Distributed multi-cell massive MIMO power allocation method based on joint optimization of energy efficiency and spectrum efficiency

Abstract

The present invention discloses a distributed multi-cell large-scale MIMO power allocation method for joint optimization of energy efficiency and spectrum efficiency, including: constructing a cell cluster and configuring an antenna array, generating a beam set through beamforming; obtaining statistical channel state information of each user in the cell cluster; performing power allocation through distributed collaboration between base stations using a deterministic equivalent method, an MM method, and an iterative water filling algorithm; the optimization goal of the power allocation optimization problem is the minimum value of the weighted sum of the energy efficiency and spectrum efficiency of each cell; and dynamically implementing multi-cell large-scale MIMO beam domain power allocation according to changes in statistical channel state information. The present invention is based on a multi-cell distributed scenario, with limited information interaction between base stations, has a small backhaul overhead, and makes full use of the user's beam domain statistical channel state information, which can effectively improve the system's energy efficiency and spectrum efficiency, achieve a balance between the two, and significantly reduce the complexity of solving the optimization problem and physical layer implementation.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-cell large-scale MIMO power allocation, and in particular to a distributed multi-cell large-scale MIMO power allocation method for joint optimization of energy efficiency and spectrum efficiency. Background Art

[0002] In a massive MIMO system, a large-scale antenna array is deployed at the base station to serve multiple users simultaneously. The use of massive MIMO technology can effectively reduce interference between users and significantly improve the energy efficiency and spectral efficiency of wireless communication systems. Beam domain transmission refers to the base station side converting the transmitted signal to the beam domain through a unified unitary transformation, making full use of the spatial angle resolution of the massive antenna array and the local characteristics of the user channel in the beam domain.

[0003] During multi-cell massive MIMO downlink transmission, the base station sends signals to users in the cell respectively. For each user in the cell, the interference signal includes two aspects: the signal sent by the base station of the cell to other users, and the signal sent by the base station of other cells to users of other cells. If a centralized method is used for downlink transmission, a large amount of large-scale matrix information needs to be exchanged between base stations. Therefore, in the massive MIMO scenario, the centralized algorithm will cause high feedback overhead and complexity. The distributed algorithm refers to the case where there is limited (or no) information exchange between different base stations, and each base station independently processes the power allocation of the cell. The distributed processing of the massive MIMO system has a small overhead and low computational complexity.

[0004] In order to better balance the energy efficiency and spectral efficiency of the system, it is necessary to design the transmission signals of different users to jointly optimize the energy efficiency and spectral efficiency of the system. Traditional optimization problems are often based on instantaneous channel state information, but in large-scale MIMO systems, it is difficult to obtain instantaneous channel state information, and when the number of antennas on the base station side is large, the complexity of the expected process in solving the user rate is very high. To this end, the present invention proposes a low-complexity distributed multi-cell large-scale MIMO power allocation method that jointly optimizes energy efficiency and spectral efficiency using statistical channel state information, where resource efficiency is defined as the weighted sum of energy efficiency and spectral efficiency. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a distributed multi-cell large-scale MIMO power allocation method that jointly optimizes energy efficiency and spectral efficiency. This method is aimed at the downlink communication scenario of the multi-cell large-scale MIMO system, can optimize the energy efficiency and spectral efficiency of the system, and reduce the complexity of implementing this optimization process, making it easy to implement.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A distributed multi-cell massive MIMO power allocation method with joint optimization of energy efficiency and spectrum efficiency, the power allocation method comprising the following steps:

[0008] Step S1: construct multiple cells into a cell cluster and configure a large-scale antenna array at the base station of each cell, and generate a beam set through beamforming;

[0009] Step S2: Each cell base station obtains statistical channel state information of users in the cell respectively;

[0010] Step S3, each cell base station performs power allocation based on the acquired statistical channel state information, which includes: first constructing an optimization problem with the optimization target being the minimum value of the resource efficiency of each cell, the optimization variable being the covariance matrix of the signal sent by each base station, and the constraint condition being that the covariance matrix of the signal sent by each base station satisfies the power constraint, and then using the deterministic equivalent method, the MM method and the iterative water filling algorithm to solve the optimization problem to obtain the optimal power allocation matrix, and each base station implements power allocation with the obtained optimal power allocation matrix; wherein the resource efficiency is the weighted sum of energy efficiency and spectral efficiency, the spectral efficiency is the reachable traversal sum rate of the cell, and the energy efficiency is the ratio of the reachable traversal sum rate of the cell to the total power consumption.

[0011] Furthermore, the power allocation method further includes:

[0012] Dynamically implement multi-cell massive MIMO beam-domain power allocation based on changes in statistical channel state information;

[0013] When a user moves during the communication process, the statistical channel state information between the base station and the user will change, and each base station will dynamically implement beam domain power allocation.

[0014] Furthermore, in step S1, a large-scale antenna array is configured in the base station of each cell, and the number of antennas is 10 2 or 10 3 The size of the beam is orders of magnitude, and a large-scale beam set capable of covering all cells is generated through beamforming;

[0015] The base station generates a large-scale beam that can cover the entire cell through the same unitary transformation. Each beam divides the spatial resources, and the base station communicates with the users of the cell in the generated beam domain.

[0016] Furthermore, in step S2, each cell base station only needs to obtain channel information of users in the cell;

[0017] The statistical channel state information of users in the cell is obtained by adopting user feedback, direct estimation by the base station, or by using uplink detection signals.

