A modeling and optimization method for multi-user communication system assisted by multi-layer intelligent metasurface

Abstract

The present invention belongs to the field of wireless communication technology, and in particular to a multi-layer intelligent metasurface assisted multi-user communication system modeling and optimization method, comprising the following steps: step one, building a system model: designing a multi-user scenario, a communication system including multi-layer RIS and MIMO base stations; using a multi-port network model, establishing a corresponding physical consistency model; step two, using a non-ideal circuit model to describe the noise and interference in the communication system; step three, signal propagation analysis: studying the propagation characteristics of the signal between the multi-layer RIS and the multi-user receiving antenna, establishing an input-output relationship, and analyzing the influence of the mutual coupling effect on signal transmission; step four, designing an optimization algorithm: proposing an alternating optimization algorithm under user fairness constraints. The present invention can effectively combine the flexibility of RIS and the advantages of MIMO technology, provide a complete and efficient solution for multi-user communication, and can improve systematization in complex wireless environments.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication technology, and specifically relates to a modeling and optimization method for a multi-layer intelligent metasurface-assisted multi-user communication system. Background Art

[0002] With the rapid development of wireless communication technology, demands for higher efficiency and quality in signal transmission are becoming increasingly stringent. Traditional antenna design and signal processing methods are no longer able to meet these requirements, necessitating the search for new solutions to improve the performance of wireless communication systems. In recent years, smart metasurfaces, as an emerging technology, have attracted widespread attention.

[0003] In the field of wireless communications, intelligent metasurfaces (RIS) can be applied in a variety of areas, including signal processing, antenna design, and beam steering. For example, the phase control properties of RIS can be used to filter and amplify signals, thereby improving signal processing efficiency and quality. RIS can also be used for phase modulation and delay adjustment of signals, enabling the processing and optimization of complex signals. In antenna design, RIS can be used to design antennas with specific radiation characteristics. By adjusting the surface current distribution of the RIS, the antenna's radiation direction and gain can be controlled, providing greater flexibility and freedom in antenna design. In particular, in multi-layer RIS applications, wave-domain signal processing on multiple layers enables more complex waveform customization and spatial resource utilization, thereby improving overall system performance. Furthermore, when combined with Multiple-Input Multiple-Output (MIMO) technology, the system can utilize multiple transmit and receive antennas within the same spectrum resources, significantly increasing data transmission rates.

[0004] However, factors such as mutual coupling and thermal noise remain significant challenges that must be considered when designing and optimizing multi-antenna systems. Therefore, further research into the integration of multi-layer RIS with electromagnetic wave propagation theory and circuit theory, and the development of physically consistent modeling methods, will provide more comprehensive analysis tools for future wireless communication systems. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-layer intelligent metasurface-assisted multi-user communication system modeling and optimization method, which can effectively combine the flexibility of RIS and the advantages of MIMO technology, provide a complete and efficient solution for multi-user communication, and improve system performance in complex wireless environments.

[0006] The technical solutions adopted by the present invention are as follows:

[0007] A multi-layer intelligent metasurface-assisted multi-user communication system modeling and optimization method includes the following steps:

[0008] Step 1: Build a system model: Design a multi-user scenario, including a communication system with multiple layers of RIS and MIMO base stations. Use a multi-port network model to define the ports of each component, including feed antennas, RIS meta-atoms, and multi-user receiving antennas, and establish a corresponding physically consistent model.

[0009] Step 2: Use non-ideal circuit models to describe noise and interference in communication systems;

[0010] Step 3: Signal Propagation Analysis: Study the signal propagation characteristics between multi-layer RIS and multi-user receiving antennas, establish input-output relationships, and analyze the impact of mutual coupling effects on signal transmission;

[0011] Step 4: Design an optimization algorithm: An alternating optimization algorithm under user fairness constraints is proposed. First, the transmit power is fixed and the phase control matrix of the RIS is optimized to improve signal transmission efficiency. Then, the phase control of the RIS is fixed and the transmit power distribution is optimized.

[0012] Furthermore, the step 1 includes the following steps:

[0013] First, a multi-user scenario is designed, which includes a communication system of multi-layer RIS and MIMO base stations. The communication system includes feed antennas, RIS atoms and multi-user receiving antennas. The multi-antenna base station BS built based on multi-layer RIS and feed antennas is designed to communicate synchronously with M users, each of whom is equipped with N R multi-user receiving antennas;

[0014] The multi-antenna base station BS is equipped with a uniform planar array, including N T ≥N R Feed antenna and L parallel RIS layers, each parallel RIS layer is embedded with N S Elementary atoms; Δ S and Δ T represents the uniform antenna spacing between the feed antenna and the RIS layer; let N T ={1,2,…,N T},L={1,2,…,L},N S ={1,2,…,N S},M={1,2,…,M},N R ={1,2,…,N R} represent the feed antenna, parallel multi-layer RIS, the meta-atom on each RIS, the user, and the set of multi-user receiving antennas respectively; the communication system is modeled as (N T +N S +MN R ) port multi-port network

[0015] Furthermore, the multi-port network in step 1 Expressed as:

[0016]

[0017] Wherein, “T”, “S” and “R” are used to represent the feed antenna, multi-layer RIS element and multi-user receiving antenna, respectively; represent the current distribution in the feed antenna element, multi-layer RIS meta-atom, and multi-user receiving antenna, respectively; Represents the voltage vector across the corresponding port; voltage (v T ,v S ,v R ) and current (i T ,i S ,i R ) is governed by Ohm's law and is expressed through the system impedance matrix are connected to each other, the matrix can be divided into different sub-matrices; among them, Represent the impedances of the feed antenna element, multi-layer RIS element-atom, and multi-user receiving antenna respectively; the diagonal elements correspond to the self-impedances of the feed antenna element, multi-layer RIS element-atom, and multi-user receiving antenna; the non-diagonal elements represent the mutual impedances between the feed antenna element, multi-layer RIS element-atom, and multi-user receiving antenna; the matrix denote the pairwise mutual impedances between the feed antenna and multi-layer RIS, the feed antenna and multiple users, and the multi-layer RIS and multiple users, respectively. Since the antenna is a reciprocal device, we can derive

[0018] In practical scenarios, the signal attenuation in the propagation channel between multiple RIS layers and multiple users is quite large, i.e., ||Z RS || F =||Z SR || F <<min(||Z R || F ,||Z S || F ). Therefore, multi-user multi-layer RIS transimpedance Z SR ≈0, where only the feed antenna affects the electromagnetic characteristics of the receiving antenna.

