A beamforming method for cell-free massive MIMO

Abstract

This invention belongs to the field of wireless communication technology, specifically relating to a beamforming method for cellless massive MIMO. The invention proposes a cascaded maximum-minimum user-access point association and beamforming method, decomposing the problem into an association stage and a beamforming stage. In the association stage, the maximum-minimum user-access point association is solved to obtain a user-access point association scheme that satisfies backhaul constraints. In the beamforming stage, the maximum-minimum beamforming problem is solved under a fixed association scheme to maximize the minimum user rate. A precise penalty function method is proposed, unifying the two stages within a binary threshold search and feasibility determination paradigm, transforming the feasibility determination problem into an unconstrained optimization problem. Finally, to avoid complex parameter tuning issues, an adaptive gradient descent algorithm is introduced to solve the unconstrained optimization problem. This invention significantly reduces complexity and enhances engineering implementability.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and specifically relates to a beamforming method for cellless massive MIMO. Background Technology

[0002] Cellular-free massive MIMO provides services to users through the collaborative efforts of multiple distributed access points, which can significantly improve coverage and macro diversity gain. However, in actual deployments, the backhaul link capacity between the CPU and each access point is limited, which restricts the number of users that each access point can serve simultaneously; at the same time, the sharing of time-frequency resources by multiple users can introduce serious interference, requiring sophisticated beamforming design.

[0003] Existing technologies, when allocating users to distributed access points and performing collaborative precoding, often result in an NP-hard problem involving combinatorial constraints and non-convex rate constraints if binary correlation variables and continuous beam variables are directly jointly optimized. This leads to high solution complexity and is not conducive to large-scale system engineering implementation. If heuristic strong channel-priority correlation is used followed by beamforming, it easily sacrifices the user experience at the edge, making it difficult to improve the performance of the worst-performing user. Therefore, a low-complexity optimization method that simultaneously balances fairness and feasibility is urgently needed. Summary of the Invention

[0004] This invention relates to a cooperative downlink transmission optimization technique for cell-free massive multiple-input multiple-output (CMIMO) systems under backhaul capacity constraints. This method maximizes the reachability rate of the worst-performing user in the system, achieving max-min fairness, while satisfying the constraints of the number of users that can be served per access point and the transmit power of each access point.

[0005] To achieve the above objectives, this invention proposes a cascaded maximum-minimum user-access point association and beamforming method, decomposing the problem into an association stage and a beamforming stage. In the association stage, the maximum-minimum user-access point association is solved to obtain a user-access point association scheme that satisfies the backhaul constraint. In the beamforming stage, the maximum-minimum beamforming problem is solved under a fixed association scheme to maximize the minimum user rate. A precise penalty function method is proposed, unifying the two stages within a binary threshold search and feasibility determination paradigm, transforming the feasibility determination problem into an unconstrained optimization problem. Finally, to avoid complex parameter tuning issues, an adaptive gradient descent algorithm is introduced to solve the unconstrained optimization problem.

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

[0007] A beamforming method for cell-free massive MIMO, wherein cell-free massive MIMO includes a CPU, One access point and The number of single-antenna users, the first Access point configuration Each antenna can serve a maximum of [number] users simultaneously. Each user, with a transmit power of no more than [number] access points. The method includes:

[0008] Constructing the channel energy matrix , The element is defined as ,in The number obtained by the CPU The access point to the first Given the channel vectors of individual users, establish a maximum and minimum user-access point association model, i.e., construct an optimization problem with the objective of maximizing the cumulative energy of the minimum user:

[0009] ,

[0010] in, and They are respectively and The List, It is determined by the associated indicator variable The matrix formed , Indicates the first The first access point service One user;

[0011] Will Relaxation as a continuous variable The relaxed convex optimization problem is obtained as follows:

[0012] ,

[0013] For convex optimization problems, binary search is used to transform the problem into a threshold feasibility determination problem, thereby obtaining a relaxed correlation solution. ;

