Multi-cell system weighting and rate maximization method based on flexible intelligent metasurface

Abstract

The invention belongs to the technical field of wireless communication, and particularly relates to a multi-cell system weighting and rate maximization method based on a flexible intelligent metasurface. According to the method, the weighted sum rate of the system is maximized by jointly optimizing the beam forming vector of the base station, the phase matrix of the FIM and the surface shape of the FIM. An alternative optimization framework is adopted, an optimization problem is decomposed into a plurality of sub-problems, and a beam forming vector, a phase matrix and a surface shape are optimized respectively. Simulation results show that the method provided by the invention can realize rapid convergence and is obviously superior to a traditional RIS auxiliary communication system in various scenes. The introduction of the FIM enables the system to effectively utilize the multipath effect, and further improves the communication efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and particularly relates to a method for maximizing the weighted sum rate of a multi-cell system based on a flexible intelligent metasurface. Background Art

[0002] With the development of 5G and 6G wireless communication technologies, the demand for network capacity and data rate is increasing continuously. In the face of a complex multi-cell environment, traditional wireless communication systems often struggle to effectively suppress inter-cell interference, especially the communication quality of users at the cell edge is poor. In recent years, reconfigurable intelligent surface (RIS) technology, as an emerging wireless communication technology, can optimize the wireless propagation environment by dynamically adjusting the phase and amplitude of electromagnetic waves, thereby improving communication performance. However, traditional RISs are usually based on rigid materials, unable to adapt to complex environmental changes and limited in performance in a multipath fading environment.

[0003] Flexible intelligent metasurface (FIM), as a new type of intelligent surface technology, can further enhance the performance of wireless communication systems by introducing the ability to dynamically adjust the surface shape, enabling it to flexibly adjust its surface shape in three-dimensional space. FIM can not only optimize signal propagation through phase adjustment but also dynamically adapt to complex propagation environments through changes in surface shape, effectively suppressing the negative impacts brought by multipath fading. Summary of the Invention

[0004] The objective of the present invention is to provide a method for maximizing the weighted sum rate in a multi-cell multi-user multiple-input single-output (MISO) system based on a flexible intelligent metasurface. By jointly optimizing the beamforming vectors of the base stations, the phase matrix of the FIM, and the surface shape of the FIM, the weighted sum rate of the system is maximized.

[0005] The technical solution adopted by the present invention is as follows:

[0006] The system model adopted by the present invention is as follows: Consider a multi-cell multi-user (MU)-MISO downlink communication system consisting of L cells, each cell contains a base station equipped with M transmit antennas, and simultaneously serves K single-antenna cell-edge users. The FIM is deployed at the cell boundary to assist communication. The FIM consists of multiple electromagnetic units whose positions can be flexibly adjusted, and each unit can dynamically adjust its position in the direction perpendicular to the surface, thereby changing the surface shape of the FIM. The number of FIM electromagnetic units is N, and the surface shape vector is d. With the aim of improving the weighted sum rate in a multi-cell multi-user communication system, an optimization model is established:

[0007]

[0008]

[0009] where represents the achievable rate of a single user. is the cascaded channel from the n-th base station to the k-th user in the l-th cell, is the direct channel from the n-th base station to the k-th user in the l-th cell, is the channel from the FIM to the k-th user in the l-th cell, is the channel from the n-th base station to the FIM, is the phase shift matrix of the FIM. is the active beamforming vector of the n-th base station for the m-th user in its cell, J l,k is the covariance of the received signal of the k-th user in the l-th cell. ω l,k represents the weight of the k-th user in the l-th cell. The three constraints are the constraint of the maximum transmit power P T,l constraint, the constraint of the FIM phase, and the constraint of the deformation range of each element of the FIM, d max represents the maximum deformation range.

