Multi-carrier space division multiple access system based on movable antenna and optimization method thereof

Abstract

The invention discloses a multi-carrier space division multiple access system based on a movable antenna and an optimization method of the multi-carrier space division multiple access system, and relates to the technical field of wireless communication. According to the method, a channel model, including time domain channel response and frequency domain channel response, under the system is provided firstly, and then the transmission rate of the system is maximized on the premise that the given transmitting power, the minimum antenna spacing and the antenna moving area are met. In order to optimize the transmission rate of the system, the invention provides an alternate optimization algorithm which sequentially and alternately optimizes precoding and antenna positions. According to the invention, the spatial degree of freedom can be fully utilized; through joint optimization of system precoding design and antenna positions, the transmission rate of the system is maximized under the condition that the system meets the constraints of given transmitting power, antenna moving areas and minimum antenna intervals.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a multi-carrier space division multiple access system based on a movable antenna and an optimization method thereof. Background Art

[0002] In the 6G era, immersive communication, ultra-large-scale connections, and ultra-high reliability and low-latency communication are basic communication scenarios, all of which require higher transmission rates than 5G [1]. In modern communication systems, large-scale multiple input multiple output (MIMO) can significantly improve the transmission rate because it can deeply tap into spatial dimension resources, allowing multiple users to communicate with the base station simultaneously on the same time-frequency resource using the spatial degrees of freedom provided by multiple antennas, thereby improving the utilization of spectrum resources. How to use more spatial degrees of freedom to improve the performance of the communication system is an issue that needs to be addressed. An intuitive solution is to add more antennas to fully utilize the spatial degrees of freedom, namely, ultra-large-scale MIMO technology [2]. However, due to power consumption, hardware cost, and high design complexity, ultra-large-scale MIMO still needs further research.

[0003] In recent years, movable antennas (MA) have become another method to utilize spatial freedom because MA can change the position of the antenna to transmit or receive the signal with the highest channel gain within the moving range [3]. Generally speaking, the antenna is connected to the RF circuit through a flexible cable, and the antenna is placed on a movable base, which is placed on a slide rail. A rope is used to connect the base and the stepper motor. When the stepper motor receives a control signal, it drives the antenna on the base to move through the rope [4]. Given that MA can achieve the same performance gain as a large number of fixed-position antennas (FPA) with a small number of antennas, it has become a research hotspot in academia in recent years. .

[0004] Reference [3] studied the MA-assisted SISO channel model in narrowband systems and theoretically proved that MA can make more effective use of spatial degrees of freedom. Reference [5] studied the MA-assisted MIMO system in downlink narrowband systems and maximized the system capacity under the constraints of transmission power and minimum antenna spacing. Reference [6] studied the MA-assisted spatial division multiple access system in uplink narrowband systems and minimized the transmission power under a fixed precoding matrix. Reference [7] studied the MA-assisted spatial division multiple access system in downlink narrowband systems and maximized the weighted rate sum under the constraints of transmission power and minimum antenna spacing. Reference [8] studied the MA-assisted SISO system in downlink multi-carrier systems and maximized the system achievable rate.

[0005] Most of the above works study narrowband system models. Although reference [8] proposed a multi-carrier system, it considered a SISO system and did not combine MA and MIMO to further utilize the spatial degrees of freedom.

[0006] [1]ITU-R,DRAFT NEW RECOMMENDATION,"Framework and overall objectives of the future development ofIMT for 2030andbeyond,"June 2023.

[0007] [2]H.Lu et al., "A Tutorial OnNear-FieldXL-MIMO Communications Towards6G," in IEEE Communications Surveys&Tutorials, doi:10.1109 / COMST.2024.3387749.

[0008] [3]L.Zhu, W.Ma and R.Zhang, "Modeling andPerformance Analysis for Movable Antenna Enabled Wireless Communications," in IEEE Transactions onWireless Communications, vol.23, no.6, pp.6234-6250, June 2024.