[0014] Through constraint-compatible discretization mapping, Under the condition of satisfying the constraint on the number of users served by each access point, it is mapped to a binary incidence matrix. ;

[0015] Get and fix Then, optimize the precoding vectors for each user at each access point. The goal is to maximize the minimum user rate while satisfying the power constraint per access point:

[0016] ,

[0017] in, , It is the first The achievable rate for each user yes Elements in;

[0018] Set rate threshold A binary search is then performed to transform the power constraint into a feasibility determination:

[0019] ,

[0020] Determine if it exists make And satisfying the power constraint, after the binary search terminates, the maximum feasible threshold is output as the maximum and minimum rates, and the corresponding... It is restored to a complex domain beam.

[0021] Furthermore, we obtain the relaxed correlation solution. The specific method is:

[0022] For any threshold The relaxed convex optimization problem is transformed into the following threshold feasibility determination problem:

[0023] ,

[0024] The feasibility determination is transformed into a problem of minimizing an exact penalty function based on the projected distance, and the exact penalty function is defined. :

[0025] ,

[0026] ,

[0027] ,

[0028] ,

[0029] in, Indicates the first The simplex set corresponding to the service capacity constraints of each access point This represents the set of constraints for the related variables. Indicates by constraints Defined set of half-spaces;

[0030] Differentiable, gradient is:

[0031] ,

[0032] Solve using gradient descent method Set search precision Given a threshold search interval Initialize the number of iterations In the In the next iteration, the threshold is taken. Determine if an association matrix exists. satisfy The update formula for gradient descent is:

[0033] ,

[0034] Adaptive step size:

[0035] ,

[0036] When reached or Stop iteration when the iteration terminates; if the penalty function value satisfies the condition after the iteration terminates. Then determine the threshold. Feasible, and make To increase the threshold; if the maximum number of iterations is reached. Still Then determine the threshold. Not feasible, and order To lower the threshold; repeat the iteration until the termination condition is met. We obtain the relaxed correlation solution. , The tolerance set.

[0037] Furthermore, to make Under the condition of satisfying the constraint on the number of users served by each access point, it is mapped to a binary incidence matrix. The specific method is:

[0038] Constructing a matrix ,in For Hadamard product, elements in This indicates that, under the meaning of satisfying maximum and minimum fairness, the th The access point should be preferentially allocated to the first one. The urgency level of each user is considered, and allocation is iteratively assigned based on the principle of prioritizing the least urgent users; specifically:

[0039] Initialize the cumulative allocation vector Binary association Correlation rating matrix ;

[0040] When there are access points that are not yet fully loaded, that is, when there are access points... Its allocated user count Perform a loop iteration:

[0041] from Select the user index with the smallest current cumulative allocation. ;

[0042] Select to make Largest access point index ;

[0043] Place And update the accumulated energy: ;

[0044] Place To avoid making duplicate selections;

[0045] If the first The action already exists If there are 1s, then the row will be... When the number of users assigned to a certain access point reaches When this occurs, it should be prohibited from being selected in subsequent iterations;

[0046] The iteration terminates when all access points reach the service user count constraint, resulting in a binary incidence matrix. .

[0047] Furthermore, determine whether it exists. make And the specific method to satisfy the power constraint is:

[0048] Will Equivalent rewriting to SOC constraints, including user The joint precoding vector is stacked with the equivalent channel vector:

[0049] ,

[0050] ,

[0051] get:

[0052] ,

[0053] in, It is the first The noise variance of an individual user, written in standard SOC form, is as follows:

[0054] ,

[0055] ,

[0056] in, It is the first The equivalent linear constraint matrix constructed from the channel vectors of each user. It is the system's joint transmit beamforming vector. It is the first Noise and interference items for individual users It is the user's received signal. It is a user's data symbol, defined as:

[0057] ,

[0058] Feasibility is determined using an exact penalty function and then solved using adaptive gradient descent for a given condition. Construct an exact penalty function :

