Cross-subcarrier precoding design method for massive MIMO-OFDM

Abstract

The present invention discloses a large-scale MIMO-OFDM cross-subcarrier precoding design method. The present invention designs a transform domain precoding vector, and the precoding vectors on different subcarriers are obtained by transforming the transform domain precoding vector. The number of transform domain precoding vectors to be designed is less than the number of subcarriers, so that the number of parameters required for the precoding design is significantly reduced. Based on the a posteriori beam domain statistical channel model, the transform domain precoding vector is optimized and designed by maximizing the traversal and rate upper bounds. First, a stable solution is obtained by using the traversal and rate minimization function and the minimum and maximum algorithm. Then, the block coordinate descent BCD method and the low-complexity algorithm of power allocation are used to reduce the problem of too large matrix inversion dimension in the stable solution. Compared with the traditional precoding design scheme, the large-scale MIMO-OFDM cross-subcarrier precoding design method proposed by the present invention reduces the computational complexity while maintaining performance close to the optimal sum rate.

Description

Technical Field

[0001] The present invention relates to wireless communication downlink precoding, and in particular to a large-scale multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) precoding method in a time division duplex (TDD) mode. Background Art

[0002] Massive multiple-input-multiple-output (MIMO) significantly improves spectrum and energy efficiency by deploying large-scale antenna arrays on the base station (BS) side to serve a large number of user terminals. It has been deeply studied and has become an important technology for future cellular systems. Massive MIMO has also been applied to many other applications and services, including the Internet of Things and drone communications. The base station uses channel state information (CSI) for precoding design to suppress interference between users. At present, most precoding-related research focuses on time division duplex (TDD) systems. By utilizing the reciprocity of uplink and downlink channels, the base station can directly estimate the downlink channel information from the uplink channel and then directly perform precoding design.

[0003] However, deploying a large-scale antenna array on the base station side will make it difficult to obtain instantaneous CSI. In addition, when the system bandwidth increases, the precoding design will bring a lot of computational overhead. Therefore, it is very important to design an efficient precoder to meet the high throughput and low complexity requirements of the massive MIMO-OFDM downlink. With the application of massive antenna arrays and broadband in 5G wireless communication systems, the traditional solution of precoding design for each subcarrier has become difficult to use due to the high hardware cost. To solve this problem, a solution of designing a frequency-flat precoder for all subcarriers has been proposed. However, the beam tilt effect caused by large antenna size and large bandwidth will cause significant performance degradation in precoding design. In order to combat beam tilt, the relevant literature uses the property that the same group of subcarrier channels have similar row space and column space to give a solution for grouping precoding design by adjacent subcarriers. So far, there is no low-complexity method for designing frequency-selective precoders using all subcarrier channels in massive MIMO-OFDM systems. Summary of the invention

[0004] Technical problem: The purpose of the present invention is to provide a large-scale MIMO-OFDM cross-subcarrier precoding design method to overcome the problem of precoding performance degradation caused by beam tilt effect, approach the optimal weighted and rate performance, and reduce the computational complexity of precoding design.

[0005] Technical solution: The present invention is a large-scale MIMO-OFDM cross-subcarrier precoding design method, comprising the following steps:

[0006] Step 1: The base station uses the channel reciprocity in the time division duplex (TDD) mode to obtain the downlink instantaneous channel information of each user terminal from the uplink channel estimation; consider the beam domain statistical channel model Get statistical channel information from where h k,m,n,c ,ω k,m,n,c and denote the channel vector, channel coupling vector and beam domain channel vector of user k on the nth OFDM symbol of the mth time slot of the cth subcarrier, respectively. V denotes the spatial sampling matrix. The superscript H, superscript *, symbol ⊙ and symbol They represent the conjugate transpose of the matrix, the conjugate of the matrix, the Hadamard product and the sample average respectively; based on the beam domain statistical channel model, the posterior beam domain statistical channel model is further obtained, and the posterior model takes into account the influence of the user's moving speed;

