Maximization method in MA and ARIS assisted multi-user communication system

Abstract

The invention discloses a maximization and minimization method in a multi-user communication system assisted by MA and ARIS, which constructs a maximization optimization problem about a minimum communication rate between a base station and multiple users on the premise of taking user fairness as a principle. Main optimization variables comprise coordinates of a mobile antenna configured by a base station, active beam forming of the base station and a reflection coefficient matrix of ARIS, an alternative optimization algorithm is adopted, an optimization sub-problem for a single optimization variable is established, an optimal solution of each optimization variable is iteratively solved, and finally the minimum communication rate between the base station and multiple users is maximized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, in particular to a maximum minimization method in a MA (Movable Antenna) and ARIS (Active Reconfigurable Intelligent Surface) assisted multi-user communication system, which realizes the active beamforming of the base station dominated by user fairness, the reflection coefficient matrix of ARIS and the optimization of MA position in a multi-user wireless communication system. BACKGROUND

[0002] In the 6G-oriented wireless communication system, although the traditional fixed antenna technology is constantly evolving by supporting millimeter wave / terahertz frequency bands, integrating large-scale MIMO and intelligent beamforming, etc., its inherent static characteristics still have significant limitations in dynamic communication scenarios. Specifically, the pointing and communication coverage of the fixed antenna cannot be flexibly adjusted, making it difficult to adapt to terminal movement and environmental changes, and easily producing signal blind areas, thereby reducing system performance.

[0003] In contrast, mobile antennas (MA) have shown great development potential due to their spatial freedom advantage. By dynamically adjusting the position, MA can real-time reconstruct the wireless channel characteristics, effectively enhance the communication coverage, improve the interference suppression capability, and eliminate the signal blind area. MA technology not only can adaptively track mobile terminals and time-varying environments to ensure the continuity of communication, but also can optimize the spatial resource allocation, significantly improve the reliability and spectral efficiency of the system. These unique advantages make it one of the most promising key enabling technologies in 5G and 6G networks.

[0004] At the same time, the active reconfigurable intelligent surface (ARIS) is an important innovation of the traditional reconfigurable intelligent surface (RIS). ARIS, while retaining the ability to control signal phase and beam, innovatively integrates a radio frequency amplification module, enabling active amplification of reflected signal power. This breakthrough effectively addresses the severe path loss problem in high-frequency communication (such as millimeter wave and terahertz frequency bands), overcoming the inherent defect of traditional passive RIS that can only control signal phase but cannot compensate for signal strength. By actively enhancing the power of reflected signals, ARIS not only significantly expands the communication coverage, but also reduces the system's demand for base station transmit power, thereby improving overall energy efficiency. Theoretical analysis and experimental research show that ARIS technology has outstanding performance advantages in high-frequency wireless communication systems, providing an innovative solution for ultra-high-speed and ultra-reliable communication in future 6G networks.

[0005] However, although the existing research has explored the MA and ARIS assisted wireless communication system to a certain extent, most of them are limited to single-user scenarios, and there are obvious deficiencies. The single-user model cannot reflect the key problems in the actual multi-user wireless communication system: first, it ignores the inevitable co-frequency interference between multiple users, while the actual system must deal with complex co-channel interference; second, it cannot consider user fairness and differentiated quality of service requirements, especially when the channel conditions of users are significantly different; third, the spatial resource allocation, MA position adjustment and ARIS reflection coefficient matrix design strategy in the single-user scenario are too idealistic to be extended to a multi-user environment. These limitations seriously restrict the application value of research results in actual networks, and systematic research in a multi-user scenario is urgently needed.

[0006] Therefore, it is essential to consider the impact of the existence of multiple users on system performance, and it is of great practical value to study a method for implementing user fairness-oriented active beamforming of the base station, reflection coefficient matrix of ARIS and MA position optimization in a MA and ARIS assisted multi-user wireless communication system. SUMMARY

[0007] The technical problem to be solved by the present application is to provide a max-min method in a MA and ARIS assisted multi-user communication system, which can realize fairness between multiple users by adjusting the active beamforming of the base station and the reflection coefficient matrix of ARIS, as well as the position of the MA equipped by the base station, that is, to maximize the minimum communication rate between the base station and multiple users.

[0008] The technical solution adopted by the present application to solve the above technical problem is: a max-min method in a MA and ARIS assisted multi-user communication system, characterized by comprising the following steps:

[0009] Step 1: Obtain the received signal-to-interference-and-noise ratio γ k at the kth user, where k = 1, 2, …, K, and K represents the number of users;

[0010] Step 2: Take γ k , k = 1, 2, …, K as the communication performance indicator, and construct a maximum optimization problem of min(γ k , k = 1, 2, …, K) under the constraint that the amplification power of ARIS is less than a preset threshold P1, that is, a maximum optimization problem of the minimum communication rate between the base station and multiple users, wherein the optimization variables in the maximum optimization problem include a vector active beamforming of the base station reflection coefficient matrix E of ARIS, wherein w kdenotes the transmit beam of the base station to the kth user; then introduce an auxiliary variable η in the maximization optimization problem, to obtain a non-convex optimization problem P1 with an auxiliary variable η, wherein the non-convex optimization problem P1 contains the signal-to-interference-and-noise ratio constraint γ k ≥ η;

[0011] Step 3: Given and E, convert the non-convex optimization problem P1 into a non-convex optimization problem P2 about optimization ; then perform a first-order Taylor expansion process on the signal-to-interference-and-noise ratio constraint in the non-convex optimization problem P2 at a feasible initial point , convert the non-convex optimization problem P2 into a convex optimization problem P3;

[0012] Step 4: Given E and the coordinates of all mobile antennas except the n th mobile antenna equipped by the base station t n , introduce K auxiliary variables in the non-convex optimization problem P1, convert the non-convex optimization problem P1 into a non-convex optimization problem P4 about optimization t n , wherein n = 1, 2, …, N, the non-convex optimization problem P4 contains the signal power constraint, the noise power constraint, the ARIS amplification power constraint, and the mobile antenna spacing constraint; then perform a second-order Taylor expansion process on the signal power constraint at a feasible initial point , a first-order Taylor expansion process at a feasible initial point , a second-order Taylor expansion process on the noise power constraint at a feasible initial point , an upper bound-minimization algorithm on the ARIS amplification power constraint at a feasible initial point , and a second-order Taylor expansion process at a feasible initial point , and a first-order Taylor expansion process on the mobile antenna spacing constraint at a feasible initial point , convert the non-convex optimization problem P4 into a convex optimization problem P5;

[0013] Step 5: Given and , introduce K auxiliary variables in the non-convex optimization problem P1, convert the non-convex optimization problem P1 into a non-convex optimization problem P6 about optimization E, wherein the non-convex optimization problem P6 contains the signal power constraint and the rank-one constraint; then perform a first-order Taylor expansion process on the signal power constraint at a feasible initial point , and a step-by-step rank-one constraint relaxation method on the rank-one constraint, convert the non-convex optimization problem P6 into a convex optimization problem P7;

[0014] Step 6: In each external iteration process, for each The inner iteration is used to solve the convex optimization problem P3, and the result of each inner iteration is obtained. The optimal solution is obtained, and the optimal solution of the inner iteration is obtained for each outer iteration when the optimal solution of the inner iteration satisfies the inner iteration condition. The optimal solution;

[0015] In each external iteration, for the coordinates of each mobile antenna equipped with the base station, an inner-layer iterative solution to the convex optimization problem P5 is used to obtain the optimal solution for the coordinates of each mobile antenna equipped with the base station at each inner-layer iteration. The optimal solution for each outer-layer iteration is obtained when the optimal solution of the inner-layer iteration satisfies the inner-layer iteration condition. The optimal solution;

[0016] In each outer iteration, for E, the inner iteration is used to solve the convex optimization problem P7 to obtain the optimal solution of E in each inner iteration. And when the optimal solution of the inner iteration satisfies the inner iteration condition, the optimal solution of E in each outer iteration is obtained.

[0017] Obtained through outer layer iteration The optimal solution The optimal solution of E is obtained when the outer iteration condition is satisfied, which is min(γ). k The maximization optimization value of (k = 1, 2, ..., K).

