A Power Allocation Method for a Low-Precision Bidirectional Cell-Free Massive MIMO System

Abstract

The present invention discloses a power allocation method for a low-precision two-way cell-free massive MIMO system, including: constructing a low-precision two-way cell-free massive MIMO system model; respectively calculating the closed-form expressions of spectral efficiency in the MAC phase and the BC phase, jointly deriving the spectral efficiency of system users in the two phases and maximizing it as the objective function of the model; setting the total power constraint condition, establishing an optimization problem model for user spectral efficiency, and using the successive approximation method to solve the model; substituting the obtained optimization parameters into the spectral efficiency in the BC phase, constructing a max-min fair resource allocation model, using the bisection method to transform the above model into a series of convex feasibility problems, and adopting an improved algorithm combining successive approximation and max-min to achieve optimal power allocation among all users and APs. The present invention constructs an optimization problem of power allocation based on spectral efficiency, obtains the optimal solution of the optimization problem through an improved algorithm, and reduces the problem of overall capacity decline caused by hardware.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a low-precision bidirectional non-cellular large-scale MIMO system power allocation method. Background Art

[0002] Cell-free massive multiple-input multiple-output (MIMO) is a new network architecture that eliminates the traditional cellular system architecture and randomly distributes numerous access points (APs). This technology can serve multiple users using the same frequency resources, offering high coverage, high throughput, and high spectral efficiency. These APs, equipped with a limited number of antennas, are compact and can be flexibly deployed across the network, providing relatively uniform service to all devices. This overcomes the shortcomings of traditional MIMO technology, such as poor service quality in the corners of cells.

[0003] Although APs have low transmit power, their large number leads to a surge in hardware costs and total transmit power. An effective solution is to use low-precision analog-to-digital converters (ADCs) on the APs, but this in turn reduces the system's spectral efficiency. Therefore, while bidirectional transmission technology is employed, total power is allocated to terminals and each AP to compensate for the system performance loss caused by reduced hardware quality. Each AP is controlled by a processor and can be treated as a whole, so a successive approximation algorithm can be used to allocate user power and total AP power. However, varying power allocation schemes between APs still lead to variations in system spectral efficiency. Applying an average power allocation to APs results in a loss of spectral efficiency.

[0004] However, the existing technology has the following disadvantages:

[0005] Existing successive approximation algorithms can only optimize power allocation for users during the multiple-access channel (MAC) phase, but cannot optimize power allocation for APs during the broadcasting (BC) phase. Adding AP power control coefficient variables to the existing optimization model not only makes it difficult to determine its convexity, but also makes it difficult to transform the original problem into a series of geometric programming problems.

[0006] Therefore, the present invention proposes an improved optimization problem model and a joint successive approximation and max-min iterative algorithm, which can further allocate power to APs, thereby overcoming the disadvantage that the existing successive approximation algorithm cannot be applied to wireless cellular systems. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a low-precision bidirectional non-cellular massive MIMO system power allocation method in response to the defects in the prior art.

[0008] The technical solution adopted by the present invention to solve its technical problem is:

[0009] The present invention provides a low-precision bidirectional non-cellular large-scale MIMO system power allocation method, the method comprising the following steps:

[0010] Step 1: Build a low-precision bidirectional non-cellular massive MIMO system model, use uplink orthogonal pilots to estimate the channel, and derive the minimum mean square error (MMSE) channel estimation method.

[0011] Step 2: Based on the constructed low-precision bidirectional non-cellular massive MIMO system model, the closed-form expressions for the MAC phase spectrum efficiency and the BC phase spectrum efficiency are calculated separately. The closed-form expressions for the user pair spectrum efficiency are derived from the two phases and maximized as the objective function of the user power and total AP power allocation optimization model.

[0012] Step 3: Set total power constraints. Based on Step 2, establish a user power and total AP power allocation optimization model to perform preliminary power resource allocation. Use successive approximation to transform this optimization problem into a series of geometric programming problems. Use an iterative algorithm to solve the model and obtain preliminary power allocation solutions for users and total APs.

[0013] In step 4, the optimization parameters obtained in step 3 are substituted into the BC phase spectrum efficiency to construct a max-min inter-AP power allocation optimization model. Using the bisection method, the model is transformed into a series of equivalent convex feasibility problems to solve the inter-AP power allocation. An improved algorithm combining joint successive approximation and max-min iteration is then used to achieve optimal power allocation for all users and APs.

