A near-field analog frequency division multiplexing method based on beam squint extension

Abstract

The present application belongs to the technical field of near-field wideband wireless communication, and particularly relates to a near-field analog frequency division multiplexing method based on beam oblique view extension. The method of the present application firstly models the signal model and the channel model of the near-field wideband multi-user OFDMA system, calculates the signal-to-noise ratio and the achievable rate of different users on each subcarrier, and maximizes the minimum achievable rate in all users under the single radio frequency chain hardware constraint by jointly optimizing the subcarrier allocation, the phase shifter phase, the true time delay parameter and the power allocation. The present application can utilize the parallel true time delay structure to generate frequency-dependent beam focusing, so that different subcarriers are focused to different near-field user positions, thereby overcoming the problems of beam focusing difficulty and user fairness deficiency in the single radio frequency chain near-field wideband multi-user system. The simulation results show that the proposed method can significantly improve the minimum user rate of the system, and the performance is better than that of other benchmark methods.

Description

Technical Field

[0001] This invention belongs to the field of near-field broadband wireless communication technology, specifically relating to a near-field analog frequency division multiplexing method based on beam-slant spread. Background Technology

[0002] With the development of high-frequency broadband wireless communication, the abundant spectrum resources in the high-frequency band provide important support for ultra-high-speed wireless transmission. However, high-frequency propagation suffers from severe path loss. To compensate for this path loss, base stations typically deploy large-scale or ultra-large-scale antenna arrays to form high-gain directional beams. As the array aperture increases, users are more likely to be located in the near-field region based on spherical wave propagation. In this case, the array response vector depends on both the user's angle and distance. Traditional far-field plane wave assumptions and angle-based beamforming methods are insufficient to accurately serve the actual user location.

[0003] In broadband systems, large bandwidth can cause a non-negligible beamsight effect, causing beamforming gain to deviate from the desired direction and leading to a degradation in system performance. Existing technologies typically consider beamsight as a detrimental factor and compensate for or suppress it through Full True-Time-Delay (Full-TTD) structures, Delay-Phase Precoding (DPP) structures, sub-connected true-time-delay structures, or other hybrid beamforming architectures.

[0004] However, in Orthogonal Frequency Division Multiple Access (OFDMA) multi-user systems, different subcarriers can be assigned to different users, and beam squint effects can cause different subcarriers to form different beam directions or focusing positions. Therefore, the frequency-dependent beam variations caused by beam squint can be combined with subcarrier allocation, allowing different subcarriers to serve users in different spatial locations, thus achieving multi-user access under limited hardware resources. Existing beam squint-based schemes are mostly based on True-Time-Delay (TDD) structures, primarily targeting far-field angular coverage, and struggle to accurately match near-field user locations determined by both angle and distance. Furthermore, existing schemes focus more on coverage and system efficiency improvements, while neglecting multi-user fairness. Therefore, there is an urgent need for a beamforming method suitable for near-field broadband OFDMA multi-user systems that actively utilizes beam squint effects under single-radio frequency (RF) chain hardware constraints to achieve fair transmission for multiple near-field users. Summary of the Invention

[0005] To address the issues in existing near-field broadband multi-user communication systems where beam squint is generally considered a detrimental effect and is compensated for or suppressed, existing beam squint utilization schemes primarily target far-field angle coverage and are ill-suited to near-field angle-range coupling characteristics, and the insufficient fair transmission performance for multi-users under single-RF-chain hardware constraints, this invention provides a near-field analog frequency division multiplexing method based on a parallel true-delay structure and beam squint extension. This invention actively utilizes the frequency-dependent beam variations generated by different subcarriers in the broadband system, jointly optimizing subcarrier allocation, phase shifter phase, true-delay parameters, and power allocation. This allows different subcarriers to form beam-focusing patterns pointing towards different near-field user locations, thereby improving the minimum achievable rate of the multi-user system under a single-RF-chain hardware architecture.