[0009] [4] L.Zhu, W.Ma and R.Zhang, "Movable Antennas for Wireless Communication: Opportunities and Challenges," in IEEE Communications Magazine, vol.62, no.6, pp.114-120, June 2024.

[0010] [5]W.Ma, L.Zhu and R.Zhang, "MIMO Capacity Characterization for MovableAntenna Systems," in IEEE Transactions onWireless Communications, vol.23, no.4, pp.3392-3407, April 2024.

[0011] [6] L.Zhu, W.Ma, B.Ning and R.Zhang, "Movable-Antenna Enhanced MultiuserCommunication via AntennaPosition Optimization," in IEEE Transactions onWirelessCommunications, vol.23, no.7, pp.7214-7229, July 2024.

[0012] [7] B. Feng, Y. Wu, X.-G.

[0013] [8] L. Zhu, W. Ma, Z. Xiao and R. Zhang, "Performance Analysis and Optimization for Movable AntennaAided Wideband Communications," in IEEE Transactions on Wireless Communications, early access, doi:10.1109 / TWC.2024.3471698. Summary of the invention

[0014] In view of this, the present invention proposes a multi-carrier space division multiple access system based on movable antennas and an optimization method thereof. The present invention takes into account the multi-carrier system, combines the advantages of MA and MIMO, and can make full use of the spatial degrees of freedom; by jointly optimizing the system precoding design and antenna position, the system maximizes the system transmission rate under the constraints of a given transmission power, antenna movement area, and minimum antenna spacing.

[0015] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0016] A multi-carrier space division multiple access system based on movable antennas is used to transmit signals to K users; the transmitting end is configured with V movable transmitting antennas, and the receiving end of each user is configured with a movable receiving antenna; the total number of subcarriers in the system is N;

[0017] For the sender:

[0018] The transmitted symbol transmitted to user k on subcarrier n is denoted as x n,k , where n = 1, 2, 3, ..., N; k = 1, 2, 3, ..., K; send signal x n,k The precoded vector w n,k After precoding modulation, the modulation symbol S corresponding to V movable transmitting antennas is obtained. v,n,k , v=1,2,3,……,V, K signals of different users of the same subcarrier belonging to the vth movable transmitting antenna are superimposed, and then the superimposed different subcarrier signals belonging to the vth movable transmitting antenna are subjected to inverse discrete Fourier transform, cyclic prefix addition, parallel-to-serial conversion, and finally modulated to a high-frequency carrier through a radio frequency link, and radiated outward from the vth movable transmitting antenna;

[0019] For the receiver of the kth user:

[0020] After the movable receiving antenna receives the signal transmitted by V movable transmitting antennas through the time domain channel, it is demodulated through the RF link, and then the cyclic prefix is ​​removed, the serial-to-parallel conversion and the Fourier transform are performed to obtain the received estimated symbol corresponding to the N subcarriers.

[0021] A method for optimizing a multi-carrier space division multiple access system based on a movable antenna is used to optimize the multi-carrier space division multiple access system based on a movable antenna to maximize the system transmission rate; specifically comprising the following steps:

[0022] Step 1, initializing antenna positions of a movable transmitting antenna and a movable receiving antenna, modeling a time domain channel response between the movable transmitting antenna and the movable receiving antenna according to the antenna positions of the movable transmitting antenna and the movable receiving antenna, and thereby obtaining a corresponding frequency domain channel response;

[0023] Step 2: Construct a system transmission rate formula based on the frequency domain channel response and the precoding vector, and record the system transmission rate formula as an optimization problem about the antenna positions of the movable transmitting antenna and the movable receiving antenna, and the precoding vector.