[0014] Furthermore, the method of step 1 of the present invention specifically includes:

[0015] The low-precision bidirectional non-cellular massive MIMO system model constructed includes L APs with M antennas and K single-antenna terminal user pairs, and M×L>>K; p During the pilot duration, the received pilot matrix expression at AP 1 is:

[0016]

[0017] Among them, ρ p is the normalized pilot power, For user T A,k and the channel vector between AP l, For user T B,k and the channel vector between the AP l side; ξ X,k is the pilot power control coefficient of T X,k and T X,k ∈ {T A,k , T B,k}}, is the orthogonal pilot sequence sent by T X,k and In addition, is the received noise matrix; after receiving the pilot signal matrix at the AP l side, it is quantized. Using the additive quantization noise model, the expression of the quantized signal is:

[0018]

[0019] where α l ∈ [0, 1] is the linear quantization coefficient related to the quantization bit b l at the AP l side. When b l takes values of 1, 2, 3, 4, 5, α l takes a series of corresponding values. When b l > 5, α l is approximately expressed as In addition, N tr,l represents the user noise matrix, and its covariance matrix expression is:

[0020]

[0021] After quantizing the signal matrix, the AP performs a demodulation operation, projects the quantized signal onto to generate the demodulated signal Based on the minimum mean square error criterion, the estimated channel A,k from user T to the AP l is expressed as:

[0022]

[0023] where β A,lk is the large-scale fading coefficient of the channel from the AP l side to T A,k .

[0024] Furthermore, the method for deriving the closed-form expression of the total system spectral efficiency in step 2 of the present invention specifically includes:

[0025] In the MAC phase, all user pairs simultaneously send data to the AP. Set the uplink data symbols sent by the kth user pair as q A,k and q B,k , satisfying The received data vector after quantization at the AP l side is expressed as:

[0026]

[0027] Among them, ρ u is the normalized uplink signal-to-noise ratio, and η X,k is the power control coefficient of user k, where 0 ≤ η X,k ≤ 1; Based on the maximum ratio combining receiver, the AP l side constructs a decoding matrix using the estimated channel, and after taking the inner product of and , it is sent to the CPU via the fronthaul link. Then the total demodulated signal of user k received by the CPU is:

[0028]

[0029] Based on the decode-and-forward protocol, the CPU sends the demodulated data symbol vector to all APs, and the APs modulate the data symbols into transmission signals using the maximum ratio transmission transmitter:

[0030]

[0031] Among them, q A = [q A,1 ...q A,K and q B = [q B,1 ...q B,K are data vectors, and η A,l = diag(η A,l1 ...η A,lK ) and η B,l = diag(η B,l1 ...η B,lK ) are the AP l power control coefficient matrices;

[0032] Using the worst-case non-coherent noise theory method, the signal-to-noise ratio expression of user T X,k in the MAC phase is:

[0033]

[0034] The total signal-to-noise ratio expression of the kth user pair in the MAC phase is:

[0035]

[0036] The signal-to-noise ratio expression of user T X,k in the BC phase is:

[0037]

[0038] ρ dis the normalized downlink signal-to-noise ratio; the total signal-to-noise ratio expression of the kth user pair in the BC phase is:

[0039]

[0040] The system throughput is affected by the combined effect of the signal-to-noise ratios in the MAC and BC phases. The closed-form expression for the spectrum efficiency of the k-th user pair is:

[0041]

[0042] where τ c is the coherence interval.

[0043] Furthermore, the method for establishing the user power and total AP power allocation optimization problem model in step 3 of the present invention is:

[0044] The upward optimization problem is transformed into a series of geometric programming problems, and the A,k , η B,k and p d Obtain the optimal solution for user power and total AP power allocation. The optimization problem is expressed as follows:

[0045]

[0046] where η A =[η A,1 ,...,η A,k ,...,η A,K ] T , η B =[η B,1 ,...,η B,k ,...,η B,K ] T Constraint 1 represents the system energy constraint, which requires the maximum total system power to be equal to P, constraint 2 represents the conditions that the power control factor should meet, and constraint 3 represents the minimum rate required for each user to reach R min ; Obviously, the above problem is not a standard optimization problem, and it is difficult to judge its convexity, so it is difficult to find its optimal solution; In order to effectively solve the above problem, the slack variable ψ is introduced k , ψ A,k and ψ B,k , reconstruct the above objective function and constraint 3 as follows:

[0047]

[0048] in,

[0049]

[0050] Among them, except b k All other parameters except are considered constants when solving the optimization problem. The objective function after the introduction of slack variables and the first two inequality constraints are not positive terms. In order to transform the above optimization problem into a geometric programming problem, the objective function and constraints are approximated by positive terms.