[0018] In step 1, Among them, h RU，k Let E represent the channel coefficients of the link from ARIS to the k-th user, and let E represent the reflection coefficient matrix of ARIS, E = diag(e1, e2, ..., e...). M ), diag(·) denotes constructing a diagonal matrix, e m =β m exp(jθ m ), j is the imaginary unit, β m and θ m This corresponds to the amplification factor and phase shift of the m-th reflecting element of ARIS, where m = 1, ..., M, and M represents the number of reflecting elements in ARIS. This represents the channel coefficients of the base station to ARIS link. This represents the channel coefficient of the link from the base station to the k-th user. This represents the vector formed by the coordinates of the N mobile antennas equipped at the base station. t n This represents the coordinates of the nth mobile antenna equipped with the base station, where n = 1, ..., N, and N represents the number of mobile antennas equipped with the base station. and This corresponds to the x-axis and y-axis coordinates of the nth mobile antenna equipped in the base station. The superscript "T" indicates the transpose operation.k denotes the transmit beam of the base station to the kth user, denotes the power of the Gaussian white noise at the ARIS, denotes the power of the Gaussian white noise at the user.

[0019] denotes the channel coefficient of the kth user link at the ARIS RU，k denotes the transmit beam of the base station to the kth user, wherein, denotes the receive response vector of the kth user link at the ARIS, which is a column vector of dimension denotes the receive response vector of the kth user link at the ARIS, which is a column vector of dimension denotes the number of receive paths of the kth user link at the ARIS, the superscript "H" denotes the conjugate transpose operation, ∑ RU，k denotes the path response matrix of the kth user link at the ARIS, ∑ RU，k is a diagonal matrix, ∑ RU，k the first element on the diagonal of ∑ follows a random variable with mean 0 and variance , and the rest of the elements follow a random variable with mean 0 and variance denotes the path loss model of the kth user link at the ARIS, d RU，k denotes the distance between the ARIS and the kth user, a RU，k denotes the path fading factor of the kth user link at the ARIS, K0denotes the average channel gain when the reference distance is d0, denotes the vector of coordinates of the M reflecting elements of the ARIS, r m denotes the coordinates of the mth reflecting element of the ARIS, and correspond to the x-axis and y-axis coordinates of the mth reflecting element of the ARIS, denotes the transmit response matrix of the kth user link at the ARIS, denotes the transmit response vector of the mth reflecting element of the ARIS to the kth user link, denotes the signal wavelength, denotes the number of transmit paths of the kth user link at the ARIS, denotes the path difference between the lth RU，k transmit path of the kth user link at the ARIS and the center position of the region S m at r r , and correspond to the path difference between the lth RU，kThe elevation and azimuth angles of the launch path, S r This represents the region where the M reflective elements of ARIS are located.

[0020] The channel coefficient of the base station to ARIS link Represented as in, This represents the receive response matrix of the base station to ARIS link. f BR (r m ) represents the received response vector of the link from the base station to the m-th reflecting element of ARIS. Represents the k-th node of the base station to ARIS link. BR The receiving path is in r m Location and Region S r The path difference at the center position, and The corresponding element represents the k-th node of the base station to ARIS link. BR The elevation and azimuth angles of the receiving path. ∑ represents the number of receive paths from the base station to the ARIS link. BR Represents the path response matrix from the base station to the ARIS link, ∑ BR Let ∑ be a diagonal matrix. BR The first element on the diagonal follows a pattern with a mean of 0 and a variance of . A random variable, with all other elements having a mean of 0 and a variance of . random variables, This represents the path loss model for the link from the base station to ARIS, d BR α represents the distance between the base station and ARIS. BR Y represents the path fading factor of the link from the base station to ARIS. BR (t) represents the transmit response matrix of the base station to the ARIS link. ζ BR (t n ) represents the transmit response vector from the nth mobile antenna equipped at the base station to the ARIS link. This indicates the number of transmission paths from the base station to the ARIS link. Indicates the lth link of the base station to ARIS BR The launch path is at t n Location and Region S t The path difference at the center position, and This corresponds to the lth link of the base station to ARIS. BRThe elevation and azimuth angles of the launch path. S t This indicates the area where the N mobile antennas equipped by the base station are located.

[0021] The channel coefficients of the base station to the k-th user link Represented as in, This represents the received response vector from the base station to the k-th user link, and its dimension is... A column vector of all 1s. ∑ represents the number of receive paths from the base station to the k-th user link. BU，k Let ∑ represent the path response matrix from the base station to the k-th user link. BU，k Let ∑ be a diagonal matrix. BU，k All elements on the diagonal have a mean of 0 and a variance of . random variables, Let d represent the path loss model of the link from the base station to the k-th user. BU，k α represents the distance between the base station and the k-th user. BU，k This represents the path fading factor of the link from the base station to the k-th user. This represents the transmit response matrix of the link from the base station to the k-th user. ζ BU，k (t n ) represents the transmit response vector from the nth mobile antenna of the base station to the kth user link. This represents the number of transmission paths from the base station to the k-th user. Represents the l-th link between the base station and the k-th user. BU，k The launch path is at t n Location and Region S t The path difference at the center location, and The corresponding term represents the l-th link from the base station to the k-th user. BU，k条 Elevation and azimuth angles of the launch path.

[0022] In step 2, the non-convex optimization problem P1 is described as follows:

[0023]

[0024] Among them, ||t n -t v ||2≥D,n,v∈{1,…,N},n≠v means that the interval between adjacent mobile antennas equipped by the base station is greater than or equal to D, P0 means the maximum transmit power of the base station, and P1 means the preset threshold of ARIS amplification power.

[0025] In step 3, the non-convex optimization problem P2 is described as follows:

[0026]

[0027] In step 3, the process of obtaining the convex optimization problem P3 is as follows:

[0028] Step 3.1: For the signal-to-interference-plus-noise ratio constraint γ k ≥η, obtained by transposition

[0029]

[0030] Step 3.2: For At a feasible initial point Perform a first-order Taylor expansion at the point to obtain in, express At a feasible initial point The first-order Taylor expansion expression at the point, Indicates taking the real part;

[0031] Step 3.3: Describe the convex optimization problem P3 as:

[0032]

[0033] In step 4, the non-convex optimization problem P4 is described as follows:

[0034]

[0035] In step 4, the process of obtaining the convex optimization problem P5 is as follows:

[0036] Step 4.1: For signal power constraints The processing procedure is as follows:

[0037] First process its right half, let get: Among them, 1 H Represents a vector consisting entirely of 1s. Indicates taking The element in the nth row and lth column, Indicates taking The element in the nth row and nth column, with the superscript "*" indicating conjugate operation, l = 1, 2, ..., N, l ≠ n. g k (t n ) is the intermediate quantity introduced; then for g k (t n At a feasible initial point Performing a second-order Taylor expansion at the point, we obtain: where represents g k (t n ) at the feasible initial point , represents g k (t n ) at , represents the gradient of , is a constant independent of t n ;

[0038] The left half of it is processed again, and k is processed by first-order Taylor expansion at the feasible initial point , where represents the first-order Taylor expansion of k at the feasible initial point ;

[0039] Step 4.2: Process the right half of the noise power constraint , , where represents the element in the nth row and the nth column of , represents the element in the nth row and the lth column of , and g k，i (t n ) is an intermediate quantity introduced; then k，i (t n ) is processed by second-order Taylor expansion at the feasible initial point ,

[0040] where represents the second-order Taylor expansion of g k，i (t n ) at the feasible initial point , represents the value of g k，i (t n ) at , represents the gradient of , is a constant independent of t n ;

[0041] Step 4.3: Process the ARIS amplification power constraint , The processing is performed, and the processing process is: and an upper bound-minimization algorithm is used to obtain a proxy upper bound at a feasible initial point wherein, is an introduced intermediate quantity, w k (n) represents the nth element in w k , represents the corresponding maximum eigenvalue, represents a unit matrix of dimension , then let and perform a second-order Taylor expansion process on at a feasible initial point to obtain: wherein, is an introduced intermediate quantity, represents the second-order Taylor expansion expression of at a feasible initial point , represents the value of at , represents the gradient of , is a constant independent of t n ;

[0042] Step 4.4: Perform a first-order Taylor expansion process on the mobile antenna spacing constraint ||t n -t v ||2≥D, n, v ∈ {1,..., N}, n≠v in n -t v ||2at a feasible initial point to obtain:

[0043] Step 4.5: The convex optimization problem P5 is described as:

[0044]

[0045] In the step 5, the non-convex optimization problem P6 is described as:

[0046] wherein,

[0047] represents a unit matrix, [·] M+1 ​This indicates retrieving the (M+1)th element.

