and change the phase shift. However, this hybrid RIS architecture requires an expensive and power-intensive RF chain to relay the signal, making it difficult to implement in practical applications. To achieve a better balance between feasibility and performance improvement, existing work has proposed the concept of active RIS. By embedding negative resistance units in each cell, active RIS can achieve both signal reflection and amplification at an acceptable power consumption. However, whether passive, HR-RIS, or active, they all require a stable power supply connection to maintain the reflection and / or amplification circuitry. This means that the implementation of these RISs relies on an external power grid or internal battery, making it difficult to provide flexible, uninterrupted communication services at low cost.

[0005] To eliminate the dependence of traditional RIS structures on the power grid / battery, existing work has proposed a self-sustaining RIS architecture using wireless technology. This self-sustaining RIS allows a portion of the cells to operate in signal reflection mode (R mode) to tune the wireless channel, while the remaining cells operate in energy harvesting mode (H mode). In H mode, the incident radio frequency signal is converted into DC power by the energy harvesting circuit. By utilizing a large number of RIS cells, this RIS achieves both self-sustainability and signal reflection.

[0006] Given that the aforementioned RIS architectures cannot simultaneously solve the dual-fading attenuation and grid / battery dependency problems faced by traditional RIS architectures, and rarely evaluate the feasibility performance of proposed RIS architectures from both optimization and analysis perspectives, while also lacking robust beamforming designs under imperfect Channel State Information (CSI), this invention prompts us to propose a novel RIS architecture and explore its application in practical networks. Summary of the Invention

[0007] This invention addresses the dual attenuation and power dependence issues faced by existing RIS (Reconstructed Signal Processing) systems by proposing a robust beamforming method for reconfigurable multifunctional smart metasurfaces. This method allows switching between an energy harvesting mode (H-mode) and a signal amplification mode (A-mode). In H-mode, cells harvest radio frequency energy from the incident signal via an embedded energy harvesting module. Simultaneously, with the assistance of a power amplifier and phase-shifting circuitry, cells operating in A-mode reflect and amplify the incident signal. This method combines signal reflection, amplification, and energy harvesting capabilities, promoting energy self-sustainability while maintaining performance advantages.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A robust beamforming method for a reconfigurable multifunctional smart metasurface, wherein the reconfigurable multifunctional smart metasurface is an MF-RIS architecture integrating signal reflection, amplification, and energy harvesting, and the robust beamforming method includes the following steps:

[0010] S1. In the case of imperfect Channel State Information (CSI), a bounded CSI model is used to characterize the uncertainty of CSI.

[0011] S2. Formulate the problem of maximizing the sum rate (SR) of a multi-user system assisted by MF-RIS;

[0012] S3. Using the S-process and generalized symbolic determinism, infinitely many non-convex constraints are approximated as semi-infinite constraints.

[0013] S4. Transform the original problem into a finite constraint problem;

[0014] S5. By iteratively optimizing the transmit beamforming and MF-RIS coefficients, the mixed-integer non-linear programming (MINLP) problem is solved, and the beamforming scheme is output.

[0015] Furthermore, step S1 introduces the following parameters to characterize the uncertainty of CSI using a bounded CSI model:

[0016] H = H + ΔH,

[0017]

[0018]

[0019] and h k These are channels h. k The estimation and corresponding estimation error, continuous set Λ h,k Collect all possible estimation errors, where ξ h,k >0 indicates the radius of the uncertainty region. Parameter g k ,ΔH,ΔG k The definition is similar.

[0020] Furthermore, the sum-rate maximization problem and constraints in the imperfect CSI case of step S2 are expressed as follows:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] Where M represents the number of units in MF-RIS, This group of units represents the number of users per antenna. The coefficient matrix of MF-RIS represents this group of users as follows:

[0031]

[0032] Where α m ∈{0,1},β m ∈[0,β max ], θ m ∈[0,2π) represents the mode indicator factor, amplitude, and phase shift of the m-th cell, respectively, β max ≥1 indicates the magnification factor. f represents the superimposed signal transmitted by the base station. k This represents the transmitted beamforming vector of user k. Data symbols representing modulation;