[0019] Furthermore, the step 2 includes the following steps:

[0020] First, the feed antenna N T The voltage source is characterized by the transmitter signal source With transmitter internal resistance R; transmitter signal source passes through noise voltage source Connected to the feed antenna, the feed antenna consists of a voltage-current pair (v T ,iT ) represents; Multilayer RIS is represented by voltage-current pair (v S ,i S ) represents each RIS atom connected to a tunable impedance, i.e. a phase shifter of the incident wave, which can be written as here, represents the reactance; given the lossless and passive characteristics of the RIS meta-atom, the noise voltage source is not included in its model; the multi-user receiving antenna can be connected through the noise voltage source Receiving antenna internal resistance R in To characterize the voltage-current pair (v R ,i R );

[0021] Multiport Network It consists only of passive components that are affected by the ambient temperature T; therefore, the impedance matrix The noise in is determined solely by the thermal noise of these components and can be determined using v N,T and v N,R Modeling; When the feed antenna and multi-user receiving antennas are mutually coupled, noise correlation will occur; the truncated Fourier transform can be used to determine the noise voltage v in the feed antenna N,T and the noise voltage v in the multi-user receiving antenna N,R The relevant power spectral density (PSD) is:

[0022]

[0023] Where t0 is time, k b is the Boltzmann constant, T is the ambient temperature, v N,T (f), v N,R (f) is v N,T , v N,R The frequency domain representation of To obtain the real part, considering the far-field communication between the feed antenna and the multi-user receiving antenna, and the existence of multi-layer RIS as an intermediate component, the cross-correlation PSD between the feed antenna and the multi-user receiving antenna is considered to be zero, that is,

[0024]

[0025] Furthermore, the step three includes the following steps:

[0026] First, the circuit model is integrated into a multi-user MIMO communication system based on multi-layer RIS; the composite signal y received by the mth user is m Usually expressed as:

[0027]

[0028] in Represents a set of symbols for each user, satisfying H m represents the channel between the feed antenna and the mth user; represents the precoding matrix at the feed antenna, n is the noise; the RMS value of the feed antenna current can be obtained by Given; can be written as a circuit model in a multi-user scenario, thus establishing the transmitter signal source v G Voltage v to the mth multi-user receiving antenna R,m Input-output relationship; for ease of analysis, use Fourier transform to convert v G and v R,m Converted to frequency domain, that is, v G (f),v R,m (f) Therefore, under the far-field assumption, the signal source v G (f) Voltage v to the mth multi-user receiving antenna R,m The input-output relationship of (f) is expressed as:

[0029] v R,m (f) = H m (f)v G (f)+n m (f),

[0030] H m (f) = -R in P m Z RS,m Φ L Z ST B,

[0031] n m (f)=(R in P m -1)v N,R +R in P m Z RS,m Φ L Z ST Bv N,T ,

[0032] Among them H m (f),n m (f) is the frequency domain distribution of the channel and noise between the feed antenna and the mth user, R in is the internal resistance, Φ L represents the phase control matrix of the lth layer RIS

[0033]

[0034] Where R is the internal resistance of the transmitter, the noise correlation matrix can be derived as follows:

[0035]

[0036] where Q m =-Z RS,m Φ L Z ST , at the signal source v G The total power budget P provided max Under this condition, the power allocated to the mth user is defined as p m , The sum of the signal-to-interference-and-noise ratio of the mth user and the achievable rate of the system is obtained as:

[0037]

[0038] It can be observed that the communication functions of the feed antenna, multi-layer RIS, and multi-user receiving antenna are basically encapsulated in H; by jointly designing the impedance and transmit power within the matrix H, the goal of beamforming can be achieved;

[0039] Next, the self-impedance and mutual coupling impedance of the feed antenna, multi-layer RIS meta-atom and multi-user receiving antenna are theoretically analyzed;

[0040] First, establish the equivalent circuit model of the antenna:

[0041]

[0042] Where V1 and I1 represent the equivalent voltage and current of the antenna, A1 represents the complex coefficient of the TM1 mode, and a is the antenna size; k0 and η0 represent the wave number and wave impedance in free space, respectively, and j represents the imaginary unit. Using basic circuit theory, the self-impedance Z Chu Written as:

[0043]

[0044] Where c is the speed of light, f is the operating frequency, and the two non-overlapping CMS antennas each have a self-impedance Z X and Z Y , and its mutual impedance is:

[0045]

[0046] The spherical coordinates are expressed as (r, θ, φ), with the rotation angles β and γ defined relative to their connecting axis r, and d being the distance between the two antennas. The above equation encapsulates the mutual impedance between the two CMS antennas, taking into account the effects of their physical parameters and the electric field. In addition, it can characterize the mutual coupling between different users.

