CN112261728A - Beam selection matrix design method based on lens array - Google Patents

Beam selection matrix design method based on lens array Download PDF

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CN112261728A
CN112261728A CN202011523683.0A CN202011523683A CN112261728A CN 112261728 A CN112261728 A CN 112261728A CN 202011523683 A CN202011523683 A CN 202011523683A CN 112261728 A CN112261728 A CN 112261728A
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user
beam selection
users
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matrix
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郭荣斌
余显斌
赵志峰
王金鹏
刘善赟
李顺斌
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Zhejiang Lab
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/50—Allocation or scheduling criteria for wireless resources
    • H04W72/53—Allocation or scheduling criteria for wireless resources based on regulatory allocation policies

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Abstract

The invention discloses a beam selection matrix design method based on a lens array, and belongs to the field of optimization algorithm design and wireless resource allocation. The method comprises the following steps: the method comprises the steps of establishing a beam selection matrix design problem, designing a beam selection matrix F by adopting a successive comparison algorithm according to channel state information, initializing system parameters, solving an optimal precoding matrix P by adopting an optimization algorithm, and executing resource allocation. Compared with the traditional beam selection algorithm, the optimization algorithm design obtained by the invention can obtain a higher system return value, namely a higher system transmission rate and better user experience.

Description

Beam selection matrix design method based on lens array
Technical Field
The invention relates to the field of wireless network resource allocation and optimization algorithm design, in particular to a beam selection matrix design method based on a lens array.
Background
Wireless data services have grown rapidly in recent years, placing increasing strain on wireless spectrum resources. Ultra-high frequency bands such as millimeter wave/terahertz and the like have therefore gained wide attention. The millimeter wave/terahertz frequency band has a great bandwidth resource, but due to the fact that attenuation in air is serious, a system needs to apply a large-scale multi-antenna array to enhance signal strength. The millimeter wave/terahertz frequency band has short wavelength, and greatly facilitates miniaturization of antenna array design, so that the millimeter wave/terahertz frequency band and the antenna array complement each other. In large-scale array systems, significant array gain and interference suppression gain can be achieved by using efficient precoding/beamforming techniques.
However, in the conventional large-scale array system design, the base station adopts a scheme of all-digital links, which means that each antenna element needs a corresponding radio frequency link (including a digital-to-analog converter, a power amplifier, a mixer, etc.), thereby greatly increasing the hardware cost and the energy consumption of the base station. In recent years, research has been proposed on the design of systems based on lens antenna arrays, which utilize the energy focusing characteristics of lens antenna arrays based on the emission/arrival angles of signals, and the hardware cost and energy consumption of the systems are effectively reduced by using switch array networks to replace phase shifters in the system design. Due to the angle-based energy focusing characteristic of the lens array, the lens array can equivalently convert the traditional spatial domain MIMO channel into the channel of the beam domain, so the beam forming vector design in the original hybrid precoding structure can be converted into a beam selection problem. However, current methods choose beams based on a maximum amplitude criterion so that as much energy of the user data stream is contained in the beam as possible. This method is simple in principle, but suffers from two disadvantages: 1) only the maximum signal energy received by each user is considered, and the interference among users is not considered; 2) different radio frequency links may select the same beam, resulting in waste of resources.
The invention provides a wave beam selection method based on interference elimination, which considers the mutual interference of different users in the same wave beam while selecting the maximum amplitude wave beam. And an optimal precoding matrix is solved through a weighted minimum mean square error algorithm, and the defects of the current method are overcome.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides an optimization algorithm based on successive comparison beam selection. Compared with the traditional resource allocation method, the method provided by the invention can rapidly select the wave beam and simultaneously solve the optimal precoding matrix, so that the method is more efficient and flexible and can greatly improve the performance of the wireless network.
In order to achieve the purpose, the invention adopts the following technical scheme: a method for designing a beam selection matrix based on a lens array is characterized in that: the method comprises the following steps:
(1) establishing and transforming a beam selection matrix joint design problem;
(1.1) considering system performance, namely the sum of the reachable rates of a system user, and establishing an optimization problem of beam selection matrix design according to the optimization principle of the system performance and the combination of the physical structure of a lens array;
(1.2) equivalently converting the optimization problem into a new optimization problem according to a weighted minimum mean square error equivalence conversion theorem;
(2) designing a beam selection matrix F by adopting a successive comparison algorithm according to the channel state information;
(3) initializing system parameters;
(4) according to the channel state information, a weighted minimum mean square error algorithm is designed to optimize an optimal precoding matrix P, in each cycle, the designed algorithm solves the optimization problem through a block coordinate descent algorithm, optimization variables to be solved are grouped according to a decoupling principle based on a rotation optimization idea, and for each group of variables, other groups of variables are fixed to be solved until the objective function value of the optimization problem is converged.