[0033] The signal received at user k is This represents the thermal noise generated on the MF-RIS, with a noise power per unit element of [value missing]. This represents the additive white Gaussian noise (AWGN) at user k with noise power, and the noise power per unit element. This represents the channels from the base station to user k, from the base station to the MF-RIS, and from the MF-RIS to user k. This is the power budget of BS. It is the feasible set of MF-RIS coefficients, Q k , The introduced auxiliary variable satisfies and in This is a combined channel from BS to user k; and ζ m For the introduced auxiliary variables, Λ h,k ,Λ g,k ,Λ G,k For all possible channel estimation errors, To reach the feasible point in the l-th iteration Located at the lower boundary of its right term, The mode indication matrix for the Mth cell, and the RF power received at the mth cell, are expressed as follows: a > 0, q > 0 are constants related to circuit characteristics such as capacitor and diode forward voltage.

[0034] Furthermore, step S3 transforms the original constraints into the following two semi-infinite constraints:

[0035]

[0036]

[0037] in These are introduced slack variables.

[0038] Furthermore, the specific process of step S3 is as follows:

[0039] First, define definition For the solution obtained in the l-th iteration, we will use the information about... The constraint is expressed as Where vector x k and the introduced coefficient A k ,a k ,a k They are represented as follows:

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] For those with infinite possibilities Λ h,k ,Λ G,k , Linear constraints are applied using the S-process to account for channel uncertainty Λ. h,k ,Λ G,k Rewritten as:

[0047] in

[0048] Then if and only if there exists υ h,k ,υ G,k When ≥0, constraints

[0049] Established;

[0050] use Rewrite constraints

[0051]

[0052]

[0053] for

[0054]

[0055]

[0056] in

[0057]

[0058]

[0059] Due to ||ΔH|| F ≤ξ H ,get and Therefore, we obtain

[0060] Using slack variable υ H,m ≥0 and υ H ≥0, the constraint is transformed into the following Linear Matrix Inequality (LMI) constraint:

[0061]

[0062]

[0063] for Λ h,k ,Λ g,k ,Λ G,k , Λ in h,k and Λ g,k CSI uncertainty in the context is addressed by introducing... and slack variables Rewrite it as:

[0064]

[0065] Using Shul's complement lemma and substituting...

[0066] The result was:

[0067]

[0068]

[0069] Introducing slack variables and Obtain the equivalent LMI for the two constraints mentioned above.

[0070] Furthermore, step S4 rewrites the original problem as follows:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] in This represents the set of slack variables.

[0083] Furthermore, step S5 uses an alternating optimization framework to decompose the reconstructed problem into two sub-problems concerning transmit beamforming and MF-RIS coefficients, and alternately optimizes transmit beamforming and MF-RIS coefficients.

[0084] Furthermore, step S5 optimizes f given the MF-RIS coefficients Θ. k In this case, the problem is a convex semidefinite programming (SDP) problem, which can be effectively solved using CVX.

[0085] Furthermore, step S5, given f k In the case of optimizing the MF-RIS coefficients Θ, where the problem is a non-convex LMI, the non-convex term υ is used. H,m (1-α m ) 2 and Each LMI is rewritten as a convex approximation by replacing the original form with its respective first-order Taylor expansion.

[0086] Furthermore, a penalty function-based approach is employed to handle unit modulus constraints. By introducing auxiliary variables The equivalent form of this constraint is:

[0087]

[0088] To address the equivalent constraints, an auxiliary variable set is introduced. satisfy Unit modulus constraint Linearization to According to the first-order Taylor expansion method, using Replace non-convex parts By introducing a set of slack variables The original problem can be transformed into a convex semidefinite programming problem, which can be effectively solved using CVX.