[0010] By jointly optimizing the beamforming vector of the base station, the phase matrix of the FIM, and the surface shape of the FIM, the weighted sum rate of the system is maximized. The solution process is to simplify the objective through the WMMSE algorithm, and then adopt an alternating optimization framework to decompose the optimization problem into multiple sub-problems, and optimize the beamforming vector, phase matrix, and surface shape respectively, which specifically includes the following steps:

[0011] S1. First, based on the weighted minimum mean square error WMMSE algorithm, by introducing the decoding vector U l,k of the k-th user in the l-th cell and the auxiliary matrix V l,k , the weighted sum rate function is rewritten as:

[0012]

[0013] where

[0014] S2. Based on the block coordinate descent method BCD, fix other variables and optimize a single variable, specifically including:

[0015] S21. Fix W, Φ, d, V, and optimize U; let the derivative of the objective function be 0 to obtain the optimal decoding vector

[0016] S22. Fix W, Φ, d, U, and optimize V; let the derivative of the objective function be 0 to obtain the optimal auxiliary matrix where is the minimum mean square error matrix;

[0017] S23. Fix V, Φ, d, U, and optimize W; the optimal W is obtained by the following method:

[0018] If Then

[0019] Otherwise Where Satisfy

[0020] S24. Fix W, V, d, U, and optimize Φ; use the Riemannian conjugate gradient (RCG) algorithm to obtain the optimal phase shift matrix Φ;

[0021] S25. Fix W, V, Φ, U, and use the gradient projection method to optimize the surface shape d;

[0022] S3. Repeat S2 until the optimization problem converges to obtain the optimal beamforming W, the optimal phase shift matrix Φ, and the optimal FIM surface shape d, and configure the multi-cell system according to the obtained parameters for downlink communication transmission.

[0023] The beneficial effects of the present invention are that the method of the present invention can converge quickly and is significantly superior to the traditional RIS-assisted communication system in various scenarios. And the introduction of FIM enables the system to effectively utilize the multipath effect and further improve the communication efficiency. Brief Description of the Drawings

[0024] Figure 1 is a flowchart of the method of the present invention.

[0025] Figure 2 is a graph of algorithm convergence under different schemes.

[0026] Figure 3 is a graph of the relationship between the weighted sum rate and the deformation range under different schemes.

[0027] Figure 4 is a graph of the relationship between the weighted sum rate and the transmit power under different schemes.

[0028] Figure 5 is a graph of the relationship between the weighted sum rate and the number of multipaths under different schemes. Detailed Embodiments

[0029] The technical solutions of the present invention will be further described below in conjunction with the drawings and embodiments.

[0030] The present invention considers a multi - cell MU - MISO downlink communication system, which consists of L cells. Each cell contains a base station equipped with M transmit antennas and serves K single - antenna edge users in the cell. The FIM is deployed at the cell boundary to assist communication. The FIM is composed of multiple electromagnetic units with flexible adjustable positions. Each unit can dynamically adjust its position in the direction perpendicular to the surface, thereby changing the surface shape of the FIM. The number of electromagnetic units of the FIM is N, and the surface shape vector is d. The channel model adopted in the present invention is as follows: The number of transmit antennas of the base station is defined as M, and these antennas are arranged in a uniform linear array with a half - wavelength spacing, and the steering vector is a ula (γ), where γ represents the transmission angle of the base station. The FIM is equivalent to a uniform planar array with a half - wavelength spacing. Assuming that the channel information is perfectly known, the steering vector is a(θ, φ, d)=a upa (θ, φ)⊙a d (θ, φ, d), where a d (θ, φ, d)=e jκd cosθcosφ , κ is the wave number, and θ and φ represent the elevation angle and azimuth angle respectively. The channel from the FIM to the k - th user in the l - th cell is expressed as where P is the number of propagation paths from the FIM to the user side, α l,k,p represent the elevation angle, azimuth angle and path loss of the p - th propagation path from the FIM to the k - th user in the l - th cell respectively. In addition, the channel from the n - th base station to the FIM is expressed as where Q is the number of propagation paths from the base station side to the FIM, β n,q represent the elevation angle, azimuth angle and path loss of the q - th propagation path from the n - th base station to the FIM. is the direct - path channel from the n - th base station to the k - th user in the l - th cell. The active beamforming vector of the n - th base station for the m - th user in its own cell is defined as W n,m , and the phase shift of the n - th element of the FIM is defined as Then the phase - shift matrix of the FIM is Subsequently, the total channel from the n - th base station to the k - th user in the l - th cell is:

[0031]

[0032] Then the achievable data rate R l,k of the k - th user in the l - th cell is expressed as:

[0033]

[0034] where J l,kLet $\mathbf{R}_{l,k}$ be the covariance of the received signal for the $k$-th user in the $l$-th cell. Then, the optimization problem of the total weighted sum rate is:

[0035]

[0036] where $\omega_{l,k}$ l,k denotes the weight of the $k$-th user in the $l$-th cell. The three constraints are the constraint on the maximum transmit power $P_l$ of the $l$-th base station, the constraint on the FIM phase, and the constraint on the deformation range of each element of the FIM. $d_{max}$ T,l represents the maximum deformation range. max As

[0037] shown, the algorithm includes the following steps: Figure 1 As shown in the figure, the algorithm includes the following steps:

[0038] S1. First, based on the weighted minimum mean square error (WMMSE) algorithm, by introducing the decoding vector $\mathbf{U}_{l,k}$ of the $k$-th user in the $l$-th cell l,k and the auxiliary matrix $\mathbf{V}_{l,k}$ l,k , the weighted sum rate function is rewritten as:

[0039]

[0040] where

[0041] S2. Based on the block coordinate descent (BCD) method, fix other variables and optimize a single variable. Specifically, it includes:

[0042] S21. Fix $\mathbf{W}$, $\boldsymbol{\varPhi}$, $d$, $\mathbf{V}$, and optimize $\mathbf{U}$. Let the derivative of the objective function be 0, and the optimal decoding vector

[0043] S22. Fix $\mathbf{W}$, $\boldsymbol{\varPhi}$, $d$, $\mathbf{U}$, and optimize $\mathbf{V}$. Let the derivative of the objective function be 0, and the optimal auxiliary matrix where is the minimum mean square error matrix;

[0044] S23. Fix $\mathbf{V}$, $\varphi$, $d$, $\mathbf{U}$, and optimize $\mathbf{W}$. The optimal $\mathbf{W}$ is obtained by the following method:

[0045] If then

[0046] Otherwise where satisfies

[0047] S24. Fix $\mathbf{W}$, $\mathbf{V}$, $d$, $\mathbf{U}$, and optimize $\boldsymbol{\varPhi}$. Use the Riemannian conjugate gradient (RCG) algorithm to obtain the optimal phase shift matrix $\boldsymbol{\varPhi}$;

[0048] S25. Fix W, V, Φ, U, and optimize the surface shape d using the gradient projection method;

[0049] S3. Repeat S2 until the optimization problem converges to obtain the optimal beamforming W, the optimal phase shift matrix Φ, and the optimal FIM surface shape d, and configure the multi-cell system according to the obtained parameters for downlink communication transmission.

[0050] Example 1:

[0051] This example verifies different schemes and the algorithm convergence under different schemes.

[0052] Simulation conditions, parameters, and performance analysis:

[0053] Fix the number of cells L = 2, with K = 2 users in each cell and the number of transmit antennas M = 2. Assume that the transmit power of each base station is the same and is denoted as P T,l = P T = 1 dBm, the noise power is -80 dBm, the number of FIM units N = 30, the wavelength is 0.01 m, the deformation range d max is one wavelength, and the number of propagation paths is P = Q = 3. In addition, the elevation angle and azimuth angle from the FIM to the user the elevation angle and azimuth angle from the base station to the FIM and the transmission angle γ of the base station are randomly and uniformly distributed within. The base stations are arranged at the centers of the cells with coordinates [200, 30], [400, 30], the FIM is placed in the middle of the two cells with coordinates [300, 30], and the users are randomly distributed in a circular area with a radius of 50 m centered on the base stations. Figure 2 The results show that the proposed algorithm has a relatively fast convergence speed, and its convergence rate is comparable to that of the RIS-based WMMSE and BCD algorithms. This indicates that introducing the FIM surface shape does not significantly increase the overall algorithm complexity. In addition, it can be observed that, compared with other baseline schemes, the introduction of FIM significantly improves the system performance. In particular, compared with the rigid RIS scheme, the proposed FIM-assisted system improves the WSR by about 33%, which highlights the advantages brought by the additional flexibility of FIM in reshaping the wireless environment.