[0048] In step 5, the process of obtaining the convex optimization problem P7 is as follows:

[0049] Step 5.1: Constrain signal power In At a feasible initial point Performing a first-order Taylor expansion at this point yields: in, express At a feasible initial point The first-order Taylor expansion is expressed at the point;

[0050] Step 5.2: Apply rank-one constraint The stepwise rank-one constraint relaxation method is used to process the relaxation, which is as follows: in, for One feasible solution, express The largest eigenvector corresponding to the largest eigenvalue. It is a feasible point for a relaxation parameter;

[0051] Step 5.3: Describe the convex optimization problem P7 as:

[0052]

[0053] The specific process of step 6 is as follows:

[0054] Step 6.1: Let s represent the number of outer iterations, and initialize s to 1;

[0055] Step 6.2: During the s-th outer iteration, This serves as the initial value required for the inner iteration during the s-th outer iteration, where s = 1. for initial value E (s-1) Let E be the initial value of E. (0) , for initial value This represents the initial value of the coordinates of the nth mobile antenna equipped at the base station. And satisfy v≠n, A×A represents region S t The area of ​​the vector, rand(1,2) represents a row vector containing two random numbers between 0 and 1, E (0) and All values ​​are random, when s>1 denotes the optimal solution of E at the (s-1)th outer iteration, (s-1) denotes the optimal solution of E at the (s-1)th outer iteration, denotes the optimal solution of E at the (s-1)th outer iteration,

[0056] Step 6.3: Inner iteration is performed on E , and the details are as follows:

[0057] Step 6.3.1: Let q denote the number of inner iteration, and the initial value of q is 1.

[0058] Step 6.3.2: Substitute E E (s-1) , into the convex optimization problem P3, and then solve it by using the interior point method to obtain the optimal solution of E at the qth inner iteration in the st outer iteration wherein, when q = 1, E is the initial value of E at the beginning of the inner iteration in the st outer iteration when q > 1, E denotes the optimal solution of E at the (q-1)th inner iteration in the st outer iteration.

[0059] Step 6.3.3: Substitute E and E into E , respectively, to obtain E and E , and then determine whether the inner iteration condition is satisfied. If yes, E is taken as the optimal solution of E at the st outer iteration and step 6.4 is executed again. If no, q = q + 1, and then return to step 6.3.2 for continuous execution, wherein, abs(·) denotes taking an absolute value, and ε1 denotes a preset first inner iteration judgment threshold.

[0060] Step 6.4: The coordinates of each mobile antenna equipped by the base station are traversed, and it is assumed that the coordinates of the nth mobile antenna are currently traversed t n , and inner iteration is performed on t n , and the details are as follows:

[0061] Step 6.4.1: Let q denote the number of inner iteration, and the initial value of q is 1.

[0062] Step 6.4.2: Substitute E E (s-1) , ​​v∈{1, …, N}, v≠n, and Substituting this into the convex optimization problem P5, and then using the interior point method to solve it, we obtain the value of t during the q-th inner iteration within the s-th outer iteration. n optimal solution Where q = 1 When t begins during the s-th outer iteration... n initial value When q > 1 This represents the time t during the (q-1)th inner iteration within the s-th outer iteration. n The optimal solution;

[0063] Step 6.4.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation and Substitute them separately In the middle, the corresponding result is and Then determine the inner iteration condition. Is it true? If it is true, then... When t is the s-th outer iteration n optimal solution Then execute step 6.4.4. If it is not true, let q = q + 1, and then return to step 6.4.2 to continue execution, where ε2 represents the preset second inner layer iteration judgment threshold;

[0064] Step 6.4.4: For t n The inner iteration ends, and... The nth element in the data is updated to... Then continue iterating through the coordinates of the next mobile antenna, let the coordinate of the next mobile antenna be t. n Then return to step 6.4.1 and continue execution until the coordinates of all moving antennas have been traversed, obtaining the optimal solution for the coordinates of all moving antennas at the s-th outer iteration, and using the vector formed by these optimal solutions as the coordinates at the s-th outer iteration. optimal solution Then proceed to step 6.5;

[0065] Step 6.5: Perform inner iterations on E, as follows:

[0066] Step 6.5.1: Let q represent the number of inner iterations, and initialize q to 1;

[0067] Step 6.5.2: [The sentence is incomplete and requires more context to translate accurately.] E (s，q-1) Substituting into the convex optimization problem P7, and then using the interior point method to solve it, we obtain the optimal solution E for the q-th inner iteration within the s-th outer iteration. (s，q) When q = 1, E (s，q-1)The initial value of E is given when the inner iteration begins during the s-th outer iteration. (s，0) E (s，0) =E (s-1) When q > 1, E (s，q-1) Let E represent the optimal solution of E in the (q-1)th inner iteration within the s-th outer iteration;

[0068] Step 6.5.3: E (s，q) and E (s，q-1) Substitute them separately In the middle, the corresponding result is and Then determine the inner iteration condition. Is it true? If it is true, then E (s，q) E is the optimal solution of E in the s-th outer iteration. (s) Then execute step 6.6. If it is not true, let q = q + 1, and then return to step 6.5.2 to continue execution. Here, ε3 represents the preset threshold for the third inner layer iteration.

[0069] Step 6.6: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] E (s) and E (s-1) Substitute them separately In the middle, the corresponding result is and Then determine the outer iteration condition. Is it true? If it is true, then... as min(γ) k The outer iteration ends when the maximum optimization value of (k = 1, 2, ..., K) is found. If the condition is not met, s = s + 1 is set, and then the process returns to step 6.2 to continue execution. Here, ε4 represents the preset outer iteration judgment threshold.

[0070] Compared with the prior art, the advantages of the present invention are as follows:

[0071] 1) The method of this invention breaks through the limitations of existing single-user research, constructs a system model in the multi-user wireless communication scenario, significantly improves the universality and practical value of the method of this invention, and can better reflect the user distribution characteristics in actual networks.

[0072] 2) The method of the present invention is for multi-user wireless communication systems. Based on the optimization framework of the maximum-minimum fairness criterion, it ensures that the communication rate of the user with the worst channel quality in the system is maximized by jointly optimizing the active beamforming of the base station and the reflection coefficient matrix of ARIS, as well as the MA position of the base station, thereby effectively improving user fairness.

[0073] 3) In high-frequency band communication such as millimeter wave and terahertz band, the signal path loss is serious, and the traditional technology is difficult to guarantee the quality of long-distance transmission. ARIS actively enhances the reflected signal power by integrating the radio frequency amplification module, directly compensates the signal path loss in the high-frequency band, and greatly expands the communication coverage. At the same time, MA shortens the equivalent distance between the terminal and the signal source by optimizing the deployment location, further reducing the base station transmission power demand. This combination not only improves the performance of high-frequency communication, but also significantly improves the system energy efficiency, providing key technical support for the green and low-carbon goal of 6G network.

[0074] 4) The method of the present application proposes a three-dimensional joint optimization framework, which optimizes the active beamforming of the base station and the reflection coefficient matrix of the ARIS, as well as the three-element parameters of the MA position equipped by the base station, establishes a multi-objective optimization model, breaks through the limitation of traditional single-dimensional optimization, and significantly improves the capacity upper bound of the multi-user wireless communication system. BRIEF DESCRIPTION OF DRAWINGS

[0075] Figure 1 The overall implementation flowchart of the method of the present application is shown in the figure.

[0076] Figure 2 The simple model diagram of the MA and ARIS assisted multi-user wireless communication system is shown in the figure.

[0077] Figure 3 The performance curve comparison diagram of the minimum communication rate between the base station and the multi-user obtained by using the method of the present application and the existing fixed antenna method and random ARIS reflection coefficient matrix method respectively with the change of the reflection element number M of ARIS is shown in the figure. DETAILED DESCRIPTION

[0078] The present application will be further described in detail below with reference to the embodiments of the drawings.