[0006] The technical solution adopted in this invention is:

[0007] A near-field analog frequency division multiplexing method based on beam-slant spread is proposed, defining the system as including a base station and For a single-antenna user, the base station is configured with one radio frequency chain and... The base station employs a parallel, true-delay-assisted analog beamforming architecture, with each antenna branch connected to a true delay unit and a phase shifter. The signals from each antenna branch are delayed by a true time delay device. Then the phase is applied by the phase shifter. After transmission to the user, a spherical wave near-field channel model is used to describe the propagation channel between the base station and the user. The goal is to maximize the minimum reachable rate among all users, and the subcarrier allocation variables are jointly optimized. Power allocation variables Phase shifter vector Sum of true delay vectors The following optimization problem is established:

[0008] ,

[0009] in, For the first The achievable rate for each user; for The definition is that when the first The subcarrier is assigned to the first When there are individual users, ;otherwise, ; It is the first The user in the first Received signal-to-noise ratio on each subcarrier; For the first The subcarrier allocated to the first Transmit power of each user; For the first The base station on each subcarrier Channel vectors for each user; For the first Structured analog beamforming vectors on each subcarrier; For the first The frequency-dependent true delay response vectors corresponding to each subcarrier; For the first The frequency of each subcarrier; This is the true time delay vector; Represents the Hadamard product; For the first Additive white Gaussian noise power at each user location; This is the maximum delay supported by the true delay unit. It is the phase shifter vector The first in One element; It is the number of subcarriers; This represents the maximum transmit power of the base station.

[0010] By solving the optimization problem, the subcarrier allocation matrix, structured analog beamforming vector, and optimal power allocation method are obtained. Based on the obtained parameters, the base station is configured to realize near-field analog frequency division multiplexing based on beam look-out spread.

[0011] Furthermore, the specific solution method for the optimization problem is a two-stage optimization solution method:

[0012] The first phase involves jointly optimizing subcarrier allocation and structured analog beamforming under equal power substitution conditions, including:

[0013] Based on the angle range of the target user region and distance range Mapping the target region to the near-field parameter domain yields the following boundary parameters:

[0014] ,

[0015] ;

[0016] set up , The subscript 'm' in 'min' and 'max' indicates the minimum or maximum value 'm' among the values ​​from 1 to M, used to select initialization parameters. The beams at both ends of the frequency band are roughly aligned with the boundary of the target user area, thus satisfying the requirement that...

[0017] ,

[0018] ;

[0019] The initial true delay vector is obtained as follows:

[0020] ,

[0021] in, Antenna spacing, The speed of light;

[0022] The initial phase shifter vector is determined by the center frequency. The following correspondence Near-field array response phase generation:

[0023] ,

[0024] in, It is the array response function;

[0025] The current structured analog beamforming vector is obtained from the true time delay vector and the phase shifter vector. Then, equal power replacement is used, setting the power on each allocated subcarrier to... , No. The subcarrier is assigned to the first The rate metric for a single user is:

[0026] ;

[0027] Get the first The equal power substitution rate for each user is:

[0028] ;

[0029] To maximize the minimum cumulative rate among all users To achieve this, we establish the subcarrier allocation problem:

[0030] ;

[0031] binary variables Relaxation as a continuous variable Solve the relaxed convex optimization problem to obtain a continuously relaxed solution. Then, based on the rate metric matrix Constructing the Refined Metric Matrix :

[0032] ;

[0033] Binary refinement is performed based on the maximum-minimum fairness principle. Specifically, each time, the user with the smallest current cumulative utility is selected, and then the subcarrier with the largest refinement metric for that user is selected from the unallocated subcarriers and allocated. This process is repeated until all subcarriers are allocated, resulting in a binary subcarrier allocation matrix that satisfies the exclusive constraint.

[0034] After fixing the subcarrier allocation matrix, define the first... The nth subcarrier is allocated to the first For each user, an ideal phase-type beamforming vector is constructed for that subcarrier:

[0035] ;

[0036] Projecting the ideal phase-type beamforming vector onto a hardware-realizable set consisting of phase shifters and true time-delay units, we establish the following projection optimization problem:

[0037] ;

[0038] After expanding the objective function and removing the constant term, the projection optimization problem is equivalent to:

[0039] ,

[0040] in For a fixed true time delay vector, the phase shifter vector has a closed-form update:

[0041] ;

[0042] For a fixed phase shifter vector, the first... The true delay update of each antenna branch is transformed into an interval One-dimensional search problem on:

[0043] ,

[0044] in, For inclusion A search set of grid points is obtained; by alternately updating the phase shifter vector and the true time delay vector until the projection optimization process converges, a simulated beamforming vector satisfying the parallel true time delay structure is obtained. ;

[0045] The second stage involves the subcarrier allocation matrix obtained in the first stage. and structured analog beamforming vector After fixing, power allocation is performed, the first... The achievable rate for each user is:

[0046] ,

[0047] The corresponding maximum-minimum fair power allocation problem is:

[0048] ,

[0049] in The introduced auxiliary variable represents the minimum common user rate that the system can guarantee, i.e., the lower bound of the rate achievable by all users. This problem is a convex optimization problem, which is solved by performing a binary search on the common rate and combining it with the reverse water injection method to obtain the optimal or near-optimal power allocation result.