[0089] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0090] This invention proposes a robust beamforming method for reconfigurable multifunctional smart metasurfaces, which improves the performance of wireless networks by intelligently reconfiguring the wireless environment. Addressing the issues of double fading attenuation and strong dependence on the power grid / battery in existing passive smart metasurfaces, a MF-RIS architecture integrating signal reflection, amplification, and energy harvesting is proposed, achieving energy self-sustainability. The asymptotic capacity of the communication network assisted by the MF-RIS architecture is analyzed. Then, aiming to achieve a self-sustaining communication system, a resource allocation problem under imperfect channel state information is constructed. By approximating the semi-infinite constraint using S-processes and generalized symbolic determinism, a highly robust beamforming scheme is proposed, overcoming unavoidable channel estimation errors and solving the double fading problem. Compared with existing self-sustaining RIS, MF-RIS better balances the relationship between energy harvesting and throughput improvement. Attached Figure Description

[0091] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0092] Figure 1 This is an architectural diagram of a reconfigurable multifunctional smart metasurface provided in an embodiment of the present invention.

[0093] Figure 2 A flowchart illustrating a robust beamforming method for a reconfigurable multifunctional smart metasurface, provided in an embodiment of the present invention. Detailed Implementation

[0094] To better understand this technical solution, the method of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0095] like Figure 1 As shown, this invention first proposes a reconfigurable multifunctional smart metasurface capable of simultaneously realizing signal reflection, amplification, and energy harvesting. From a wireless communication perspective, the physical implementation and operating protocol of MF-RIS are presented, and the communication network and various parameters of MF-RIS are defined.

[0096] This invention considers an MF-RIS-assisted multi-user downlink communication network, wherein MF-RIS is deployed to assist wireless communication from an N-antenna base station (BS) to K single-antenna users. The set of users is represented as... This invention assumes that the MF-RIS is equipped with M units, using This indicates the group of units.

[0097] These M units are divided into two groups: one group operates in H mode and the other in A mode. Specifically, the units operating in H mode extract radio frequency energy from the received signal to support the operation of MF-RIS. Simultaneously, the units operating in A mode reflect and amplify the incident signal. The MF-RIS coefficient matrix is ​​represented as follows: Where α m ∈{0,1},β m ∈[0,β max ], θ m ∈[0,2π) represent the mode indicator factor, amplitude, and phase shift of the m-th cell, respectively. Here, α m =1 indicates that the m-th unit is operating in mode A, α m =0 indicates that it is working in H mode, β max ≥1 indicates the magnification factor.

[0098] The superimposed signal transmitted by the base station is represented as Where f k It is the transmitted beamforming vector of user k. The modulated data symbol is independent of k. The signal received at user k can be represented as:

[0099]

[0100] in This represents the thermal noise generated on the MF-RIS, with the noise power of each unit being... This represents additive white Gaussian noise at user k, with noise power of... besides, Let the channels from BS to user k, from BS to MF-RIS, and from MF-RIS to user k be defined respectively. For the combined channel from BS to user k, the achievable data rate of user k can be expressed as:

[0101]

[0102] This invention defines Let M be the mode indication matrix for the Mth cell. Then, the received RF power at the mth cell is expressed as:

[0103]

[0104] Among them, the expectation operator Used for w and n sBased on logistic functions, this invention applies a nonlinear energy harvesting model to the proposed MF-RIS. Specifically, the total power harvested in the m-th cell is expressed as:

[0105]

[0106] Where Y m Indicates about The logical function is given by Z, which represents a constant that determines the maximum sampling power. Ω is then determined by... The given values ​​of a > 0 and q > 0 are related to circuit characteristics such as the capacitor and diode forward voltage. In practice, parameters Z, a, and q can be obtained using standard curve fitting tools.

[0107] To achieve self-sustainability of MF-RIS, the total power consumed by MF-RIS should not exceed the power it harvests, as given by the following formula:

[0108]

[0109] Among them, P b ,P DC ,P C These represent the power consumption of each phase shifter, the DC bias power consumption of the amplifier circuit, and the power consumption of the RF-DC power conversion circuit, respectively. Here, ξ represents the reciprocal of the amplifier efficiency. This indicates the output power of the MF-RIS.

[0110] This invention analyzes the achievable capacity performance of MF-RIS and compares it with that of self-sustaining RIS, demonstrating that the proposed MF-RIS outperforms the self-sustaining RIS in terms of asymptotic signal-to-noise ratio.