[0079] The overall implementation flowchart of the MA and ARIS assisted multi-user communication system maximum minimization method proposed by the present application is shown in the figure. Figure 1 The method is suitable for the MA and ARIS assisted multi-user wireless communication system, as shown in the figure. Figure 2 In this embodiment, N=4, M=4, in the present application, it is assumed that the N mobile antennas equipped by the base station are distributed in the area S t , and can be in the area S tThe antenna can move freely within the region, with the spacing between adjacent mobile antennas greater than or equal to D. In this embodiment, D = 0.5λ, where λ represents the signal wavelength, and in this embodiment, λ = 0.125 meters. A = 4λ is set, and the region S... t The x-axis range is -A / 2 to A / 2, and the y-axis range is -A / 2 to A / 2. The M reflective elements of ARIS are set to be distributed at fixed intervals in an A×A region S. r Within a fixed interval of 0.5λ, the method includes the following steps:

[0080] Step 1: Obtain the received signal-to-interference-plus-noise ratio γ at the k-th user. k , where k = 1, 2, ... K, and K represents the number of users.

[0081] In this embodiment, in step 1, Where |·| denotes modulo, h RU，k Let E represent the channel coefficients of the link from ARIS to the k-th user, and let E represent the reflection coefficient matrix of ARIS, E = diag(e1, e2, ..., e...). M E is a diagonal matrix of dimension M×M, and diag(·) denotes constructing the diagonal matrix. m =β m exp(jθ m ), exp(·) denotes an exponential function with the natural constant as the base, where the natural constant is 2.71, j is the imaginary unit, and β m and θ m This corresponds to the amplification factor and phase shift of the m-th reflecting element of ARIS, where m = 1, ..., M, and M represents the number of reflecting elements in ARIS. This represents the channel coefficient of the base station to ARIS link. This represents the channel coefficient of the link from the base station to the k-th user. This represents the vector formed by the coordinates of the N mobile antennas equipped at the base station. t n This represents the coordinates of the nth mobile antenna equipped with the base station, where n = 1, ..., N, and N represents the number of mobile antennas equipped with the base station. and This corresponds to the x-axis and y-axis coordinates of the nth mobile antenna equipped in the base station. The superscript "T" indicates the transpose operation. k w represents the transmit beam from the base station to the k-th user. i This represents the transmission beam from the base station to the i-th user, where i = 1, 2, ..., K, i ≠ k. This represents the power of the Gaussian white noise at ARIS. This represents the power of the Gaussian white noise at the user's location, which is taken as... ||·||2 represents the two-norm.

[0082] In the present embodiment, the channel coefficient h RU，k represents wherein, represents the received response vector of the ARIS to the kth user link, which is a column vector of dimension of all 1s, represents the number of received paths of the ARIS to the kth user link, which is taken as the superscript "H" represents the conjugate transpose operation, ∑ RU，k represents the path response matrix of the ARIS to the kth user link, ∑ RU，k is a diagonal matrix, ∑ RU，k the first element on the diagonal of ∑ obeys a random variable with mean 0 and variance and the remaining elements obey a random variable with mean 0 and variance represents the path loss model of the ARIS to the kth user link, d RU，k represents the distance between the ARIS and the kth user, a RU，k represents the path fading factor of the ARIS to the kth user link, which is taken as d RU，k = 40 meters, a RU，k = 3, K0 represents the average channel gain when the reference distance is d0, which is taken as K0 = -30 dB, d0 = 1 meter in the present embodiment, represents the vector composed of the coordinates of the M reflecting elements of the ARIS, r m represents the coordinates of the mth reflecting element of the ARIS, and correspond to the x-axis coordinate and the y-axis coordinate of the mth reflecting element of the ARIS, represents the transmit response matrix of the ARIS to the kth user link, represents the transmit response vector of the mth reflecting element of the ARIS to the kth user link, λ represents the signal wavelength, which is taken as λ = 0.125 meters in the present embodiment, represents the number of transmit paths of the ARIS to the kth user link, which is taken as represents the path difference at r RU，k between the lth m transmit path of the ARIS to the kth user link and the center position of the region S r , and The corresponding term represents the l-th link from ARIS to the k-th user. RU，k The elevation and azimuth angles of the launch path are specified in this embodiment. and All are random numbers in [0, 2π], S r This represents the region where the M reflective elements of ARIS are located.

[0083] In this embodiment, the channel coefficient of the base station to ARIS link Represented as in, This represents the receive response matrix of the base station to ARIS link. f BR (r m ) represents the received response vector of the link from the base station to the m-th reflecting element of ARIS. Represents the k-th node of the base station to ARIS link. BR The receiving path is in r m Location and Region S r The path difference at the center position, and The corresponding element represents the k-th node of the base station to ARIS link. BR The elevation and azimuth angles of the receiving path are specified in this embodiment. and All are random numbers in the range [0, 2π]. This represents the number of receive paths from the base station to the ARIS link; in this embodiment, it is taken as... ∑ BR Represents the path response matrix from the base station to the ARIS link, ∑ BR Let ∑ be a diagonal matrix. BR The first element on the diagonal follows a pattern with a mean of 0 and a variance of . A random variable, with all other elements having a mean of 0 and a variance of . random variables, This represents the path loss model for the link from the base station to ARIS, d BR α represents the distance between the base station and ARIS. BR This represents the path fading factor of the link from the base station to ARIS. In this embodiment, we take d. BR =30 meters, α BR =2.2, This represents the transmit response matrix of the base station to ARIS link. ζ BR (t n ) represents the transmit response vector from the nth mobile antenna equipped at the base station to the ARIS link. This represents the number of transmission paths from the base station to the ARIS link; in this embodiment, it is taken as... Indicates the lth link of the base station to ARIS BR The launch path is at t n Location and Region S t The path difference at the center location, and This corresponds to the lth link of the base station to ARIS. BR The elevation and azimuth angles of the launch path are specified in this embodiment. and All are random numbers in the range [0, 2π]. S t This indicates the area where the N mobile antennas equipped by the base station are located.

[0084] In this embodiment, the channel coefficient of the link from the base station to the k-th user is... Represented as in, This represents the received response vector from the base station to the k-th user link, and its dimension is... A column vector of all 1s. This represents the number of receive paths from the base station to the k-th user link. In this embodiment, we take... ∑ BU，k Let ∑ represent the path response matrix from the base station to the k-th user link. BU，k Let ∑ be a diagonal matrix. BU，k All elements on the diagonal have a mean of 0 and a variance of . random variables, Let d represent the path loss model of the link from the base station to the k-th user. BU，k α represents the distance between the base station and the k-th user. BU，k This represents the path fading factor from the base station to the k-th user link, which is taken as d in this embodiment. BU，k =70 meters, α BU，k =3, This represents the transmit response matrix of the link from the base station to the k-th user. ζ BU，k (t n ) represents the transmit response vector from the nth mobile antenna of the base station to the kth user link. This represents the number of transmission paths from the base station to the k-th user link. In this embodiment, we take... Represents the l-th link between the base station and the k-th user. BU，k The launch path is at t nLocation and Region S t The path difference at the center location, and The corresponding term represents the l-th link from the base station to the k-th user. BU，k The elevation and azimuth angles of the launch path are specified in this embodiment. and All are random numbers in the range [0, 2π].

[0085] Step 2: with γ k Let k = 1, 2, ..., K be used as communication performance indicators. A framework is constructed to minimize (γ) under the constraint that the ARIS amplification power is less than a preset threshold P1. k The optimization problem for maximizing the minimum communication rate between a base station and multiple users (k = 1, 2, ..., K) is called the optimization problem for maximizing the minimum communication rate between a base station and multiple users. The optimization variables in this problem include a vector composed of the coordinates of the N mobile antennas equipped at the base station. Active beamforming of base stations The reflection coefficient matrix E of ARIS, where w k Let represent the transmit beam from the base station to the k-th user; then, an auxiliary variable η is introduced into the maximization optimization problem, resulting in a non-convex optimization problem P1 with the auxiliary variable η, where the non-convex optimization problem P1 includes the signal-to-interference-plus-noise ratio constraint γ. k ≥η.

