CN110912599B - Mixed wave beam shaping method in multi-input multi-output multi-user communication system - Google Patents
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Abstract
The invention discloses a mixed wave beam forming method in a multi-input multi-output multi-user communication system, which comprises the following steps: (S1) solving a complete digital beam forming B under multiple users; (S2) according to the complete digital beam forming B, adopting an alternating minimum algorithm to solve the mixed beam forming; the hybrid beamforming includes an optimal analog beamforming matrix a and a digital beamforming matrix D. According to the invention, the complete digital beamforming is firstly solved to form an expression containing matrix inversion, and the matrix inversion is converted to an expression based on Neumann series solving, so that matrix singular value decomposition and matrix inversion with high calculation complexity are avoided. Then in the design of the hybrid beamforming, the whole framework adopts an alternating minimization idea, and when the hybrid beamforming is solved, a gradient projection method is adopted, so that the method can be used for quickly converging and the calculation complexity is reduced.
Description
Technical Field
The invention relates to the technical field of communication, in particular to a hybrid beamforming method in a multi-input multi-output multi-user communication system.
Background
Massive multiple input multiple output (Massive MIMO) is recognized as a key technology of the 5G mobile communication system. The hybrid beamforming combines analog beamforming and baseband beamforming, can effectively reduce the number of radio frequency chains required by complete digital beamforming, and is as close to the spectral efficiency performance of the complete digital beamforming as possible, thereby attracting wide attention in millimeter wave Massive MIMO communication systems. The hybrid beamforming is obtained by taking complete digital beamforming as an optimization target and generally adopting a block diagonal (Block Diagonalization, BD) method of singular value decomposition (Singular Value Decomposition, SVD). Because the antenna scale and the dimensionality of the channel transmission matrix are large, the acquisition of singular value decomposition of complete digital beamforming can generate higher computational complexity; although the popular optimization (Manifold Optimization, MO for short) and punishment double decomposition (Penalty Dual Decomposition, PDD for short) hybrid beamforming algorithm can effectively improve the spectrum efficiency of the millimeter wave communication system, the problem of high computational complexity is not improved obviously.
Disclosure of Invention
Aiming at the high complexity problem of the design and the acquisition of the complete digital beamforming of the hybrid beamforming, the invention provides a hybrid beamforming method in a multi-input multi-output multi-user communication system, and the method of Neumann series approximate inversion replaces singular value decomposition to obtain the complete digital beamforming with low complexity; and then, adopting an alternating minimum algorithm based on gradient projection to obtain mixed beam forming so as to reduce the operation complexity.
The invention is realized by the following technical scheme:
a method of hybrid beamforming in a multiple-input multiple-output multiple-user communication system, comprising the steps of:
(S1) solving the complete digital beam forming under multiple users, wherein the calculation formula of the complete digital beam forming B is as follows:
B＝H H (HH H ) -1 M
wherein,,
H k a downlink channel for a kth user, K being the number of users; matrix HH H Inverse matrix (HH) H ) -1 Calculating by adopting a Neumann series approximation inversion-based method; the matrix M is:
wherein M is k The expression of (2) is
U k Sum sigma k Respectively is pair [ (HH) H ) -1 ] k Unitary matrix and diagonal matrix obtained by singular value decomposition, < ->
Is (HH) H ) -1 The block is divided into sub-matrices of diagonal directions,namely pair belongs to (HH) H ) -1 Element h of (2) i,j ，[(HH H ) -1 ] k From h i,j Composition, where N r (k-1)+1≤i,j≤N r k,1≤k≤K；N r The number of antennas configured for each user; s is(s) r Number of data streams at each user;
(S2) according to the complete digital beam forming B, adopting an alternating minimum algorithm to solve the mixed beam forming; the hybrid beamforming includes an optimal analog beamforming matrix a and a digital beamforming matrix D.
A further improvement of the invention is that matrix HH is solved by adopting a method based on Neumann series approximation inversion H Inverse matrix (HH) H ) -1 The method comprises the following steps:
(S11) assume p=hh H T=i- βp; inverse matrix P of matrix P -1 The Neumann series expression of (c) is:
wherein: l is the order of the matrix polynomial, alpha n Is a polynomial coefficient, and is combined and expressed as alpha= [ alpha ] 1 ,...,α L ] T ；
(S12) solving the optimal beta and alpha, and substituting the beta and alpha into Neumann series to obtain an inverse matrix P -1 The method comprises the steps of carrying out a first treatment on the surface of the The solution formula for β and α is:
α＝G -1 ω
wherein: ρ is the signal to noise ratio; in massive MIMO systems, when N t And KN r At a constant rate
In the event of an increase in the volume,
the feature distribution convergence function of (1) is:
wherein (x) + ＝max{0,x},
Wherein N is t 、N r The number of antennas equipped for the base station and the number of antennas equipped for the user, respectively.