[0018] Furthermore, in step S3, the optimization problem is solved by using the deterministic equivalent method, the MM method and the iterative water filling algorithm to obtain the optimal power allocation matrix, which specifically includes:

[0019] First, according to the large-dimensional random matrix theory, the system spectral efficiency is calculated using the beam domain statistical channel state information obtained in step S2, which includes: introducing deterministic equivalent auxiliary variables, determining the deterministic equivalent values ​​of the reachable traversal and the rate, and then calculating the deterministic equivalent value of the objective function, and then converting the optimization problem into a concave function through MM transformation;

[0020] Then, the sub-problems after MM transformation are converted into the problem of solving the power allocation matrix of each cell separately, and other cell parameters are regarded as constants when solving the optimization problem of the cell. For the power allocation problem of each cell, it is decomposed into an inner optimization sub-problem and an outer optimization sub-problem. The optimization goal of the inner optimization sub-problem is to solve the optimal power allocation matrix that maximizes the system and rate, and the optimization goal of the outer optimization sub-problem is to solve the optimal transmission power that maximizes resource efficiency.

[0021] Finally, the iterative water injection algorithm is used to solve the inner optimization subproblem, and the gradient method is used to update the transmit power according to the inner optimization result. If the transmit power converges, the iteration is terminated and the result of the inner subproblem is used as the result of the cell optimization problem.

[0022] Furthermore, in step S3, the optimization problem is constructed by the following method:

[0023] Define the kth user in the uth cell as (k,u), and assume that the signal sent by the base station to user (k,u) is x k,u , the signal covariance matrix is The set of transmitted signal covariance matrices is Then the traversal rate of user (k,u) is expressed as:

[0024]

[0025] In formula (1), Among them, the represents the interference plus noise covariance matrix of user (k,u), σ 2 is the noise variance, log is the logarithmic operation, det means taking the determinant of the matrix, N k,u ×N k,u The identity matrix of Represents the matrix G k,u,v Perform conjugate transpose;

[0026] For the u-th cell, its power consumption model is:

[0027]

[0028] In formula (2), tr{·} represents the operation of taking the matrix trace, is the signal transmission power of the cell, ξ u is the base station amplification factor, P c,u is the dynamic power dissipated in each antenna, P s,u is the static circuit power dissipated in the hardware;

[0029] The energy efficiency of the u-th cell is expressed as the ratio of the sum of the rates of all users in the cell to the total power consumption multiplied by the bandwidth W:

[0030]

[0031] In formula (3), EE u (Λ) represents energy efficiency;

[0032] Resource efficiency is defined as the weighted sum of energy efficiency and spectrum efficiency, and its specific expression is:

[0033]

[0034] In formula (4),

[0035]

[0036]

[0037]

[0038] P tot,u =ξ u P max,u +MP c,u +P s,u ;

[0039] Among them, SE u (Λ) represents the spectral efficiency of cell u, and the auxiliary function f k,u (Λ) represents the subtracted term of the achievable rate of user (k,u) in formula (1), and the auxiliary function g k,u (Λ) represents the subtraction term of the achievable rate of user (k,u) in formula (1), P tot,u is a constant normalization factor, β is a weight factor, P max,u is the transmission power constraint of the base station in the u-th cell;

[0040] In order to solve the optimal power allocation matrix, a multi-cell massive MIMO beam domain power allocation problem is constructed:

[0041]

[0042] In formula (5), min is the minimum value operation.

[0043] Furthermore, in step S3, the optimization problem is solved by using the deterministic equivalent method, the MM method and the iterative water filling algorithm to obtain the optimal power allocation matrix, which specifically includes:

[0044] Step S301: Initialize the covariance matrix Λ of the transmitted signal (0) , set the number of iterations to indicate l = 0, and the initial resource efficiency is Among them, the covariance matrix Λ of the initial transmission signal (0) When , power is allocated to the N beams with the strongest beam gain according to the beam domain statistical channel state information, and N is selected using the greedy algorithm;

[0045] Step S302: Calculate the user rate R k,u The subtracted term f in the expression (Λ) k,u The deterministic equivalent value of (Λ) specifically includes:

[0046] Step S3021, introduce and iteratively calculate the following four deterministic equivalent auxiliary variables, expressed as:

[0047]

[0048]

[0049]

[0050]

[0051] in, N k,u ×N k,u The identity matrix, I M is the M×M identity matrix, Λ k,u is the power allocation matrix of user (k,u), T k,u (X) and F k,u (X) is the diagonal matrix function of user (k,u), which is M-dimensional and N-dimensional respectively. k,u dimensional matrix, X refers to the general function variable, and its diagonal elements are expressed as:

[0052] [T k,u (X)] m,m =tr{diag[Ω k,u,u ] :,m X};

[0053]

[0054] During the iteration process, the four auxiliary variables will tend to converge, and the iteration will stop when the change value of the auxiliary variable is less than the given threshold;

[0055] Step S3022, f k,u Deterministic equivalent value of (Λ) It is expressed as:

[0056]

[0057] Step S303: Set the user rate to R k,u The subtrahend term of (Λ) is g k,u (Λ), which is expressed as:

[0058]

[0059] Then calculate the derivative terms needed in the MM iterative algorithm:

[0060]

[0061] In formula (7), Represents the matrix Ω k,u,j The nth row vector of represents the power allocation matrix of user (p,q) at the lth iteration;

[0062] Step S304: According to the MM iterative algorithm, the user rate g k,u The terms in (Λ) are replaced by their first-order Taylor expansions The specific expression is:

[0063]

[0064] In formula (7), Λ i,j represents the power allocation matrix of user (i, j);

[0065] Step S305: f k,u (Λ) is replaced by its deterministic equivalent Then the optimization problem of maximizing the minimum resource efficiency becomes the following form:

[0066]

[0067] Step S306: Use the distributed iterative water injection algorithm to solve the above problem and obtain the solution Λ of the optimization problem in this iteration. (l+1) ;

[0068] Step S307: Using the solution Λ of this iteration (l+1) Calculate the new energy efficiency value for each cell:

[0069]

[0070] Step S308: The minimum resource value obtained in the l+1th iteration The result of the first iteration Compare and if the difference between the two results is less than the set threshold ε1, terminate the iteration and use the power allocation matrix obtained in step S307 as the final solution; otherwise, add 1 to the number of iterations l, jump back to step S302 and substitute the solution of this iteration, recalculate the deterministic equivalent value of the user rate and the first-order Taylor expansion term of the MM algorithm, and repeat the above steps.