[0086] In this embodiment, in step 2, the non-convex optimization problem P1 is described as follows:

[0087]

[0088] Where max is the maximization function, st means "constrained by...", and S t t represents the area where the N mobile antennas equipped with the base station are located. n t represents the coordinates of the nth mobile antenna equipped with the base station. v Represents the coordinates of the v-th mobile antenna equipped with the base station, ||t n -t v ||2≥D, n, v∈{1,…,N}, n≠v indicates that the spacing between adjacent mobile antennas equipped by the base station is greater than or equal to D, and P0 represents the maximum transmit power of the base station. In this embodiment, P0=20dBm. This represents the channel coefficient of the base station to ARIS link. This represents the power of the Gaussian white noise at ARIS. For ARIS amplification power constraint, P1 represents the preset threshold of ARIS amplification power, which is taken as 15dBm in this embodiment. ||·||2 represents the L2 norm operation. FThis represents the F-norm operation.

[0089] Step 3: In the given In the case of E, the nonconvex optimization problem P1 is transformed into an optimization problem with respect to E. The nonconvex optimization problem P2 is then solved; the signal-to-interference-plus-noise ratio (SIR) constraint in the nonconvex optimization problem P2 is then applied at a feasible initial point. A first-order Taylor expansion is performed to transform the non-convex optimization problem P2 into a convex optimization problem P3.

[0090] In this embodiment, in step 3, the non-convex optimization problem P2 is described as follows:

[0091]

[0092] In this embodiment, the process of obtaining the convex optimization problem P3 in step 3 is as follows:

[0093] Step 3.1: For the signal-to-interference-plus-noise ratio constraint γ k ≥η, obtained by transposition

[0094]

[0095] Step 3.2: For At a feasible initial point Perform a first-order Taylor expansion at the point to obtain in, express At a feasible initial point The first-order Taylor expansion expression at the point, This indicates taking the real part.

[0096] Step 3.3: Describe the convex optimization problem P3 as:

[0097]

[0098] Step 4: In the given E and the coordinates t of the nth mobile antenna (excluding the base station). n All other moving antennas t v Given coordinates where v∈{1,…,N}, v≠n, introduce K auxiliary variables into the nonconvex optimization problem P1. Transform the nonconvex optimization problem P1 into an optimization problem t. n The nonconvex optimization problem P4, where n = 1, 2, ..., N, includes signal power constraints, noise power constraints, ARIS amplification power constraints, and moving antenna spacing constraints. Then, the signal power constraints are applied at a feasible initial point. Perform a second-order Taylor expansion at the point and at a feasible initial point At the feasible initial point At the feasible initial point At the feasible initial point At the feasible initial point At the feasible initial point

[0099] In this embodiment, in step 4, the non-convex optimization problem P4 is described as:

[0100]

[0101] In this embodiment, in step 4, the process of obtaining the convex optimization problem P5 is as follows:

[0102] Step 4.1: For the signal power constraint The process is as follows:

[0103] First, process the right half, let Get: Where, 1 H represents a full 1 vector, represents the element in the nth row and the lth column of , the superscript "*" represents the conjugate operation, l = 1, 2,..., N, l ≠ n, represents the element in the nth row and the nth column of , the superscript "*" represents the conjugate operation, l = 1, 2,..., N, l ≠ n, g k (t n ) is an intermediate quantity introduced; then perform a second-order Taylor expansion on g k (t n ) at the feasible initial point , to get: Where, represents the second-order Taylor expansion expression of g k ( t n) at the feasible initial point , g k (t n ) is the value of g n (t k ) at , g k (t k，i ) is the gradient of , and is a constant independent of t n .

[0104] Then process the left half, and perform a second-order Taylor expansion on ηz k at the feasible initial point Performing a first-order Taylor expansion at this point yields: in, Represents ηz k At a feasible initial point The first-order Taylor expansion is expressed at the point.

[0105] Step 4.2: Constraining Noise Power The right half is processed as follows: Let get: in, Indicates taking The element in the nth row and nth column, Indicates taking The element in the nth row and lth column, g k，i (t n ) is the intermediate quantity introduced; then for g k，i (t n At a feasible initial point Performing a second-order Taylor expansion at the point, we obtain: in, G represents k，i (t n At a feasible initial point The second-order Taylor expansion is expressed at the point. G represents k，i (t n )exist The value at that location, express gradient, For a with t n Irrelevant constants.

[0106] Step 4.3: Constraining ARIS Amplification Power In The processing procedure is as follows: [Instructions to be made] And an upper bound minimization algorithm is used at a feasible initial point. Get Agent upper boundary in, As an intermediate variable, Tr(·) represents finding the trace of the matrix. ζ BR (t j′ ) is ζ BR (t n t in ) n Replace with the coordinates t of the j′-th mobile antenna equipped at the base station. j′ , obtained, w k (n) represents wk The nth element in w k (j′) represents w k The j′-th element in express The corresponding largest eigenvalue, The dimension is The identity matrix, For ζ BR (t n t in ) n Replace with get, Indicates w k The l-th element, ζ BR (t l ) is ζ BR (t n t in ) n Replace with the coordinates t of the l-th mobile antenna equipped with the base station. l Get; then let And on At a feasible initial point Performing a second-order Taylor expansion at the point, we obtain: in, This is an intermediate quantity that is introduced. express At a feasible initial point The second-order Taylor expansion is expressed at the point. express exist The value at that location, express gradient, For a with t n Irrelevant constants.

[0107] Step 4.4: Constrain the spacing between the moving antennas ||t n -t v ||t||t in ||2≥D, n, v∈{1,…,N}, n≠v n -t v ||2 at a feasible initial point Performing a first-order Taylor expansion at this point yields:

[0108] Step 4.5: Describe the convex optimization problem P5 as:

[0109] Step 5: In the given and In the case of introducing K auxiliary variables into the nonconvex optimization problem P1 The non-convex optimization problem P1 is converted into a non-convex optimization problem P6 about optimization E, wherein the non-convex optimization problem P6 contains the signal power constraint and the rank-one constraint; then the signal power constraint is processed by first-order Taylor expansion at a feasible initial point The rank-one constraint is processed by a step-by-step rank-one constraint relaxation method, and the non-convex optimization problem P6 is converted into a convex optimization problem P7.

[0110] In this embodiment, in step 5, the non-convex optimization problem P6 is described as:

[0111] wherein,

[0112] denotes a unit matrix, [·] M+1 denotes taking the M+1th element, rank(·) denotes the rank of a matrix.

[0113] In this embodiment, in step 5, the process of obtaining the convex optimization problem P7 is as follows:

[0114] Step 5.1: the signal power constraint in the convex optimization problem P7 is processed by first-order Taylor expansion at a feasible initial point to obtain: wherein, denotes the first-order Taylor expansion expression of at the feasible initial point .

[0115] Step 5.2: the rank-one constraint in the convex optimization problem P7 is processed by a step-by-step rank-one constraint relaxation method, and the relaxation is wherein, is a feasible solution of , denotes the maximum eigenvector corresponding to the maximum eigenvalue of , and is a feasible point of a relaxation parameter.

[0116] Step 5.3: the convex optimization problem P7 is described as:

[0117]

[0118] Step 6: in each external iteration process, the inner layer iteration is used to solve the convex optimization problem P3 for , to obtain the optimal solution of in each inner layer iteration, and the optimal solution of in each external iteration is obtained when the optimal solution of the inner layer iteration satisfies the inner layer iteration condition. ​​

[0119] In each external iteration, for the coordinates of each mobile antenna equipped with the base station, an inner-layer iterative solution to the convex optimization problem P5 is used to obtain the optimal solution for the coordinates of each mobile antenna equipped with the base station at each inner-layer iteration. The optimal solution for each outer-layer iteration is obtained when the optimal solution of the inner-layer iteration satisfies the inner-layer iteration condition. The optimal solution.

[0120] In each outer iteration, for E, the inner iteration is used to solve the convex optimization problem P7 to obtain the optimal solution of E in each inner iteration. And when the optimal solution of the inner iteration satisfies the inner iteration condition, the optimal solution of E in each outer iteration is obtained.

[0121] Obtained through outer iteration The optimal solution The optimal solution of E is obtained when the outer iteration condition is satisfied, which is min(γ). k The maximization optimization value of (k = 1, 2, ..., K).

[0122] In this embodiment, the specific process of step 6 is as follows:

[0123] Step 6.1: Let s represent the number of outer iterations, and the initial value of s is 1.