[0024] Step 3: Consider the antenna positions of the movable transmitting antenna and the movable receiving antenna as fixed values ​​and solve the optimization problem Converted to an optimization problem about the precoding vector Then we will optimize the problem Converted to an optimization problem about power allocation constructing a plurality of precoding vectors according to the obtained power allocation results;

[0025] Step 4: For each precoding vector, the precoding vector is considered as a constant value and the optimization problem is Transformed into an optimization problem regarding the antenna positions of the movable transmitting antenna and the movable receiving antenna

[0026] Step 5: Repeat steps 2 to 4 until the problem is optimized. The calculation results of convergence are obtained, and for each precoding vector corresponding to the converged calculation results, the precoding vector corresponding to the largest converged calculation result is recorded as the final precoding vector;

[0027] Step 6, determine whether the antenna positions of the movable transmitting antenna and the movable receiving antenna corresponding to the final precoding vector meet the constraints. If so, record them as the final antenna positions of the movable transmitting antenna and the movable receiving antenna, and complete the optimization of the multi-carrier space division multiple access system based on the movable antenna. Otherwise, project them into the feasible domain of the constraints, and record the projected antenna positions of the movable transmitting antenna and the movable receiving antenna as the final positions, and complete the optimization of the multi-carrier space division multiple access system based on the movable antenna.

[0028] Furthermore, the specific method of step 1 is:

[0029] Step 101: for the time domain channel between the movable receiving antenna and the movable transmitting antenna of the kth user receiving end, model it as a finite-length delay tap response H k :

[0030]

[0031] in represents the time domain channel response for the kth user at the dth delay tap, D represents the total number of delay taps, 1<D<N, d=1,2,…,D;

[0032] Step 102: h d,k Divide into three parts and multiply them, that is, the transmitting end field response model F d, k(t), far-field wireless channel modelΣ d,k and the receiving end field response model g d,k (r):

[0033]

[0034]

[0035] Where j represents the imaginary unit, L represents the total number of scattering paths, ∑ d,kThe diagonal elements of represent the response coefficient of each scattering path for the kth user in the dth delay path; λ represents the central carrier wavelength of the entire transmission signal bandwidth; the movable transmitting antenna and the movable receiving antenna establish a local Cartesian coordinate system within their respective moving ranges, and set the reference point as the origin, and obtain the antenna position t of the V movable transmitting antennas v =[x v ,y v ] T , the antenna position r of the kth user's movable receiving antenna k =[x k ,y k ] T ;

[0036]

[0037] denote the azimuth and elevation of the arrival angle and the azimuth and elevation of the departure angle of the lth scattering path for the kth user in the dth delay path, respectively, l = 1, 2, 3, ..., L;

[0038] Step 103, calculate H k The corresponding frequency domain channel response

[0039]

[0040] where F N represents the N-dimensional discrete Fourier transform matrix, represents the frequency domain channel response for the k-th user at the n-th subcarrier.

[0041] Furthermore, the specific method of step 2 is:

[0042]

[0043] Among them, ∑ i≠k represents i=1,2,3,……,K, and i≠k; σ 2 represents the additive white Gaussian noise power; P max Indicates the maximum transmit power of the system, represents any movable transmitting antenna except the vth movable transmitting antenna, A represents the minimum spacing distance between movable transmitting antennas, and They respectively represent the moving ranges of the movable transmitting antenna and the movable receiving antenna.

[0044] Furthermore, the specific method of step 3 is:

[0045] Step 301: Optimize the problem Converted to an optimization problem about the precoding vector

[0046]

[0047] Step 302: Optimize the problem Converted to an optimization problem about power allocation

[0048]

[0049] in represents the power allocation vector;

[0050]

[0051] p n,k represents the power of the nth subcarrier allocated to the kth user;

[0052] Step 303, using the CVX solver to solve the optimization problem Perform multiple iterations to obtain the final power allocation vector. represents the power allocation result of the mth iteration, The initial value is After the final iteration The corresponding final power allocation result p is recorded as n,k , i=1,2,3,……,K;

[0053] Step 304: construct maximum ratio combining precoding vectors Zero-forcing precoding vector and the regularized zero-forcing precoding vector

[0054]

[0055]

[0056] in, γ is the regularization coefficient; I K represents the K-order identity matrix;