[0071] Furthermore, in step S306, a distributed algorithm is used, with cells as units, and each cell performs power allocation calculations separately, and the power allocation matrix set of cell u is expressed as The set of power allocation matrices excluding all users in the u-th cell is denoted as

[0072] Furthermore, in step S306, each cell independently performs the following method:

[0073] Step S3061: When the uth cell performs power allocation, the parameters from other cells are regarded as constants, that is, Then the objective function of the u-th cell is expressed as:

[0074]

[0075] Correspondingly, the maximum resource efficiency problem of the u-th cell is:

[0076]

[0077] Step S3062: For problem (12), transform it into two nested sub-problems, where:

[0078] The inner optimization problem is defined as:

[0079]

[0080] In formula (13), Indicates that at a given transmission power P T,u The maximum spectral efficiency of the system under

[0081] The outer optimization problem is defined as:

[0082]

[0083] In formula (14), Indicates that at a given transmission power P T,uMaximum system energy efficiency under

[0084] Step S3063: Initialize a transmission power P T,u (0) and the step size s required by the gradient method, set the iteration indicator n = 0;

[0085] Step S3064: Set P T,u =P T,u (n), Substitution problem Then set the iteration indicator t = 0 and let the auxiliary matrix in, The collection is

[0086] Step S3065: Use KKT conditions to obtain the problem The equivalent fractional equation, X k The mth diagonal element of satisfies the following formula:

[0087]

[0088] In formula (15), γ k,u,m and x k,m They are Γ k,u and X k The m-th diagonal element of and are the derivative of the MM algorithm of user (a,u) and the deterministic equivalent auxiliary matrix, Ω a,u,u is the statistical channel information matrix from base station u to user (a,u), θ u is a Lagrange multiplier that satisfies the condition

[0089] Auxiliary variable ν k,m It is used to represent the critical value of the Lagrange multiplier, which is specifically expressed as:

[0090]

[0091] The auxiliary function is defined as follows:

[0092]

[0093]

[0094] in, represents the set of all power allocation matrices except the u-th cell at the l-th MM iteration, Represents the matrix Ω a,u,q The nth row vector of a,u,qis the statistical channel information matrix from base station q to user (a,u), Represents a set with k, m, a as parameters;

[0095] Step S3066: Use Newton's method to solve the above fractional equation to obtain the value of the auxiliary matrix, and update the water injection result to X (t+1) ;

[0096] Step S3067: X obtained in the t+1th iteration (t+1) The calculated objective function is compared with the objective function obtained in the tth iteration. If the difference between the two is less than or equal to the set threshold ε2, the iteration is terminated and the value of the auxiliary matrix obtained in step S3066 is used as the optimal solution of the power allocation matrix. Otherwise, increase the number of iterations by 1 and jump back to step S3066;

[0097] Step S3068: Solution of the optimal power allocation matrix obtained in step S3067 and the value of the Lagrange multiplier θ u , calculate the derivative value required by the gradient method, which is expressed as:

[0098]

[0099] In formula (17),

[0100] Step S3069: Update the transmit power using the gradient method, which is expressed as:

[0101]

[0102] Step S30610: The transmission power P obtained in the n+1th iteration is T,u (n+1) and the result P obtained by the nth iteration T,u (n) is compared. If the difference between the two is less than a certain set threshold ε3, the iteration is terminated and the solution of the power allocation matrix obtained in step S3067 is replaced by As a question otherwise, increase the number of iterations by 1 and jump back to step S3064.

[0103] The beneficial effects of the present invention are:

[0104] 1. In the present invention, the base station communicates with users in the cell in the beam domain, which can match the spatial characteristics of the massive MIMO wireless channel, thereby obtaining the improvement of energy efficiency and spectral efficiency brought by the use of a massive antenna array;

[0105] 2. In the present invention, each base station obtains the beam domain statistical channel state information of each user through sparse detection signals. Therefore, this method is applicable to time division duplex and frequency division duplex systems, and can make full use of the beam domain statistical channel state information of users in the local cell and users in other cells.

[0106] 3. The present invention utilizes the iterative algorithm of the deterministic equivalent method, the MM iterative algorithm and the iterative water filling algorithm to perform distributed multi-cell large-scale MIMO beam domain power allocation, which can achieve a balance between system energy efficiency and spectral efficiency, and significantly reduce the complexity of solving the optimization problem and the physical layer implementation, thereby speeding up the calculation speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 A schematic diagram of the flow of the distributed multi-cell large-scale MIMO power allocation method for joint optimization of energy efficiency and spectrum efficiency provided in Example 1;

[0108] Figure 2 This is a flow chart of a distributed iterative algorithm based on a deterministic equivalent method and an MM iterative algorithm provided in Example 1;

[0109] Figure 3 This is a schematic diagram of the process based on the iterative water injection algorithm provided in Example 1. DETAILED DESCRIPTION

[0110] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0111] See also Figure 1-Figure 3 This embodiment provides a distributed multi-cell large-scale MIMO power allocation method with joint optimization of energy efficiency and spectrum efficiency, the method comprising the following steps:

[0112] Step S1: construct a cell cluster and configure the antenna array, and generate a beam set through beamforming:

[0113] Specifically, in this embodiment, step S1 specifically includes:

[0114] Several cells are constructed into a cell cluster, and the base stations of each cell in the cell cluster are equipped with large-scale antenna arrays, where the number of antennas is 10 2 or 10 3 The size of the beam is orders of magnitude, and a large-scale beam set capable of covering all cells is generated through beamforming;

[0115] The base station generates a large-scale beam that can cover the entire cell through the same unitary transformation. Each beam divides the spatial resources, and the base station communicates with the users of the cell in the generated beam domain.