[0124] Step 6.2: During the s-th outer iteration, E (s-1) , This serves as the initial value required for the inner iteration during the s-th outer iteration, where s = 1. for initial value E (s-1) Let E be the initial value of E. (0) , for initial value This represents the initial value of the coordinates of the nth mobile antenna equipped at the base station. And satisfy v≠n, A×A represents region S t The area of ​​the array is given by `rand(1,2)`, which represents a row vector containing two random numbers between 0 and 1. E represents the initial value of the coordinates of the v-th mobile antenna equipped at the base station. (0) and All values ​​are random, when s>1 Indicates the time of the (s-1)th outer iteration The optimal solution, E (s-1) This represents the optimal solution of E in the (s-1)th outer iteration. Indicates the time of the (s-1)th outer iteration The optimal solution.

[0125] Step 6.3: For Perform inner layer iterations as follows:

[0126] Step 6.3.1: Let q represent the number of inner iterations, and the initial value of q is 1.

[0127] Step 6.3.2: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] E (s-1) , Substituting into the convex optimization problem P3 and then using the interior point method to solve it, we obtain the result of the q-th inner iteration within the s-th outer iteration. optimal solution Where q = 1 When the inner iteration begins during the s-th outer iteration... initial value When q > 1 This indicates the time of the (q-1)th inner iteration within the s-th outer iteration. The optimal solution.

[0128] Step 6.3.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] and Substitute them separately In the middle, the corresponding result is and Where min is the minimization function; then the inner iteration conditions are judged. Is it true? If it is true, then... When the s-th outer iteration optimal solution Then execute step 6.4. If the condition is not met, let q = q + 1, and then return to step 6.3.2 to continue execution. Here, abs(·) represents taking the absolute value, and ε1 represents the preset threshold for the first inner layer iteration judgment. In this embodiment, ε1 = 10. -4 In q = q + 1, the "=" sign is the assignment operator.

[0129] Step 6.4: Traverse the coordinates of each mobile antenna equipped with the base station. Let the coordinates t of the nth mobile antenna being traversed. n , for t n Perform inner layer iterations as follows:

[0130] Step 6.4.1: Let q represent the number of inner iterations, and the initial value of q is 1.

[0131] Step 6.4.2: [The sentence is incomplete and requires more context to translate accurately.] E (s-1) , v∈{1, …, N}, v≠n, and Substitute into the convex optimization problem P5, and then solve it by using the interior point method to obtain the optimal solution of t n at the qth inner iteration of the st outer iteration wherein v≠n is the vth element in q=1 is the initial value of t n at the start of the inner iteration in the st outer iteration is the nth element in q>1 denotes the optimal solution of t n at the (q-1)th inner iteration of the st outer iteration.

[0132] Step 6.4.3: Substitute and into to obtain and respectively, and then determine whether the inner iteration condition is met. If yes, take as the optimal solution of t n at the st outer iteration and execute Step 6.4.4 again, and if not, set q=q+1 and return to Step 6.4.2 for continuous execution, wherein ε2 represents a preset second inner iteration judgment threshold, and in this embodiment, ε2=10 -4 .

[0133] Step 6.4.4: The inner iteration of t n is completed, the nth element in is updated to and then the coordinates of the next mobile antenna are traversed, and the coordinates of the next mobile antenna are set as t n . Then return to Step 6.4.1 for continuous execution until the coordinates of all mobile antennas are traversed, the optimal solution of the coordinates of all mobile antennas at the st outer iteration is obtained, and the vector composed of these optimal solutions is taken as the optimal solution of t at the st outer iteration . Then execute Step 6.5.

[0134] Step 6.5: Perform inner iteration on E, as follows:

[0135] Step 6.5.1: Let q represent the number of inner iterations, and the initial value of q is 1.

[0136] Step 6.5.2: Substitute E (s，q-1)Substituting into the convex optimization problem P7, and then using the interior point method to solve it, we obtain the optimal solution E for the q-th inner iteration within the s-th outer iteration. (s，q) When q = 1, E (s，q-1) The initial value of E is given when the inner iteration begins during the s-th outer iteration. (s，0) E (s，0) =E (s-1) When q > 1, E (s，q-1) Let E represent the optimal solution of E in the (q-1)th inner iteration within the s-th outer iteration.

[0137] Step 6.5.3: E (s，q) and E (s，q-1) Substitute them separately In the middle, the corresponding result is and Then determine the inner iteration condition. Is it true? If it is true, then E (s，q) E is the optimal solution of E in the s-th outer iteration. (s) Then execute step 6.6. If the condition is not met, set q = q + 1, and return to step 6.5.2 to continue execution. Here, ε3 represents the preset threshold for the third inner layer iteration judgment. In this embodiment, ε3 = 10. -4 .

[0138] Step 6.6: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] E (s) and E (s-1) Substitute them separately In the middle, the corresponding result is and Then determine the outer iteration condition. Is it true? If it is true, then... as min(γ) k The outer iteration ends when the maximum optimization value of (k = 1, 2, ..., K) is found. If the condition is not met, then s = s + 1, and the process returns to step 6.2 to continue execution. Here, ε4 represents the preset outer iteration judgment threshold, which is taken as ε4 = 10 in this embodiment. -4 In s = s + 1, the "=" sign is the assignment operator.

[0139] The feasibility and effectiveness of the method of the present invention will be further illustrated by the following simulation.

[0140] Figure 3A performance curve comparison chart of minimum communication rate R between base station and multi-users obtained by using the method of the application and the existing fixed antenna method and random ARIS reflection coefficient matrix method respectively is given. The fixed antenna method refers to equipping the base station with a traditional fixed antenna, and the random ARIS reflection coefficient matrix method refers to that the reflection coefficient matrix of ARIS is randomly generated without optimization. In the simulation, the number of reflection elements M of ARIS varies from 2 to 10 from small to large. Figure 3 It can be seen from the simulation results that the minimum communication rate R between the base station and the multi-users obtained by using the three methods increases with the increase of the number of reflection elements M of ARIS, which is mainly due to that a larger M has finer control ability and stronger spatial freedom. A larger M can form a higher-precision reflection coefficient matrix, more concentratedly guide the signal energy to the users, and effectively improve the received signal-to-interference-and-noise ratio. At the same time, the increased reflection paths provide more abundant channel control dimensions, which can better coordinate the interference between multi-users and realize more efficient spatial reuse. In addition, a larger M can also produce a channel hardening effect, reduce the influence of small-scale fading, and make the communication link more stable and reliable, thereby further improving the minimum communication rate R between the base station and the multi-users. The results show that the calculation performance of the method of the application is better than that of the existing fixed antenna method and random ARIS reflection coefficient matrix method.