[0050] The beneficial effects of this invention are as follows: The near-field broadband OFDMA multi-user fair beamforming method and system proposed in this invention, based on parallel true time delay structure and beam squint effect, can transform beam squint in broadband systems from a traditional harmful effect into a usable frequency-dependent beam focusing capability, enabling different subcarriers to be focused on different near-field user spatial locations; it can serve multiple spatially distributed users under single-RF chain hardware constraints, reducing the number of RF chains and hardware complexity; it can simultaneously consider the angle and distance information of near-field users, overcoming the problem that far-field angle coverage methods are difficult to adapt to near-field scenarios; and it can improve the minimum reachable rate of all users in the system and improve multi-user fairness by jointly optimizing subcarrier allocation, simulating beamforming, and power allocation. Attached Figure Description

[0051] Figure 1 A schematic diagram of a beamforming structure based on parallel TTD considered for the present invention.

[0052] Figure 2 In order to be in m、 dB and A comparative schematic diagram of polar coordinate beam patterns under the given conditions, wherein (a) is the beam pattern of the method proposed in this invention, (b) is the beam pattern of the method using only phase shifters, (c) is the beam pattern of the CFB method, and (d) is the beam pattern of the THzPrism method.

[0053] Figure 3 For when The diagram shows the curve of the system's minimum rate as a function of the signal-to-noise ratio.

[0054] Figure 4 For when At dB, the system minimum rate varies with the number of users. A schematic diagram of the changing curve. Detailed Implementation

[0055] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings and simulation examples.

[0056] This invention is applicable to parallel true-delay assisted near-field broadband OFDMA multi-user downlink systems. The base station is configured with one radio frequency chain and... A uniform linear array composed of antenna elements is used to serve Single-antenna user. Total system bandwidth. Classified as The subcarrier, the The frequency of each subcarrier is

[0057]

[0058] The base station employs a parallel true-delay-assisted analog beamforming architecture. Each phase shifter applies a frequency-independent phase. , No. Each true delay unit applies a delay. Therefore, the first The structured analog beamforming vectors on each subcarrier are

[0059]

[0060] in

[0061] set up Represents the subcarrier allocation variable, when the... The subcarrier is assigned to the first When there are individual users, ;otherwise, Each subcarrier is allocated to only one user, i.e.

[0062]

[0063] No. The transmitted signal on each subcarrier can be represented as

[0064]

[0065] in, For transmission power, To send to the Data symbols for each user. The user in the first The received signal on each subcarrier is

[0066]

[0067] in, It is additive white Gaussian noise. Since each subcarrier is allocated to only one user, there is no multi-user interference on the same subcarrier. The user in the first The received signal-to-noise ratio on each subcarrier is

[0068]

[0069] No. The achievable rate for each user is

[0070]

[0071] In near-field scenarios, the array response depends not only on the user's angle but also on the user's distance. For arrays located in polar coordinates... The user or scattering point at the location, the first The distance from each antenna element to that location is

[0072]

[0073] Under the second-order Taylor approximation, we have

[0074]

[0075] Therefore, the near-field array response can be approximated as:

[0076]

[0077] Base station to the The user in the first The channel on each subcarrier can be modeled as follows:

[0078]

[0079] in, Rice factor, The total number of paths, and The first The complex gain and propagation delay of each path, Indicates the line-of-sight path.

[0080] This invention aims to maximize the minimum reachable rate for all users by jointly optimizing subcarrier allocation, power allocation, phase shifter phase, and true delay parameters, establishing the following optimization problem:

[0081]

[0082] Because the above problem simultaneously involves binary subcarrier allocation variables, constant-mode phase shifter constraints, true delay range constraints, and power constraints, and the phase shifter vector... With true time delay vector pass Because the components are mutually coupled, this problem is a mixed-integer non-convex optimization problem, which is difficult to solve directly. This invention employs a two-stage optimization method to solve it.