[0051] For the objective function 1+ψ k , using monomials At the point Approximation is made near For the first inequality constraint a 1,k η A,k +a 2,k η B,k , since for any set of positive numbers the arithmetic mean is greater than or equal to the geometric mean, then:

[0052]

[0053] in When η A,k , η B,k Approximately equal to η A,k , η B,k When , the geometric mean is used to replace the arithmetic mean in the first inequality constraint; for the second inequality constraint, Approach in is the initialization value; through local approximation, the original optimization problem can be transformed into a geometric programming problem. In order to control the accuracy of the geometric programming problem, the parameters with initial values must be limited in range. The above optimization problem is transformed into:

[0054]

[0055] Among them, θ>0 is the asymptotic precision control coefficient. The larger θ is, the faster the convergence speed is, but the lower the accuracy is.

[0056] Furthermore, the method for solving the problem using the successive approximation method in step 3 of the present invention specifically includes:

[0057] Using the successive approximation algorithm, the original optimization problem is transformed into a series of geometric programming problems for solution. First, the parameters are initialized, which requires that the total uplink and downlink power are equal and the uplink total power is evenly distributed among users, expressed as:

[0058] and Using average power distribution to find and

[0059] Define parameters ε1 and θ, and let i = 1; Iterate i. When i = 1, calculate μ using the initial parameters k , χ X,k , and then solve the geometric programming problem to obtain the local optimal solution and When i > 1, let Solve When the difference between adjacent local optimal solutions is less than ε1, exit the iteration, and the global optimal solution is the local optimal solution of the last iteration.

[0060] Furthermore, the method for constructing the power allocation model between APs based on max - min in step 4 of the present invention specifically includes:

[0061] Through η A,lk , η B,lk Obtain the optimal solution of power allocation between APs, and the optimization problem is expressed as:

[0062]

[0063] The above optimization problem is a non - convex model. Define And introduce in the slack variable υ l , and the above optimization problem is re - described as:

[0064]

[0065] The objective function of the above problem model is quasiconvex. Therefore, use the bisection method to solve the optimization problem In each iteration step, the following convex feasibility problem needs to be solved:

[0066]

[0067] where

[0068] Set The upper and lower bounds t in the objective function of the problem upp and t low , and set Solve the feasibility problem If the problem is feasible, increase the lower bound, i.e., t low = t. If the problem is infeasible, decrease the upper bound, i.e., t max = t, and re - let Judge feasibility; until t upp - tlow > ε2 to end the iteration.

[0069] Further, the improved algorithm that combines successive approximation and max-min iteration in step 4 of the present invention specifically includes:

[0070] The combined successive approximation algorithm and the max-min iteration algorithm jointly iteratively optimize the power allocation for all users and all APs; similarly, initialize the iteration count j and the tolerance ε3; when j = 1, perform an average power allocation for the APs, that is When j > 1, let η X,lk be the solution of the max-min power control algorithm Solve for η using the successive approximation algorithm X,k , ρ d the optimal solution and substitute it into the max-min power control algorithm; find the optimal solution of η X,lk the optimal solution and substitute it back into the successive approximation algorithm; when stop the iteration to obtain the power allocation results for all users and all APs.

[0071] The beneficial effects produced by the present invention are:

[0072] The improvements of the present invention in the combined successive approximation algorithm include: regarding all APs as a whole, treating the downlink power control factor as a constant, and only optimizing the total AP power, so that the successive approximation algorithm can be applied to the low-precision two-way cell-free power optimization problem model. The improvements in the downlink max-min power control algorithm include: transforming the quasiconvex form of the objective function into a convex second-order cone form, and then transforming the original problem into a feasibility problem for solution. Finally, iteratively solve the successive approximation algorithm and the max-min power control algorithm to iteratively optimize the user and AP power control factors, and ultimately achieve the optimization of system power allocation.