[0007] Step 2: Design the transform domain precoding vector {q k,i |1≤i≤N}, where the subscript i represents the index of the transform domain precoding vector designed for user k, i ranges from 1 to N, N is the total number of transform domain precoding vectors designed for user k, and the value of N can be set by yourself; it is converted into the precoding vector of user k on the cth subcarrier through a transformation matrix The precoding vector obtained after transformation It has frequency selectivity; it calculates the power allocation factor of the transform domain precoding vector to be designed based on the instantaneous channel information and statistical channel information. Where ε is obtained by stacking N power allocation coefficients, and the superscript T represents the transposition operation. represents a complex vector of dimension N;

[0008] Step 3: The base station performs large-scale MIMO-OFDM cross-subcarrier precoding design based on the power allocation factor combined with instantaneous channel information and statistical channel information.

[0009] The massive MIMO-OFDM system is equipped with a base station with a uniform planar array antenna UPA, K users are randomly distributed in the cell, and the cross-subcarrier precoding vector satisfies a total power constraint.

[0010] The transform domain precoding vector {q k,i |1≤i≤N}, and transform it into a precoding vector on each subcarrier through a transformation matrix The specific expression is

[0011]

[0012] in represents the vector obtained by stacking subcarriers for the kth user, N v Represents the total number of subcarriers used for transmission, and the Kronecker product operation is It is obtained by stacking the transform domain precoding vector of user k; the i-th column of the deterministic matrix F is in Represents the elements of the i-th column; define the matrix is the transformation matrix, where The dimension is the number of transmitting antennas M t The unit matrix can be further obtained

[0013]

[0014] The block matrix is defined as The cth sub-block is M t dimensional unit matrix.

[0015] In step 2, the power allocation factor of the transform domain precoding vector to be designed is calculated based on the instantaneous channel information and the statistical channel information. The following steps are involved:

[0016] Step 2.1: Set the number of iterations d = 0; initialize the transform domain precoding vector q k,i [d], 1≤k≤K, 1≤i≤N and power allocation factor ε i [d] and normalize the transform domain precoding vector to Make it meet the unit energy condition;

[0017] Step 2.2: Calculate the matrix function D in the minimization function of the traversal and rate upper bound based on the normalized transform domain precoding vector p [d] and A p [d], where d represents the dth iteration;

[0018] Step 2.3: Calculate the final power allocation factor iterative formula ε[d+1]=(D p [d]+μ * I N ) -1 A p [d]ε[d], where μ * represents the optimal Lagrange multiplier;

[0019] Step 2.4: Multiply the power allocation factor by the normalized transform domain precoding vector to obtain the transform domain precoding vector after power allocation

[0020] The traversal and rate upper bound minimization function in step 2.2 is a concave quadratic function tangent to the original objective function obtained by the relationship between the matrix weighted and minimum mean square error MSE minimization problem and the weighted traversal and rate maximization problem.

[0021] Calculate the power allocation factor of the transform domain precoding vector to be designed, and separate the constraints of the transform domain precoding vector in each coordinate direction, so as to simplify the precoding design using the block coordinate descent BCD method. In step 3, the transform-based cross-subcarrier precoding design based on the power allocation factor combined with the instantaneous channel information and the statistical channel information specifically includes the following steps:

[0022] Step 3.1: Calculate the noise plus interference covariance r using the transform domain precoding vector after power allocation k,c and the equivalent channel covariance

[0023] Step 3.2: Calculate the matrix function A in the minimization function k,c [d] and D c [d];

[0024] Step 3.3: Use block coordinate descent (BCD) to obtain the optimal iterative update formula of the transform domain precoding vector;

[0025] Step 3.4: According to Update the power allocation factor.

[0026] In step 3.3, the BCD algorithm is used to optimize the original q k becomes q k The i-th component q k,i To reduce the matrix inversion dimension in the design process, the optimal iterative update formula of the transform domain precoding vector is finally obtained as follows:

[0027]

[0028] in and is calculated from the matrix in the minimization function, and the superscript ij represents the block matrix index. represents the optimal Lagrange multiplier of the i-th coordinate, w k is the weight factor of user k.