[0116] According to the multi-cell massive MIMO downlink communication scenario, each base station is configured with a massive antenna array with M transmit antennas, where M is 10 2 or 10 3 If there are U cells in total, the u-th cell contains K u target users, then the set of users is Each user configures N k,u Root receiving antenna.

[0117] Step S2: Each cell base station obtains statistical channel state information of users in the cell respectively;

[0118] Specifically, distributed collaboration is performed between cells, and each cell base station only needs to obtain channel information of users in the cell. In this embodiment, the statistical channel state information of users in the cell is obtained by adopting user feedback, direct estimation by the base station, or uplink detection signals.

[0119] Step S3: Each cell base station performs distributed multi-cell large-scale MIMO beam domain power allocation with joint optimization of energy efficiency and spectrum efficiency based on the statistical channel state information of users in the cell and a small amount of information exchanged between other base stations:

[0120] Specifically, in this embodiment, step S3 includes:

[0121] Power allocation with joint optimization of energy efficiency and spectrum efficiency is performed using deterministic equivalent method, MM method and iterative water filling algorithm;

[0122] The optimization goal of the power allocation optimization problem is to minimize the resource efficiency of each cell. Resource efficiency is the weighted sum of energy efficiency and spectrum efficiency, where spectrum efficiency is the reachable traversal sum rate of the cell, and energy efficiency is the ratio of the reachable traversal sum rate of the cell to the total power consumption. The optimization variable is the covariance matrix of the signal sent by each base station, and the constraint condition is that the covariance matrix of the signal sent by each base station satisfies the power constraint. The power allocation problem is solved based on a distributed method.

[0123] More specifically, step S3 includes the following sub-steps:

[0124] Step S301: According to the large-dimensional random matrix theory, the system spectral effect is calculated by using the beam domain statistical channel state information, so as to achieve the deterministic equivalent value of the ergodic sum rate, thereby calculating the deterministic equivalent value of the objective function; and the sum rate is converted into a concave function by using the MM transform;

[0125] Step S302: convert the sub-problem after MM transformation into a problem of solving the power allocation matrix of each cell respectively, and regard other cell parameters as constants when solving the optimization problem of the cell; for the power allocation problem of each cell, decompose it into an inner optimization sub-problem and an outer optimization sub-problem; wherein the optimization goal of the inner optimization sub-problem is to solve the optimal power allocation matrix that maximizes the system and rate, and the optimization goal of the outer optimization sub-problem is to solve the optimal transmission power that maximizes resource efficiency;

[0126] Step S303: using an iterative water filling algorithm to solve the inner optimization sub-problem, and using a gradient method to update the transmission power according to the inner optimization result;

[0127] If the transmit power converges, the iteration ends and the result of the inner sub-problem is used as the result of the cell optimization problem.

[0128] Step S4: dynamically implement multi-cell massive MIMO beam domain power allocation according to changes in statistical channel state information:

[0129] Specifically, in this embodiment, step S4 specifically includes: when the user moves during the communication process, the statistical channel state information between the base station and the user will change, each base station dynamically implements beam domain power allocation, and the distributed multi-cell large-scale MIMO power allocation process with joint optimization of energy efficiency and spectral efficiency is dynamically updated.

[0130] The above are specific steps of the method of this embodiment. The method of this embodiment is described in more detail below in conjunction with a specific scenario, including:

[0131] Part 1: Building a multi-cell massive MIMO beam-domain communication model

[0132] Specifically, consider a multi-cell massive MIMO scenario where a massive antenna array with M transmit antennas is configured on the base station side, and M is 10 2 or 10 3 Order of magnitude, on the user side, there are K u target users, each user is configured with N k,u Root receiving antenna.

[0133] In the channel detection phase, each user sends an uplink detection signal to the base station. The base station estimates the beam domain statistical channel state information based on the received detection signal. The statistical channel state information from the base station in the vth cell to the kth user in the uth cell is:

[0134]

[0135] In formula (1), G k,u,vis the beam domain channel matrix from the base station of the νth cell to the kth user of the uth cell, represents the expectation operation, ⊙ represents the Hadamard product of the matrix, is the matrix G k,u,v The conjugate matrix of .

[0136] Each base station transforms the spatial domain signal sent to each user into the beam domain through a unified unitary transformation, and sends a signal to each user in the cell. The kth user in the uth cell is defined as (k,u). Assume that the signal sent by the base station to user (k,u) is x k,u , the signal covariance matrix is The set of transmitted signal covariance matrices is Then the traversal rate of user (k,u) can be expressed as:

[0137]

[0138] In formula (2), σ 2 is the noise variance, log is the logarithmic operation, det means taking the determinant of the matrix, N k,u ×N k,u The identity matrix of Represents the matrix G k,u,v Perform conjugate transpose; is the interference plus noise covariance matrix of user (k,u).