A further improvement of the invention is that in the process of adopting an alternate minimum algorithm to solve the mixed beam forming, the matrix A is initialized arbitrarily (p) P=0 and for each iteration p the following steps are performed:
(S21) according to the full digital beamforming B and the analog beamforming matrix A (p) Calculating a digital beamforming matrix D (p+1) The objective function is:
(S22) according to the digital beamforming matrix D (p+1) And finish the processAll-digital beamforming B solving analog beamforming matrix A (p+1) The objective function is:
wherein, the analog beam forming matrix A (p+1) Solving an objective function of the model by adopting an iteration method;
(S23) if the number of alternate passes p reaches a predetermined value, simulating the beamforming matrix A (p+1) Digital beamforming matrix D (p+1) As a calculation result; otherwise, the process goes to step (S21).
A further improvement of the invention is that, based on the full digital beamforming B and the analog beamforming matrix a (p) Calculating a digital beamforming matrix D (p+1) The process of (1) specifically comprises the following steps:
(S211) according to formula D (p+1) ＝(A (p) ) -1 B calculating an unmodified digital beamforming matrix D (p+1) ；
(S212) shaping matrix D of unmodified digital wave beam (p+1) Multiplying by a scaling factor
Obtaining a digital beam forming matrix D which meets the power constraint condition after correction (p+1) The method comprises the steps of carrying out a first treatment on the surface of the Wherein s is t ＝Ks r For the data flow at the base station, satisfy
Is a power constraint of (a).
A further development of the invention is that, according to the digital beamforming matrix D (p+1) Solving analog beamforming matrix a with full digital beamforming B (p+1) The process of (1) specifically comprises the following steps:
(S221) vectorizing the full digital beamforming B to obtain a vector u=vec (B); and randomly initializing the phase
And calculate the projection matrix +.>
(S222) calculating an intermediate solution
Wherein μ is the linear search step along the opposite direction of the gradient, +.>
For along->
Is the fastest falling search direction of (1),
(S223) if the iteration number is smaller than the target value, projecting the obtained intermediate solution onto a unit modulus circle
And jumping to a value step (S222); if the number of iterations reaches the target value, then go to step (S224);
(S224) converting the intermediate solution obtained finally into matrix to obtain output analog beam forming matrix
Wherein (1)>
Representing the mapping vector as a function of the matrix.
A further improvement of the present invention is that the linear search step employed in step (S222)
And μ is less than or equal to Lipschitz constant ζ, expressed as:
wherein: wherein r is 1 ,...,r u Is the row sum of the projection matrix G;
N r the number of antennas configured for each user; />
The number of radio frequency chains equipped for the base station, τ is the maximum boundary of a constant ζ, taking ζ=τ; />
To adjust the parameters, it is used to ensure that μ is less than or equal to the constant ζ.
The invention has the advantages that: according to the invention, the complete digital beamforming is firstly solved to form an expression containing matrix inversion, and the matrix inversion is converted to an expression based on Neumann series solving, so that matrix singular value decomposition and matrix inversion with high calculation complexity are avoided. Then in the design of the hybrid beamforming, the whole framework adopts an alternating minimization idea, and when the hybrid beamforming is solved, a gradient projection method is adopted, so that the method can be used for quickly converging and the calculation complexity is reduced.
Drawings
Fig. 1 is a flow chart of a hybrid beamforming method in a multiple-input multiple-output (memo) multi-user communication system;
fig. 2 is a block diagram of a multi-user MIMO system;
FIG. 3 is a comparison of the present invention with another prior art full digital beamforming algorithm;
FIG. 4 is a graph of user and rate transformation at different iterations in step (S22);
fig. 5 is a graph of sum rate comparisons under different algorithms.