[0057] Furthermore, the specific method of step 4 is:

[0058] Step 401, optimize the problem Transformed into an optimization problem regarding the antenna positions of the movable transmitting antenna and the movable receiving antenna

[0059]

[0060] Step 402, let

[0061] make in

[0062] Step 403, according to the chain rule:

[0063]

[0064] in

[0065]

[0066] also

[0067]

[0068]

[0069] Except All elements outside are 0;

[0070]

[0071] Step 404: Update the antenna positions of the movable transmitting antenna and the movable receiving antenna:

[0072]

[0073] in,

[0074]

[0075]

[0076] α represents the gradient update step size, Represents the boundary function: If the updated antenna position exceeds or If the moving range is larger than the moving range, the updated antenna position is modified to the nearest moving range boundary point.

[0077] Furthermore, the specific method of step 6 is:

[0078] The antenna position of the movable transmitting antenna corresponding to the final precoding vector is recorded as If it satisfies Then it is recorded as the final antenna position of the movable transmitting antenna and the movable receiving antenna, and the optimization of the multi-carrier space division multiple access system based on the movable antenna is completed;

[0079] Otherwise, project it into the feasible domain of the constraints and construct the optimization problem

[0080]

[0081] in, express The antenna position of the vth movable transmitting antenna, express The antenna position of any movable transmitting antenna except the vth movable transmitting antenna;

[0082] Use CVX solvers to solve optimization problems Perform multiple iterations to obtain the final antenna position of the movable transmitting antenna Complete the optimization of multi-carrier spatial division multiple access system based on movable antenna.

[0083] Due to the adoption of the above technical solution, the beneficial effects of the present invention compared with the prior art are:

[0084] 1. The present invention takes into account the multi-carrier system, combines the advantages of MA and MIMO, and can fully utilize the spatial freedom.

[0085] 2. The present invention jointly optimizes the system precoding design and antenna position, so that the system can maximize the system transmission rate while satisfying the constraints of given transmission power, antenna movement area and minimum antenna spacing. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 The system model diagram of a multi-carrier space division multiple access system based on a movable antenna in an embodiment of the present invention.

[0087] Figure 2 This is a simulation diagram of transmission rate comparison with different transmission power levels in an embodiment of the present invention.

[0088] Figure 3 This is a simulation diagram of transmission rate comparison with different numbers of transmitting antennas in an embodiment of the present invention. DETAILED DESCRIPTION

[0089] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0090] A multi-carrier space division multiple access system based on movable antennas, such as Figure 1 As shown:

[0091] Figure 1The system model of a multi-carrier space division multiple access system based on MA transmitting signals to K users is shown, where the transmitter is equipped with V movable antennas, the receiver is equipped with one movable antenna, the total number of subcarriers in the system is N, and the bandwidth of each subcarrier is W. n,k represents the modulation symbol transmitted to user k on carrier n, w n,k Represents the corresponding precoding vector. The transmission symbols of different users are transmitted to the corresponding antenna ports after precoding modulation for superposition, inverse discrete Fourier transform, adding cyclic prefix, parallel-to-serial conversion and other processes, and finally modulated to a high-frequency carrier through the RF link and radiated outward from the transmitting antenna. After the user end receives the signal through the time domain channel, it performs an inverse transform opposite to that of the transmitter, and finally obtains the demodulated symbol. Assume that the distance between each user and the transmitter is d k , then the path loss at the transmitting and receiving ends is expressed as Among them C 0 represents the average channel attenuation at a distance of 1 meter, and β represents the path loss exponent factor.

[0092] For user k, the time domain baseband equivalent channel model between the transceivers is modeled as a finite-length delay tap response, i.e. in represents the time domain channel response of the dth delay tap, and D represents the total number of delay taps. According to the characteristics of multi-carrier system signal transmission, the frequency domain channel response and the time domain channel response are a pair of Fourier transform pairs, so the frequency response of the channel is

[0093]

[0094] Among them, F N represents the N-dimensional discrete Fourier transform matrix, Represents the frequency domain channel response of the nth carrier. After the introduction of MA technology, the antenna can move within a certain range. The transmitting and receiving antennas establish a local Cartesian coordinate system within their respective moving ranges and set the reference point as the origin. d,k It is divided into three models and multiplied, namely the transmitter field response model, the far-field wireless channel model and the receiver field response model.