[0073] Aiming at the shortcoming that the existing two-way cell-free massive MIMO power allocation technology cannot perform power allocation for APs, the present invention proposes a combined successive approximation and max-min iteration power allocation algorithm. Construct an optimization problem for spectral efficiency based on the MAC phase and the BC phase, perform power allocation for all users and APs, and thus can reduce the problem of overall capacity degradation caused by hardware. The present invention can be applied to a two-way low-precision cell-free massive MIMO communication transmission system. The main parameter in the algorithm involved in the present invention is the large-scale fading coefficient, and the large-scale fading coefficient remains unchanged in many adjacent coherent time intervals. Therefore, the optimization problem involved in the patent is simplified and has good operability. Description of the Drawings

[0074] The present invention will be further described below in conjunction with the accompanying drawings and embodiments. In the accompanying drawings:

[0075] Figure 1 is the overall method flowchart of the embodiment of the present invention;

[0076] Figure 2 is the flowchart of the improved joint successive approximation and max - min iterative power allocation algorithm of the embodiment of the present invention;

[0077] Figure 3 is the application scenario diagram of the embodiment of the present invention;

[0078] Figure 4 is the comparison diagram of the algorithm simulation results of the embodiment of the present invention. Specific embodiments

[0079] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0080] As Figure 1 shown, the power allocation method for a low - precision two - way cell - free massive MIMO system according to the embodiment of the present invention includes the following steps:

[0081] Step 1: Construct a low - precision two - way cell - free massive MIMO system model, perform channel estimation on the system using uplink orthogonal pilots, and derive the minimum mean square error estimated channel;

[0082] Step 2: Based on the constructed low - precision two - way cell - free massive MIMO system model, calculate the closed - form expressions of the spectral efficiency in the MAC phase and the closed - form expressions of the spectral efficiency in the BC phase respectively. Combine the two phases to derive the closed - form expression of the total spectral efficiency of the system and maximize it as the objective function of the user power and total AP power allocation optimization problem model;

[0083] Step 3: Set the total power constraint condition, establish a user power and total AP power allocation optimization problem model based on Step 2, and perform preliminary power resource allocation; use the successive approximation method to transform the above - mentioned optimization problem into a series of geometric programming problems, and solve the model through an iterative algorithm to obtain the preliminary allocation scheme of the power among users and the total AP power;

[0084] In step 4, the optimized parameters obtained in step 3 are substituted into the BC phase spectrum efficiency to construct a max-min inter-AP power allocation optimization model. Using the bisection method, the model is transformed into a series of equivalent convex feasibility problems to solve the inter-AP power allocation. An improved algorithm combining joint successive approximation and max-min iteration is then used to achieve optimal power allocation for all users and all APs.

[0085] The method of step 1 specifically includes:

[0086] The low-precision bidirectional non-cellular massive MIMO system model constructed includes L APs with M antennas and K single-antenna terminal user pairs, and M×L>>K; p During the pilot duration, the received pilot matrix expression at AP 1 is:

[0087]

[0088] Among them, ρ p is the normalized pilot power, For user T A,k and the channel vector between AP l, For user T B,k and the channel vector between AP l; X,k T X,k The pilot power control coefficient and T X,k ∈{T A,k ,T B,k}, T X,k The orthogonal pilot sequence sent and also, is the receiving noise matrix; after receiving the pilot signal matrix at the AP l end, it is quantized and the additive quantization noise model is used. The quantized signal expression is:

[0089]

[0090] where α l ∈[0,1] is the AP l end and the quantization bit b l The linear quantization coefficients are related to the l When the value is 1, 2, 3, 4, or 5, α l The corresponding value is:

[0091] 0.6366,0.8825,0.96546,0.990503,0.997501;

[0092] When b l >5, α l Approximately expressed as In addition, Ntr,l Denote the user noise matrix, and its covariance matrix expression is:

[0093]

[0094] After quantizing the signal matrix, the AP performs a demodulation operation, projects the quantized signal onto to generate a demodulated signal Based on the minimum mean square error criterion, the estimated channel between user T A,k and AP l is The expression is:

[0095]

[0096] where β A,lk is the large-scale fading coefficient of the channel from AP l to T A,k The method for deriving the closed-form expression of the total spectral efficiency of the system in step 2 specifically includes:

[0097] In the multiple access channel (MAC) phase, all user pairs simultaneously send data to the AP. Set the uplink data symbol sent by the kth user pair as q