Detailed Description
Examples: as shown in fig. 1, the massive MIMO multi-user downlink communication system model generally includes: base station is equipped with N t K users all configure N for the root transmitting antenna r A root antenna. The number of radio frequency chains configured by the base station and the user is respectively
And
the number of data streams at the base station and each user is s, respectively t ，s r . The kth user receives a signal of
Wherein->
For transmitting data vectors>
Is a white gaussian noise, which is a white gaussian noise,
digital beam forming matrix of base station and user terminal respectively, < > in->
The analog beamforming matrices of the base station and the user side, respectively. Then the spectral efficiency of the kth user can be expressed as:
in the above model, sum rate
The mixed beam forming method in the multi-input multi-output multi-user communication system is mainly used for solving the analog beam forming matrix A and the digital beam forming matrix D in the model. The method is used for a downlink transmission scene of a single cell and multiple users, has the problems of inter-user interference and high complexity of beamforming design, and firstly adopts a block diagonal beamforming method based on Neumann series approximate inversion to obtain low-complexity complete digital beamforming, and carries out diagonalization treatment on a channel matrix based on a zero forcing idea to equivalent an MIMO channel into a plurality of parallel independent space subchannels so as to eliminate multi-user interference; and then, the mixed wave beam forming design is carried out based on an alternating minimum algorithm of gradient projection, so that the operation complexity is further reduced. The embodiment of the invention can reduce the calculation complexity under the condition of ensuring smaller loss of frequency spectrum and rate performance.
Specifically, the hybrid beamforming method in the mimo-multiuser communication system of the present embodiment includes the following steps:
(S1) solving the complete digital beam forming under multiple users, wherein the calculation formula of the complete digital beam forming B is as follows:
B＝H H (HH H ) -1 M (2)
wherein,,
H k a downlink channel for a kth user, K being the number of users; matrix HH H Inverse matrix (HH) H ) -1 Calculating by adopting a Neumann series approximation inversion-based method; the matrix M is:
wherein M is k The expression of (2) is
U k Sum sigma k Respectively is pair [ (HH) H ) -1 ] k Unitary matrix and diagonal matrix obtained by singular value decomposition, < ->
Is (HH) H ) -1 Block diagonal submatrices, i.e. pairs belonging to (HH H ) -1 Element h of (2) i,j ，[(HH H ) -1 ] k From h i,j Composition of the compositionWherein N is r (k-1)+1≤i,j≤N r k,1≤k≤K；N r The number of antennas configured for each user; s is(s) r Number of data streams at each user;
(S2) according to the complete digital beam forming B, adopting an alternating minimum algorithm to solve the mixed beam forming; the hybrid beamforming includes an optimal analog beamforming matrix a and a digital beamforming matrix D.
In the above step (S1), the direct solution (HH) H ) -1 Is relatively complex, and therefore solves (HH H ) -1 And converting into matrix polynomial approximation solution. If matrix
And->
Then Z is nonsingular and the inverse of Z can be represented by a Neumann series of +.>
Assuming p=hh H T=i- βp, β being a parameter satisfying the quotation. The following formula is satisfied:
wherein: l is the order of the matrix polynomial, alpha n Is a polynomial coefficient, and can be expressed as alpha= [ alpha ] 1 ,...,α L ] T 。
Solving the optimal beta and alpha can be expressed as an optimization problem of formula (5), and solving beta and alpha can be calculated as P -1 I.e. (HH) H ) -1 . In solving (HH) H ) -1 Since β and α are obtained in advance, the computation complexity is multiplied by the polynomial matrix only, and the inverse matrix can be approximated by the first three terms of the Neumann series.
Wherein: ρ r (. Cndot.) is the radius of the matrix spectrum.
However, the solving process of the formula (5) has a large calculation amount, and in this embodiment, the solving formulas of β and α are:
α＝G -1 ω (7)
wherein: ρ is the signal to noise ratio; in massive MIMO systems, when N t And KN r At a constant rate
In the event of an increase in the volume,
the feature distribution convergence function of (1) is:
wherein (x) + ＝max{0,x},
Wherein N is t 、N r The number of antennas equipped for the base station and the number of antennas equipped for the user, respectively.