[0029] Beneficial effects: Compared with the prior art, the present invention has the following advantages: This design method represents the precoding vector on the subcarrier as the product of the transformation matrix and the transform domain precoding vector. Since the number of transform domain precoding vectors is much less than the number of subcarriers, the number of parameters required for design can be significantly reduced. A low-complexity solution for solving the transform domain precoding vector is given by using the block coordinate descent BCD algorithm combined with power allocation. Compared with the traditional precoding design scheme, the design algorithm proposed in the present invention reduces the computational complexity while maintaining near-optimal and rate performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flow chart of a large-scale MIMO-OFDM cross-subcarrier precoding design method of the present invention;

[0031] Figure 2 This is a comparison diagram of the rate performance of the massive MIMO-OFDM cross-subcarrier precoding and group precoding of the present invention under similar complexity;

[0032] Figure 3 This is a comparison diagram of the rate performance of large-scale MIMO-OFDM cross-subcarrier precoding and group precoding under the same number of precodings of the present invention;

[0033] Figure 4 This is a comparison chart of the massive MIMO-OFDM cross-subcarrier precoding, SLNR precoding, and RZF precoding and rate performance of the present invention. DETAILED DESCRIPTION

[0034] In order to enable those skilled in the art to better understand the purpose, structure and function of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0035] 1. System Configuration

[0036] Consider a massive MIMO-OFDM communication system consisting of a base station and K users. The base station is equipped with a massive uniform array antenna array (UPA), and the number of vertical antennas is M. z , the number of antennas in the horizontal direction is M x , the total number of antennas on the base station side is M t =M z M x Consider N c Subcarrier and N g OFDM modulation with cyclic prefix, assuming N v subcarriers are used for transmission, the remaining N c -N vsubcarriers are set as the guard bandwidth. Considering the time division duplex TDD system, the system Doppler resource consists of several time slots, each of which contains N b The channel parameters remain constant within an OFDM symbol and vary between symbols.

[0037] 2. Beam-Domain Statistical Channel Model

[0038] The channel beam domain expression of the kth user on the cth subcarrier of the nth OFDM symbol in the mth time slot can be written as follows

[0039]

[0040] The beam domain channel is m k is a fixed vector w k,m,n,c is an element that satisfies The spatial sampling matrix is ​​denoted as V, which indicates the direction of the sampling beam. Further, the channel coupling vector is defined as

[0041]

[0042] According to existing literature, the beam domain channel The channel coupling vector ω is related to OFDM symbols and subcarriers. k,m,n,c Independent of OFDM symbols and subcarriers. For simplicity, let ω k =ω k,m,n,c Indicates statistical CSI.

[0043] Based on the a priori channel model obtained before channel estimation, the Gauss-Markov process is used to obtain the a posteriori channel model. After performing channel estimation on the first OFDM symbol, the a posteriori beam-domain statistical channel model of the downlink channel can be obtained as

[0044]

[0045] where ρ k is a coefficient related to the speed of user k. Specifically, in a quasi-static scenario, ρ k Close to 1, when the user is in a high mobility scenario, ρ k tends to a very small value. By adjusting ρ k The value of can be used to model user channels with different mobile speeds.

[0046] Further, the posterior channel is decomposed into

[0047]

[0048] in and Denote the deterministic part and random part of the downlink channel respectively. Define the function for

[0049]

[0050] in is a matrix parameter. Further, define for

[0051]

[0052] Where diag() means diagonalizing the vector.

[0053] 3. Cross-subcarrier precoding design

[0054] 3.1 Problem Statement

[0055] For simplicity, h is omitted k,m,n,c The subscripts m and n in the equation are as follows. The received signal of user k at the cth subcarrier is expressed as

[0056]

[0057] in and x k,c They represent the precoding vector and the transmitted signal of user k on the cth subcarrier respectively. Noise scalar z k,c satisfy Distribution. is Gaussian noise, then the interference plus noise covariance can be expressed as

[0058]

[0059] Assume r k,c It can be obtained on the user k side, so the traversal rate of user k is

[0060]

[0061] The goal of precoding design is to obtain the precoding vector that maximizes the weighted traversal and rate.