[0139] For the u-th cell, its power consumption model is:

[0140]

[0141] In formula (3), tr{·} represents the operation of taking the matrix trace, is the signal transmission power of the cell, ξ u (>1) is the base station amplification factor, P c,u is the dynamic power dissipated in each antenna, P s,u is the static circuit power dissipated in the hardware.

[0142] The energy efficiency of the u-th cell is expressed as the ratio of the sum of the rates of all users in the cell to the total power consumption multiplied by the bandwidth W:

[0143]

[0144] In formula (4), EE u (Λ) represents energy efficiency;

[0145] In order to better balance the energy efficiency and spectrum efficiency of the system, a new optimization goal is proposed, called resource efficiency. Specifically, resource efficiency is defined as the weighted sum of energy efficiency and spectrum efficiency, and its specific expression is:

[0146]

[0147] In formula (5),

[0148]

[0149]

[0150]

[0151] P tot,u =ξ u P max,u +MP c,u +P s,u ;

[0152] Among them, SE u (Λ) represents the spectral effect of cell u. For the convenience of the subsequent steps, an auxiliary function f is defined k,u (Λ) and g k,u (Λ), respectively represent the subtracted and minus terms of the achievable rate of user (k,u) in formula (2), P tot,u is a constant normalization factor, in order to normalize the units of energy efficiency and spectrum efficiency in formula (5) to bits / Joule / Hz. β is the weight factor, P max,u is the transmission power constraint of the base station in the u-th cell.

[0153] Considering the energy efficiency and spectrum efficiency balance problem in multi-cell massive MIMO communication, in order to solve the optimal power allocation matrix, the multi-cell massive MIMO beam domain power allocation problem is constructed:

[0154]

[0155] In formula (6), min is the minimum value operation.

[0156] Since the objective function of the above problem is non-convex, it is difficult to obtain a global optimal solution, and the implementation complexity is very high. To this end, this embodiment proposes a distributed multi-cell large-scale MIMO power allocation method that jointly optimizes energy efficiency and spectrum efficiency using beam domain statistical channel state information. Specifically, this method includes an iterative algorithm based on deterministic equivalence and MM methods and an iterative water injection algorithm.

[0157] Part II: Iterative Algorithms Based on Deterministic Equivalence and MM Methods

[0158] When calculating the rate of cell users, it is necessary to traverse the channel and calculate the expected value. Since there is no closed-form expression for the expectation, Monte-Carlo simulation calculation is required. In order to avoid the high-complexity expectation calculation, the present invention uses large-dimensional matrix random theory to calculate the deterministic equivalent expression of the objective function to reduce the computational complexity. The deterministic equivalent method only uses statistical channel state information and iteratively calculates the deterministic equivalent auxiliary variables to obtain the approximate result of the objective function value. At the same time, since the deterministic equivalent result can well approximate the accurate expression of the rate term, the deterministic equivalent method can be used simultaneously in the power allocation method based on the MM iterative algorithm.

[0159] The implementation process based on the deterministic equivalent method and the MM iterative algorithm is as follows: Figure 2 As shown, it specifically includes the following steps:

[0160] Step S301: Initialize the covariance matrix Λ of the transmitted signal (0) , set the number of iterations to indicate l = 0, and the initial resource efficiency is Among them, the covariance matrix Λ of the initial transmission signal (0) When , power can be allocated to the N beams with the strongest beam gain according to the beam domain statistical channel state information, and N is selected using a greedy algorithm.

[0161] Step S302: Calculate the user rate R k,u The subtracted term f in the expression (Λ) k,u The deterministic equivalent value of (Λ) specifically includes:

[0162] Step S3021, introduce and iteratively calculate the following four deterministic equivalent auxiliary variables, expressed as:

[0163]

[0164]

[0165]

[0166]

[0167] in, N k,u ×N k,u The identity matrix, I M is the M×M identity matrix, Λ k,u is the power allocation matrix of user (k,u), T k,u (X) and F k,u (X) is the diagonal matrix function of user (k,u), and X refers to the general function variable. k,udimensional matrix, its diagonal elements can be expressed as:

[0168] [T k,u (X)] m,m =tr{diag[Ω k,u,u ] :,m X};

[0169]

[0170] During the iteration process, the four auxiliary variables will tend to converge, and the iteration will stop when the change value of the auxiliary variable is less than the given threshold.

[0171] Step S3022, f k,u Deterministic equivalent value of (Λ) It can be expressed as:

[0172]

[0173] Step S303: Set the user rate to R k,u The subtrahend term of (Λ) is g k,u (Λ), which is expressed as:

[0174]

[0175] Then calculate the derivative terms needed in the MM iterative algorithm:

[0176]

[0177] In formula (8), Represents the matrix Ω k,u,j The nth row vector of represents the power allocation matrix of user (p,q) at the lth iteration.

[0178] Step S304: According to the MM iterative algorithm, the derivative term calculated using formula (8) Set the user rate g k,u The terms in (Λ) are replaced by their first-order Taylor expansions The specific expression is:

[0179]

[0180] In formula (9), Λ i,j represents the power allocation matrix of user (i, j).

[0181] Step S305: f k,u (Λ) is replaced by its deterministic equivalent That is, formula (7), then the optimization problem of maximizing the minimum resource efficiency becomes the following form:

[0182]

[0183] Step S306: Use the distributed iterative water injection algorithm to solve the above problem and obtain the solution Λ of the optimization problem in this iteration. (l+1) .

[0184] Step S307: Using the solution Λ of this iteration (l+1) Calculate the new energy efficiency value for each cell:

[0185]

[0186] Step S308: The minimum resource value obtained in the l+1th iteration The result of the first iteration Compare and if the difference between the two results is less than the set threshold ε1, the iteration is terminated and the power allocation matrix obtained in step S307 is used as the final solution;

[0187] Otherwise, the number of iterations l is increased by 1, and the process jumps back to step S302 and substitutes the solution of this iteration, recalculates the deterministic equivalent value of the user rate and the first-order Taylor expansion term of the MM algorithm, and repeats the above steps.