Preferably, the optimization problem in said sub-step (1.1) comprises an objective function, variable modeling and constraint assumptions.
Preferably, the objective function in the new optimization problem in said sub-step (1.2) is a convex function.
Preferably, the step (2) comprises the following substeps:
(2.1) channel vector according to beam domain between each user and base station
Figure 591366DEST_PATH_IMAGE001
Condition of (2), counter quantity
Figure 242927DEST_PATH_IMAGE001
The amplitude of the wave beam in (1) is arranged in descending order, and for the Kth user, the corresponding strongest wave beam number is used
Figure 22664DEST_PATH_IMAGE002
Is shown in which
Figure 214611DEST_PATH_IMAGE003
，
Figure 763404DEST_PATH_IMAGE004
The number of antenna elements of the base station is the number, and then all users are grouped according to the strongest wave beams corresponding to all users;
(2.2) if
Figure 976080DEST_PATH_IMAGE005
The strongest beam numbers corresponding to other users are all not consistent, then user k belongs to non-interfering packets, i.e.
Figure 977534DEST_PATH_IMAGE006
And for aggregation of non-interfering users
Figure 504330DEST_PATH_IMAGE007
Means that, for a non-interfering user, the strongest beam of the user is directly selected
Figure 907630DEST_PATH_IMAGE008
；
(2.3) if the strongest beam of user k is coincident with other users, then user k belongs to the interfered user, i.e. user k is a user with interference
Figure 432152DEST_PATH_IMAGE009
And for sets of interfering users
Figure 983219DEST_PATH_IMAGE010
Indicating that, for users with interference, selection is made
Figure 454652DEST_PATH_IMAGE011
A beam to serve them, wherein
Figure 509195DEST_PATH_IMAGE011
Representation collection
Figure 735777DEST_PATH_IMAGE010
The number of medium beams and assembling these beams from the set
Figure 711824DEST_PATH_IMAGE012
Are selected one by one, wherein
Figure 783685DEST_PATH_IMAGE013
Show that
Figure 161576DEST_PATH_IMAGE014
From a collection of elements
Figure 824639DEST_PATH_IMAGE015
And (4) removing. In the invention, a beam which increases the system performance to the maximum is selected based on a successive comparison method.
(2.4) after all the interference-free users are selected, the optimal wave beam corresponding to the interference-free users is selected
Figure 287981DEST_PATH_IMAGE016
After that, we need to get from the rest
Figure 897954DEST_PATH_IMAGE017
Selecting from one beam
Figure 192669DEST_PATH_IMAGE018
A beam of waves to try bestInterference between user beams is reduced. Without loss of generality, a baseband precoding matrix P is set as a zero-forcing precoding matrix, and then the zero-forcing precoding matrix is selected one by one based on a successive comparison idea
Figure 698737DEST_PATH_IMAGE019
And a beam. In each selection we select the one that gives the best achievable rate for the system from the remaining selectable beams. Until all the beams corresponding to each user are selected, we can obtain a beam selection matrix F.
Preferably, the system parameter in the step (3) is variable
Figure 446113DEST_PATH_IMAGE020
And auxiliary variables
Figure 63039DEST_PATH_IMAGE021
Initialization of
Figure 946682DEST_PATH_IMAGE022
Wherein P represents the full digital pre-coding matrix at the base station side, and after initialization, the matrix is initialized to satisfy the constraint
Figure 685968DEST_PATH_IMAGE023
Is determined by the random value of (a),
Figure 858323DEST_PATH_IMAGE024
and
Figure 75678DEST_PATH_IMAGE025
weight factors and receiver gains for the k-th user, respectively, while initializing auxiliary variables
Figure 548247DEST_PATH_IMAGE026
Wherein
Figure 989593DEST_PATH_IMAGE027
Is used to measure the upper bound of the variation value of the objective function of the optimization problem.