[0047] Then the propagation channel model between the feed antenna, multi-layer RIS and multiple users is derived. First, the propagation channel between the feed antenna and the first layer of RIS is analyzed. To determine the transimpedance between the feed antenna and the meta-atom on the first layer of RIS in the near field; assuming that the feed antenna is parallel to the first layer of RIS, the configuration parameters in the mutual impedance between the antennas can be set to and The corresponding (N S ,N T )Transimpedance and (N T ,N S )Transimpedance are equal to:

[0048]

[0049] in, It is the Nth T The feed antenna and the Nth S The distance between the meta-atoms is calculated. Next, the RIS inter-layer propagation channel model is analyzed. According to the Rayleigh-Sommerfeld diffraction equation, each meta-atom on the RIS layer can be regarded as a secondary wave source. Its inter-layer transimpedance is:

[0050]

[0051] where a s represents the area of ​​each meta-atom, d l Indicates the distance between layers, Indicates the Nth layer on the (l-1)th layer RIS S The Nth meta-atom on the lth layer of RIS S The distance between the ' meta-atoms; then the correlated Rayleigh fading channel is used to represent the channel from the last layer RIS to the mth user, denoted as Taking antenna coupling into account, the spatial channel correlation can be characterized in terms of the impedance matrix; this is because the impedance matrix exhibits the same correlation characteristics as the isotropic ambient noise, which are described by the real part of the impedance matrix; therefore, Defined as:

[0052]

[0053] in, is an independent and identically distributed Rayleigh fading channel, α is the path loss exponent, d RS is the distance between the last layer RIS and the mth user.

[0054] Furthermore, the step 4 includes the following steps:

[0055] First, the total rate of all users is maximized by jointly optimizing the transmit power of the feed antenna and the wave domain beamforming of the multi-layer RIS. When solving the optimization problem, the SINR constraint Γ of the mth user must be ensured. m Minimum to ensure user fairness; at the same time, constrain the maximum transmission power of the feed antenna; the main challenge lies in the multi-layer structure of the multi-layer RIS; to solve this problem, an effective algorithm is designed to optimize the transmission power p of each layer of RIS through alternating optimization. t =[p1,p2,…,p M ] T and the phase control matrix; it can be formulated as the following non-convex optimization problem:

[0056]

[0057] First, the phase control matrix is ​​optimized. Given the transmission power distribution p t , optimize the phase control matrix of each RIS layer; transform equation H m Z in (f) ST Expand, that is:

[0058]

[0059] Based on the multi-layer structure, the gradient ascent iterative algorithm is used to optimize the phase control matrix of each layer; l ) and the gradient of the l-th layer adjustable impedance matrix is The adjustable impedance matrix of the l-th layer RIS at iteration t+1 is:

[0060]

[0061] Among them, since the adjustable impedance of RIS must be a strictly imaginary number, the operator is added In addition, μ l >0 is the Armijo step size, which is determined by the backtracking line search in each iteration; the above formula is iteratively executed until the increment of the sum rate rises below the predetermined threshold and convergence is achieved;

[0062] Then the transmit power allocation is carried out, and the transmit power allocation is derived through the obtained multi-layer RIS phase control matrix; is a fully Hermitian matrix, and assume that R n is reversible, and the achievable rate of the mth user can be further expressed as:

[0063]

[0064] Take the above formula as p i The function is rewritten as:

[0065]

[0066] R m Represents the difference between two concave functions, which is a non-concave function; using continuous convex approximation, h2(p i ) performs a first-order Taylor expansion:

[0067]

[0068] where p i (t) Indicates p i The value at the tth iteration; therefore, P1 can be approximately reformulated as P1.1, which can be expressed as

[0069]

[0070] This problem is a standard convex optimization problem and can be solved using the CVX toolbox to obtain the transmit power allocation.

[0071] Furthermore, the number of atoms in the RIS layer is greater than 50.

[0072] Furthermore, the number of atoms in the RIS layer is 80.

[0073] The technical effects achieved by the present invention are:

[0074] The multi-layer intelligent metasurface-assisted multi-user communication system modeling and optimization method of the present invention effectively combines the flexibility of RIS and the advantages of MIMO technology, providing a complete and efficient solution for multi-user communication and improving system performance in complex wireless environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 The present invention is a multi-user communication system model based on multi-layer RIS;

[0076] Figure 2 The present invention is an equivalent circuit model of a multi-user communication system based on a multi-layer RIS;

[0077] Figure 3 is a comparison diagram of the achievable rate of the communication system of the present invention and the number of layers of multi-layer RIS;

[0078] Figure 4 is a comparison diagram of the achievable rate and the total transmission power of the communication system of the present invention;

[0079] Figure 5 is a comparison diagram of the achievable rate of the communication system of the present invention and the distance between the layers of the multi-layer RIS;

[0080] Figure 6This is a comparison diagram of the achievable rate of the communication system of the present invention and the number of atoms in the RIS layer;

[0081] Figure 7 is the achievable rate and of the system with antenna efficiency compensation of the present invention. DETAILED DESCRIPTION

[0082] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is described in detail below with reference to the following examples. It should be understood that the following text is only used to describe one or more specific embodiments of the present invention and does not strictly limit the scope of protection of the present invention.

[0083] like Figure 1-7 As shown, a multi-layer intelligent metasurface assisted multi-user communication system modeling and optimization method includes the following steps:

[0084] Step 1: Build a system model: Design a multi-user scenario, including a communication system with multiple layers of RIS and MIMO base stations. Use a multi-port network model to define the ports of each component, including feed antennas, RIS meta-atoms, and multi-user receiving antennas, and establish a corresponding physically consistent model.

[0085] Specifically, the step 1 includes the following steps:

[0086] First, a multi-user scenario is designed, which includes a communication system with multiple layers of RIS and MIMO base stations. The overall architecture of the communication system is as follows: Figure 1 As shown, it includes feed antennas, RIS meta-atoms and multi-user receiving antennas, where the multi-antenna base station (BS) built based on multi-layer RIS and feed antennas is designed to communicate synchronously with M users, each of whom is equipped with N R Multi-user receiving antennas.