[0062]

[0063] where w k represents the weight factor, and P represents the total power. The above problem can be considered as a cross-subcarrier joint precoding design.

[0064] make represents the vector obtained by stacking subcarriers for the kth user. The transform domain precoding vector of user k is defined as {q k,i|1≤i≤N}, further, let p k for

[0065]

[0066] where the vector It is obtained by stacking the transform domain precoding vector of user k. The deterministic matrix The i-th column of Defining the Matrix is the transformation matrix. Assume that the matrix F is a partial DFT matrix. Further, the precoding vector Can write

[0067]

[0068] Block Matrix is defined as The cth sub-block is the unit matrix. In the following derivation, let Let's recalculate r k,c as follows

[0069]

[0070] Let the equivalent channel total covariance be Recalculate for

[0071]

[0072] Next, the cross-subcarrier precoding design problem is transformed into solving the optimal stacked transform domain precoding vector to maximize the weighted traversal and rate

[0073]

[0074] Assume N≤N v To reduce the redundancy caused by precoding design for each subcarrier. To further avoid complex expectation operations, the convex function property of logdet(·) is used to derive The upper bound of

[0075]

[0076] Define the upper bound of the weighted traversal and rate as

[0077]

[0078] Then, the problem statement can be simplified to

[0079]

[0080] It can be found that the above problem is still difficult to solve, because the vectors q of different users k In r k,c The objective function is simplified by minimizing the function.

[0081] 3.2 Minimum function under the MM framework

[0082] First, the MM algorithm is introduced. Under the current iteration of MM, a lower bound function tangent to the original objective function is found. Then the lower bound function is maximized in the next iteration. As the number of iterations increases, the value of the original objective function increases monotonically. The convergence of the algorithm ensures that the original optimization problem can reach a stable point. Define the transform domain precoding vector sequence as Then the sequence of transform domain precoding vectors at the dth iteration is Real-valued functions is considered to be the minimum function of the weighted traversal and rate at the dth iteration of the transform domain precoding vector sequence if all of the following conditions are met:

[0083]

[0084] Furthermore, the transform domain precoding vector sequence can be updated in the next iteration as follows

[0085]

[0086] At this point, the following inequality shows that the weighted traversal and rate are monotonically increasing:

[0087]

[0088] In addition, the objective function has a finite upper bound due to the power constraint. Therefore, the objective function value converges. It also converges because the minimization function is a concave function. Eventually, as the number of iterations increases, the transform domain precoding vector sequence converges to a stable point.

[0089] According to the last few definitions in Chapter 2, we can get the following r k,c and Calculation

[0090]

[0091]

[0092] matrix The calculation is as follows

[0093]

[0094] Inspired by the matrix weighted sum minimization mean square error MSE minimization problem and the relationship between weighted traversal and rate maximization problems, the minimization function that satisfies the conditions can be obtained as

[0095]

[0096] where the constant γ[d] is independent of q k , and there are

[0097]

[0098]

[0099]

[0100] The specific derivation is omitted here for simplicity. It can be found that the minimization function is a concave quadratic function, and the transform domain precoding vectors of different users are decoupled in the minimization function. Therefore, setting the minimization function as the objective function will make the problem simpler. The problem statement can be further simplified as

[0101]

[0102] The above concave quadratic optimization problem can be solved by the Lagrange multiplier method, and the Lagrange equation is constructed as follows

[0103]

[0104] Where μ is the Lagrange multiplier. Further, the stable solution of the optimization problem is obtained as:

[0105] Theorem 1. The stable point can be obtained by minimizing the concave quadratic optimization problem constructed by the function. The specific structure is shown below

[0106]

[0107] The matrix and The definition is as follows

[0108]

[0109]

[0110] The optimal Lagrange multiplier μ * It can be obtained by dichotomy.