[0059] ,

[0060] ,

[0061] ,

[0062] Differentiable, gradient is:

[0063] ,

[0064] The update formula for gradient descent is: Adaptive step size is When it reaches or Stop iterating when the threshold is reached, and give the threshold accordingly. The feasibility conclusions were obtained, and then the maximum and minimum rates and beam vectors were derived. When the iteration terminates, if the penalty function value satisfies Then determine the threshold. Feasible, and make To increase the threshold; if the maximum number of iterations is reached. Still Then determine the threshold. Not feasible, and order To lower the threshold; repeat the iteration until the termination condition is met. The maximum and minimum rates and beam vectors are obtained. , The tolerance set.

[0065] The beneficial effects of this invention are as follows: compared with the prior art, this invention can strictly control the number of users served and the power output of each access point under the condition of limited backhaul, while improving system performance with the maximum and minimum criteria; the structure of cascading and unified feasibility judgment avoids directly solving the combinatorial nonconvex problem, significantly reducing complexity and enhancing engineering feasibility; the adaptive gradient descent method is introduced to solve the constructed unconstrained optimization problem, achieving high solution efficiency without the need for manual parameter tuning. Attached Figure Description

[0066] Figure 1 A diagram showing the comparison of maximum and minimum reachable speeds for different numbers of users;

[0067] Figure 2 A diagram showing the comparison of maximum and minimum achievable rates for different numbers of antennas per access point;

[0068] Figure 3 A schematic diagram comparing the maximum and minimum achievable rates at different transmit powers for each access point;

[0069] Figure 4 This is a schematic diagram illustrating the convergence of the feasible threshold over time during the binary search process. Detailed Implementation

[0070] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings:

[0071] This invention considers a Multiple-Input Multiple-Output (MIMO) communication system, which is... , Access points and The user consists of a single antenna, the first Access point configuration Root antenna. The first The received signal for a user can be represented as:

[0072] (1)

[0073] in For the first Data symbols for each user, It is noise. For the first The access point to the first Channel vectors for each user For the first The access point to the first Precoded vectors for each user For the correlation indicator variable, Indicates the first The first access point service One user.

[0074] No. The reachable rate for a user is defined as:

[0075] (2)

[0076] in:

[0077] (3)

[0078] Backhaul limitation is reflected in the maximum number of simultaneous services per access point. Each user, and the transmit power of each access point cannot exceed [number] users; Therefore, the system should satisfy the following constraints:

[0079] (4)

[0080] Under this constraint, solve directly The joint optimization includes binary variables and non-convex rate constraints, for Difficult problems make it hard to guarantee the quality of solutions.

[0081] To address the above problems, this invention proposes a two-stage solution method.

[0082] Phase 1: Association of Maximum and Minimum Users and Access Points

[0083] Constructing the channel energy matrix Its elements are defined as Based on this, a maximum and minimum user-access point association model is established to maximize the cumulative service quality of the minimum user while ensuring that the number of users served by each access point does not exceed a certain limit. The problem is structured as follows:

[0084] (5)

[0085] in and They are respectively and The List.

[0086] Binary association variables Relaxation as a continuous variable The problem is convex.

[0087] (6)

[0088] The following section will introduce a low-complexity algorithm for solving the above problem, obtaining the relaxed optimal solution. Later, through constraint-compatible discretization mapping, we can... Under the condition of satisfying the constraint on the number of users served by each access point, it is mapped to a binary incidence matrix. .

[0089] Phase 2: Fixed-association maximum and minimum beamforming.

[0090] Fixed first stage output Then, solve:

[0091] (7)

[0092] in Let the constraint set be defined as follows: .