[0087] The multi-antenna base station BS is equipped with a uniform planar array consisting of N T ≥N R Feed antenna and L parallel RIS layers, each parallel RIS layer is embedded with N S Δ S and Δ T Denotes the uniform antenna spacing between the feed antenna and the RIS layer. Let N T ={1,2,…,N T},L={1,2,…,L},N S ={1,2,…,N S},M={1,2,…,M},N R ={1,2,…,N R} represent the feed antenna, parallel multi-layer RIS, meta-atom on each RIS, user, and the set of multi-user receiving antennas. The system can be modeled as (NT +N S +MN R ) port multi-port network like Figure 2 As shown, that is:

[0088]

[0089] Among them, "T", "S" and "R" are used to represent the feed antenna, multi-layer RIS element and multi-user receiving antenna, respectively. represent the current distribution in the feed antenna element, multi-layer RIS meta-atom, and multi-user receiving antenna, respectively. Represents the voltage vector across the corresponding port. Voltage (v T ,v S ,v R ) and current (i T ,i S ,i R ) is governed by Ohm's law and is expressed through the system impedance matrix are connected to each other, the matrix can be divided into different sub-matrices. Among them, Represent the impedances of the feed antenna element, multi-layer RIS element-atom, and multi-user receive antenna, respectively. The diagonal elements correspond to the self-impedances of the feed antenna element, multi-layer RIS element-atom, and multi-user receive antenna. The off-diagonal elements represent the mutual impedances between the feed antenna element, multi-layer RIS element-atom, and multi-user receive antenna. The matrix They represent the pairwise mutual impedances between the feed antenna and multi-layer RIS, the feed antenna and multiple users, and the multi-layer RIS and multiple users, respectively. Since the antenna is a reciprocal device, we can derive

[0090] In practical scenarios, the signal attenuation in the propagation channel between multiple RIS layers and multiple users is quite large, i.e.

[0091] ||Z RS || F =||Z SR || F <<min(||Z R || F ,||Z S || F ). Therefore, multi-user multi-layer RIS transimpedance Z SR ≈0, where only the feed antenna affects the electromagnetic characteristics of the receiving antenna.

[0092] In this step, we model a multi-user communication system with a multi-antenna base station configured with multiple layers of RIS. We also establish a multi-port network model to describe the voltage and current relationships between the base station, the RIS layers, and the multiple user receiving antennas.

[0093] Step 2: Use non-ideal circuit models to describe noise and interference in communication systems.

[0094] Specifically, the step 2 includes the following steps:

[0095] like Figure 2 As shown, the feed antenna N T The voltage source is characterized by the transmitter signal source With transmitter internal resistance R. The transmitter signal source passes through the noise voltage source Connected to the feed antenna, the feed antenna consists of a voltage-current pair (v T ,i T ) is expressed by voltage-current pair (v S ,i S ). Each RIS atom is connected to a tunable impedance, i.e., a phase shifter of the incident wave, which can be written as here, represents the reactance. Given the lossless and passive nature of the RIS meta-atom, the noise voltage source is not included in its model. The multi-user receiving antenna can be connected to the Receiving antenna internal resistance R in To characterize the voltage-current pair (v R ,i R ).

[0096] Multiport Network It consists only of passive components that are affected by the ambient temperature T. Therefore, the impedance matrix The noise in is determined solely by the thermal noise of these components and can be determined using v N,T and v N,R When the feed antenna and the multi-user receiving antenna are coupled, noise correlation occurs. The truncated Fourier transform can be used to determine the noise voltage v in the feed antenna. N,T and the noise voltage v in the multi-user receiving antenna N,R The relevant power spectral density (PSD) is:

[0097]

[0098] Where t0 is time, k b is the Boltzmann constant, T is the ambient temperature, v N,T (f), v N,R (f) is v N,T , v N,R The frequency domain representation of To obtain the real part, considering the far-field communication between the feed antenna and the multi-user receiving antenna, and the existence of multi-layer RIS as an intermediate component, the cross-correlation PSD between the feed antenna and the multi-user receiving antenna is considered to be zero, that is:

[0099]

[0100] `This step is mainly for the multi-port network model built in step 1 Consider the non-ideal voltage source of the feed antenna and the current-voltage pairs of the multilayer RIS. Analyze the impact of thermal noise and establish a noise correlation model.

[0101] Step 3: Signal propagation analysis: Study the propagation characteristics of signals between multi-layer RIS and multi-user receiving antennas, establish input-output relationships, and analyze the impact of mutual coupling effects on signal transmission.

[0102] Specifically, the step three includes the following steps:

[0103] First, the circuit model is integrated into a multi-user MIMO communication system based on multi-layer RIS. The composite signal y received by the mth user is m It can usually be expressed as:

[0104] y m =H m Wx+n

[0105] in Represents a set of symbols for each user, satisfying H m represents the channel between the feed antenna and the mth user. represents the precoding matrix at the feed antenna, and n is the noise. The RMS value of the feed antenna current can be obtained by Given. Combined Figure 2 , can be written as a circuit model in a multi-user scenario, thereby establishing the transmitter signal source v G Voltage v to the mth multi-user receiving antenna R,m The input-output relationship of v is obtained by Fourier transform. G and v R,m Converted to frequency domain, that is, v G (f),v R,m (f) Therefore, under the far-field assumption, the signal source v G (f) Voltage v to the mth multi-user receiving antenna R,m The input-output relationship of (f) can be expressed as:

[0106] v R,m (f) = H m (f)v G (f)+n m (f),

[0107] H m (f) = -Rin P m Z RS,m Φ L Z ST B,

[0108] n m (f)=(R in P m -1)v N,R +R in P m Z RS,m Φ L Z ST Bv N,T ,

[0109] Among them H m (f),n m (f) is the frequency domain distribution of the channel and noise between the feed antenna and the mth user, R in is the internal resistance, Φ L represents the phase control matrix of the lth layer RIS

[0110]

[0111] Where R is the internal resistance of the transmitter. The noise correlation matrix can be derived as follows:

[0112]

[0113] where Q m =-Z RS,m Φ L Z ST . At the signal source v G The total power budget P provided max Under this condition, the power allocated to the mth user is defined as p m , The signal-to-interference-and-noise ratio ρ of the mth user can be obtained m The sum of the rates achievable by the system, R, is:

[0114]

[0115] It can be observed that the communication functions of the feed antenna, multi-layer RIS, and multi-user receive antennas are essentially encapsulated in H. By jointly designing the impedance and transmit power within the matrix H, the goal of beamforming can be achieved.