[0188] Specifically, in this embodiment, the threshold ε1 can be set by a technician according to actual conditions, and the specific value is not limited in this embodiment.

[0189] Part III: Distributed Algorithm Based on Iterative Water Injection Algorithm

[0190] The sub-optimization problem after deterministic equivalence and MM algorithm is a maximum-minimum problem, and its objective function is a discontinuous minimum function. In order to solve this problem, a distributed algorithm is adopted, with cells as units, and each cell performs power allocation calculations separately.

[0191] For convenience of representation, the power allocation matrix set of cell u is expressed as The set of power allocation matrices excluding all users in the u-th cell is denoted as

[0192] The implementation process of the distributed algorithm based on iterative water injection algorithm is as follows: Figure 3 As shown, each cell u executes the algorithm when performing power allocation in the cell. The algorithm includes the following steps:

[0193] Step S3061: When the uth cell performs power allocation, the parameters from other cells are regarded as constants, that is, Then the objective function of the u-th cell can be expressed as:

[0194]

[0195] Correspondingly, the maximum resource efficiency problem of the u-th cell is:

[0196]

[0197] The above problem can be solved by iteratively optimizing two nested subproblems.

[0198] Step S3062: For problem (13), transform it into two nested sub-problems, where:

[0199] The inner optimization problem can be defined as:

[0200]

[0201] In formula (14), Indicates that at a given transmission power P T,u The maximum spectral efficiency of the system under .

[0202] The outer optimization problem can be defined as:

[0203]

[0204] In formula (15), Indicates that at a given transmission power P T,u Maximum system energy efficiency under .

[0205] Step S3063: Initialize a transmission power P T,u (0) and the step size s required by the gradient method, set the iteration indicator n = 0;

[0206] Step S3064: Set P T,u =P T,u (n), Substitution problem Then set the iteration indicator t = 0 and let the auxiliary matrix in, The collection is

[0207] Step S3065: Use KKT conditions to obtain the problem The equivalent fractional equation, X k The mth diagonal element x k,m Satisfy the following formula:

[0208]

[0209] In formula (16), for convenience of expression, we define γ k,u,m and x k,m for Γ k,uand X k The m-th diagonal element of and are the derivative of the MM algorithm of user (a,u) and the deterministic equivalent auxiliary matrix, Ω a,u,u is the statistical channel information matrix from base station u to user (a,u). u is a Lagrange multiplier that satisfies the condition

[0210] Auxiliary variable ν k,m Used to represent the critical value of the Lagrange multiplier, expressed as:

[0211]

[0212] The auxiliary function is defined as follows:

[0213]

[0214]

[0215] In the formula represents the set of all power allocation matrices except the u-th cell at the l-th MM iteration, Represents the matrix Ω a,u,q The nth row vector of a,u,q is the statistical channel information matrix from base station q to user (a,u), Represents a set with k, m, and a as parameters.

[0216] Step S3066: Use Newton's method to solve the above fractional equation to obtain the value of the auxiliary matrix, and update the water injection result to X (t+1) .

[0217] Step S3067: X obtained in the t+1th iteration (t+1) The calculated objective function is compared with the objective function obtained in the tth iteration. If the difference between the two is less than or equal to the set threshold ε2, the iteration is terminated and the value of the auxiliary matrix obtained in step S3066 is used as the optimal solution of the power allocation matrix.

[0218] Otherwise, increase the number of iterations by 1 and jump back to step S3066.

[0219] The threshold ε2 may be set by those skilled in the art according to actual conditions.

[0220] Step S3068: Solution of the optimal power allocation matrix obtained in step S3067 and the value of the Lagrange multiplier θ u, calculate the derivative value required by the gradient method, which is expressed as:

[0221]

[0222] In formula (18),

[0223] Step S3069: Update the transmit power using the gradient method, which is expressed as:

[0224]

[0225] Step S30610: The transmission power P obtained in the n+1th iteration is T,u (n+1) and the result P obtained by the nth iteration T,u (n) is compared. If the difference between the two is less than a certain set threshold ε3, the iteration is terminated and the solution of the power allocation matrix obtained in step S3067 is replaced by As a question The solution;

[0226] Otherwise, the number of iterations is increased by 1, and the process jumps back to step S3064. The threshold ε3 can be set by those skilled in the art according to actual conditions.

[0227] Part IV: Dynamic Implementation of Distributed Multi-Cell Massive MIMO Beam-Domain Power Allocation

[0228] During the movement of each user, as the beam domain statistical channel state information between the base station and the user changes, the base station side repeats the above steps according to the updated statistical channel state information, and dynamically implements distributed multi-cell large-scale MIMO power allocation based on the deterministic equivalent method, MM iterative algorithm and iterative water filling algorithm, thereby realizing dynamic update of the transmission process.

[0229] In summary, since the changes in beam domain statistical channel state information are related to the specific application scenarios, the base station updates the statistical channel state information according to the application scenarios and the corresponding time intervals. Its typical statistical time window is several times or dozens of times the short-term transmission time window. The acquisition of relevant statistical channel state information is also carried out over a larger time width. The distributed multi-cell large-scale MIMO power allocation based on the deterministic equivalent method, MM iterative algorithm and iterative water filling algorithm is dynamically implemented. This method can significantly improve the resource efficiency of the system.

[0230] The matters not described in detail in the present invention are all known technologies to those skilled in the art.