[0083] The first phase involves jointly optimizing subcarrier allocation and structured simulated beamforming under equal power substitution conditions. Firstly, based on the angular range of the target user area... and distance range Map the target region to the near-field parameter domain:

[0084]

[0085]

[0086] set up , Select initialization parameters. This ensures that the beams at both ends of the frequency band are roughly aligned with the boundary of the target user area, thus satisfying the requirement that...

[0087]

[0088]

[0089] Therefore, the true delay vector is initialized as follows:

[0090]

[0091] The initial phase shifter vector is determined by the center frequency. The following correspondence Near-field array response phase generation:

[0092]

[0093] Given the current structured simulation beamforming vector Then, equal power replacement is used, setting the power on each allocated subcarrier to... . No. The subcarrier is assigned to the first The rate metric for a single user is:

[0094]

[0095] Therefore, the first The equal power substitution rate for each user is:

[0096]

[0097] This invention addresses the subcarrier allocation problem by aiming to maximize the minimum cumulative rate among all users:

[0098]

[0099] To reduce the solution complexity, binary variables are... Relaxation as a continuous variable Solve the relaxed convex optimization problem to obtain a continuously relaxed solution. Then, based on the rate metric matrix... Construct the refined metric matrix:

[0100]

[0101] Binary refinement is performed based on the maximum-minimum fairness principle. Specifically, each time, the user with the smallest current cumulative utility is selected, and then the subcarrier with the largest refinement metric for that user is selected from the unallocated subcarriers for allocation. This process is repeated until all subcarriers are allocated, resulting in a binary subcarrier allocation matrix that satisfies the exclusive constraint.

[0102] After fixing the subcarrier allocation matrix, let the first... The nth subcarrier is allocated to the first For each user, an ideal phase-type beamforming vector is constructed for that subcarrier:

[0103]

[0104] This ideal beamforming vector can phase-align the target user channel, but it typically does not satisfy the requirements of a parallel true-delay hardware architecture. Therefore, this invention projects the ideal phase-type beamforming vector onto a hardware-realizable set consisting of phase shifters and true-delay units, establishing the following projection optimization problem:

[0105]

[0106] After expanding the objective function and removing the constant term, the above problem is equivalent to:

[0107]

[0108] in For a fixed true time delay vector, the phase shifter vector has a closed-form update:

[0109]

[0110] For a fixed phase shifter vector, the first The true delay update of each antenna branch can be transformed into an interval One-dimensional search problem on:

[0111]

[0112] in, For inclusion A search set of grid points is obtained. By alternately updating the phase shifter vector and the true time delay vector until the projection optimization process converges, a simulated beamforming vector that satisfies the parallel true time delay structure is obtained.

[0113] The second stage involves the subcarrier allocation matrix obtained in the first stage. and structured analog beamforming vector After fixing, power allocation is performed. At this time, the [number]th [unit]... The achievable rate for each user is:

[0114]

[0115] The corresponding maximum-minimum fair power allocation problem is:

[0116]

[0117] This problem is a convex optimization problem, which can be solved by performing a binary search on the common rate and combining it with the reverse water injection method to obtain the optimal or near-optimal power allocation result.

[0118] To verify the effectiveness of the proposed near-field broadband OFDMA multi-user fair beamforming method based on parallel true time delay structure and beam squint effect, numerical simulation experiments were conducted. Unless otherwise specified, the base station adopts a structure composed of... A uniform linear array composed of antenna elements, and served by a single radio frequency chain. Single-antenna user. The number of system subcarriers is set to... The center carrier frequency is set to The total system bandwidth is set to Maximum true delay is set to The maximum transmit power of the base station is normalized to Each user's propagation channel contains Path, Rice factor set to .

[0119] This simulation considers a near-field multi-user communication scenario, where users are randomly distributed within an angular range. and distance range Inside. Let the array aperture be... ,in , Under the above parameters, the corresponding Fresnel distance and Rayleigh distance of the system are respectively

[0120] Because the user's distance range is located and Therefore, this simulation scenario belongs to a typical near-field communication region, where the user channel depends not only on the angle but also on the distance. In the simulation, the signal-to-noise ratio is defined as...

[0121]

[0122] in This indicates that the noise power is the same at all user locations.