[0116] Next, we conduct a theoretical analysis of the self-impedance and mutual coupling impedance of the feed antenna, multi-layer RIS meta-atom, and multi-user receiving antenna. First, we establish the equivalent circuit model of the antenna:

[0117]

[0118] Where V1 and I1 represent the equivalent voltage and current of the antenna, A1 represents the complex coefficient of the TM1 mode, a is the antenna size, k0 and η0 represent the wave number and wave impedance in free space, respectively, and j represents the imaginary unit. Using basic circuit theory, the self-impedance Z Chu Written as:

[0119]

[0120] Where c is the speed of light, f is the operating frequency, [V], [A], [Ω] are the units of voltage, current and impedance, and the two non-overlapping CMS antennas each have a self-impedance Z X and Z Y , and its mutual impedance is:

[0121]

[0122] The spherical coordinates are expressed as (r, θ, φ), with the rotation angles β and γ defined relative to the connecting axis r, and d being the distance between the two antennas. The above equation encapsulates the mutual impedance between the two CMS antennas, taking into account the effects of their physical parameters and the electric field. Furthermore, it can characterize the mutual coupling between different users.

[0123] Then the propagation channel model between the feed antenna, multi-layer RIS and multiple users is derived, and the propagation channel analysis between the feed antenna and the first layer of RIS is first performed. To determine the transimpedance between the feed antenna and the meta-atom on the first layer of RIS in the near field. Assuming that the feed antenna is parallel to the first layer of RIS, the configuration parameters in the mutual impedance between the antennas can be set to and The corresponding (N S ,N T )Transimpedance and (N T ,N S )Transimpedance are equal to:

[0124]

[0125] in, It is the Nth T The feed antenna and the Nth S The distance between the meta-atoms. Next, we analyze the RIS inter-layer propagation channel model. According to the Rayleigh-Sommerfeld diffraction equation, each meta-atom on the RIS layer can be regarded as a secondary wave source. Its inter-layer transimpedance is:

[0126]

[0127] where as represents the area of ​​each meta-atom, d l Indicates the distance between layers, Indicates the Nth layer on the (l-1)th layer RIS S The Nth meta-atom on the lth layer of RIS S The distance between the ' meta-atoms. Then the correlated Rayleigh fading channel is used to represent the channel from the last layer RIS to the mth user, which is denoted as Taking antenna coupling into account, the spatial channel correlation can be characterized in terms of an impedance matrix. This is because the impedance matrix exhibits the same correlation characteristics as isotropic ambient noise, which are described by the real part of the impedance matrix. Therefore, Defined as:

[0128]

[0129] in, is an independent and identically distributed Rayleigh fading channel, α is the path loss exponent, d RS is the distance between the last layer RIS and the mth user.

[0130] This step primarily establishes the input-output relationship between the voltage from the transmitting signal source and the multi-user receiving antenna. The voltage signal is converted to the frequency domain using a Fourier transform to simplify analysis. Next, a system analysis is conducted under physical constraints to investigate the self-impedance, coupled impedance, and propagation model of the feed antenna, multi-layer RIS elements, and multi-user receiving antenna.

[0131] Step 4: Design an optimization algorithm: An alternating optimization algorithm under user fairness constraints is proposed. First, the transmit power is fixed and the phase control matrix of the RIS is optimized to improve signal transmission efficiency. Then, the phase control of the RIS is fixed and the transmit power distribution is optimized.

[0132] The step 4 includes the following steps:

[0133] First, the total rate of all users is maximized by jointly optimizing the transmit power of the feed antenna and the wave domain beamforming of the multi-layer RIS. When solving the optimization problem, the SINR constraint Γ of the mth user must be ensured. m Minimize to ensure user fairness. At the same time, constrain the maximum transmission power of the feed antenna. The main challenge lies in the multi-layer structure of the multi-layer RIS. To solve this problem, an effective algorithm is designed to optimize the transmission power p of each layer of RIS through alternating optimization. t =[p1,p2,…,p M ] T and the phase control matrix. It can be formulated as the following non-convex optimization problem:

[0134]

[0135] First, the phase control matrix is ​​optimized. Given the transmission power distribution p t , optimize the phase control matrix of each RIS layer. m Z in (f) ST Expand, that is:

[0136]

[0137] Based on the multi-layer structure, the gradient ascent iterative algorithm is used to optimize the phase control matrix of each layer. l ) and the gradient of the l-th layer adjustable impedance matrix is The adjustable impedance matrix of the l-th layer RIS at iteration t+1 is:

[0138]

[0139] Among them, since the adjustable impedance of RIS must be a strictly imaginary number, the operator is added In addition, μ l >0 is the Armijo step size, which is determined by backtracking line search in each iteration. The above formula is iteratively executed until the increment of the sum rate rises below a predetermined threshold, reaching convergence.