Claims

1. A max-minimization method in a MA and ARIS assisted multi-user communication system, characterized by The method comprises the following steps: Step 1: Obtain the received signal-to-interference-and-noise ratio γ at the kth user k where k = 1, 2, …, K, and K represents the number of users. Step 2: γ k , k = 1, 2, …, K as a communication performance index, a maximum optimization problem of min(γ k , k = 1, 2, …, K) under the constraint that the amplification power of the ARIS is less than a preset threshold P1 is constructed, that is, a maximum optimization problem of the minimum communication rate between the base station and the multiple users, wherein the optimization variable in the maximum optimization problem includes a vector Active beamforming of the base station Reflection coefficient matrix E of the ARIS, wherein w k represents a transmission beam of the base station to the kth user; then an auxiliary variable η is introduced in the maximum optimization problem, to obtain a non-convex optimization problem P1 with the auxiliary variable η, wherein the non-convex optimization problem P1 includes a signal-to-interference-and-noise ratio constraint γ k ≥ η. Step 3: In the case of given and E, the non-convex optimization problem P1 is converted into a non-convex optimization problem P2 with respect to optimization of the signal-to-interference-plus-noise ratio constraint in the non-convex optimization problem P2 at a feasible initial point is converted into a convex optimization problem P3 by a first-order Taylor expansion process. Step 4: In the case of given E and the coordinates t of the nth mobile antenna equipped by the base station, and the coordinates of all the remaining mobile antennas except the base station n K auxiliary variables are introduced in the non-convex optimization problem P1 The non-convex optimization problem P1 is converted into a non-convex optimization problem P4 about the optimization of t n , n = 1, 2, …, N, wherein the non-convex optimization problem P4 contains the signal power constraint, the noise power constraint, the ARIS amplification power constraint, and the mobile antenna spacing constraint; then the second-order Taylor expansion processing is performed on the signal power constraint at the feasible initial point , the first-order Taylor expansion processing is performed on the signal power constraint at the feasible initial point , the second-order Taylor expansion processing is performed on the noise power constraint at the feasible initial point , the upper bound-minimization algorithm is adopted for the ARIS amplification power constraint at the feasible initial point , and the second-order Taylor expansion processing is performed on the noise power constraint at the feasible initial point , the first-order Taylor expansion processing is performed on the mobile antenna spacing constraint at the feasible initial point , the non-convex optimization problem P4 is converted into a convex optimization problem P5. Step 5: Given and , introduce K auxiliary variables in the non-convex optimization problem P1, convert the non-convex optimization problem P1 into a non-convex optimization problem P6 about optimization E, wherein the non-convex optimization problem P6 contains a signal power constraint, a rank-one constraint; then perform a first-order Taylor expansion process on the signal power constraint at a feasible initial point , and use a step-by-step rank-one constraint relaxation method to process the rank-one constraint, convert the non-convex optimization problem P6 into a convex optimization problem P7; Step 6: In each outer iteration, solve the convex optimization problem P3 with respect to using the inner layer iteration to obtain the optimal solution of in each inner iteration, and obtain the optimal solution of in each outer iteration when the optimal solution of the inner iteration satisfies the inner iteration condition. In each outer iteration process, for the coordinates of each mobile antenna equipped by the base station, the inner iteration is used to solve the convex optimization problem P5, to obtain the optimal solution of the coordinates of each mobile antenna equipped by the base station at each inner iteration, and to obtain the optimal solution of the coordinates of each mobile antenna equipped by the base station at each outer iteration when the optimal solution of the inner iteration satisfies the inner iteration condition. ​ In each outer iteration, the inner iteration is used to solve the convex optimization problem P7 for E, to obtain the optimal solution of E in each inner iteration, and to obtain the optimal solution of E in each outer iteration when the optimal solution of the inner iteration meets the inner iteration condition; The outer layer iteration obtains The optimal solution of E satisfies the outer layer iteration condition, and min(γ The optimal solution of E satisfies the outer layer iteration condition, and min(γ k The maximum optimization value of min(γ 2. The MA and ARIS assisted multi-user communication system maximum minimization method according to claim 1, characterized in that in step 1, where h RU,k denotes the channel coefficient of the ARIS to the kth user link, E denotes the reflection coefficient matrix of the ARIS, E = diag(e1, e2, …, e M ), diag(·) denotes constructing a diagonal matrix, e m = β m exp(jθ m ), j is the imaginary unit, β m and θ m correspond to the amplification coefficient and phase shift of the mth reflecting element of the ARIS, m = 1, …, M, M denotes the number of reflecting elements of the ARIS, denotes the channel coefficient of the base station to the ARIS link, denotes the channel coefficient of the base station to the kth user link, denotes a vector composed of the coordinates of the N mobile antennas equipped by the base station, t n denotes the coordinates of the nth mobile antenna equipped by the base station, n = 1, …, N, N denotes the number of mobile antennas equipped by the base station, and correspond to the x-axis coordinate and y-axis coordinate of the nth mobile antenna equipped by the base station, the superscript "T" denotes the transpose operation, w k denotes the transmit beam of the base station to the kth user, denotes the power of the Gaussian white noise at the ARIS, denotes the power of the Gaussian white noise at the user.

3. The MA and ARIS assisted multi-user communication system maximum minimization method of claim 2, wherein The channel coefficient h from ARIS to the k-th user link RU,k Represented as in, This represents the received response vector from ARIS to the k-th user link, and its dimension is... A column vector of all 1s This represents the number of receive paths from ARIS to the k-th user link, with the superscript "H" indicating the conjugate transpose operation. Σ RU,k Σ represents the path response matrix from ARIS to the k-th user link. RU,k Let Σ be a diagonal matrix. RU,k The first element on the diagonal follows a pattern with a mean of 0 and a variance of . A random variable, with all other elements having a mean of 0 and a variance of . random variables, Let d represent the path loss model for the link from ARIS to the k-th user. RU,k Let α represent the distance between ARIS and the k-th user. RU,k Let Ki represent the path fading factor from ARIS to the k-th user link, and K0 represent the average channel gain at a reference distance of d0. This represents a vector consisting of the coordinates of the M reflective elements of ARIS. r m This represents the coordinates of the m-th reflecting element in ARIS. and This corresponds to the x-axis and y-axis coordinates of the m-th reflective element in ARIS. This represents the transmit response matrix from ARIS to the k-th user link. This represents the transmit response vector from the m-th reflecting element to the k-th user link in ARIS. λ represents the signal wavelength. This represents the number of transmit paths from ARIS to the k-th user link. Indicates the l-th link from ARIS to the k-th user. RU,k The launch path is in r m Location and Region S r The path difference at the center position, and The corresponding term represents the l-th link from ARIS to the k-th user. RU,k The elevation and azimuth angles of the launch path, S r This represents the region where the M reflective elements of ARIS are located.

4. The MA and ARIS assisted multi-user communication system maximum minimization method of claim 3, wherein channel coefficients of the base station-to-ARIS link denote wherein denote the received response matrix of the base station-to-ARIS link, f BR denote m the received response vector of the mthreflective element link of the base station-to-ARIS link, denote the path difference at r BR of the k m threceiving path of the base station-to-ARIS link at the center position of the region S r , and denote the elevation and azimuth of the k BR threceiving path of the base station-to-ARIS link, denote the number of receiving paths of the base station-to-ARIS link, BR denote the path response matrix of the base station-to-ARIS link, BR is a diagonal matrix, BR the 1stelement on the diagonal of Σ obeys a random variable with mean 0 and variance and the rest of the elements obey a random variable with mean 0 and variance denote the path loss model of the base station-to-ARIS link, BR denote the distance between the base station and the ARIS, BR denote the path fading factor of the base station-to-ARIS link, denote the transmitted response matrix of the base station-to-ARIS link, ζ BR (t n ) denote the transmitted response vector of the nthmobile antenna equipped by the base station to the ARIS link, denote the number of transmitting paths of the base station-to-ARIS link, denote the path difference at t n of the l t thtransmitting path of the base station-to-ARIS link at the center position of the region S BR , and denote the elevation and azimuth of the l t thtransmitting path of the base station-to-ARIS link, S BU,k denote the region where the N mobile antennas equipped by the base station are located.

5. The MA and ARIS assisted multi-user communication system maximum minimization method of claim 4, wherein a channel coefficient of the base station to the kth user link denotes wherein denotes a received response vector of the base station to the kth user link, which is a column vector of dimension is an all-one column vector, denotes a number of received paths of the base station to the kth user link, Σ BU,k denotes a path response matrix of the base station to the kth user link, Σ BU,k is a diagonal matrix, Σ BU,k all elements on the diagonal of Σ are random variables with mean 0 and variance denotes a path loss model of the base station to the kth user link, d BU,k denotes a distance of the base station to the kth user, α BU,k denotes a path fading factor of the base station to the kth user link, denotes a transmit response matrix of the base station to the kth user link, ζ BU,k (t n ) denotes a transmit response vector of the nth mobile antenna of the base station to the kth user link, denotes a number of transmit paths of the base station to the kth user link, denotes a path difference of the lth BU,k transmit path of the base station to the kth user link at t n to the center position of the region S t , and correspond to an elevation angle and an azimuth angle of the lth BU,k transmit path of the base station to the kth user link.

6. The MA and ARIS assisted multi-user communication system maximum minimization method of claim 5, wherein In the step 2, the non-convex optimization problem P1 is described as: s.t.γ k ≥η,k= 1,2,... K, where ||t n -t v ||2≥D,n,v∈{1,…,N},n≠v represents that the interval between adjacent mobile antennas equipped by the base station is greater than or equal to D, P0 represents the maximum transmission power of the base station, and P1 represents a preset threshold of the ARIS amplification power.