[0123] To illustrate the performance advantages of this invention, three typical schemes are selected as comparison methods. The first is a scheme that uses only phase shifters, denoted as the PS-only scheme. In this scheme, all true delay units are turned off, i.e., ... The remaining subcarrier allocation and power allocation processes remain unchanged. The second type is the center-focused beamforming scheme, denoted as the CFB scheme, which fixes the beam to the center of the user area in the angle-range domain. The third type is the THzPrism scheme, which uses a serial true delay-assisted beamforming structure. The direction of the center beam is determined by a phase shifter, and a frequency-dependent angle spread is introduced by a true delay unit to cover the target user's angular region.

[0124] Figure 2 It shows the distance Signal-to-noise ratio Number of users Under the given conditions, near-field polar coordinate beam patterns obtained by different methods are shown. The angles of the four users are... Uniformly distributed within the range. (By) Figure 2 As can be seen from (a) in the figure, the method proposed in this invention can utilize the frequency-dependent beam variations on different subcarriers to focus beam energy onto the near-field angle-range positions of different users, thereby forming multiple precisely focused beams oriented towards the users. In this simulation example, the minimum user rate corresponding to the method proposed in this invention reaches This demonstrates better multi-user fairness. In contrast, the PS-only scheme, lacking the frequency-dependent phase modulation capability generated by the true delay unit, results in significant overlap of multiple beam peaks, making it difficult to effectively distinguish between different users; the CFB scheme mainly concentrates beam energy at the center of the user area, making it difficult to simultaneously accommodate multiple users distributed at different angles and distances; while the THzPrism scheme can form a certain degree of frequency-dependent beam splitting, it mainly focuses on far-field angle coverage and does not consider changes in the near-field distance dimension, thus making it difficult for beams of different frequency components to accurately match the near-field spatial positions of actual users.

[0125] Figure 3 This shows when the number of users is Simulation results showing the minimum achievable rate of the system as a function of the signal-to-noise ratio. It can be seen that as... As the signal-to-noise ratio (SNR) increases, the minimum achievable rate of each scheme shows an upward trend. Compared with the comparative schemes, the method proposed in this invention achieves the highest minimum user rate across the entire SNR range, with a more significant performance advantage in the high SNR region. This is because this invention, through joint optimization of subcarrier allocation, phase shifter phase, true delay parameters, and power allocation, can transform the beam-squinting effect of different subcarriers into usable frequency-dependent near-field focusing capabilities, thereby enabling different users to obtain higher effective array gain on their allocated subcarriers. The CFB scheme, due to its fixed beam focusing position, is difficult to adapt to the spatial distribution of multiple users, thus exhibiting the lowest performance. Although the PS-only scheme and the THzPrism scheme can achieve certain beamforming gains, their minimum rates are still lower than the method proposed in this invention because they fail to fully utilize the near-field angle-range coupling characteristics.

[0126] Figure 4 It shows in Under these conditions, the minimum achievable rate of the system varies with the number of users. Simulation results show that as the number of users increases, limited subcarrier and power resources need to be shared among more users, thus reducing the minimum achievable rate for all schemes. However, the method proposed in this invention consistently maintains the highest minimum user rate under different user numbers, demonstrating its ability to maintain good maximum-minimum fairness performance even with increased system load. This is because this invention not only avoids multi-user interference on the same subcarrier through OFDMA, but also actively regulates the near-field focusing direction of different subcarriers through a parallel true-delay structure, enabling each subcarrier to more effectively serve users in different spatial locations. In contrast, the CFB scheme struggles to adapt to changes in spatial distribution due to an increase in the number of users, the PS-only scheme is limited by a frequency-independent phase shifter structure, and the THzPrism scheme primarily achieves angular domain coverage rather than near-field angle-range joint focusing; therefore, all three are inferior to the method proposed in this invention in terms of multi-user fair transmission performance.

[0127] In summary, simulation results demonstrate that the proposed near-field broadband OFDMA multi-user fair beamforming method can fully utilize the beam squint effect in broadband systems under the constraints of a single radio chain and parallel true delay hardware, achieving spatial focusing of different subcarriers on different near-field users. Compared with methods using only phase shifters, CFB methods, and THzPrism methods, this invention has significant advantages in beam focusing accuracy, minimum user rate, and multi-user fairness, verifying the effectiveness and practicality of the proposed method in near-field broadband multi-user communication systems.