[0111] This stable point is obtained by considering the CSI on all subcarriers, so the potential performance gain of precoding can be explored.

[0112] 3.3 Low Complexity Precoding Design

[0113] The dimension of the matrix inversion in the stable solution is NM t , which makes the computational complexity become unacceptable as N increases. Next, we change the optimization objective from the original q k becomes q k The i-th component q k,i Then, a low-complexity cross-subcarrier precoding design scheme is obtained by using the block coordinate descent (BCD) algorithm combined with power allocation.

[0114] The block coordinate descent (BCD) iterative algorithm finds the minimum of the objective function by continuously minimizing the coordinate directions. For each iteration, one coordinate is set as the optimization variable. Then, the coordinate hyperplane of the optimization variable is minimized while fixing the remaining coordinates, and the remaining coordinates are updated in a cyclic manner. Specifically, the sequence is defined is the i-th coordinate. Set To optimize the variables, the remaining coordinates are obtained from the previous iteration. At this time, the minimization function can be expressed as

[0115]

[0116] It can be found that -g is a k,i Differentiable convex function. At this point, the block coordinate descent (BCD) algorithm cannot be directly applied because different coordinates are coupled in the total power constraint. Therefore, power allocation is required to separate the restricted set of coordinates.

[0117] The power allocation coefficient of the i-th coordinate is defined as ε i , the power allocation coefficients are stacked to obtain Define the matrix function as follows

[0118]

[0119]

[0120] The matrix A' k,c and D' c A after substituting the power allocation coefficient k,c and D c The optimal power allocation coefficient is given as follows

[0121] Theorem 2. The optimal power allocation coefficient is calculated as follows

[0122] ε[d+1]=(D p [d]+μ * I N ) -1 A p [d]ε[d] (37)

[0123] The matrix D p [d] and A p The i-th and j-th elements of [d] are represented as

[0124]

[0125]

[0126] The normalized transform domain precoding vector is expressed as

[0127] The transform domain precoding vector after power allocation is Will Substituting into the minimization function we can get

[0128]

[0129] The block matrix and The i-th, j-th block matrix of

[0130]

[0131]

[0132] Define the i-th coordinate of the d-th iteration as After obtaining the power allocation factor, the BCD algorithm is used to construct the optimization problem

[0133]

[0134] Noting that the power constraints at different coordinates are decoupled, the stable solution to this problem is given below:

[0135] Theorem 3. After applying the block coordinate descent BCD algorithm, the stable solution of the optimization problem is

[0136]

[0137] It can be found that after applying the block coordinate descent BCD algorithm, the dimension of the matrix inversion in the stable solution is reduced to M t .

[0138] In summary, the low-complexity large-scale MIMO-OFDM cross-subcarrier precoding design method can be summarized as follows:

[0139] Step 1: Set d = 0. Initialize the power allocation coefficient ε i [d] and the transform domain precoding vector q k,i [d];

[0140] Step 2: q k,i[d] Normalized to unit energy

[0141] Step 3: Calculate the matrix and

[0142] Step 4: Update the power allocation coefficient ε[d+1];

[0143] Step 5: Update the transform domain precoding vector q after power allocation k,i [d];

[0144] Step 6: Calculate the interference plus noise covariance r k,c and the equivalent channel total covariance

[0145] Step 7: Calculate the matrix A k,c [d] and D c [d];

[0146] Step 8: Update the transform domain precoding vector q after power allocation k,i [d+1];

[0147] Step 9: Update the power allocation coefficient ε[d+1] and set d=d+1. ;

[0148] Step 10: Repeat steps 2-9 until convergence.

[0149] 4. Technical Effect

[0150] In order to enable those skilled in the art to better understand the solution of the present invention, a large-scale MIMO-OFDM cross-subcarrier precoding design method used in this embodiment under a specific system configuration is provided below.