[0140] Then, the transmit power allocation is carried out and the transmit power allocation is derived through the obtained multi-layer RIS phase control matrix. is a fully Hermitian matrix, and assume that R n is reversible, and the achievable rate of the mth user can be further expressed as:

[0141]

[0142] Take the above formula as p i The function is rewritten as:

[0143]

[0144] R m Represents the difference between two concave functions, which is a non-concave function. Using continuous convex approximation, h2(p i ) performs a first-order Taylor expansion:

[0145]

[0146] where p i (t) Indicates p i The value at the tth iteration. Therefore, P1 can be approximately reformulated as P1.1, which can be expressed as

[0147]

[0148] This problem is a standard convex optimization problem and can be solved using the CVX toolbox to obtain the transmit power allocation.

[0149] This step mainly optimizes the transmit power of the feed antenna and the beamforming performed by the multi-layer RIS in the wave domain. The transmit power and the phase control matrix of each layer of RIS are optimized through alternating optimization to maximize the total rate of all users.

[0150] In order to verify the technical effect of this technical solution, this technical solution conducts the following simulation experiments, and the simulation conditions are:

[0151] Set up a three-dimensional coordinate system, in which the feed antenna and each layer of RIS are uniform planar arrays deployed parallel to the xy plane. The BS of the multi-layer RIS is centered at (0m, 10m, 0m), and M users are evenly distributed in a circle with a radius of 50m centered at (0m, 0m, 0m). A multi-layer RIS-assisted multi-user communication system is proposed, whose operating frequency is f0 = 28GHz, corresponding to a wavelength of λ = 10.7mm. Unless otherwise specified, 4 feed antennas and seven RIS layers are configured, and each RIS layer consists of 100 meta-atoms. The number of users is 4, and each user has 4 antennas. The distance between adjacent RIS layers is λ / 3. The transmission power is P max =20dBm, the path loss exponent is α=3.5, and the receiver sensitivity is σ 2 =-110dBm. The feed antenna size is The size of the meta-atom is Where ζ(·) is the Riemann zeta function and the maximum number of iterations is 60. Minimum SINR constraint Γ m All simulation results are obtained by averaging 100 independent experiments.

[0152] from Figure 3 It can be seen that when the RIS atomic spacing remains unchanged, the system achievable rate and the system achievable rate increase with the increase of the number of RIS layers; when the number of RIS layers remains unchanged, the system achievable rate and the system achievable rate increase with the decrease of the RIS atomic spacing. This is due to the higher spatial resolution and broadband gain brought by the mutual coupling effect. Under the same conditions, the system achievable rate and the system achievable rate obtained by the proposed alternating optimization algorithm are higher than those of the uniform power allocation algorithm, such as in Δ S =λ / 2, when the number of multi-layer RIS layers is 6, the proposed alternating optimization algorithm achieves a system achievable rate that is 2 bit / s / Hz higher than that of the uniform power allocation algorithm.

[0153] from Figure 4It can be seen that as the total transmit power increases, the system achievable rate and sum also increase. Furthermore, under the same conditions, the proposed alternating optimization algorithm achieves a higher system achievable rate and sum than the uniform power allocation algorithm. When the total transmit power is less than 10dBm, the smaller M, the higher the system achievable rate and sum. When the total transmit power is greater than 10dBm, the larger M, the higher the system achievable rate and sum.

[0154] from Figure 5 It can be seen that there exists an optimal interlayer distance at which the system's achievable rate reaches its maximum. For example, in a 10×10 meta-atom configuration, the optimal interlayer distance is approximately λ / 3. When the interlayer distance exceeds this optimal value, the system's achievable rate begins to decline. This decline is primarily due to increased interlayer propagation loss, which cannot be fully compensated by the number of multi-layer RIS meta-atoms. Furthermore, as the number of meta-atoms increases, the optimal interlayer distance also increases, thereby increasing the system's achievable rate. For example, in a 7×7 meta-atom configuration, the optimal interlayer distance is approximately 0.2λ, and the system's achievable rate is 17.5 bits / s / Hz; while in a 12×12 meta-atom configuration, the optimal interlayer distance is approximately 0.4λ, and the system's achievable rate is 19.9 bits / s / Hz.

[0155] from Figure 6 It can be seen that as the number of RIS layer atoms increases, the system achievable rates for different algorithms also increase. The figure shows that the proposed alternating optimization algorithm outperforms other algorithms when the number of RIS layer atoms is greater than 50. When the number of atoms is 80, the proposed algorithm achieves a system achievable rate that is 1 bit / s / Hz higher than the uniform power allocation algorithm, 2 bit / s / Hz higher than the iterative water filling algorithm, 7 bit / s / Hz higher than the codebook method, and 8 bit / s / Hz higher than the random phase method. The proposed algorithm demonstrates superior power allocation and anti-interference capabilities.

[0156] from Figure 7 It can be seen that after considering the antenna radiation efficiency loss, the system achievable rates and the proposed alternating optimization algorithm, iterative water filling algorithm, and uniform power distribution algorithm all decrease, which is due to the spatial correlation and impedance mismatch caused by mutual coupling. T =λ / 4 is still larger than Δ T =λ / 2, the system can reach a high rate, which indirectly shows the gain that can be brought by a good mutual coupling design.

[0157] This paper constructs a multi-user communication scenario assisted by a multi-layer intelligent metasurface and proposes a modeling and optimization method for a multi-user communication system assisted by a multi-layer intelligent metasurface. Once deployed, this invention leverages the technical characteristics of intelligent metasurfaces to achieve dynamic signal control and optimized transmission. Furthermore, intelligent metasurfaces can be used to design antennas with specific radiation characteristics and dynamically control electromagnetic waves by adjusting their surface current distribution, thereby improving the coverage and signal quality of wireless communication systems.

[0158] In summary, the present invention effectively combines the flexibility of RIS and the advantages of MIMO technology, provides a complete and efficient solution for multi-user communication, and can improve system performance in complex wireless environments.

[0159] The foregoing is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained herein shall, unless otherwise specified or limited, be implemented in accordance with conventional means in the art.