[0054] Example 2:

[0055] This example verifies different schemes and the relationship between the weighted sum rate and the deformation range under different schemes.

[0056] Simulation conditions, parameters, and performance analysis:

[0057] Fix the number of cells L = 2, with K = 2 users in each cell and the number of transmit antennas M = 2. Assume that the transmit power of each base station is the same and is denoted as P T,l = P T= 1 dBm, noise power -80 dBm, number of FIM units N = 30, wavelength 0.01 m, number of propagation paths P = Q = 3. In addition, the elevation and azimuth angles from the FIM to the user The elevation and azimuth angles from the base station to the FIM and the transmission angle γ of the base station are randomly and uniformly distributed within. The base stations are arranged at the center of the cell, with coordinates [200, 30], [400, 30], the FIM is placed in the middle of the two cells, with coordinates [300, 30], and the users are randomly distributed in a circular area with a radius of 50 m centered on the base station. Figure 2 Shows the relationship between the surface shape deformation range and the weighted sum rate. The experiment considers two different settings: (i) N = 16, (ii) N = 24. First, as the deformation range increases, the weighted sum rate increases accordingly because the FIM has greater flexibility to adjust its surface shape, thus improving the system performance. Second, we observe the diminishing returns effect. The reason for this phenomenon is that the FIM surface shape vector is embedded in the complex exponential term of the multipath beam steering vector. Since the digital system cannot accurately represent irrational numbers, the objective function is periodic with respect to the surface shape. Therefore, after reaching the first global optimum point, further increasing the deformation range will not bring additional performance gain, resulting in the curve tending to be flat. Based on this observation, we can obtain the optimal surface shape within a small deformation range of about one wavelength scale, which reflects the advantages of the FIM in practical applications and its deployment potential in the real world. Third, comparing different N values, it can be found that a larger N will bring a higher sum rate, which is consistent with expectations. Finally, when comparing the performance of the FIM and the rigid RIS, we find that as N increases, the performance gap between the two also expands. Specifically: when N = 16, the sum rate gap between the FIM and the RIS is 0.11 bit / s / Hz, and when N = 24, this gap expands to 0.26 bit / s / Hz. The fundamental reason is that as N increases, the number of channels remains unchanged, while the dimension of the surface shape vector increases, enabling the FIM to more flexibly optimize the wireless environment and further improve the system performance.

[0058] Example 3:

[0059] This example verifies different schemes and the relationship between the weighted sum rate and the deformation range under different schemes.

[0060] Simulation conditions, parameters, and performance analysis:

[0061] Fix the number of cells L = 2, each cell has K = 2 users, and the number of transmit antennas M = 2. Assume that the transmit power of each base station is the same and is denoted as P T,l = P T, the noise power is -80 dBm, the number of FIM units N = 30, the wavelength is 0.01 m, and the deformation range is d max is one wavelength, and the number of propagation paths is P = Q = 3. In addition, the elevation angle and azimuth angle from the FIM to the user the elevation angle and azimuth angle from the base station to the FIM and the transmission angle γ of the base station are randomly and uniformly distributed within. The base stations are arranged at the center of the cell, with coordinates [200, 30], [400, 30], the FIM is placed in the middle of the two cells, with coordinates [300, 30], and the users are randomly distributed in a circular area with a radius of 50 m centered on the base station. Figure 3 shows the weighted sum rate of different schemes varying with the transmit power P T changing. It can be observed that as P T increases, the performance of each scheme improves. In addition, if neither the phase shift matrix nor the FIM surface shape is optimized, then the deployment of the FIM hardly brings any performance gain. It is worth noting that even with phase shift optimization, under the randomly deformed FIM surface shape, the system performance is still lower than that of the rigid RIS. This is because the randomly deformed surface may disrupt the coherent synthesis of multipath signals, resulting in performance degradation. In contrast, the optimized FIM surface can effectively align the multipath components, so that the FIM-assisted system is always superior to the rigid RIS-assisted system when the transmit power increases.