[0095]

[0096] where ∑ d,k =diag{b 1,d,k ,…,b L,d,k} represents the diagonal matrix of the far-field wireless channel between the transceiver reference points, whose diagonal elements represent the response coefficient of each transmission path, and each diagonal element has a mean of 0 and a variance of q d / L complex Gaussian random distribution. drepresents the normalized power delay spectrum, and L represents the total number of scattering paths. v =[x v ,y v ] T ,r k =[x k ,y k ] T They represent the antenna position of the vth antenna at the transmitting end and the antenna position of user k at the receiving end relative to the reference point respectively. represents the receiving end field response model, Represents the field response model matrix of the transmitting end. Since the antenna movement area is much smaller than the signal transmission distance, the transmitted and received signals are approximately plane waves. The movement of the antenna does not change the amplitude, arrival angle and departure angle of the signal, but only affects the phase of the signal. Based on the above analysis, we can get

[0097]

[0098] Where λ represents the center carrier wavelength of the entire transmission signal bandwidth, and different antenna positions affect the phase change of the signal at the transmitting and receiving ends.

[0099]

[0100] They represent the azimuth and elevation of the arrival angle and the azimuth and elevation of the departure angle of the lth scattering path for the kth user in the dth delay path, respectively. Each scattering path angle obeys a uniform distribution of [0,2π).

[0101] Based on the above analysis, the transmission rate of the MA-assisted multi-carrier space division multiplexing system can be obtained as follows:

[0102]

[0103] σ 2 represents the additive white Gaussian noise power.

[0104] An optimization method for a multi-carrier space division multiple access system based on a movable antenna:

[0105] This patent takes maximizing the system transmission rate as the optimization goal, and jointly optimizes the precoding and the position of the transmitting and receiving antennas under the premise of satisfying the given transmission power, the minimum antenna spacing and the antenna movement area. This optimization problem is recorded as The optimization mathematical model is

[0106]

[0107] Where P max represents the maximum transmission power of the system, A represents the minimum separation distance of the antenna, and represents the moving area of ​​the transmitting and receiving antennas. Since the optimization variables (W, t, r) are coupled together, The problem is a joint non-convex problem. At the same time, the non-convexity of the objective function and the constraint (6c) also increases the difficulty of solving it.

[0108] Solving the optimization problem:

[0109] This patent proposes an alternating optimization (AO) algorithm to solve non-convex problems The core idea is to use an alternating method to optimize W, t and r respectively.

[0110] Precoding Optimization

[0111] For given t and r, the problem Transformed into a fractional programming problem

[0112]

[0113] This technique considers three different linear precoding techniques, including maximum ratio transmission (MRT), zero forcing (ZF) and regularized zero forcing (RZF). but

[0114]

[0115] According to formulas (8), (9), and (10), we can get three corresponding W n,k ;

[0116] Where γ is the regularization coefficient, I K represents the K-order unit matrix; p n,k represents the power of the nth subcarrier allocated to the kth user. (5) Re-expressed as

[0117]

[0118] The above formula is a convex difference function, which is linearized using the first-order Taylor expansion of the subtrahend.

[0119]

[0120] Define the right side of the above inequality as ζ n,k ,in represents the power allocation result of the mth iteration. Therefore, after fixed linear precoding, the problem Convert to

[0121]

[0122] in Represents the power allocation vector. The final power allocation result can be obtained by multiple iterations. The objective function and constraints in the optimization problem are both convex functions, so CVX can be used to solve and obtain the final result.