7. The MA and ARIS assisted multi-user communication system maximum minimization method of claim 6, wherein In the step 3, the non-convex optimization problem P2 is described as: In the step 3, the obtaining process of the convex optimization problem P3 is as follows: Step 3.1 : For the SINR constraint γ k ≥ η, transposing gives where, Step 3.2: On at a feasible initial point a first order Taylor expansion is performed to obtain where denotes a first order Taylor expansion representation of at a feasible initial point denotes taking the real part; Step 3.3: the convex optimization problem P3 is described as:

8. The MA and ARIS assisted multi-user communication system maximum minimization method of claim 7, wherein In the step 4, the non-convex optimization problem P4 is described as: In the step 4, the obtaining process of the convex optimization problem P5 is as follows: Step 4.1 : For signal power constraint The process is: First, process the right half, let Obtained: wherein, 1 H denotes an all-one vector, denotes the element in the nth row and the 1th column of denotes the element in the nth row and the 1th column of denotes the element in the nth row and the nth column of denotes the element in the nth row and the nth column of l = 1,2,...,N, l≠n, g k (t n ) is an introduced intermediate variable; then the second-order Taylor expansion is performed on g k (t n ) at the feasible initial point , and the following equation is obtained: where, denotes g k (t n ) the second order Taylor expansion representation of g at a feasible initial point denotes g k (t n ) the value of g at denotes the gradient of g is a constant independent of t n ;​ Reprocess its left half, ηz k At a feasible initial point A first-order Taylor expansion is performed at the feasible initial point where, denotes ηz k At a feasible initial point A first-order Taylor expansion expression at the feasible initial point Step 4.2: the noise power constraint The right half is processed as follows: Let get: in, Indicates taking The element in the nth row and nth column, Indicates taking The element in the nth row and lth column, g k,i (t n ) is the intermediate quantity introduced; then for g k,i (t n At a feasible initial point Performing a second-order Taylor expansion at the point, we obtain: in, G represents k,i (t n At a feasible initial point The second-order Taylor expansion is expressed at the point. G represents k,i (t n )exist The value at that location, express gradient, For a with t n Irrelevant constants; Step 4.3: Handling ARIS power amplification constraints ​​​​​ wherein, is an introduced intermediate quantity, w k (n) denotes the nth element in w k , denotes the corresponding largest eigenvalue, denotes the identity matrix of dimension ​ Let and at a feasible initial point be expanded in a second order Taylor expansion to obtain where is an introduced intermediate quantity, denotes a second order Taylor expansion representation at a feasible initial point denotes the value at denotes the gradient of denotes the gradient of is a constant independent of t n . Step 4.4: On inter-mobile antenna spacing constraint ||t n -t v ||2≥D,n,v∈{1,…,N},n≠v||t n -t v ||2at a feasible initial point A first order Taylor expansion is performed at the feasible initial point, resulting in: Step 4.5: the convex optimization problem P5 is described as:

9. The MA and ARIS assisted multi-user communication system maximum minimization method of claim 8, wherein In the step 5, the non-convex optimization problem P6 is described as: wherein I denotes the identity matrix, [·] M+1 denotes taking the M+1th element, In the step 5, the obtaining process of the convex optimization problem P7 is as follows: Step 5.1: Signal power constraint In the case of At a feasible initial point A first order Taylor expansion is performed at the feasible initial point to obtain: Example 1 at a feasible initial point a first-order Taylor expansion expression; Step 5.2: Apply rank-one constraint The stepwise rank-one constraint relaxation method is used to process the relaxation, which is as follows: in, for One feasible solution, express The largest eigenvector corresponding to the largest eigenvalue. It is a feasible point for a relaxation parameter; Step 5.3: the convex optimization problem P7 is described as:

10. The MA and ARIS assisted multi-user communication system maximum minimization method of claim 9, wherein The specific process of the step 6 is as follows: Step 6.1: let s represent the number of outer iterations, and the initial value of s is 1; Step 6.2: In the s-th outer iteration, set E (s-1) , as the initial value required by the inner iteration in the s-th outer iteration, where s = 1 is the initial value of E E (s-1) is the initial value of E (0) , is the initial value of E represents the initial value of the coordinates of the n-th mobile antenna equipped by the base station, and satisfies v≠n, AxA represents the area of the region S t , rand(l,2) represents a row vector containing two random numbers between 0 and 1, E (0) and are random values, s > 1 represents the optimal solution of in the s-1-th outer iteration, E (s-1) represents the optimal solution of E in the s-1-th outer iteration, represents the optimal solution of in the s-1-th outer iteration; Step 6.3: Inner iteration on is performed as follows: Step 6.3.1: let q represent the number of inner iterations, and the initial value of q is 1; Step 6.3.2: Substitute into the convex optimization problem P3, and solve it by using the interior point method to obtain the optimal solution of E (s-1) , in the qth inner iteration of the st outer iteration where q = 1 is the initial value of in the qth inner iteration of the st outer iteration where q = 1 is the initial value of in the qth inner iteration of the st outer iteration q > 1 is the optimal solution of in the qth inner iteration of the st outer iteration q > 1 is the optimal solution of q > 1 is the optimal solution of Step 6.3.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] and Substitute them separately In the middle, the corresponding result is and Then determine the inner iteration condition. Is it true? If it is true, then... When the s-th outer iteration optimal solution Then execute step 6.

4. If it is not true, let q = q + 1, and then return to step 6.3.2 to continue execution. Here, abs(·) means taking the absolute value, and ε1 means the preset threshold for the first inner layer iteration judgment. Step 6.4: Traverse the coordinates of each mobile antenna equipped by the base station, and suppose that the coordinates of the nth mobile antenna are currently being traversed, denoted as t n , for t n , perform inner iteration, specifically as follows: Step 6.4.1: let q represent the number of inner iterations, and the initial value of q is 1; Step 6.4.2: [The sentence is incomplete and requires more context to translate accurately.] E (s-1) , v∈{1,···,N},v≠n, and Substituting this into the convex optimization problem P5, and then using the interior point method to solve it, we obtain the value of t during the q-th inner iteration within the s-th outer iteration. n optimal solution Where q = 1 When t begins during the s-th outer iteration... n initial value When q > 1 This represents the time t during the (q-1)th inner iteration within the s-th outer iteration. n The optimal solution; Step 6.4.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation and Substitute them separately In the middle, the corresponding result is and Then determine the inner iteration condition. Is it true? If it is true, then... When t is the s-th outer iteration n optimal solution Then execute step 6.4.

4. If it is not true, let q = q + 1, and then return to step 6.4.2 to continue execution, where ε2 represents the preset second inner layer iteration judgment threshold; Step 6.4.4: For t n The inner iteration ends, and... The nth element in the data is updated to... Then continue iterating through the coordinates of the next mobile antenna, let the coordinate of the next mobile antenna be t. n Then return to step 6.4.1 and continue execution until the coordinates of all moving antennas have been traversed, obtaining the optimal solution for the coordinates of all moving antennas at the s-th outer iteration, and using the vector formed by these optimal solutions as the coordinates at the s-th outer iteration. optimal solution Then proceed to step 6.5; Step 6.5: the inner iteration is performed on E, and the specific process is as follows: Step 6.5.1: let q represent the number of inner iterations, and the initial value of q is 1; Step 6.5.2: [The sentence is incomplete and requires more context to translate accurately.] E (s,q-1) Substituting into the convex optimization problem P7, and then using the interior point method to solve it, we obtain the optimal solution E for the q-th inner iteration within the s-th outer iteration. (s,q) When q = 1, E (s,q-1) The initial value of E is given when the inner iteration begins during the s-th outer iteration. (s,0) E (s,0) =E (s-1) When q > 1, E (s,q-1) Let E represent the optimal solution of E in the (q-1)th inner iteration within the s-th outer iteration; Step 6.5.3: Substitute E (s,q) and E (s,q-1) into respectively, to obtain and Then determine whether the inner iteration condition is satisfied, if yes, take E (s,q) as the optimal solution E (s) of E in the s-th outer iteration, and execute Step 6.6 again, if not, let q = q + 1, and return to Step 6.5.2 for continuous execution, wherein ε3 represents a preset third inner iteration determination threshold. Step 6.6: Substitute E (s) and E (s-1) into respectively, to obtain and Then determine whether the outer iteration condition is satisfied. If satisfied, take as the maximum optimization value of min(γ k ,k=1,2,…K), and the outer iteration ends. If not satisfied, let s=s+1, and then return to Step 6.2 for continuous execution, where ε4 represents a preset outer iteration judgment threshold.

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