[0151] Using the QuaDRiGa channel model to generate channels, we consider a massive MIMO-OFDM system where the base station antennas are configured as M t =128, where M x =16,M z = 8 UPA, users are randomly distributed on the base station side. The number of samples and the sampling interval are set to 1000 and 2s respectively. Assume N v = 24 subcarriers are used for transmission, and the simulation scenario is set to "3GPP_3D_Uma_NLOS". The signal-to-noise ratio range is set from -10dB to 20dB.

[0152] Figure 2 The comparison curves of the sum rate performance of large-scale MIMO-OFDM cross-subcarrier precoding and subcarrier group precoding are given under similar complexity. Irepresents the number of group precoding groups, and the same linear curves correspond to similar complexity. It is observed that the massive MIMO-OFDM cross-subcarrier precoding scheme is better than the subcarrier group precoding scheme. Specifically, when SNR = 20dB, the sum rate performance of massive MIMO-OFDM cross-subcarrier precoding when N = 3 is better than that of group precoding when N I = 6, the sum rate performance is 30% higher. In addition, compared with the scheme of precoding each subcarrier, the proposed scheme can significantly reduce the complexity while achieving acceptable performance. It is noted that the proposed scheme also has good performance when N = 1, which reflects that jointly considering all subcarrier CSIs will bring certain performance gains.

[0153] Figure 3 The comparison curves of the sum rate performance of large-scale MIMO-OFDM cross-subcarrier precoding and subcarrier group precoding are given under the same number of precoding designs. It is observed that when N=N I When , the massive MIMO-OFDM cross-subcarrier precoding scheme has a more obvious advantage in sum and rate performance compared with subcarrier group precoding. In general, the proposed scheme can achieve better performance by combining all subcarrier CSIs to design a transform domain precoding vector with a smaller number of subcarriers.

[0154] Figure 4 The performance comparison curves of massive MIMO-OFDM cross-subcarrier precoding, instantaneous CSI-based SLNR precoding and RZF precoding in different mobile scenarios are given. For SLNR precoding, the calculation formula is given as

[0155]

[0156] where u max (·) and ζ represent the maximum eigenvector and power coefficient respectively. Set the user moving speed to 30, 120 and 240 km / h. Set the transform domain precoding vector N = 3, and the number of groups of SLNR and RZF N I =6. It is observed that the proposed scheme is significantly better than the instantaneous CSI-based precoding scheme. Specifically, the sum rate of the proposed scheme is 1.23 times that of the SLNR precoding when SNR=20db and the user moving speed is 30kmph. The gain increases to 1.42 when the user moving speed reaches 250kmph. Massive MIMO-OFDM cross-subcarrier precoding can achieve better performance with fewer precoders than group instantaneous CSI-based precoding, and the performance gain increases with the increase of user moving speed.