In the implementation process of the step (S1), the method specifically comprises the following steps:
step 1, input matrix H, calculate (HH H ) -1
Step 3, outputting a complete digital beam forming matrix B=H H (HH H ) -1 M
In the above step (S1), the downlink channel H of the kth user k Can be represented by a millimeter wave channel geometry channel model, wherein the downlink channel of the kth user is as follows
Wherein L is k Is the number of scattering paths that are present,
for the complex path gain of the kth user,
a r (θ k,l )∈[0,2π]，/>
and theta k,l The departure angle (AoD) and the arrival angle (AoA) of the first scattering path of the millimeter wave channel are shown, respectively. />
And a r (θ k,l ) Is the array response vector for AoD and AoA corresponding to the first scattering path. Assume that both the base station and the user side employ a Uniform Linear Array (ULA), therefore +.>
And a r (θ k,l ) Can be expressed as
In the process of respectively solving the mixed beamforming by adopting the alternating minimum algorithm in the step (S2), the matrix A is initialized at will (p) P=0 and for each iteration p the following steps are performed:
(S21) according to the full digital beamforming B and the analog beamforming matrix A (p) Calculating a digital beamforming matrix D (p+1) The objective function is:
(S22) according to the digital beamforming matrix D (p+1) Solving analog beamforming matrix a with full digital beamforming B (p+1) The objective function is:
wherein, the analog beam forming matrix A (p+1) Solving an objective function of the model by adopting an iteration method;
(S23) if the number of alternate passes p reaches a predetermined value, simulating the beamforming matrix A (p+1) Digital beamforming matrix D (p+1) As a calculation result; otherwise, the process goes to step (S21). In this embodiment, the maximum value of the alternate pass p is 40.
In the above step (S2), after the complete digital beamforming matrix is obtained, the solution of the base station optimal analog beamforming matrix a and the digital beamforming matrix D can be expressed as
Wherein: d= [ D ] 1 D 2 ... D K ]. The above expression adopts an alternating minimum algorithm to respectively solve the optimal analog beamforming matrix A and the digital beamforming matrix D. Sequentially executing the step (S21) and the step (S22) in each alternating operation process; in this embodiment, the above alternating operation is performed at most 40 times.
In the process of executing the step (S21), the solving process of the objective function (formula 17) can be converted into a linear least squares solving problem, and the optimal digital beamforming matrix D can be calculated (p+1) ＝(A (p) ) -1 B. However, the power constraint in equation (18) is not considered in equation (17). In order to satisfy the constraint in equation (18), D to be obtained is required (p+1) Multiplying by a scaling factor
Wherein s is t ＝Ks r For the data flow at the base station, satisfy +.>
Is a power constraint of (a).
The process of solving the objective function in step (S21) specifically includes the steps of:
(S211) according to formula D (p+1) ＝(A (p) ) -1 B calculating an unmodified digital beamforming matrix D (p+1) ；
(S212) shaping matrix D of unmodified digital wave beam (p+1) Multiplying by a scaling factor
Obtaining a digital beam forming matrix D which meets the power constraint condition after correction (p+1) 。
Digital beamforming matrix D (p+1) After the calculation is completed, D is maintained in the following alternate operation (p+1) Invariably, solve for A by equation (17) (p+1) . However, the analog beamforming matrix a (p+1) There is a constant modulus constraint in equation (18) such that the solving process of the objective function in step (S22) is a non-convex constraint problem with high computational complexity. Therefore, it needs to be converted into an iterative method to solve.
Solving an analog beamforming matrix A (p+1) The basic idea of (a) is as follows: vectorizing matrix B, and randomly setting initialization phase
Taking the value and calculating the projection matrix +.>
Subsequently, an intermediate solution is obtained by a gradient descent method
Where μ is the linear search step along the opposite direction of the gradient,
for along->
The fastest declining search direction of (2); then the resulting intermediate solution is projected onto a unit modulus circle to get the next solution +.>
Iterative update ζ (t+1) And->
Until a defined stopping criterion is fulfilled.
Solving the search step μ in the gradient projection method generally involves matrix singular value decomposition, with the arrangement of
As long as μ is guaranteed to be less than or equal to the Lipschitz constant ζ, the projection gradient method will iteratively converge to a Karush-Kuhn-Tucker point, given by equation (19):
wherein: wherein r is 1 ,...,r u Is the row sum of the projection matrix G;
N r the number of antennas configured for each user; />
The number of radio frequency chains equipped for the base station, τ, is the maximum boundary of a constant ζ, which has been demonstrated in the literature to take ζ=τ; />
The parameter is adjusted to ensure that μ is less than or equal to the constant ζ.