[0098] and q A,k and q B,k , satisfying The received data vector after quantization at the AP l side is expressed as:

[0099]

[0100] where ρ u is the normalized uplink signal-to-noise ratio, and η X,k is the power control coefficient of user pair k, 0 ≤ η X,k ≤ 1; Based on the maximum ratio combining receiver, the AP l side constructs a decoding matrix using the estimated channel, and after taking the inner product of and it is sent to the CPU via the fronthaul link. Then the total demodulated signal of user pair k received by the CPU is:

[0101]

[0102] Based on the decode-and-forward protocol, the CPU sends the demodulated data symbol vector to all APs, and the APs modulate the data symbols into transmission signals using the maximum ratio transmission transmitter:

[0103]

[0104] where q A = [q A,1 ...q A,K and qB = [q B,1 ...q B,K is the data vector, η A,l = diag(η A,l1 ...η A,lK ) and η B,l = diag(η B,l1 ...η B,lK ) is the AP l power control coefficient matrix;

[0105] Using the worst non - coherent noise theory method, the signal - to - noise ratio expression of user T in the k - th user pair X,k in the MAC phase is:

[0106]

[0107] The total signal - to - noise ratio expression of the k - th user pair in the MAC phase is:

[0108]

[0109] User T X,k in the broadcast BC phase has the signal - to - noise ratio expression:

[0110]

[0111] ρ d is the normalized downlink signal - to - noise ratio. The total signal - to - noise ratio expression of the k - th user pair in the BC phase is:

[0112]

[0113] The system throughput is affected by the combined signal - to - noise ratios in the MAC and BC phases. The closed - form expression of the spectral efficiency of the k - th user pair is:

[0114]

[0115] where τ c is the coherence interval.

[0116] The method for establishing the total spectral efficiency optimization problem model in step 3 is:

[0117] Transform the user power and total AP power allocation optimization problem into a series of geometric programming problems, and obtain the optimal solutions of user power and total AP power allocation through η A,k , η B,k and p d . The optimization problem is expressed as follows:

[0118]

[0119] where η A= [η A,1 ,..., η A,k ,..., η A,K T , η B = [η B,1 ,..., η B,k ,..., η B,K T ; Constraint 1 represents the system energy constraint, which requires that the maximum total power of the system be equal to P. Constraint 2 represents the condition that the power control factor should satisfy. Constraint 3 represents that the minimum rate required for each user is R min ; Obviously, the above problem is not a standard optimization problem, and it is difficult to judge its convexity and concavity. Therefore, it is difficult to find its optimal solution. To effectively solve the above problem, slack variables ψ k , ψ A,k and ψ B,k are introduced to represent and respectively. The above objective function and constraint condition 3 are reconstructed as:

[0120]

[0121] where

[0122]

[0123] where, except for b k the rest of the parameters are regarded as constants when solving the optimization problem. The objective function and the first two inequality constraint conditions after introducing the slack variables are not positive polynomials. To transform the above optimization problem into a geometric programming problem, the objective function and the constraint conditions are approximated by positive polynomials;

[0124] For 1 + ψ k in the objective function, it is approximated by the monomial near the point where For a 1,k η A,k + a 2,k η B,k in the first inequality constraint condition, since for any set of positive numbers, the arithmetic mean is greater than or equal to the geometric mean, therefore:

[0125]

[0126] where When η A,k , η B,k is approximately equal to η A,k , η​​B,k When , the geometric mean is used to replace the arithmetic mean in the first inequality constraint; for the second inequality constraint, Approach in is the initialization value; through local approximation, the original optimization problem is transformed into a geometric programming problem. In order to control the accuracy of the geometric programming problem, the parameters with initial values must be limited in range. Then the above optimization problem is transformed into:

[0127]

[0128] Among them, θ>0 is the asymptotic precision control coefficient. The larger θ is, the faster the convergence speed is, but the lower the accuracy is.

[0129] The method for solving the problem using the successive approximation method in step 3 specifically includes:

[0130] Using the successive approximation algorithm, the original optimization problem is transformed into a series of geometric programming problems for solution. First, the parameters are initialized, which requires that the total uplink and downlink power are equal and the uplink total power is evenly distributed among users, expressed as:

[0131] and Using average power distribution to find and

[0132] Define parameters ε1 and θ, let i = 1; iterate i, when i = 1, use the initialization parameters to calculate μ k , χ X,k , and then solve the geometric programming problem Find the local optimal solution and When i>1, let solve When the difference between adjacent local optimal solutions is less than ε1, the iteration is exited and the global optimal solution is the local optimal solution of the last iteration.