[0111] Next, an asymptotic capacity performance analysis of this invention is performed. This invention analyzes the performance gain achieved by MF-RIS in a single-user single-input single-output (SISO) system. Considering the capacity of the MF-RIS auxiliary channel, it is assumed that the direct link is blocked and the reflection link is a line-of-sight link. Given the mode indication matrix α = diag(α1, α2, ..., α... M The signal received at the user's location is given by the following formula:

[0112]

[0113] Where p represents the base station's transmit power.

[0114]

[0115] here

[0116] g=|g1|1M ⊙exp(jarg(g))=[g1,g2,...,g M ] T ,

[0117] h = |h1|1 M ⊙exp(jarg(h))=[h1,h2,...,h M ] T ,

[0118] These represent the channel vectors from MF-RIS to the user and from BS to MF-RIS, respectively. Let represent the AWGN noise at the user's location. Then, the problem of maximizing the signal-to-noise ratio (SNR) can be constructed as follows:

[0119]

[0120]

[0121]

[0122]

[0123] in Let represent the maximum output power of MF-RIS. Using Lagrange duality, the optimal transmit power and phase shift for this problem are expressed as:

[0124]

[0125] Assume the number of MF-RIS units operating in A mode and H mode are respectively and The optimal amplitude coefficient for the original problem can be given by the following formula:

[0126]

[0127] in

[0128]

[0129] In order to analyze the asymptotic capacity achievable by MF-RIS, this invention assumes... and Therefore, the asymptotic signal-to-noise ratio can be expressed as:

[0130]

[0131] For the MF-RIS auxiliary system under consideration, the optimal number of reflection units can be determined by... Restore it to an integer to obtain it. Represented as... Then, M A,2 The value is calculated as follows:

[0132]

[0133] Next, this invention analyzes the asymptotic performance of self-sustaining RIS. Assume the number of cells operating in H mode and R mode are M respectively. H and M A Given the pattern index matrix α, the signal-to-noise ratio maximization problem is formulated as:

[0134]

[0135]

[0136]

[0137]

[0138] Similarly, using Lagrange duality, the optimal solution to the above problem can be obtained as follows:

[0139]

[0140] The asymptotic signal-to-noise ratio of the self-sustaining RIS-assisted system under consideration is:

[0141]

[0142] Furthermore, the optimal number of units for operation in R mode is:

[0143]

[0144] By solving γ MF ≥γ SE The present invention yields a number of reflection units required for MF-RIS that are superior to those required for self-persistent RIS, and the results are as follows:

[0145]

[0146] in For a more intuitive comparison, this invention sets... M H =200, P b =1.5mW, P C =2.1μW, P DC =0.3mW, β max =20dB, ξ=1.1. Then, we obtain the result when M AWhen the signal-to-noise ratio is ≤26, the asymptotic signal-to-noise ratio performance of the MF-RIS is better than that of its self-sustaining RIS counterpart, i.e., the above-mentioned M A The inequality holds. In particular, for a practical RIS model, such as M... A =10, the present invention obtains γ MF ≈33.4dB, γ SE ≈22.9dB, where the former is about 11.2 times larger than the latter.

[0147] like Figure 2 As shown, this invention proposes a robust beamforming method for reconfigurable multifunctional smart metasurfaces, achieving the maximum realizability and rate for the user, comprising the following steps:

[0148] S1. In the case of imperfect CSI, a bounded CSI model is used to characterize the uncertainty of CSI.

[0149] Due to unavoidable channel estimation and quantization errors, achieving perfect CSI is quite difficult. Therefore, this invention proposes a robust beamforming scheme that takes into account imperfect CSI.

[0150] First, consider the optimization problem under perfect CSI, which can be expressed as:

[0151]

[0152]

[0153]

[0154]

[0155] in, It is the power budget of the base station;

[0156] It is the feasible set of MF-RIS coefficients.