[0231] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A distributed multi-cell massive MIMO power allocation method with joint optimization of energy efficiency and spectrum efficiency, characterized in that: The power allocation method comprises the following steps: Step S1: construct multiple cells into a cell cluster and configure a large-scale antenna array at the base station of each cell, and generate a beam set through beamforming; Step S2: Each cell base station obtains statistical channel state information of users in the cell respectively; Step S3, each cell base station performs power allocation based on the acquired statistical channel state information, which includes: first constructing an optimization problem with the optimization target being the minimum value of the resource efficiency of each cell, the optimization variable being the covariance matrix of the signal sent by each base station, and the constraint condition being that the covariance matrix of the signal sent by each base station satisfies the power constraint, and then using the deterministic equivalent method, the MM method and the iterative water filling algorithm to solve the optimization problem, and obtain the optimal power allocation matrix, and each base station implements power allocation with the obtained optimal power allocation matrix; wherein the resource efficiency is the weighted sum of energy efficiency and spectral efficiency, the spectral efficiency is the reachable traversal sum rate of the cell, and the energy efficiency is the ratio of the reachable traversal sum rate of the cell to the total power consumption; In step S3, the optimization problem is solved by using the deterministic equivalent method, the MM method and the iterative water filling algorithm to obtain the optimal power allocation matrix, which specifically includes: First, according to the large-dimensional random matrix theory, the system spectral efficiency is calculated using the beam domain statistical channel state information obtained in step S2, which includes: introducing deterministic equivalent auxiliary variables, determining the deterministic equivalent values ​​of the reachable traversal and the rate, and then calculating the deterministic equivalent value of the objective function, and then converting the optimization problem into a concave function through MM transformation; Then, the sub-problems after MM transformation are converted into the problem of solving the power allocation matrix of each cell separately, and other cell parameters are regarded as constants when solving the optimization problem of the cell. For the power allocation problem of each cell, it is decomposed into an inner optimization sub-problem and an outer optimization sub-problem. The optimization goal of the inner optimization sub-problem is to solve the optimal power allocation matrix that maximizes the system and rate, and the optimization goal of the outer optimization sub-problem is to solve the optimal transmission power that maximizes resource efficiency. Finally, the iterative water injection algorithm is used to solve the inner optimization subproblem, and the gradient method is used to update the transmit power according to the inner optimization result. If the transmit power converges, the iteration ends and the result of the inner subproblem is used as the result of the cell optimization problem. In step S3, the optimization problem is constructed by the following method: Define the kth user in the uth cell as (k,u), and assume that the signal sent by the base station to user (k,u) is x k,u , the signal covariance matrix is The set of transmitted signal covariance matrices is Then the traversal rate of user (k,u) is expressed as: In formula (1), Among them, the represents the interference plus noise covariance matrix of user (k,u), σ 2 is the noise variance, log is the logarithmic operation, det means taking the determinant of the matrix, N k,u ×N k,u The identity matrix of Represents the matrix G k,u,v Perform conjugate transpose; For the u-th cell, its power consumption model is: In formula (2), tr{·} represents the operation of taking the matrix trace, is the signal transmission power of the cell, ξ u is the base station amplification factor, P c,u is the dynamic power dissipated in each antenna, P s,u is the static circuit power dissipated in the hardware; The energy efficiency of the u-th cell is expressed as the ratio of the sum of the rates of all users in the cell to the total power consumption multiplied by the bandwidth W: In formula (3), EE u (Λ) represents energy efficiency; Resource efficiency is defined as the weighted sum of energy efficiency and spectrum efficiency, and its specific expression is: In formula (4), P tot,u =ξ u P max,u +MP c,u +P s,u ; Among them, SE u (Λ) represents the spectral efficiency of cell u, and the auxiliary function f k,u (Λ) represents the subtracted term of the achievable rate of user (k,u) in formula (1), and the auxiliary function g k,u (Λ) represents the subtraction term of the achievable rate of user (k,u) in formula (1), P tot,u is a constant normalization factor, β is a weight factor, P max,u is the transmission power constraint of the base station in the u-th cell; In order to solve the optimal power allocation matrix, a multi-cell massive MIMO beam domain power allocation problem is constructed: In formula (5), min is the minimum value operation; In step S3, the optimization problem is solved by using the deterministic equivalent method, the MM method and the iterative water filling algorithm to obtain the optimal power allocation matrix, which specifically includes: Step S301: Initialize the covariance matrix Λ of the transmitted signal (0) , set the number of iterations to indicate l = 0, and the initial resource efficiency is Among them, the covariance matrix Λ of the initial transmission signal (0) When , power is allocated to the N beams with the strongest beam gain according to the beam domain statistical channel state information, and N is selected using the greedy algorithm; Step S302: Calculate user rate R k,u The subtracted term f in the expression (Λ) k,u The deterministic equivalent value of (Λ) specifically includes: Step S3021, introduce and iteratively calculate the following four deterministic equivalent auxiliary variables, expressed as: in, N k,u ×N k,u The identity matrix, I M is the M×M identity matrix, Λ k,u is the power allocation matrix of user (k,u), T k,u (X) and F k,u (X) is the diagonal matrix function of user (k,u), which is M-dimensional and N-dimensional respectively. k,u dimensional matrix, X refers to the general function variable, and its diagonal elements are expressed as: [T k,u (X)] m,m =tr{diag[Ω k,u,u ] :,m X}; During the iteration process, the four auxiliary variables will tend to converge, and the iteration will stop when the change value of the auxiliary variable is less than the given threshold; Step S3022, f k,u Deterministic equivalent value of (Λ) It is expressed as: Step