[0133] The above successive approximation algorithm is expressed as follows using sub-algorithm 1:

[0134]

[0135] The method for constructing the max-min based inter-AP power allocation model in step 4 specifically includes:

[0136] The downlink power control factor η A,lk , η B,lk To obtain the optimal solution for power allocation between APs, the optimization problem is expressed as:

[0137]

[0138] The above optimization problem is a non-convex model, and define and introduce in the slack variable υ l , and the above optimization problem is re-described as:

[0139]

[0140] The objective function of the above problem model is quasiconvex, so the bisection method is used to solve the optimization problem In each iteration step, the following convex feasibility problem needs to be solved:

[0141]

[0142] where

[0143] As Figure 2 shown, the improved algorithm that adopts joint successive approximation and max-min iteration in step 4 specifically includes:

[0144] First, set the upper and lower bounds t in the objective function of the problem upp and t l o w , and set to solve the feasibility problem If the problem is feasible, then increase the lower bound, i.e., t l o w = t. If the problem is infeasible, then decrease the upper bound, i.e., t max = t, and re-let to judge feasibility; until t upp - t low > ε2 to end the iteration;

[0145] The specific steps are shown in sub-algorithm 2:

[0146]

[0147] The joint successive approximation algorithm and the max-min iteration algorithm perform joint iterative optimization on the power allocation of all users and APs; similarly, initialize the iteration number j and the tolerance ε3; when j = 1, perform equal power allocation for the AP, i.e., When j > 1, let η X,lk be the solution of the max-min power control algorithm Solve for η X,k , ρd The optimal solution And bring it into sub-algorithm 2; find η X,lk The optimal solution And bring it back into Sub-Algorithm 1; when When , the iteration stops and the power allocation results of all users and APs are obtained.

[0148] The above iteration is expressed as comprehensive algorithm 1:

[0149]

[0150]

[0151] like Figure 3 As shown, in another specific embodiment of the present invention, the system scenario used is 1km 2 There are 10 APs randomly distributed in the range, and each AP works in time division duplex mode to serve 10 user pairs. Simulation parameters P = 35dB, τ c =200, τ p =2K. The large-scale fading model is: β X,lk =PL X,lk ·z X,lk Among them, PL X,lk From AP l to user T X,k The path loss between X,lk represents shadow fading with a standard deviation of σ = 8 dB. Specifically, in Algorithm 1, the maximum number of iterations is I = 50, the iteration step is θ = 1.1, and the convergence tolerances for the three algorithms are set to ε1 = 0.02, ε2 = 0.0002, and ε3 = 0.0002, respectively. All multi-antenna APs are connected to the CPU via a fronthaul link to facilitate channel estimation.

[0152] like Figure 4 As shown in the figure, the effectiveness of the low-precision bidirectional non-cellular large-scale MIMO system power allocation method proposed in this patent is verified through simulation on the Matlab platform. In the equal power allocation scheme, all users use the same power control coefficient, and the total power in the MAC stage is the same as the total power in the BC stage. In the figure, b represents the quantization bit. Figure 4 As shown in the figure, the spectrum efficiency is significantly improved after the introduction of the improved method, and the larger the number of quantization bits, the more obvious the improvement effect.

[0153] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all such improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A power allocation method for a low-precision two-way cell-free massive MIMO system, characterized in that The method includes the following steps: Step 1: Construct a low-precision two-way cell-free massive MIMO system model, estimate the channel using uplink orthogonal pilots, and derive the minimum mean square error (MMSE) estimated channel; Step 2: Based on the constructed low-precision two-way cell-free massive MIMO system model, calculate the closed-form expressions of the spectral efficiency in the MAC phase and the BC phase respectively, jointly derive the closed-form expression of the spectral efficiency for users, and maximize it as the objective function of the user power and total AP power allocation optimization problem model; Step 3: Set the total power constraint condition, establish the user power and total AP power allocation optimization problem model based on Step 2, and perform preliminary power resource allocation; use the successive approximation method to transform the above optimization problem into a series of geometric programming problems, and solve the model through an iterative algorithm to obtain the preliminary allocation scheme of the power among users and the total AP power; Step 4: Substitute the optimized parameters obtained in Step 3 into the spectral efficiency in the BC phase, construct the max-min based AP power allocation optimization problem model, use the bisection method to transform the above model into a series of convex feasibility problems, solve the AP power allocation, and then use the improved algorithm combining successive approximation and max-min iteration to achieve the optimal power allocation among all users and all APs.