[0157] Before addressing the problem, this invention first transforms it into a more manageable form. To handle the objective function, this invention introduces an auxiliary variable Q. k , satisfy and Based on these variable definitions, the present invention obtains the following new constraints:

[0158]

[0159]

[0160] To address the non-convexity of this constraint, this invention employs the Successive Convex Approximation (SCA) technique. Based on the fact that the first-order Taylor expansion of a convex function is a globally underestimated quantization, the feasible point is reached in the l-th iteration. The lower bound of the terms on its right is given by the following equation:

[0161]

[0162] To facilitate the derivation of constraints:

[0163]

[0164] The received RF power and output power are first rewritten as follows:

[0165]

[0166]

[0167] Then, by introducing auxiliary variables and ζ m The original constraint is equivalently rewritten as:

[0168]

[0169]

[0170]

[0171] in Because the first constraint in the above equation is still non-convex, this invention approximates it using a first-order Taylor expansion. For any feasible point in the l-th iteration... The lower bound is determined by Provided.

[0172] Now define Define an auxiliary variable set and define it. The problem has been rephrased as:

[0173]

[0174]

[0175]

[0176]

[0177]

[0178]

[0179]

[0180]

[0181] Next, a bounded CSI model is used to characterize the uncertainty of CSI, given by the following equation:

[0182] H = H + ΔH

[0183]

[0184]

[0185] in This is the cascaded channel from BS to user k. and Δh k These are channels h. k The estimation and corresponding estimation error of the continuous set Λ. h,k Collect all possible estimation errors, where ξ h,k >0 indicates the radius of the uncertainty region. Parameter Δg k ,ΔH,ΔG k The definition is similar.

[0186] S2. Formulate the SR maximization problem of MF-RIS-assisted multi-user systems.

[0187] The problem of maximizing SR under imperfect CSI is constructed as follows:

[0188]

[0189]

[0190]

[0191]

[0192]

[0193]

[0194]

[0195]

[0196]

[0197] The difficulty in solving this problem lies in the infinite number of non-convex constraints caused by CSI imperfections. To address this, this invention uses S-processes and generalized symbolic determinism to... ζ m , The relevant constraints are transformed into a tractable form. Then, the reconstructed problem is decomposed into two subproblems using an alternating optimization (AO) framework. Next, the transmit beamforming and MF-RIS coefficients are alternately optimized.

[0198] S3. By using the S-process and generalized symbolic determinism, the infinite number of non-convex constraints caused by CSI imperfections are approximated as semi-infinite constraints, thereby transforming the original problem into a finite constraint problem.

[0199] By definition And will Let be the solution obtained in the l-th iteration, with constraints. Λ h，k Λ G，k , It is equivalently linearized as:

[0200]

[0201] Where vector x k and the introduced coefficient A k ,a k ,a k They are given by the following formulas respectively:

[0202]

[0203]

[0204]

[0205]

[0206]

[0207]

[0208] At this point, linear constraints Λ h,k ,Λ G,k , There are still infinite possibilities. For ease of derivation, this invention uses the S-process to further transform it into a processable form.

[0209] To apply the S-process to this constraint, this invention incorporates the channel uncertainty Λ h,k ,Λ G,k Rewritten as the following quadratic expression:

[0210]

[0211] in

[0212] Then, based on the S process, if and only if there exists υ h,k ,υ G,k When ≥0, the constraint holds, such that:

[0213]

[0214] Similarly, using constraint Λ H , and Λ H They were rewritten as:

[0215]

[0216]

[0217] in

[0218]

[0219]

[0220] Based on |ΔH| F ≤ξ H The present invention obtains and

[0221] Therefore, the present invention has:

[0222]

[0223] Based on the above equation and the S-process, a slack variable υ is introduced. H,m ≥0 and υ H ≥0, constraint

[0224]

[0225]

[0226] It is transformed into the following linear matrix inequality LMI constraint:

[0227]

[0228]

[0229] Next, the present invention considers constraints. Λ h,k ,Λ g,k ,ΛG,k , LMIΛ h,k and Λ g,k CSI uncertainty.