[0093] To unify the solution of the maximum / minimum and convex constraint structures corresponding to (6) and (7), the user-access point association problem and beam waveform of this invention are both abstracted into the following general form problem:

[0094] (8)

[0095] To solve the maximum-minimum problem shown in equation (8), this invention adopts a binary search approach, which is equivalent to transforming it into solving a problem with a given threshold. The feasibility determination problem. For any threshold The following feasibility assessment is constructed:

[0096] (9)

[0097] Furthermore, the feasibility determination is transformed into a problem of minimizing an exact penalty function based on the projected distance, where the penalty function is defined as:

[0098] (10)

[0099] in This represents the projection operator. During the association phase, Indicates the first The simplex set corresponding to the service capacity constraints of each access point, i.e. ; The set of constraints representing the related variables, i.e. , Indicates by constraints A defined set of half-spaces. During the beamforming stage, Indicates the first The set of power constraints for each access point, i.e. , Indicates a rate threshold constraint The second-order cone set obtained through equivalent transformation.

[0100] By minimizing And determine whether its minimum value is not greater than a preset threshold. This enables rapid feasibility assessment, and iterative processing is performed using an adaptive gradient descent method.

[0101] (11)

[0102] When the iteration terminates, if the penalty function value satisfies Then determine the threshold. Feasible, and make To increase the threshold; if the maximum number of iterations is reached. Still Then determine the threshold. Not feasible, and order To lower the threshold, repeat the iteration until the termination condition is met. The solution is obtained. . The tolerance set.

[0103] This invention addresses the problem of user-access point association and beamforming in cell-free massive MIMO systems with limited backhaul, considering multiple-input multiple-output (MIMO) communication systems. , Access points and The user consists of a single antenna, the first Access point configuration Root antenna. The first The access point and the first The channel between users is Assuming this is known. The backhaul limit requires each access point to serve a maximum of [number missing]. For each user, the transmit power of each access point cannot exceed [number]. Therefore, the downlink system targeted by this invention satisfies:

[0104] (12)

[0105] Step S1: Parameter Initialization and Channel Acquisition. Set system parameters. Maximum number of users that each access point can serve simultaneously , No. Power limit of each access point , No. noise variance of individual users Binary search accuracy Feasibility assessment threshold and the maximum number of gradient iterations CPU obtains .

[0106] After obtaining the system parameters and channel information, calculate the channel energy matrix. : And with the objective of maximizing the minimum cumulative energy of users, the following optimization problem is constructed:

[0107] (13)

[0108] in and They are respectively and The List.

[0109] Binary association variables Relaxation as a continuous variable The relaxed convex optimization problem is obtained as follows:

[0110] (14)

[0111] The problem is transformed into a threshold feasibility determination problem by using binary search, and the feasibility determination of the associated threshold is achieved by using an exact penalty function and adaptive gradient descent.

[0112] For any threshold The relaxed convex optimization problem is transformed into the following threshold feasibility determination problem:

[0113] (15)

[0114] Set search precision Given a threshold search interval Initialize the number of iterations. In the first In the next iteration, the threshold is taken. Determine if an association matrix exists. satisfy .

[0115] To achieve rapid feasibility determination of the association threshold, this invention constructs an accurate penalty function:

[0116] (16)

[0117] Indicates the first The simplex set corresponding to the service capacity constraints of each access point, i.e. ; The set of constraints representing the related variables, i.e. , Indicates by constraints The defined set of half-spaces, i.e. .

[0118] It is differentiable, and its gradient is:

[0119] (17)

[0120] Problem (16) is solved using the gradient descent method. The update formula for gradient descent is:

[0121] (18)

[0122] To improve convergence speed and ensure global convergence of the algorithm, an adaptive step size is adopted:

[0123] (19)

[0124] When reached or Stop iteration when the iteration terminates. If the penalty function value satisfies the condition after iteration terminates... Then determine the threshold. Feasible, and make To increase the threshold; if the maximum number of iterations is reached. Still Then determine the threshold. Not feasible, and order To lower the threshold, repeat the iteration until the termination condition is met. We obtain the relaxed correlation solution. . The tolerance set.