2. The power allocation method for a low-precision two-way cell-free massive MIMO system according to claim 1, characterized in that, The method of Step 1 specifically includes: The constructed low-precision two-way cell-free massive MIMO system model includes L APs with M antennas each and K single-antenna terminal user pairs, and M×L >> K; the received pilot matrix expression at the l-th AP is: Among them, ρ p is the normalized pilot power, τ p is the pilot length, For user T A,k and the channel vector between AP l, For user T B,k and the channel vector between AP l; X,k T X,k The pilot power control coefficient and T X,k ∈{T A,k ,T B,k }, T X,k The orthogonal pilot sequence sent and also, is the receiving noise matrix; after receiving the pilot signal matrix at the AP l end, it is quantized and the additive quantization noise model is used. The quantized signal expression is: where α l ∈[0,1] is the AP l end and the quantization bit b l The linear quantization coefficients are related to the l When the value is 1, 2, 3, 4, or 5, α l Take a series of values corresponding to it, when b l >5, α l Approximately expressed as In addition, N tr,l Represents the user noise matrix, and its covariance matrix expression is: After quantizing the signal matrix, AP performs demodulation and projects the quantized signal onto On, generate demodulated signal Based on the minimum mean square error criterion, user T A,k Estimated channel between AP l The expression is: Among them β A,lk is the large-scale fading coefficient of the AP l-end to T A,k channel.

3. The low-precision bidirectional non-cellular massive MIMO system power allocation method according to claim 2, characterized in that: The method of deriving the closed-form expression of the total system spectral efficiency in Step 2 specifically includes: In the MAC phase, all user pairs send data to the AP simultaneously. Let the uplink data symbol sent by the k-th user pair be q A,k and q B,k , satisfying where X ∈ {A, B}; the quantized received data vector at the AP l side is represented as: Among them, ρ u is the normalized uplink signal-to-noise ratio, η X,k is the power control coefficient of user k, 0≤η X,k ≤1; Based on the maximum ratio joint receiver, AP l uses the estimated channel to construct a decoding matrix and converts and After the inner product is performed and sent to the CPU via the forward link, the total demodulated signal received by the CPU for user k is: Based on the decode-and-forward protocol, the CPU demodulates the data symbol vector and sends it to all APs, and the APs modulate the data symbols into transmission signals using a maximum ratio transmission transmitter; where q A = [q A,1 ...q A,K and q B = [q B,1 ...q B,K are data vectors, ηA,l = diag(ηA,l1...ηA,lK) and η B,l = diag(η B,l1 ...η B,lK ) are the power control coefficient matrices at the AP l end; H l and G l are estimated channel matrices; Using the worst incoherent noise theory method, user T X,k The signal-to-noise ratio expression in the MAC stage is: The expression of the total signal-to-noise ratio (SNR) of the k-th user pair in the MAC phase is: User T X,k The signal-to-noise ratio expression in the BC stage is: Among them ρ d is the normalized downlink signal-to-noise ratio; the total signal-to-noise ratio expression of user pair k in the BC phase is as follows: The system throughput is affected by the combined SNR in the MAC phase and the BC phase, and the closed-form expression of the spectral efficiency of the k-th user pair is: where τ c is the coherence interval.