Claims

1. A method for designing cross-subcarrier precoding for massive MIMO-OFDM, characterized in that: The steps include: Step 1: The base station uses the channel reciprocity in the time division duplex (TDD) mode to obtain the downlink instantaneous channel information of each user terminal from the uplink channel estimation; consider the beam domain statistical channel model Get statistical channel information from in and denote the channel vector, channel coupling vector and beam domain channel vector of user k in the nth OFDM symbol of the mth time slot of the cth subcarrier, respectively; V denotes the spatial sampling matrix; the superscript H, superscript *, symbol ⊙ and symbol E{·} denote the conjugate transpose, matrix conjugate, Hadamard product and sample average of the matrix, respectively; based on the beam domain statistical channel model, the a posteriori beam domain statistical channel model is further obtained, and the a posteriori beam domain statistical channel model takes into account the influence of the user's moving speed; Step 2: Design the transform domain precoding vector {q k,i |1≤i≤N}, where the subscript i represents the index of the number of transform domain precoding vectors designed for user k, i ranges from 1 to N, N is the total number of transform domain precoding vectors designed for user k, and the value of N can be set by yourself; it is converted into the precoding vector of user k on the cth subcarrier through a transformation matrix The precoding vector obtained after transformation It has frequency selectivity; it calculates the power allocation factor of the transform domain precoding vector to be designed based on the instantaneous channel information and statistical channel information. Where ε is obtained by stacking N power allocation coefficients, and the superscript T represents the transposition operation. represents a complex vector of dimension N; Step 3: The base station performs large-scale MIMO-OFDM cross-subcarrier precoding design based on the power allocation factor combined with instantaneous channel information and statistical channel information; The transform domain precoding vector {q k,i |1≤i≤N}, and transform it into a precoding vector on each subcarrier through a transformation matrix The specific expression is in represents the vector obtained by stacking subcarriers for the kth user, N v Represents the total number of subcarriers used for transmission, and the Kronecker product operation is It is obtained by stacking the transform domain precoding vector of user k; the i-th column of the deterministic matrix F is in Represents the elements of the i-th column; define the matrix is the transformation matrix, where The dimension is the number of transmitting antennas M t The unit matrix can be further obtained The block matrix is defined as The cth sub-block is M t dimensional unit matrix; In step 2, the power allocation factor of the transform domain precoding vector to be designed is calculated based on the instantaneous channel information and the statistical channel information. The following steps are involved: Step 2.1: Set the number of iterations d = 0; initialize the transform domain precoding vector q k,i [d], 1≤k≤K, 1≤i≤N and power allocation factor ε i [d] and normalize the transform domain precoding vector to Make it meet the unit energy condition; Step 2.2: Calculate the matrix function D in the minimization function of the traversal and rate upper bound based on the normalized transform domain precoding vector p [d] and A p [d], where d represents the dth iteration; Step 2.3: Calculate the final power allocation factor iterative formula ε[d+1]=(D p [d]+μ * I N ) -1 A p [d]ε[d], where μ * represents the optimal Lagrange multiplier; Step 2.4: Multiply the power allocation factor by the normalized transform domain precoding vector to obtain the transform domain precoding vector after power allocation In step 3, the cross-subcarrier precoding design is performed according to the power allocation factor combined with the instantaneous channel information and the statistical channel information, and specifically includes the following steps: Step 3.1: Calculate the noise plus interference covariance r using the transform domain precoding vector after power allocation k,c and the equivalent channel covariance Step 3.2: Calculate the matrix function A in the minimization function k,c [d] and D c [d]; Step 3.3: Use block coordinate descent (BCD) to obtain the optimal iterative update formula of the transform domain precoding vector; Step 3.4: According to Update the power allocation factor.

2. The method for designing cross-subcarrier precoding for massive MIMO-OFDM according to claim 1, characterized in that: The massive MIMO-OFDM system is equipped with a base station equipped with a uniform planar array antenna (UPA), and K users are randomly distributed in the cell; the cross-subcarrier precoding vector satisfies a total power constraint.

3. The method for designing cross-subcarrier precoding for massive MIMO-OFDM according to claim 1, characterized in that: The traversal and rate upper bound minimization function in step 2.2 is a concave quadratic function tangent to the original objective function obtained by the relationship between the matrix weighted and minimum mean square error MSE minimization problem and the weighted traversal and rate maximization problem.

4. The method for designing cross-subcarrier precoding for massive MIMO-OFDM according to claim 1, characterized in that: The power allocation factor of the transform domain precoding vector to be designed is calculated, and the constraints of the transform domain precoding vector in each coordinate direction are separated so as to simplify the precoding design by using the block coordinate descent (BCD) method.

5. The method for designing cross-subcarrier precoding for massive MIMO-OFDM according to claim 1, characterized in that: In step 3.3, the block coordinate descent BCD algorithm is used to optimize the original q k becomes q k The i-th component q k,i To reduce the matrix inversion dimension in the design process, the optimal iterative update formula of the transform domain precoding vector is finally obtained as follows: in and is calculated from the matrix in the minimization function, and the superscript ij represents the block matrix index. represents the optimal Lagrange multiplier of the i-th coordinate, w k is the weight factor of user k.

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