[0125] The projection operators in the exact penalty function all have analytical expressions. (Set of half-spaces) The projection satisfies:

[0126] (20)

[0127] Simplex set The projection satisfies:

[0128] ,(twenty one)

[0129] Constraint Set The projection satisfies:

[0130] ,(twenty two)

[0131] Step S3: Relax the association Mapping to binary association .

[0132] Construct the matrix: ,in For Hadamard product, This indicates that, under the meaning of satisfying maximum and minimum fairness, the th The access point should be preferentially allocated to the first one. The algorithm assigns tasks based on the urgency of each user's needs, iteratively prioritizing the least urgent users. Specifically:

[0133] Initialize the cumulative allocation vector Binary association Correlation rating matrix .

[0134] When there are access points that are not yet fully loaded, that is, when there are access points... Its allocated user count Perform a loop iteration:

[0135] from Select the user index with the smallest current cumulative allocation. ;

[0136] Select to make Largest access point index ;

[0137] Place And update the accumulated energy: ;

[0138] Place To avoid making duplicate selections;

[0139] If the first The action already exists If there are 1s, then the row will be... When the number of users assigned to a certain access point reaches... If this condition is met, it should be prevented from being selected in subsequent iterations.

[0140] The iteration terminates when all access points reach the service user count constraint, and the output is a binary correlation matrix. .

[0141] Step S4: Constructing the threshold feasibility problem of maximum and minimum beamforming under fixed binary correlation.

[0142] The binary incidence matrix is ​​obtained in the first stage. After that, fix Remain unchanged, optimize the precoding vectors for each user at each access point. The goal is to maximize the minimum user rate while satisfying the power constraint per access point:

[0143] ,(twenty three)

[0144] in .

[0145] For rate threshold Perform a binary search to convert it into a feasibility determination:

[0146] ,(twenty four)

[0147] Determine if it exists make And it meets the power constraint.

[0148] Step S5: ... Equivalently rewritten as SOC constraints.

[0149] users The joint precoding vector is stacked with the equivalent channel vector:

[0150] (25)

[0151] Phase ambiguity guarantees For real numbers, we can obtain:

[0152] (26)

[0153] The above formula can be written in standard SOC form:

[0154] (27)

[0155] in,

[0156] (28)

[0157] And define:

[0158] (29)

[0159] Step S6: Use the exact penalty function to determine feasibility and solve it using adaptive gradient descent.

[0160] For a given Construct the exact penalty function:

[0161] (30)

[0162] It is differentiable, and its gradient is:

[0163] (31)

[0164] In the implementation, gradient iteration is performed using equation (18), and during iteration, the adaptive step size of equation (19) is used to improve the convergence speed.

[0165] When reached or Stop iterating when the threshold is reached, and give the threshold accordingly. The feasibility conclusions were obtained, and then the maximum and minimum rates and beam vectors were derived. When the iteration terminates, if the penalty function value satisfies Then determine the threshold. Feasible, and make To increase the threshold; if the maximum number of iterations is reached. Still Then determine the threshold. Not feasible, and order To lower the threshold, repeat the iteration until the termination condition is met. The maximum and minimum rates and beam vectors are obtained. . The tolerance set.

[0166] The projection operator in the exact penalty function takes the following form. (Second-order cone set) The projection satisfies:

[0167] (32)

[0168] Power Ball The projection satisfies:

[0169] (33)

[0170] Step S7: Output the results.

[0171] After the binary search terminates, the maximum feasible threshold is output as the maximum and minimum rates, and the corresponding... The result of the second stage is to restore it to a complex domain beam.

[0172] The simulation fixes the number of access points to be [number]. Each access point is configured One antenna, number of users Furthermore, different values ​​were used in different experiments; the backhaul constraint was achieved by limiting the maximum number of users served by each access point, setting the upper limit of users served by each access point to be [value missing]. The maximum transmit power for each access point is set to... All access points and users are randomly distributed in... Within the square area, the carrier frequency is set to The system bandwidth is set to The noise power is fixed at .