4. The power allocation method for a low-precision two-way cell-free massive MIMO system according to claim 3, wherein The method of establishing the user power and total AP power allocation optimization problem model in Step 3 is: The optimization problem of user power and total AP power allocation is transformed into a series of geometric programming problems, and the A,k , η B,k and p d Obtain the optimal solution for user power and total AP power allocation. The optimization problem is expressed as follows: subject to 0 ≤ η A ≤ 1, 0 ≤ η B ≤ 1, 0 ≤ p d R k ≥R min ,k=1,...,K where η A =[η A,1 ,..., η A,k ,..., η A,K T , η B =[η B,1 ,..., η B,k ,..., η B,K T ; Constraint 1 represents the system energy constraint, which requires that the maximum total power of the system is equal to P. Constraint 2 represents the condition that the power control factor should satisfy. Constraint 3 represents that the minimum rate required for each user is R min ; Obviously, the above problem is not a standard optimization problem, and it is difficult to judge its convexity or concavity. Therefore, it is very difficult to find its optimal solution. To effectively solve the above problem, slack variables ψ k , ψ A,k and ψ B,k are introduced, and the above objective function and constraint conditions are reconstructed as:​​ subject to Among them, where, except for b k all other parameters are regarded as constants when solving the optimization problem; the objective function and the first two inequality constraint conditions after introducing slack variables are not positive polynomials. In order to transform the above optimization problem into a geometric programming problem, positive polynomials are used to approximate the objective function and the first two constraint conditions; For 1 + ψ in the objective function k , use the monomial to approximate near the point , where For a in the first inequality constraint 1,k η A,k + a 2,k η B,k , since for any set of positive numbers, the arithmetic mean is greater than or equal to the geometric mean, so: Among them When η A,k , η B,k approaches η A,k , η B,k , use the above geometric mean to replace the arithmetic mean in the first inequality constraint; for the second inequality constraint, use to approach ψ Ak , +ψ Bk , +, ψ kA ψ, where is the initial value; through local approximation, the original optimization problem can be transformed into a geometric programming problem. To control the accuracy of the geometric programming problem, the range of the parameters with initial values needs to be limited. The above optimization problem is transformed into: subject to 0≤η A ≤1,0≤η B ≤1,0≤p d , where θ > 0 is the asymptotic precision control coefficient. The larger θ is, the faster the convergence speed, but the lower the accuracy.

5. The low-precision bidirectional non-cellular massive MIMO system power allocation method according to claim 4, characterized in that: The method of using the successive approximation method to solve in Step 3 specifically includes: Use the successive approximation algorithm to transform the original optimization problem into a series of geometric programming problems for solution; first, initialize the parameters, that is, require the total power in the MAC phase and the BC phase to be equal and evenly distribute the uplink total power among users, expressed as: and Using average power distribution to find and Define parameters ε1, θ and the number of iterations i. When i = 1, use the initialization parameters to calculate μ k , χ X，k , and then solve the geometric programming problem Find the local optimal solution and When i>1, let solve When the difference between two adjacent local optimal solutions is less than ε1, the iteration is exited and the global optimal solution is the local optimal solution of the last iteration.

6. The low-precision bidirectional non-cellular massive MIMO system power allocation method according to claim 5, characterized in that: The method of constructing the max-min based AP power allocation model in Step 4 specifically includes: By η A,lk , η B,lk To obtain the optimal solution for power allocation between APs, the optimization problem is expressed as: subject to 0≤η X,lk ,k=1,...,K,l=1,...,L,X=A,B The above optimization problem is a non-convex model, and define and introduce in the slack variable υ l , and the above optimization problem is re-described as: subject to 0<υ l <1,l=1,...,L k=1,...,K,l=1,...,L,X=A,B The objective function of the above problem model is quasiconvex, so the bisection method is used to solve the optimization problem In each iteration step, the following convex feasibility problem needs to be solved: 0 < υ l <1, l = 1, ..., L k = 1, ..., K, l = 1, ..., L, X = A, B in set up In the objective function of the problem The upper and lower bounds of t upp and t low , and set Solve feasibility issues like If the problem is feasible, then improve the lower bound, i.e., t low =t, if If the problem is infeasible, then reduce the upper bound, i.e., t max = t, and then re-set judge Feasibility; until t upp -t low >ε2 ends the iteration.

7. The power allocation method for a low-precision two-way cell-free massive MIMO system according to claim 6, characterized in that The improved algorithm combining successive approximation and max-min iteration in Step 4 specifically includes: Jointly optimize the power allocation of all users and all APs through joint iterative optimization of the successive approximation algorithm and the max-min iterative algorithm; similarly, initialize the number of iterations j and the tolerance ε3; when j = 1, perform average power allocation for the APs, that is When j > 1, let η X,lk be the solution of the max-min power control algorithm Solve for η using the successive approximation algorithm X,k , ρ d the optimal solution and substitute it into the max-min power control algorithm; use the max-min algorithm to find the optimal solution of η X,lk the optimal solution and substitute it back into the successive approximation algorithm; when is satisfied, stop the iteration and obtain the power allocation results of all users and all APs.

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