Preferably, the step (4) specifically includes the following substeps:
(4.1) fixing other variables, and independently solving the gain of the receiver at the user end
Figure 711561DEST_PATH_IMAGE028
Obtained by examining its first-order optimum conditions
Figure 670290DEST_PATH_IMAGE029
Closed-form solution:
Figure 262945DEST_PATH_IMAGE030
wherein
Figure 344034DEST_PATH_IMAGE031
Is the intermediate variable(s) of the variable,
Figure 490981DEST_PATH_IMAGE032
the ith column of the matrix is represented,
Figure 315718DEST_PATH_IMAGE033
，
(4.2) fixing other variables, solving the weight factors separately
Figure 231721DEST_PATH_IMAGE034
By checking its first-order optimum condition, obtain
Figure 218132DEST_PATH_IMAGE034
Closed-form solution of (c):
Figure 852376DEST_PATH_IMAGE035
(4.3) fixing other variables, solving the precoding matrix P independently, and obtaining the following by checking first-order optimal conditions:
Figure 215224DEST_PATH_IMAGE036
wherein the content of the first and second substances,
Figure 516892DEST_PATH_IMAGE037
for lagrange multipliers, the need is satisfied
Figure 470942DEST_PATH_IMAGE038
If, if
Figure 592481DEST_PATH_IMAGE039
The solution corresponding to P satisfies the constraint of the problem, that is, the solution of the problem, if the constraint is not satisfied, the solution can be determined according to the relaxation condition
Figure 759021DEST_PATH_IMAGE040
And obtaining the solution of P.
(4.4) enter the next cycle until
Figure 384037DEST_PATH_IMAGE041
At this time, the values of the beam selection matrix F and the baseband precoding matrix P are the solutions of the optimization problem.
Preferably, the condition for the algorithm to loop out is
Figure 977829DEST_PATH_IMAGE042
。
Compared with the prior art, the invention has the beneficial effects that:
(1) compared with a successive comparison algorithm (without optimizing a precoding matrix) and an algorithm based on maximum beam amplitude selection, the optimization algorithm design obtained by the invention can obtain a higher system report value, namely a higher system transmission rate and better user experience.
(2) The method designs the beam selection matrix based on the successive comparison method, and optimally designs the pre-coding matrix by adopting a weighted minimum mean square error algorithm.
Drawings
FIG. 1 is a schematic diagram of a lens array based communication system;
FIG. 2 is a flowchart of a method for jointly designing beam selection and precoding matrix optimization according to the present invention;
fig. 3 shows the variation of the achievable performance of the system of the method of the present invention and the zero-forcing precoding algorithm based on the all-digital structure, the beam selection algorithm based on the successive comparison (non-optimized precoding matrix), the beam selection algorithm based on the maximum energy principle in the wireless resource allocation process when the signal-to-noise ratio of the receiving end is from 0dB to 30 dB.
Detailed Description
In order to explain technical contents, structural features, and objects and effects of the technical solutions in detail, the following detailed description is given with reference to the accompanying drawings.
Referring to fig. 1, taking a downlink millimeter wave MIMO communication system as an example, the communication system includes a base station and a plurality of single-antenna users, wherein a lens antenna array is configured at the front end of the radio frequency at the base station side, which includes
Figure 586665DEST_PATH_IMAGE043
A bar radio frequency link and
Figure 494578DEST_PATH_IMAGE044
and each antenna array element simultaneously serves K single-antenna users. In order to serve each user, the number of radio frequency links needs to be satisfied
Figure 301997DEST_PATH_IMAGE045
. Without loss of generality, we assume here that
Figure 4374DEST_PATH_IMAGE046
. To describe the performance of the communication system, we analyze the data changes during the communication. In a downlink, a base station generates K independent data streams, the data streams are firstly subjected to digital precoding at a baseband and then simultaneously transmitted to all users, and a transmission signal after precoding is as follows:
Figure 100506DEST_PATH_IMAGE047
wherein the content of the first and second substances,
Figure 608848DEST_PATH_IMAGE048
is the complex baseband signal of the kth user with a mean value of 0 modulo 1, i.e.