Claims

1. A near-field analog frequency division multiplexing method based on beamout spread, defining the system as including a base station and A single-antenna user, characterized in that... The base station is configured with a radio frequency chain and by The base station employs a parallel, true-delay-assisted analog beamforming architecture, with each antenna branch connected to a true delay unit and a phase shifter. The signals from each antenna branch are delayed by a true time delay device. Then the phase is applied by the phase shifter. After transmission to the user, a spherical wave near-field channel model is used to describe the propagation channel between the base station and the user. The goal is to maximize the minimum reachable rate among all users, and the subcarrier allocation variables are jointly optimized. Power allocation variables Phase shifter vector Sum of true delay vectors The following optimization problem is established: ， in, For the first The achievable rate for each user; for The definition is that when the first The subcarrier is assigned to the first When there are individual users, ;otherwise, ; It is the first The user in the first Received signal-to-noise ratio on each subcarrier; For the first The subcarrier allocated to the first Transmit power of each user; For the first The base station on each subcarrier Channel vectors for each user; For the first Structured analog beamforming vectors on each subcarrier; For the first The frequency-dependent true delay response vectors corresponding to each subcarrier; For the first The frequency of each subcarrier; This is the true time delay vector; Represents the Hadamard product; For the first Additive white Gaussian noise power at each user location; This is the maximum delay supported by the true delay unit. It is the phase shifter vector The first in One element; It is the number of subcarriers; This represents the maximum transmit power of the base station. By solving the optimization problem, the subcarrier allocation matrix, structured analog beamforming vector, and optimal power allocation method are obtained. Based on the obtained parameters, the base station is configured to realize near-field analog frequency division multiplexing based on beam look-out spread.

2. The near-field analog frequency division multiplexing method based on beam-slant spread according to claim 1, characterized in that, The specific solution method for the optimization problem is a two-stage optimization solution method: The first phase involves jointly optimizing subcarrier allocation and structured analog beamforming under equal power substitution conditions, including: Based on the angle range of the target user region and distance range Mapping the target region to the near-field parameter domain yields the following boundary parameters: ， ； set up , Select initialization parameters The beams at both ends of the frequency band are roughly aligned with the boundary of the target user area, thus satisfying the requirement that... ， ； The initial true delay vector is obtained as follows: ， in, Antenna spacing, The speed of light; The initial phase shifter vector is determined by the center frequency. The following correspondence Near-field array response phase generation: ， in, It is the array response function; The current structured analog beamforming vector is obtained from the true time delay vector and the phase shifter vector. Then, equal power replacement is used, setting the power on each allocated subcarrier to... , No. The subcarrier is assigned to the first The rate metric for a single user is: ； Get the first The equal power substitution rate for each user is: ； To maximize the minimum cumulative rate among all users To achieve this, we establish the subcarrier allocation problem: ； binary variables Relaxation as a continuous variable Solve the relaxed convex optimization problem to obtain a continuously relaxed solution. Then, based on the rate metric matrix Constructing the Refined Metric Matrix : ； Binary refinement is performed based on the maximum-minimum fairness principle. Specifically, each time, the user with the smallest current cumulative utility is selected, and then the subcarrier with the largest refinement metric for that user is selected from the unallocated subcarriers and allocated. This process is repeated until all subcarriers are allocated, resulting in a binary subcarrier allocation matrix that satisfies the exclusive constraint. After fixing the subcarrier allocation matrix, define the first... The nth subcarrier is allocated to the first For each user, an ideal phase-type beamforming vector is constructed for that subcarrier: ； Projecting the ideal phase-type beamforming vector onto a hardware-realizable set consisting of phase shifters and true time-delay units, we establish the following projection optimization problem: ； After expanding the objective function and removing the constant term, the projection optimization problem is equivalent to: ， in For a fixed true time delay vector, the phase shifter vector has a closed-form update: ； For a fixed phase shifter vector, the first... The true delay update of each antenna branch is transformed into an interval One-dimensional search problem on: ， in, For inclusion A search set of grid points is obtained; by alternately updating the phase shifter vector and the true time delay vector until the projection optimization process converges, a simulated beamforming vector satisfying the parallel true time delay structure is obtained. ; The second stage involves the subcarrier allocation matrix obtained in the first stage. and structured analog beamforming vectors After fixing, power allocation is performed, the first... The achievable rate for each user is: ， The corresponding maximum-minimum fair power allocation problem is: ， in The introduced auxiliary variable represents the minimum common user rate that the system can guarantee, i.e., the lower bound of the rate that all users can reach. This problem is a convex optimization problem, which is solved by performing a binary search on the common rate and combining it with the reverse water injection method to obtain the optimal or near-optimal power allocation result.

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