[0123] Specifically, the CVX solution can refer to reference [9]:

[0124] [9] M. Grant and S. Boyd, "CVX: Matlab software for disciplinedconvexprogramming, version 2.1," https: / / cvxr.com / cvx, Mar. 2014.

[0125] Optimization of antenna position:

[0126] For a given precoding W, the antenna position optimization problem can be expressed as

[0127]

[0128] It should be noted that both the objective function and constraint (6c) are non-convex. To solve this difficulty, this patent first solves the partial derivative of the objective function for each optimization variable, and then uses the gradient ascent method to update the antenna position. Finally, the antenna position is projected onto the feasible domain of constraint (6c). Due to the non-convexity of (6c), (6c) is linearized using a first-order Taylor expansion.

[0129] make but

[0130]

[0131] in According to the chain rule,

[0132]

[0133] in Note that the vth element in the time domain channel response of user k is only related to t v and r k Therefore, the vth element only needs to be solved for t v and r k The gradient of , the gradient of other variables is zero. From the above analysis, we can get:

[0134]

[0135]

[0136] in According to the chain rule of gradients, The antenna position t can be obtained by solving (1), (16) and (5) in sequence v The gradient of is obtained, that is,

[0137]

[0138] Calculating (18), (20), (21), (22), (23), (16), (24) in sequence yields Through The same calculation steps are used to replace t in (20)-(24) v Change to r k , x v Change to x k ,y v Change to y k , and we can obtain it by calculating (19), (20), (21), (22), (23), (17), and (24) in sequence.

[0139] Therefore, the update formula for the antenna position is

[0140]

[0141] in α represents the gradient update step size, t q and r q represents the position of the transmitting and receiving antennas at the qth iteration, represents the boundary function. If the updated position exceeds the moving range, the updated position is modified to a boundary point to satisfy constraint (6d).

[0142] Alternately optimize precoding and antenna position, and assume that the transmitting antenna position when the objective function converges is When the antenna position at convergence satisfies constraint (6c), the final antenna position Otherwise, the gradient projection method is needed to solve the final antenna position. Since there is only one antenna at the receiving end, there is no constraint (6c). For the non-convexity of constraint (6c), a first-order Taylor expansion is used for linearization.

[0143]

[0144] For the convergence results obtained By solving the optimization problem The antenna position that satisfies constraint (6c) is obtained.

[0145]

[0146] The optimization objective function and constraints are both convex functions, so CVX can be used to solve and obtain the final result.

[0147] In summary, the problem solved by this patent design is The pseudo code is given below:

[0148]

[0149]

[0150] Simulation Results

[0151] According to the system parameters in Table 1, the algorithm proposed in this patent is used to perform simulation experiments. All simulation results are obtained by taking the average value after more than 1,000 independent channels. In order to verify the effectiveness of the proposed algorithm, this technology is compared with the FPA system to verify the effectiveness of antenna position optimization.

[0152] Table 1

[0153]

[0154]

[0155] Figure 2 The relationship between the system transmission rate and the transmission power is shown. It can be seen that as the transmission power increases, the transmission rate of all schemes increases accordingly. Under the same precoding, the transmission rate of the MA system is always greater than that of the FPA system, which proves the effectiveness of the algorithm proposed in this patent and shows that the MA technology can use more spatial degrees of freedom to improve the system transmission rate. In addition, when the precoding technology remains unchanged, the MA technology can further enhance the transmission rate. Therefore, under low transmission rate requirements, the MA system can reduce the complexity of the precoding design.

[0156] Figure 3 The relationship between the system transmission rate and the number of transmitting antennas is shown. In order to fully utilize the gain of space division multiple access, the number of users is always equal to the number of antennas. It can be seen that as the number of antennas increases, the transmission rate of all schemes increases accordingly, and the relationship is approximately linear. Compared with the FPA system, the transmission rate of the MA system is always faster, which proves the effectiveness of the algorithm proposed in this patent, and also shows that the MA technology can further utilize the gain brought by multiple antennas on the basis of the FPA system.