[0173] The simulation results demonstrate the advantages of the present invention. Methods and sorting-based Methods, and a maximum-minimum beamforming method with infinite backhaul capacity. Compare them. Based on sorting. The method first sorts users based on the channel strength between each user and each access point; then, for each access point, the one with the highest channel quality is selected. Establishing service relationships between users, that is, setting the associated variables corresponding to the selected users. The remaining users are set to This ensures that each access point can serve a maximum of [number] services. User-specific backhaul constraints. Unlimited backhaul capacity. The method assumes unlimited backhaul capacity, allowing each access point to serve all users simultaneously; that is, it directly sets all associated variables... .

[0174] Figure 1 This shows the number of antennas at each access point. Power of each access point Under these conditions, the maximum and minimum reachable rates vary with the number of users. The changes. Only one service is provided at each access point. Under the condition of one user, the solution of the present invention can still obtain the same Similar maximum and minimum achievable rates, and significantly better than . Figure 2 Showing the number of users Power of each access point Under these conditions, the maximum and minimum reachable rates vary with the number of antennas at each access point. The results show that the performance of all three methods increases with the number of antennas; the growth trend of the proposed solution is similar to... Consistent, and consistently outperforms other antennas of different sizes. This demonstrates that the present invention has stable gain and scalability under different antenna configurations. Figure 3 This shows the number of antennas at each access point. Number of users Under the given conditions, the maximum and minimum reachable rates change with increasing transmit power at each access point. As transmit power increases, the maximum and minimum reachable rates for all three schemes rise, indicating that increasing transmit power effectively improves the quality for the worst-case user. A comparison shows that... The performance is consistently the highest, which can be considered the theoretical upper limit; this invention's solution Always better The result is stable and close to the theoretical upper limit, indicating that the present invention can significantly improve user speed under constrained conditions. Figure 4The paper describes the convergence of the feasibility threshold over time during the binary search process using three algorithms. Results show that, compared to schemes using general solvers such as HSDE and ADMM to solve feasibility subproblems, this invention, based on the precise penalty function of projected distance and adaptive gradient descent, only requires closed projection and gradient updates, significantly reducing the cumulative running time of feasibility determination and binary search. This results in lower computational overhead when achieving similar maximum and minimum reachability rates.

[0175] In summary, this invention, in cellless massive MIMO networks with limited backhaul, achieves near-infinite maximum and minimum reachable rates by employing a cascaded framework of maximum and minimum user-access point association and maximum and minimum beamforming, even with each access point only allowed to serve a limited number of users. Furthermore, it demonstrates higher computational efficiency in feasibility assessment and binary search processes, verifying the effectiveness of this invention in improving user experience and engineering feasibility in weak networks.

Claims

1. A beamforming method for cell-free massive MIMO, wherein cell-free massive MIMO includes a CPU, One access point and The number of single-antenna users, the first Access point configuration Each antenna can serve a maximum of [number] users simultaneously. Each user, with a transmit power of no more than [number] access points. Its characteristics are, The method includes: Constructing the channel energy matrix , The element is defined as ,in The number obtained by the CPU The access point to the first Given the channel vectors of individual users, establish a maximum and minimum user-access point association model, i.e., construct an optimization problem with the objective of maximizing the cumulative energy of the minimum user: ， in, and They are respectively and The List, It is determined by the associated indicator variable The matrix formed , Indicates the first The first access point service One user; Will Relaxation as a continuous variable The relaxed convex optimization problem is obtained as follows: ， For convex optimization problems, binary search is used to transform the problem into a threshold feasibility determination problem, thereby obtaining a relaxed correlation solution. ; Through constraint-compatible discretization mapping, Under the condition of satisfying the constraint on the number of users served by each access point, it is mapped to a binary incidence matrix. ; Get and fix Then, optimize the precoding vectors for each user at each access point. The goal is to maximize the minimum user rate while satisfying the power constraint per access point: ， in, , It is the first The achievable rate for each user yes Elements in; Set rate threshold A binary search is then performed to transform the power constraint into a feasibility determination: ， Determine if it exists make And satisfying the power constraint, after the binary search terminates, the maximum feasible threshold is output as the maximum and minimum rates, and the corresponding... It is restored to a complex domain beam.