S303: Set the user rate to R k,u The subtrahend term of (Λ) is g k,u (Λ), which is expressed as: Then calculate the derivative terms needed in the MM iterative algorithm: In formula (7), Represents the matrix Ω k,u,j The nth row vector of represents the power allocation matrix of user (p,q) at the lth iteration; Step S304: According to the MM iterative algorithm, the user rate g k,u The terms in (Λ) are replaced by their first-order Taylor expansions The specific expression is: In formula (7), Λ i,j represents the power allocation matrix of user (i, j); Step S305: f k,u (Λ) is replaced by its deterministic equivalent Then the optimization problem of maximizing the minimum resource efficiency becomes the following form: Step S306: Use the distributed iterative water injection algorithm to solve the above problem and obtain the solution Λ of the optimization problem in this iteration. (l+1) ; Step S307: Using the solution Λ obtained in this iteration (l+1) Calculate the new energy efficiency value for each cell: Step S308: The minimum resource value obtained in the l+1th iteration The result of the first iteration Compare, if the difference between the two results is less than the set threshold ε1, then terminate the iteration and use the power allocation matrix obtained in step S307 as the final solution; otherwise, add 1 to the number of iterations l, jump back to step S302 and substitute the solution of this iteration, recalculate the deterministic equivalent value of the user rate and the first-order Taylor expansion term of the MM algorithm, and repeat the above steps; In step S306, a distributed algorithm is used, with cells as units, and each cell performs power allocation calculations separately, and the power allocation matrix set of cell u is expressed as The set of power allocation matrices excluding all users in the u-th cell is denoted as In step S306, each cell independently performs the following method: Step S3061: When the uth cell performs power allocation, the parameters from other cells are regarded as constants, that is, Then the objective function of the u-th cell is expressed as: Correspondingly, the maximum resource efficiency problem of the u-th cell is: Step S3062: For problem (12), transform it into two nested sub-problems, where: The inner optimization problem is defined as: In formula (13), Indicates that at a given transmission power P T,u The maximum spectral efficiency of the system under The outer optimization problem is defined as: In formula (14), Indicates that at a given transmission power P T,u Maximum system energy efficiency under Step S3063: Initialize a transmission power P T,u (0) and the step size s required by the gradient method, set the iteration indicator n = 0; Step S3064: Set P T,u =P T,u (n), Substitution problem In the example above, we set the iteration indicator t = 0 and let the auxiliary matrix in, The collection is Step S3065: Use KKT conditions to obtain the problem The equivalent fractional equation, X k The mth diagonal element of satisfies the following formula: In formula (15), γ k,u,m and x k,m They are Γ k,u and X k The mth diagonal element of and are the derivative of the MM algorithm of user (a,u) and the deterministic equivalent auxiliary matrix, Ω a,u,u is the statistical channel information matrix from base station u to user (a,u), θ u is a Lagrange multiplier that satisfies the condition Auxiliary variable ν k,m It is used to represent the critical value of the Lagrange multiplier, which is specifically expressed as: The auxiliary function is defined as follows: in, represents the set of all power allocation matrices except the u-th cell at the l-th MM iteration, Represents the matrix Ω a,u,q The nth row vector of a,u,q is the statistical channel information matrix from base station q to user (a,u), Represents a set with k, m, a as parameters; Step S3066: Use Newton's method to solve the above fractional equation to obtain the value of the auxiliary matrix, and update the water injection result to X (t+1) ; Step S3067: X obtained in the t+1th iteration (t+1) The calculated objective function is compared with the objective function obtained in the tth iteration. If the difference between the two is less than or equal to the set threshold ε2, the iteration is terminated and the value of the auxiliary matrix obtained in step S3066 is used as the optimal solution of the power allocation matrix. Otherwise, increase the number of iterations by 1 and jump back to step S3066; Step S3068: Solution of the optimal power allocation matrix obtained in step S3067 and the value of the Lagrange multiplier θ u , calculate the derivative value required by the gradient method, which is expressed as: In formula (17), Step S3069: Update the transmit power using the gradient method, which is expressed as: Step S30610: The transmission power P obtained in the n+1th iteration is T,u (n+1) and the result P obtained by the nth iteration T,u (n) is compared. If the difference between the two is less than a certain set threshold ε3, the iteration is terminated and the solution of the power allocation matrix obtained in step S3067 is replaced by As a question otherwise, increase the number of iterations by 1 and jump back to step S3064.

2. The distributed multi-cell massive MIMO power allocation method with joint optimization of energy efficiency and spectrum efficiency according to claim 1 is characterized in that: The power allocation method further comprises: Dynamically implement multi-cell massive MIMO beam-domain power allocation based on changes in statistical channel state information; When a user moves during the communication process, the statistical channel state information between the base station and the user will change, and each base station will dynamically implement beam domain power allocation.

3. The distributed multi-cell massive MIMO power allocation method with joint optimization of energy efficiency and spectrum efficiency according to claim 1 is characterized in that: In step S1, a large-scale antenna array is configured in the base station of each cell, and the number of antennas is 10 2 or 10 3 The size of the beam is orders of magnitude, and a large-scale beam set capable of covering all cells is generated through beamforming; The base station generates a large-scale beam that can cover the entire cell through the same unitary transformation. Each beam divides the spatial resources, and the base station communicates with the users of the cell in the generated beam domain.

4. The distributed multi-cell massive MIMO power allocation method with joint optimization of energy efficiency and spectrum efficiency according to claim 1, characterized in that: In step S2, each cell base station only needs to obtain channel information of users in the cell; The statistical channel state information of users in the cell is obtained by adopting user feedback, direct estimation by the base station, or by using uplink detection signals.

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