[0157] Those skilled in the art will appreciate that the embodiments described are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to the embodiments described. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A multi-carrier space division multiple access system based on a movable antenna for transmitting signals to K users; characterized in that: The transmitting end is equipped with V movable transmitting antennas, and each user's receiving end is equipped with a movable receiving antenna; the total number of subcarriers in the system is N; For the sender: The transmitted symbol transmitted to user k on subcarrier n is denoted as x n,k , where n = 1, 2, 3, ..., N; k = 1, 2, 3, ..., K; send signal x n,k The precoded vector w n,k After precoding modulation, the modulation symbol S corresponding to V movable transmitting antennas is obtained. v,n,k , v=1,2,3,……,V, K signals of different users of the same subcarrier belonging to the vth movable transmitting antenna are superimposed, and then the superimposed different subcarrier signals belonging to the vth movable transmitting antenna are subjected to inverse discrete Fourier transform, cyclic prefix addition, parallel-to-serial conversion, and finally modulated to a high-frequency carrier through a radio frequency link, and radiated outward from the vth movable transmitting antenna; For the receiver of the kth user: After the movable receiving antenna receives the signal transmitted by V movable transmitting antennas through the time domain channel, it is demodulated through the RF link, and then the cyclic prefix is ​​removed, the serial-to-parallel conversion and the Fourier transform are performed to obtain the received estimated symbol corresponding to the N subcarriers.

2. An optimization method for a multi-carrier space division multiple access system based on a movable antenna, characterized in that: Used to optimize a multi-carrier space division multiple access system based on a movable antenna as described in claim 1 to maximize the system transmission rate; specifically comprising the following steps: Step 1, initializing antenna positions of a movable transmitting antenna and a movable receiving antenna, modeling a time domain channel response between the movable transmitting antenna and the movable receiving antenna according to the antenna positions of the movable transmitting antenna and the movable receiving antenna, and thereby obtaining a corresponding frequency domain channel response; Step 2: Construct a system transmission rate formula based on the frequency domain channel response and the precoding vector, and record the system transmission rate formula as an optimization problem about the antenna positions of the movable transmitting antenna and the movable receiving antenna, and the precoding vector. Step 3: Consider the antenna positions of the movable transmitting antenna and the movable receiving antenna as fixed values ​​and solve the optimization problem Converted to an optimization problem about the precoding vector Then we will optimize the problem Converted to an optimization problem about power allocation constructing a plurality of precoding vectors according to the obtained power allocation results; Step 4: For each precoding vector, the precoding vector is considered as a constant value and the optimization problem is Transformed into an optimization problem regarding the antenna positions of the movable transmitting antenna and the movable receiving antenna Step 5: Repeat steps 2 to 4 until the problem is optimized. The calculation results of convergence are obtained, and for each precoding vector corresponding to the converged calculation results, the precoding vector corresponding to the largest converged calculation result is recorded as the final precoding vector; Step 6, determine whether the antenna positions of the movable transmitting antenna and the movable receiving antenna corresponding to the final precoding vector meet the constraints. If so, record them as the final antenna positions of the movable transmitting antenna and the movable receiving antenna, and complete the optimization of the multi-carrier space division multiple access system based on the movable antenna. Otherwise, project them into the feasible domain of the constraints, and record the projected antenna positions of the movable transmitting antenna and the movable receiving antenna as the final positions, and complete the optimization of the multi-carrier space division multiple access system based on the movable antenna.