Figure DEST_PATH_IMAGE049
。
Figure 208456DEST_PATH_IMAGE050
Represents a baseband precoding matrix, and
Figure DEST_PATH_IMAGE051
it is the precoding vector corresponding to the kth user. The data signals are sent to a radio frequency link after baseband digital precoding, and then are connected with different antenna array elements through an analog switch array. We assume that the channel is flat fading, then all K users receive
Figure 878472DEST_PATH_IMAGE052
The dimensional signal vector y of (a) can be expressed as:
Figure DEST_PATH_IMAGE053
wherein
Figure 258638DEST_PATH_IMAGE054
A beam-domain channel matrix is represented,
Figure DEST_PATH_IMAGE055
a beam selection matrix is represented whose elements correspond to the opening and closing of the switches in the analog switch array subject to a 0-1 constraint. We use
Figure 39512DEST_PATH_IMAGE056
To represent
Figure DEST_PATH_IMAGE057
Additive Gaussian noise of dimension, the mean value is 0, and the variance satisfies
Figure 555944DEST_PATH_IMAGE058
. Next we are right toThe beam domain channel matrix H is described.
The lens antenna array can convert the traditional spatial domain channel into a beam domain channel H through a discrete Fourier transform:
Figure DEST_PATH_IMAGE059
wherein
Figure 600124DEST_PATH_IMAGE060
Is a DFT matrix equivalent to the lens array.
Figure DEST_PATH_IMAGE061
The space-domain channel vector between a base station and a kth user is represented, and because the lens array is often applied to ultra-high frequency bands such as millimeter wave/terahertz, a relatively classic Saleh-Vallenzuela channel model is adopted:
Figure 467585DEST_PATH_IMAGE062
wherein
Figure DEST_PATH_IMAGE063
And
Figure 52150DEST_PATH_IMAGE064
respectively, the line-of-sight channel and the l-th non-line-of-sight channel vectors between the base station and the k-th user, and, correspondingly,
Figure DEST_PATH_IMAGE065
and
Figure 626351DEST_PATH_IMAGE066
respectively representing the complex gains of line-of-sight and non-line-of-sight channels,
Figure DEST_PATH_IMAGE067
and
Figure 903749DEST_PATH_IMAGE068
representing the corresponding spatial direction.
Fig. 2 is a flowchart of a joint design method of precoding and beam selection matrix based on lens array, which specifically includes the following steps:
(1) the method specifically comprises the following substeps of establishing and converting a beam selection matrix design problem:
(1.1) according to the optimization principle of system performance, combining the physical structure of the lens array, establishing a design theoretical model of the beam selection matrix, wherein the design theoretical model comprises an objective function, variable modeling and constraint assumptions. In the present invention, we aim to maximize the system achievable rate, and we propose the system user rate maximization problem according to shannon's theorem as follows:
Figure DEST_PATH_IMAGE069
and (1.2) equivalently converting the original optimization problem into a new optimization problem according to a weighted minimum mean square error equivalence conversion theorem, wherein an objective function in the new optimization problem is a convex function. The optimization problem after transformation is as follows:
Figure 727348DEST_PATH_IMAGE070
(2) a beam selection matrix F is designed by adopting a successive comparison algorithm according to the channel state information, and the method specifically comprises the following substeps:
(2.1) channel vector according to beam domain between each user and base station
Figure DEST_PATH_IMAGE071
In the case of (2), the amplitudes (modulo complex) of the elements in the vector (one element corresponding to one selectable beam) are sorted in descending order. For the kth user, the strongest beam (i.e., the largest element in the channel vector) corresponding to the kth user is numbered
Figure 318867DEST_PATH_IMAGE072
Is shown in which
Figure DEST_PATH_IMAGE073
. Users can be grouped when we get the strongest beams for all users.
(2.2) if
Figure 544312DEST_PATH_IMAGE074
The strongest wave beam numbers corresponding to other users are not consistent, then the user k is said to belong to the non-interference user group, namely
Figure DEST_PATH_IMAGE075
. For the aggregation of all non-interfering users
Figure 992611DEST_PATH_IMAGE076
And (4) showing. For a non-interfering user, we directly choose the strongest beam of that user
Figure DEST_PATH_IMAGE077
Since it does not cause interference to other users.
(2.3) if the strongest beam of user k coincides with the other users, we call this user the interfering user, i.e. the user k is a member of the set
Figure 303506DEST_PATH_IMAGE078
. For sets of all users with interference
Figure DEST_PATH_IMAGE079
And (4) showing. For users with interference, we need to select
Figure 229874DEST_PATH_IMAGE080
A beam to serve them (
Figure 778667DEST_PATH_IMAGE080
Representing the number of elements in the set). These beams are from the set
Figure DEST_PATH_IMAGE081
Are selected one by one, note that
Figure 194605DEST_PATH_IMAGE082
Represents to be assembled
Figure DEST_PATH_IMAGE083
From a collection of elements
Figure 196059DEST_PATH_IMAGE084
In the invention, a beam which increases the system performance to the maximum is selected based on a successive comparison method.