In the implementation process, the analog beamforming matrix A is solved (p+1) The process of (1) specifically comprises the following steps:
(S221) vectorizing the full digital beamforming B to obtain a vector u=vec (B); and randomly initializing the phase
And calculate the projection matrix +.>
(S222) calculating an intermediate solution
Wherein μ is the linear search step along the opposite direction of the gradient, +.>
For along->
Is the fastest falling search direction of (1),
(S223) if the iteration number is smaller than the target value, projecting the obtained intermediate solution onto a unit modulus circle
And jumping to a value step (S222); if the iteration number reaches the target value, the process goes to step (S224);
(S224) converting the intermediate solution obtained finally into matrix to obtain output analog beam forming matrix
Wherein (1)>
Representing the mapping vector as a function of the matrix.
In a specific embodiment, as shown in fig. 1, consider a single-cell multi-user downlink communication scenario, where the following is set forth in the simulation environment: number of base station transmitting antennas N t Number of receive antennas per user n=128 r Number of users k=4, emission angle and arrival angle are distributed in [0,2 pi ]]In, base station antenna spacing d=λ/2, data stream s for each user r Data flow s of base station =4 t ＝Ks r Total transmit power p=ks r Scattering path L between base station and each user k =8. The specific parameters are shown in Table 1 below:
TABLE 1
The method is used for solving the optimal mixed beam forming while ensuring the maximization of the sum rate performance, namely solving the optimal digital beam forming and analog beam forming. Generally, the known complete digital beamforming is needed in the process of solving the hybrid beamforming, so that the process of solving the optimal hybrid beamforming is divided into two steps, wherein the first step adopts a block diagonal beamforming method based on Neumann series approximation inversion to obtain the complete digital beamforming, and the second step adopts an alternating minimum method based on gradient projection to obtain the hybrid beamforming.
Fig. 3 is a block diagonal beamforming method based on singular value decomposition and a method based on Neumann series approximation inversion for solving the sum rate performance comparison of complete digital beamforming, and it can be seen that the method and the rate performance of the present invention are close to those based on singular value decomposition. Because the invention adopts Neumann series approximation inversion to replace singular value decomposition, compared with a method based on singular value decomposition, the invention has lower calculation complexity. The following mixed beam forming design part is used for complete digital beam forming as comparison, and the complete digital beam forming is obtained by solving based on Neumann series approximation inversion method.
In the hybrid beamforming design, fig. 4 is a graph showing the gradient projection method proposed in step (S22) of the present patent, and the rate transformation curve under different iteration times, and it can be seen from the graph that the method of the present invention can converge rapidly, and the performance of the optimal all-digital beamforming is very close only when t=2. Then, as the iteration number increases, the performance is improved, but not greatly improved. To facilitate comparison with the manifold optimization method and to demonstrate performance advantages, t=10 is set in the following simulation.
FIG. 5 is a schematic view of the process
The comparison of the sum rate performance of the gradient projection method, the Manifold Optimization (MO) method under multi-user and the Orthogonal Matching Pursuit (OMP) method is presented below, and the performance of the gradient projection method is better than that of the orthogonal matching pursuit method. Compared with MO method, the sum rate is slightly reduced, but the calculation complexity is lower than MO algorithm, in the simulation environment of the inventionThe computational complexity of analog beamforming is 49% of MO algorithm.
In summary, in the downlink wireless communication system of the multi-user millimeter wave MIMO system, aiming at the high computational complexity of the interference among users and the design of complete digital beamforming and hybrid beamforming, in the technical scheme of the invention, a complete digital beamforming algorithm with low complexity is improved first, then a hybrid beamforming matrix is designed based on an alternate minimization algorithm, and an algorithm based on gradient projection is provided to determine analog beamforming, so that the computational complexity can be reduced under the condition of ensuring less loss of rate performance.
The above embodiments of the present invention do not limit the scope of the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of the present invention.