3. The optimization method of a multi-carrier space division multiple access system based on a movable antenna according to claim 2, characterized in that: The specific method of step 1 is: Step 101: for the time domain channel between the movable receiving antenna and the movable transmitting antenna of the kth user receiving end, model it as a finite-length delay tap response H k : in represents the time domain channel response for the kth user at the dth delay tap, D represents the total number of delay taps, 1<D<N, d=1,2,…,D; Step 102: h d,k Divide into three parts and multiply them, that is, the transmitting end field response model F d,k (t), far-field wireless channel model∑ d,k and the receiving end field response model g d,k (r): ∑ d,k =diag{b 1,d,k ,b 2,d,k ,…,b L,d,k }; Where j represents the imaginary unit, L represents the total number of scattering paths, ∑ d,k The diagonal elements of represent the response coefficient of each scattering path for the kth user in the dth delay path; λ represents the central carrier wavelength of the entire transmission signal bandwidth; the movable transmitting antenna and the movable receiving antenna establish a local Cartesian coordinate system within their respective moving ranges, and set the reference point as the origin, and obtain the antenna position t of the V movable transmitting antennas v =[x v ,y v ] T , the antenna position r of the kth user's movable receiving antenna k =[x k ,y k ] T ; denote the azimuth and elevation of the arrival angle and the azimuth and elevation of the departure angle of the lth scattering path for the kth user in the dth delay path, respectively, l = 1, 2, 3, ..., L; Step 103, calculate H k The corresponding frequency domain channel response where F N represents the N-dimensional discrete Fourier transform matrix, represents the frequency domain channel response for the k-th user at the n-th subcarrier.

4. The optimization method of a multi-carrier space division multiple access system based on a movable antenna according to claim 3, characterized in that: The specific method of step 2 is: Among them, ∑ i≠k represents i=1,2,3,……,K, and i≠k; σ 2 represents the additive white Gaussian noise power; P max Indicates the maximum transmit power of the system, represents any movable transmitting antenna except the vth movable transmitting antenna, A represents the minimum spacing distance between movable transmitting antennas, and They respectively represent the moving ranges of the movable transmitting antenna and the movable receiving antenna.

5. The optimization method of a multi-carrier space division multiple access system based on a movable antenna according to claim 4, characterized in that: The specific method of step 3 is: Step 301: Optimize the problem Converted to an optimization problem about the precoding vector Step 302: Optimize the problem Converted to an optimization problem about power allocation in represents the power allocation vector; p n,k represents the power of the nth subcarrier allocated to the kth user; Step 303, using the CVX solver to solve the optimization problem Perform multiple iterations to obtain the final power allocation vector. represents the power allocation result of the mth iteration, The initial value is After the final iteration The corresponding final power allocation result p is recorded as n,k , i=1,2,3,……,K; Step 304: construct maximum ratio combining precoding vectors Zero-forcing precoding vector and the regularized zero-forcing precoding vector in, γ is the regularization coefficient; I K represents the K-order identity matrix; 6. The optimization method of a multi-carrier space division multiple access system based on a movable antenna according to claim 5, characterized in that: The specific method of step 4 is: Step 401, optimize the problem Transformed into an optimization problem regarding the antenna positions of the movable transmitting antenna and the movable receiving antenna Step 402, let w n,i =u n,i +jz n,i ; make in Step 403, according to the chain rule: in also Except All elements outside of are 0; Step 404: Update the antenna positions of the movable transmitting antenna and the movable receiving antenna: in, α represents the gradient update step size, Represents the boundary function: If the updated antenna position exceeds or If the moving range is larger than the moving range, the updated antenna position is modified to the nearest moving range boundary point.

7. The optimization method of a multi-carrier space division multiple access system based on a movable antenna according to claim 6, characterized in that: Step 6: The antenna position of the movable transmitting antenna corresponding to the final precoding vector is recorded as If it satisfies Then it is recorded as the final antenna position of the movable transmitting antenna and the movable receiving antenna, and the optimization of the multi-carrier space division multiple access system based on the movable antenna is completed; Otherwise, project it into the feasible domain of the constraint and construct the optimization problem in, express The antenna position of the vth movable transmitting antenna, express The antenna position of any movable transmitting antenna except the vth movable transmitting antenna; Use CVX solvers to solve optimization problems Perform multiple iterations to obtain the final antenna position of the movable transmitting antenna Complete the optimization of multi-carrier spatial division multiple access system based on movable antenna.

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