2. The beamforming method for cell-free massive MIMO according to claim 1, characterized in that, Obtain the relaxed correlation solution The specific method is: For any threshold The relaxed convex optimization problem is transformed into the following threshold feasibility determination problem: ， The feasibility determination is transformed into a problem of minimizing an exact penalty function based on the projected distance, and the exact penalty function is defined. : ， ， ， ， in, Indicates the first The simplex set corresponding to the service capacity constraints of each access point This represents the set of constraints for the related variables. Indicates by constraints Defined set of half-spaces; Differentiable, gradient is: ， Solve using gradient descent method Set search precision Given a threshold search interval Initialize the number of iterations In the In the next iteration, the threshold is taken. Determine if an association matrix exists. satisfy The update formula for gradient descent is: ， Adaptive step size: ， When reached or Stop iteration when the iteration terminates; if the penalty function value satisfies the condition after the iteration terminates. Then determine the threshold. Feasible, and make To increase the threshold; if the maximum number of iterations is reached. Still Then determine the threshold. Not feasible, and order To lower the threshold; repeat the iteration until the termination condition is met. We obtain the relaxed correlation solution. , The tolerance set.

3. The beamforming method for cell-free massive MIMO according to claim 2, characterized in that, make Under the condition of satisfying the constraint on the number of users served by each access point, it is mapped to a binary incidence matrix. The specific method is: Constructing a matrix ,in For Hadamard product, elements in This indicates that, under the meaning of satisfying maximum and minimum fairness, the th The access point should be preferentially allocated to the first one. The urgency level of each user is considered, and allocation is iteratively assigned based on the principle of prioritizing the least urgent users; specifically: Initialize the cumulative allocation vector Binary association Correlation rating matrix ; When there are access points that are not yet fully loaded, that is, when there are access points... Its allocated user count Perform a loop iteration: from Select the user index with the smallest current cumulative allocation. ; Select to make Largest access point index ; Place And update the accumulated energy: ; Place To avoid making duplicate selections; If the first The action already exists If there are a "1", then the row will be... ; When the number of users assigned to a certain access point reaches When this occurs, it should be prohibited from being selected in subsequent iterations; The iteration terminates when all access points reach the service user count constraint, resulting in a binary incidence matrix. .

4. The beamforming method for cell-free massive MIMO according to claim 3, characterized in that, Determine if it exists make And the specific method to satisfy the power constraint is: Will Equivalent rewriting to SOC constraints, including user The joint precoding vector is stacked with the equivalent channel vector: ， ， get: ， in, It is the first The noise variance of an individual user, written in standard SOC form, is as follows: ， ， in, It is the first The equivalent linear constraint matrix constructed from the channel vectors of each user. It is the system's joint transmit beamforming vector. It is the first Noise and interference items for individual users It is the user's received signal. It is a user's data symbol, defined as: ， Feasibility is determined using an exact penalty function and then solved using adaptive gradient descent for a given condition. Construct an exact penalty function : ， ， ， Differentiable, gradient is: ， The update formula for gradient descent is: Adaptive step size is When it reaches or Stop iterating when the threshold is reached, and give the threshold accordingly. The feasibility conclusions were obtained, and then the maximum and minimum rates and beam vectors were derived. When the iteration terminates, if the penalty function value satisfies Then determine the threshold. Feasible, and make To increase the threshold; if the maximum number of iterations is reached. Still Then determine the threshold. Not feasible, and order To lower the threshold; repeat the iteration until the termination condition is met. The maximum and minimum rates and beam vectors are obtained. , The tolerance set.

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