[0062] Example 4:

[0063] This example verifies different schemes and the relationship between the weighted sum rate and the number of multipaths under different schemes.

[0064] Simulation conditions, parameters and performance analysis:

[0065] Fix the number of cells L = 2, each cell has K = 2 users, and the number of transmit antennas M = 2. Assume that the transmit power of each base station is the same and is denoted as P T,l = P T = 1 dBm, the noise power is -80 dBm, the number of FIM units N = 30, the wavelength is 0.01 m, and the deformation range d max is one wavelength. In addition, the elevation angle and azimuth angle from the FIM to the user the elevation angle and azimuth angle from the base station to the FIM and the transmission angle γ of the base station are randomly and uniformly distributed within. The base stations are arranged at the center of the cell, with coordinates [200, 30], [400, 30], the FIM is placed in the middle of the two cells, with coordinates [300, 30], and the users are randomly distributed in a circular area with a radius of 50 m centered on the base station. Figure 4The performance of the FIM in mitigating the impact of multipath propagation was verified. The results show that as the number of propagation paths P and Q increases, the performance gain of the FIM in terms of sum rate also increases significantly, far exceeding that of the RIS-based scheme. This proves the effectiveness of the FIM in reducing the negative impact of multipath fading. It is worth noting that if the surface shape is not optimized (i.e., a random surface shape is adopted), as the number of paths increases, the system cannot guarantee that the sum rate will still increase, and even a performance degradation may occur.

Claims

1. A weighted sum rate maximization method for a multi-cell system based on a flexible intelligent metasurface, wherein the multi-cell system is a multi-cell MU-MISO downlink communication system, which consists of L cells, each of which contains a base station, and the base station is equipped with M transmitting antennas, and provides services for K single-antenna cell single-antenna edge users at the same time; characterized in that: FIM is deployed at the cell boundary to assist communication. FIM consists of multiple electromagnetic units with flexible position adjustment. Each unit can dynamically adjust its position in the direction perpendicular to the surface, thereby changing the surface shape of FIM. The number of FIM electromagnetic units is N, and the surface shape vector is d. With the purpose of improving the weighted sum rate in a multi-cell multi-user communication system, an optimization model is established: in represents the achievable rate for a single user, is the cascade channel from the nth base station to the kth user in the lth cell, is the direct channel from the nth base station to the kth user in the lth cell, is the channel from FIM to the kth user in the lth cell, is the channel from the nth base station to FIM, is the phase shift matrix of FIM, is the active beamforming vector of the nth base station for the mth user in its cell, J l,k is the covariance of the received signal of the kth user in the lth cell, ω l,k represents the weight of the kth user in the lth cell, and the three constraints are the maximum transmission power P T,l The constraints of FIM phase and the deformation range of each FIM element, d max Indicates the maximum deformation range; By jointly optimizing the beamforming vector of the base station, the phase matrix of the FIM, and the surface shape of the FIM, the weighted sum rate of the system is maximized. The solution process specifically includes the following steps: S1, based on the weighted minimum mean square error WMMSE algorithm, by introducing the decoding vector U of the kth user in the lth cell l,k and the auxiliary matrix V l,k , rewrite the weighted sum rate function as: in S2, based on the block coordinate descent method BCD, fix other variables and optimize a single variable, including: S21. Fix W, Φ, d, V, optimize U; set the derivative of the objective function to 0, and obtain the optimal decoding vector S22, fix W, Φ, d, U, optimize V; set the derivative of the objective function to 0, and obtain the optimal auxiliary matrix in is the minimum mean square error matrix; S23. Fix V, Φ, d, U and optimize W. The optimal W is obtained by the following method: like but otherwise in satisfy S24, fix W, V, d, U, optimize Φ; use the Riemann conjugate gradient RCG algorithm to obtain the optimal phase shift matrix Φ; S25, fix W, V, Φ, U, and use the gradient projection method to optimize the surface shape d; S3. Repeat S2 until the optimization problem converges, and the optimal beamforming W, the optimal phase shift matrix φ, and the optimal FIM surface shape d are obtained. The multi-cell system is configured according to the obtained parameters for downlink communication transmission.

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