[0230] By defining a matrix And introduce slack variables The constraint can be rewritten as:

[0231]

[0232] Then, the present invention uses the Schul complement lemma to equivalently rewrite the above constraints as follows:

[0233]

[0234]

[0235] The present invention further inserts into the above formula Then, the above constraints are restated as follows:

[0236]

[0237]

[0238] The aforementioned constraints remain difficult to handle due to the presence of multiple complex-valued uncertainties. Here, the present invention transforms them into a finite number of constraints by applying a general symbolic determinism lemma. Given matrix D and... And D = D H The following is a semi-infinite LMI:

[0239]

[0240] If and only if there exists When it was established, it made

[0241]

[0242] To constrain

[0243]

[0244] For example, we can observe that the constraint can be rewritten by setting the parameters as follows:

[0245] G1=[Δh k 0],

[0246] E1 = -[0 F -k ],F1=I K , E2 = -[0 F-k F2 = [v 0]

[0247] The original constraints are then equivalently transformed into the following LMI:

[0248]

[0249] in and These are the introduced slack variables. Similarly, given the introduced slack variables... constraint

[0250]

[0251] The equivalent LMI is:

[0252]

[0253] Finally, by replacing the original constraints with the LMI constraints mentioned above, the original problem is reformulated as follows:

[0254]

[0255]

[0256]

[0257]

[0258]

[0259]

[0260]

[0261]

[0262]

[0263]

[0264]

[0265] in This represents the set of slack variables. The resulting multivariate optimization problem can be solved using the AO method.

[0266] S5. The resulting MINLP problem is solved by iteratively optimizing the transmit beamforming and MF-RIS coefficients.

[0267] Next, the transmit beamforming and MF-RIS coefficients will be jointly designed.

[0268] First, we need to optimize f given Θ. k With a fixed MF-RIS coefficient Θ, the transmit beamforming optimization problem under imperfect CSI is expressed as:

[0269]

[0270]

[0271]

[0272]

[0273]

[0274]

[0275]

[0276]

[0277]

[0278]

[0279] This is an SDP problem, so it can be solved efficiently with CVX.

[0280] Next, given f k Optimization Θ: Given f k The MF-RIS coefficient optimization problem is formulated as follows:

[0281]

[0282]

[0283]

[0284]

[0285]

[0286]

[0287]

[0288]

[0289]

[0290]

[0291]

[0292] The difficulty in solving this problem lies in non-convex LMIs.

[0293]

[0294]

[0295] Highly coupled unit modulus constraint and the binary constraint α m ∈{0,1},β m ∈[0,β max ], By using the non-convex term υ in the first expression H,m (1-α m ) 2 and Replace them with their first-order Taylor expansions respectively. and LMIs are rewritten as their convex approximations, where This is a feasible point in the l-th iteration. The expressions for the convex approximation are as follows:

[0296]

[0297]

[0298] Next, a penalty function-based method will be used to handle the constraints:

[0299]

[0300] By introducing auxiliary variables The equivalent form of this constraint obtained by the present invention is:

[0301]

[0302] With the help of auxiliary variable set satisfy Unit modulus constraint Linearization to According to the first-order Taylor expansion, this invention uses Approximate non-convex part By introducing a set of slack variables The original problem is transformed into:

[0303]

[0304]

[0305]

[0306]

[0307]

[0308]

[0309]

[0310]

[0311]

[0312]

[0313]

[0314]

[0315] This problem is a convex SDP, which can be solved efficiently using CVX.