Claims (2)
1. A method for hybrid beamforming in a multiple-input multiple-output (memo) multi-user communication system, comprising the steps of:
(S1) solving the complete digital beam forming under multiple users, wherein the calculation formula of the complete digital beam forming B is as follows:
B＝H H (HH H ) -1 M
wherein,,
H k a downlink channel for a kth user, K being the number of users; matrix HH H Inverse matrix (HH) H ) -1 Calculating by adopting a Neumann series approximation inversion-based method; the matrix M is:
wherein M is k The expression of (2) is
U k Sum sigma k Respectively is pair [ (HH) H ) -1 ] k Unitary matrix and diagonal matrix obtained by singular value decomposition, < ->
Is (HH) H ) -1 Block diagonal submatrices, i.e. pairs belonging to (HH H ) -1 Element h of (2) i,j ，[(HH H ) -1 ] k From h i,j Composition, where N r (k-1)+1≤i,j≤N r k,1≤k≤K；N r The number of antennas configured for each user; s is(s) r Number of data streams at each user;
solving matrix HH by adopting Neumann series approximation inversion-based method H Inverse matrix (HH) H ) -1 The method comprises the following steps:
(S11) assume p=hh H T=i- βp; inverse matrix P of matrix P -1 The Neumann series expression of (c) is:
wherein: l is the order of the matrix polynomial, alpha n Is a polynomial coefficient, and is combined and expressed as alpha= [ alpha ] 1 ,...,α L ] T ；
(S12) solving the optimal beta and alpha, and substituting the beta and alpha into Neumann series to obtain an inverse matrix P -1 The method comprises the steps of carrying out a first treatment on the surface of the The solution formula for β and α is:
α＝G -1 ω
wherein: ρ is the signal to noise ratio; in massive MIMO systems, when N t And KN r At a constant rate
In the event of an increase in the volume,
the feature distribution convergence function of (1) is:
wherein (x) + ＝max{0,x},
Wherein N is t 、N r The number of antennas respectively equipped for the base station and the number of antennas equipped for the user;
(S2) according to the complete digital beam forming B, adopting an alternating minimum algorithm to solve the mixed beam forming; the mixed beamforming comprises an optimal analog beamforming matrix A and a digital beamforming matrix D;
in the process of solving the mixed beam forming by adopting the alternating minimum algorithm, the matrix A is initialized at will (p) P=0 and for each iteration p the following steps are performed:
(S21) according to the full digital beamforming B and the analog beamforming matrix A (p) Calculating a digital beamforming matrix D (p +1) The objective function is:
(S22) according to the digital beamforming matrix D (p+1) Solving analog beamforming matrix a with full digital beamforming B (p +1) The objective function is:
wherein, the analog beam forming matrix A (p+1) Solving an objective function of the model by adopting an iteration method;
(S23) if the number of alternate passes p reaches a predetermined value, simulating the beamforming matrix A (p+1) Digital beamforming matrix D (p+1) As a calculation result; otherwise, jumping to the step (S21);
from a complete digital beamforming B and an analog beamforming matrix A (p) Calculating a digital beamforming matrix D (p+1) The process of (1) specifically comprises the following steps:
(S211) according to formula D (p+1) ＝(A (p) ) -1 B calculating an unmodified digital beamforming matrix D (p+1) ；
(S212) shaping matrix D of unmodified digital wave beam (p+1) Multiplying by a scaling factor
Obtaining a digital beam forming matrix D which meets the power constraint condition after correction (p+1) The method comprises the steps of carrying out a first treatment on the surface of the Wherein s is t ＝Ks r For the data flow at the base station, satisfy
Is a power constraint of (2);
from a digital beamforming matrix D (p+1) Solving analog beamforming matrix a with full digital beamforming B (p+1) The process of (1) specifically comprises the following steps:
(S221) vectorizing the full digital beamforming B to obtain a vector u=vec (B); and randomly initializing the phase
And calculate the projection matrix +.>
(S222) calculating an intermediate solution
Wherein μ is the linear search step along the opposite direction of the gradient, +.>
For along->
Is the fastest falling search direction of (1),
(S223) if the iteration number is smaller than the target value, projecting the obtained intermediate solution onto a unit modulus circle
And jumping to a value step (S222); if the iteration number reaches the target value, the process goes to step (S224);
(S224) converting the intermediate solution obtained finally into matrix to obtain output analog beam forming matrix
Wherein (1)>
Representing the mapping vector as a function of the matrix.
2. The method of hybrid beamforming in a mimo-multiuser communication system according to claim 1, wherein the linear search step employed in step (S222) is
And μ is less than or equal to Lipschitz constant ζ, expressed as:
wherein: wherein r is 1 ,...,r u Is the row sum of the projection matrix G;
N r the number of antennas configured for each user;
the number of radio frequency chains equipped for the base station, τ is the maximum boundary of a constant ζ, taking ζ=τ; />
To adjust the parameters, it is used to ensure that μ is less than or equal to the constant ζ.
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