(2.4) after all the interference-free users are selected, the optimal wave beam corresponding to the interference-free users is selected
Figure DEST_PATH_IMAGE085
After that, we need to get from the rest
Figure 722855DEST_PATH_IMAGE086
Selecting from one beam
Figure DEST_PATH_IMAGE087
Individual beams to minimize interference between user beams. Without loss of generality, we first set the baseband precoding matrix P as a zero-forcing precoding matrix, and the optimization problem of selecting the remaining beams at this time can be written as:
Figure 657313DEST_PATH_IMAGE088
wherein D is selected from
Figure DEST_PATH_IMAGE089
Select out of one wave beam
Figure 447415DEST_PATH_IMAGE090
One possible solution for each of the beams is,
Figure DEST_PATH_IMAGE091
represents an upper bound on the transmit power of the base station, and
Figure 732902DEST_PATH_IMAGE092
presentation instrumentThere is a beam domain channel matrix corresponding to the selected beam.
In the beam selection of the interference user, the interference user is selected one by one based on the idea of successive comparison
Figure DEST_PATH_IMAGE093
And a beam. In each selection we select the one that gives the best achievable rate for the system from the remaining selectable beams, which is equivalent to making it the best possible to achieve the rate for the system
Figure 1073DEST_PATH_IMAGE094
And (4) minimizing. By way of example, in the first selection,
Figure DEST_PATH_IMAGE095
should be selected according to the following formula:
Figure 258879DEST_PATH_IMAGE096
wherein
Figure DEST_PATH_IMAGE097
，
Figure 16619DEST_PATH_IMAGE098
ϵ is an arbitrarily small parameter (e.g., taking the beam domain channel matrix corresponding to the selected non-interfering user beam)
Figure DEST_PATH_IMAGE099
) To ensure that matrix inversion is feasible. When in use
Figure 727086DEST_PATH_IMAGE100
Solved, i.e. after the beam corresponding to the first interfering user is selected, we can update the sum of G
Figure DEST_PATH_IMAGE101
：
Figure 595685DEST_PATH_IMAGE102
By analogy, we can select all
Figure DEST_PATH_IMAGE103
The beams corresponding to the non-interfering users are obtained, and then K beams corresponding to all the users are obtained.
(3) After the beam selection matrix F is determined, the original optimization problem is simplified into a new problem, and then variables need to be adjusted
Figure 973577DEST_PATH_IMAGE104
Initializing to satisfy
Figure DEST_PATH_IMAGE105
Wherein P represents the all-digital precoding matrix at the base station side,
Figure 839902DEST_PATH_IMAGE106
and
Figure DEST_PATH_IMAGE107
respectively, the weight factor and the receiver gain for the kth user. Initializing auxiliary variables
Figure 365561DEST_PATH_IMAGE108
Wherein
Figure DEST_PATH_IMAGE109
The method is used for measuring the upper bound of the change value of the objective function of the optimization problem and is used for setting the iteration termination condition of the algorithm.
(4) And designing a weighted minimum mean square error algorithm to optimize the optimal precoding matrix P according to the channel state information. In each cycle, the designed algorithm solves the optimization problem through a block coordinate descent algorithm, the optimization variables to be solved are grouped according to a decoupling principle based on a rotation optimization idea, and the variables of other groups are fixed and solved aiming at each group of variables. Until the objective function value of the optimization problem converges. The method specifically comprises the following substeps:
(4.1) fixing the otherVariables, solved separately
Figure 975534DEST_PATH_IMAGE110
By checking its first-order optimum, it can be directly obtained
Figure 473511DEST_PATH_IMAGE110
Closed-form solution of (c):
Figure DEST_PATH_IMAGE111
wherein
Figure 510737DEST_PATH_IMAGE112
，
Figure DEST_PATH_IMAGE113
Representing the ith column of matrix V.