[0316] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. However, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A robust beamforming method for reconfigurable multifunctional smart metasurfaces, characterized in that, The reconfigurable multifunctional smart metasurface is an MF-RIS architecture that integrates signal reflection, amplification, and energy harvesting. The robust beamforming method includes the following steps: S1. In the case of imperfect channel state information, a bounded CSI model is used to characterize the uncertainty of CSI; step S1 introduces the following parameters to use a bounded CSI model to characterize the uncertainty of CSI: and These are channels The estimation and corresponding estimation error, continuous set Collect all possible estimation errors, where Indicates the radius of the region of uncertainty; S2. Formulate the sum-rate maximization problem of the MF-RIS-assisted multi-user system; the sum-rate maximization problem and constraints under the imperfect CSI case are expressed as follows: in Indicates the number of cells in MF-RIS. This group of units represents Indicates the number of users per antenna. The coefficient matrix of MF-RIS represents this group of users as follows: in They represent the first The mode indicator factor, amplitude, and phase shift of each unit. Indicates the magnification factor. This indicates the superimposed signal sent by the base station. Indicates user The transmitted beamforming vector, Data symbols representing modulation; In users The signal received at the location is This represents the thermal noise generated on the MF-RIS, with a noise power per unit element of [value missing]. Indicates users with noise power Additive white Gaussian noise at the location, noise power per unit element This represents the distance from the base station to user k, from the base station to the MF-RIS, and from the MF-RIS to the user. The channel, This is the power budget of BS. It is the feasible set of MF-RIS coefficients, Q k , The introduced auxiliary variable satisfies and ,in From BBS to user Combined channels; and For the introduced auxiliary variables, For all possible channel estimation errors, In the first In the next iteration, at the feasible point Located at the lower boundary of its right term, For the first The pattern indication matrix of the nth unit, in the nth The radio frequency power received at each unit is expressed as: It is a constant related to the circuit characteristics of the capacitor and diode forward voltage; S3. Using the S-process and generalized symbolic determinism, infinitely many non-convex constraints are approximated as semi-infinite constraints. S4. Transform the sum rate maximization problem in step S2 under the imperfect CSI condition into a finite constraint problem; S5. Using an alternating optimization framework, decompose the finite constraint problem in step S4 into two sub-problems concerning transmit beamforming and MF-RIS coefficients. Alternately optimize transmit beamforming and MF-RIS coefficients, and solve the mixed-integer nonlinear programming problem by iteratively optimizing transmit beamforming and MF-RIS coefficients, outputting the beamforming scheme. The mixed-integer nonlinear programming problem is designed as follows: given MF-RIS coefficients... Optimize the transmit beam under the circumstances The problem and in a given transmission beam Optimize MF-RIS coefficients under certain conditions The problem.

2. The robust beamforming method for reconfigurable multifunctional smart metasurfaces according to claim 1, characterized in that, Step S3 transforms the constraints of step S2 into the following two semi-infinite constraints: in , , These are introduced slack variables.

3. The robust beamforming method for reconfigurable multifunctional smart metasurfaces according to claim 2, characterized in that, The specific process of step S3 is as follows: First, define ,definition In the first The solution obtained in the next iteration will be about The constraint is expressed as Where vector and the introduced coefficients They are represented as follows: For those with infinite possibilities Linear constraints are applied using the S-process to account for channel uncertainty. Rewritten as: in Then if and only if exists At that time, constraints Established; use Rewrite constraints for in because ,get and Therefore, we get ; Use slack variables and The constraints are transformed into the following linear matrix inequality constraints: for In and CSI uncertainty in the context is addressed by introducing... and slack variables Rewrite it as: Using the Schuler complement lemma and substituting... The result was: Introducing slack variables , and Thus, we obtain the equivalent linear matrix inequalities for the two constraints mentioned above.

4. The robust beamforming method for reconfigurable multifunctional smart metasurfaces according to claim 3, characterized in that, Step S4 rewrites the sum-rate maximization problem in the imperfect CSI case of step S2 into a finite-constraint problem: in This represents the set of slack variables.

5. The robust beamforming method for reconfigurable multifunctional smart metasurfaces according to claim 4, characterized in that, Step S5: Given MF-RIS coefficients Optimize under the circumstances At this point, the finite constraint problem in step S4 is a convex semidefinite programming problem.

6. The robust beamforming method for reconfigurable multifunctional smart metasurfaces according to claim 4, characterized in that, Step S5 is given Optimize MF-RIS coefficients under the following conditions At this point, the finite constraint problem in step S4 is a non-convex linear matrix inequality, which is solved by addressing the non-convex terms. and Each of these is replaced with its own first-order Taylor expansion, thus rewriting the linear matrix inequalities as their respective convex approximations.

7. The robust beamforming method for reconfigurable multifunctional smart metasurfaces according to claim 6, characterized in that, A penalty function-based approach is used to handle unit modulus constraints. By introducing auxiliary variables The equivalent form of the constraint is: To address the equivalent constraints, an auxiliary variable set is introduced. ,satisfy Unit module constraint Linearization to According to the first-order Taylor expansion method, using Replace non-convex parts By introducing a set of slack variables The problem in step S2 is transformed into a convex semidefinite programming problem.

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