Claims

1. A multi-layer intelligent metasurface-assisted multi-user communication system modeling and optimization method, characterized by: The following steps are involved: Step 1: Build a system model: Design a multi-user scenario, including a communication system with multiple layers of RIS and MIMO base stations; Using a multi-port network model, define the ports of each component, including the feed antenna, RIS meta-atom, and multi-user receiving antenna, and establish the corresponding physically consistent model; Step 2: Use non-ideal circuit models to describe noise and interference in communication systems; Step 3: Signal Propagation Analysis: Study the signal propagation characteristics between multi-layer RIS and multi-user receiving antennas, establish input-output relationships, and analyze the impact of mutual coupling effects on signal transmission; Step 4: Design an optimization algorithm: An alternating optimization algorithm under user fairness constraints is proposed. First, the transmit power is fixed and the RIS phase control matrix is ​​optimized to improve signal transmission efficiency. Then, the RIS phase control is fixed and the transmit power distribution is optimized. The step 1 comprises the following steps: First, a multi-user scenario is designed, which includes a communication system of multi-layer RIS and MIMO base stations. The communication system includes feed antennas, RIS atoms and multi-user receiving antennas. The multi-antenna base station BS built based on multi-layer RIS and feed antennas is designed to communicate synchronously with M users, each of whom is equipped with N R multi-user receiving antennas; The multi-antenna base station BS is equipped with a uniform planar array, including N T ≥N R Feed antenna and L parallel RIS layers, each parallel RIS layer is embedded with N S Elementary atoms; Δ S and Δ T represents the uniform antenna spacing between the feed antenna and the RIS layer; let N T ={1,2,…,N T },L={1,2,…,L},N S ={1,2,…,N S },M={1,2,…,M},N R ={1,2,…,N R } represent the feed antenna, parallel multi-layer RIS, the meta-atom on each RIS, the user, and the set of multi-user receiving antennas respectively; the communication system is modeled as (N T +N S +MN R ) port multi-port network The multi-port network in step 1 Expressed as: Where "T", "S", and "R" are used to represent the feed antenna, multi-layer RIS element, and multi-user receiving antenna, respectively; represent the current distribution in the feed antenna element, multi-layer RIS meta-atom, and multi-user receiving antenna, respectively; Represents the voltage vector across the corresponding port; voltage (v T ,v S ,v R ) and current (i T ,i S ,i R ) is governed by Ohm's law and is expressed through the system impedance matrix are connected to each other, the matrix can be divided into different sub-matrices; among them, Represent the impedances of the feed antenna element, multi-layer RIS element-atom, and multi-user receiving antenna respectively; the diagonal elements correspond to the self-impedances of the feed antenna element, multi-layer RIS element-atom, and multi-user receiving antenna; the non-diagonal elements represent the mutual impedances between the feed antenna element, multi-layer RIS element-atom, and multi-user receiving antenna; the matrix denote the pairwise mutual impedances between the feed antenna and multi-layer RIS, the feed antenna and multiple users, and the multi-layer RIS and multiple users, respectively. Since the antenna is a reciprocal device, we can derive In practical scenarios, the signal attenuation in the propagation channel between multiple RIS layers and multiple users is quite large, i.e., ||Z RS || F =||Z SR || F <<min(||Z R || F ,||Z S || F ). Therefore, multi-user multi-layer RIS transimpedance Z SR ≈0, where only the feed antenna affects the electromagnetic characteristics of the receiving antenna; The second step comprises the following steps: First, the feed antenna N T The voltage source is characterized by the transmitter signal source With transmitter internal resistance R; transmitter signal source passes through noise voltage source Connected to the feed antenna, the feed antenna consists of a voltage-current pair (v T ,i T ) represents; Multilayer RIS is represented by voltage-current pair (v S ,i S ) represents each RIS atom connected to a tunable impedance, i.e. a phase shifter of the incident wave, which can be written as here, represents the reactance; given the lossless and passive characteristics of the RIS meta-atom, the noise voltage source is not included in its model; the multi-user receiving antenna can be connected through the noise voltage source Receiving antenna internal resistance R in To characterize the voltage-current pair (v R ,i R ); Multiport Network It consists only of passive components that are affected by the ambient temperature T; therefore, the impedance matrix The noise in is determined solely by the thermal noise of these components and can be determined using v N,T and v N,R Modeling; When the feed antenna and multi-user receiving antennas are mutually coupled, noise correlation will occur; the truncated Fourier transform can be used to determine the noise voltage v in the feed antenna N,T and the noise voltage v in the multi-user receiving antenna N,R The relevant power spectral density (PSD) is: Where t0 is time, k b is the Boltzmann constant, T is the ambient temperature, v N,T (f), v N,R (f) is v N,T , v N,R The frequency domain representation of To obtain the real part, considering the far-field communication between the feed antenna and the multi-user receiving antenna, and the existence of multi-layer RIS as an intermediate component, the cross-correlation PSD between the feed antenna and the multi-user receiving antenna is considered to be zero, that is, ； The step three comprises the following steps: First, the circuit model is integrated into a multi-user MIMO communication system based on multi-layer RIS; the composite signal y received by the mth user is m Usually expressed as: in Represents a set of symbols for each user, satisfying H m represents the channel between the feed antenna and the mth user; represents the precoding matrix at the feed antenna, n is the noise; the RMS value of the feed antenna current can be obtained by Given; can be written as a circuit model in a multi-user scenario, thus establishing the transmitter signal source v G Voltage v to the mth multi-user receiving antenna R,m Input-output relationship; for ease of analysis, use Fourier transform to convert v G and v R,m Converted to frequency domain, that is, v G (f),v R,m (f) Therefore, under the far-field assumption, the signal source v G (f) Voltage v to the mth multi-user receiving antenna R,m The input-output relationship of (f) is expressed as: v R,m (f)=H m (f)v G (f)+n m (f), H m (f)=-R in P m Z RS,m Φ L Z ST B, n m (f)=(R in P m -1)v N,R +R in P m Z RS,m Φ L Z ST Bv N,T , Among them H m (f),n m (f) is the frequency domain distribution of the channel and noise between the feed antenna and the mth user, R in is the internal resistance, Φ L represents the phase control matrix of the lth layer RIS Where R is the internal resistance of the transmitter, the noise correlation matrix can be derived as follows: where Q m =-Z RS,m Φ L Z ST , at the signal source v G The total power budget P provided max Under this condition, the power allocated to the mth user is defined as p m , The sum of the signal-to-interference-and-noise ratio of the mth user and the achievable rate of the system is obtained as: It can be observed that the communication functions of the feed antenna, multi-layer RIS, and multi-user receiving antenna are basically encapsulated in H; by jointly designing the impedance and transmit power within the matrix H, the goal of beamforming can be achieved; Next, the self-impedance and mutual coupling impedance of the feed antenna, multi-layer RIS meta-atom and multi-user receiving antenna are theoretically analyzed; First, establish the equivalent circuit model of the antenna: Where V1 and I1 represent the equivalent voltage and current of the antenna, A1 represents the complex coefficient of the TM1 mode, and a is the antenna size; k0 and η0 represent the wave number and wave impedance in free space, respectively, and j represents the imaginary unit. Using basic circuit theory, the self-impedance Z Chu Written as: Where c is the speed of light, f is the operating frequency, and the two non-overlapping CMS antennas each have a self-impedance Z X and Z Y , and its mutual impedance is: The spherical coordinates are expressed as (r, θ, φ), with the rotation angles β and γ defined relative to their connecting axis r, and d being the distance between the two antennas. The above equation encapsulates the mutual impedance between the two CMS antennas, taking into account the effects of their physical parameters and the electric field. In addition, it can characterize the mutual coupling between different users. Then the propagation channel model between the feed antenna, multi-layer RIS and multiple users is derived. First, the propagation channel between the feed antenna and the first layer of RIS is analyzed. To determine the transimpedance between the feed antenna and the meta-atom on the first layer of RIS in the near field; assuming that the feed antenna is parallel to the first layer of RIS, the configuration parameters in the mutual impedance between the antennas can be set to and The corresponding (N S ,N T )Transimpedance and (N T ,N S )Transimpedance are equal to: in, It is the Nth T The feed antenna and the Nth S The distance between the meta-atoms is calculated. Next, the RIS inter-layer propagation channel model is analyzed. According to the Rayleigh-Sommerfeld diffraction equation, each meta-atom on the RIS layer can be regarded as a secondary wave source. Its inter-layer transimpedance is: where a s represents the area of ​​each meta-atom, d l Indicates the distance between layers, Indicates the Nth layer on the (l-1)th layer RIS S The Nth meta-atom on the lth layer of RIS S The distance between the ' meta-atoms; then the correlated Rayleigh fading channel is used to represent the channel from the last layer RIS to the mth user, denoted as Taking antenna coupling into account, the spatial channel correlation can be characterized in terms of the impedance matrix; this is because the impedance matrix exhibits the same correlation characteristics as the isotropic ambient noise, which are described by the real part of the impedance matrix; therefore, Defined as: in, is an independent and identically distributed Rayleigh fading channel, α is the path loss exponent, d RS is the distance between the last layer RIS and the mth user; The step 4 includes the following steps: First, the total rate of all users is maximized by jointly optimizing the transmit power of the feed antenna and the wave domain beamforming of the multi-layer RIS. When solving the optimization problem, the SINR constraint Γ of the mth user must be ensured. m Minimum to ensure user fairness; at the same time, constrain the maximum transmission power of the feed antenna; the main challenge lies in the multi-layer structure of the multi-layer RIS; to solve this problem, an effective algorithm is designed to optimize the transmission power p of each layer of RIS through alternating optimization. t =[p1,p2,…,p M ] T and the phase control matrix; it can be formulated as the following non-convex optimization problem: First, the phase control matrix is ​​optimized. Given the transmission power distribution p t , optimize the phase control matrix of each RIS layer; transform equation H m Z in (f) ST Expand, that is: Based on the multi-layer structure, the gradient ascent iterative algorithm is used to optimize the phase control matrix of each layer; l ) and the gradient of the l-th layer adjustable impedance matrix is The adjustable impedance matrix of the l-th layer RIS at iteration t+1 is: Among them, since the adjustable impedance of RIS must be a strictly imaginary number, the operator is added In addition, μ l >0 is the Armijo step size, which is determined by the backtracking line search in each iteration; the above formula is iteratively executed until the increment of the sum rate rises below the predetermined threshold and convergence is achieved; Then the transmit power allocation is carried out, and the transmit power allocation is derived through the obtained multi-layer RIS phase control matrix; is a fully Hermitian matrix, and assume that R n is reversible, and the achievable rate of the mth user can be further expressed as: Take the above formula as p i The function is rewritten as: R m Represents the difference between two concave functions, which is a non-concave function; using continuous convex approximation, h2(p i ) performs a first-order Taylor expansion: where p i (t) Indicates p i The value at the tth iteration; therefore, P1 can be approximately reformulated as P1.1, which can be expressed as This problem is a standard convex optimization problem and can be solved using the CVX toolbox to obtain the transmit power allocation.

2. The multi-layer intelligent metasurface-assisted multi-user communication system modeling and optimization method according to claim 1 is characterized by: The number of atoms in the RIS layer is greater than 50.

3. The multi-layer intelligent metasurface-assisted multi-user communication system modeling and optimization method according to claim 2 is characterized by: The number of atoms in the RIS layer is 80.

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