(4.2) fixing other variables and solving separately
Figure 461376DEST_PATH_IMAGE114
By checking its first-order optimum, it can be directly obtained
Figure 140619DEST_PATH_IMAGE114
Closed-form solution of (c):
Figure DEST_PATH_IMAGE115
(4.3) fixing other variables, solving P independently, and obtaining the following by checking first-order optimal conditions:
Figure 24261DEST_PATH_IMAGE116
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE117
for lagrange multipliers, the need is satisfied
Figure 497968DEST_PATH_IMAGE118
If, if
Figure DEST_PATH_IMAGE119
The solution corresponding to P satisfies the constraint of the problem, that is, the solution of the problem, if the constraint is not satisfied, the solution can be determined according to the relaxation condition
Figure 467061DEST_PATH_IMAGE120
To obtain
Figure DEST_PATH_IMAGE121
And then obtaining a solution of P.
(4.4) enter the next cycle until
Figure 418836DEST_PATH_IMAGE122
At this time, the values of the beam selection matrix F and the baseband precoding matrix P are the solutions of the optimization problem, and the algorithm cycle end condition is an iteration end parameter
Figure DEST_PATH_IMAGE123
。
To evaluate the technical effect of the proposed invention, in this example we simulated the invention, and we first simulated the performance of the invention and then compared it with other solutions that exist today. The simulation parameters of the system are set as follows: the base station lens antenna array comprises
Figure 422564DEST_PATH_IMAGE124
An antenna element, and
Figure DEST_PATH_IMAGE125
and one radio frequency link for serving K = 16 users. The parameters of the channel model are set as follows: 1) there is one LOS channel, and 2 NLOS channels; 2) channel fading satisfaction of LOS and NLOS channels
Figure 4856DEST_PATH_IMAGE126
(ii) a 3) Launch angles for LOS and NLOS channels
Figure DEST_PATH_IMAGE127
And
Figure 461245DEST_PATH_IMAGE128
compliance
Figure DEST_PATH_IMAGE129
Random uniform distribution of (1); 4) the channel parameters are independent of each other. For the algorithm proposed by the present invention, we set the iteration termination parameter
Figure 482290DEST_PATH_IMAGE130
。
In fig. 3, we analyze the proposed beam selection matrix design method and compared with the existing base, we observe the system performance of these methods as a function of the signal-to-noise ratio. For each signal-to-noise ratio, 100 random channels are selected and the results are averaged, so that the performances of different schemes are objectively analyzed, in order to better explain the value of the method, a zero-forcing precoding algorithm under a full-digital structure is simulated, from the simulation results, the full-digital zero-forcing precoding scheme is taken as the upper bound of the system performance, the performance is followed by the optimization method provided by the invention, and then the successive comparison beam selection method and the maximum beam selection method of the unoptimized precoding matrix are followed, so that the advantages brought by the method are explained.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents or improvements made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1. A method for designing a beam selection matrix based on a lens array is characterized in that: the method comprises the following steps:
(1) establishing and transforming a beam selection matrix design problem;
(1.1) considering system performance, namely the sum of the reachable rates of a system user, and establishing an optimization problem of beam selection matrix design according to the optimization principle of the system performance and the combination of the physical structure of a lens array;
(1.2) equivalently converting the optimization problem into a new optimization problem according to a weighted minimum mean square error equivalence conversion theorem;
(2) designing a beam selection matrix F by adopting a successive comparison algorithm according to the channel state information;
(3) initializing system parameters;
(4) according to the channel state information, a weighted minimum mean square error algorithm is designed to optimize an optimal precoding matrix P, in each cycle, the designed algorithm solves the optimization problem through a block coordinate descent algorithm, optimization variables to be solved are grouped according to a decoupling principle based on a rotation optimization idea, and for each group of variables, other groups of variables are fixed to be solved until the objective function value of the optimization problem is converged.
2. The method of claim 1, wherein the method further comprises: the optimization problem in said sub-step (1.1) comprises an objective function, variable modeling and constraint assumptions.
3. The method of claim 1, wherein the method further comprises: the objective function in the new optimization problem in sub-step (1.2) is a convex function.
4. The method of claim 1, wherein the method further comprises: the step (2) comprises the following substeps:
(2.1) channel vector according to beam domain between each user and base station
Figure 928662DEST_PATH_IMAGE001
Condition of (2), counter quantity
Figure 539771DEST_PATH_IMAGE001
The amplitudes of the beams in (1) are sorted in descending order, pairFor the Kth user, the corresponding strongest beam number is used
Figure 158972DEST_PATH_IMAGE002
Is shown in which
Figure 957163DEST_PATH_IMAGE003
Grouping all users according to the strongest wave beams corresponding to all users;
(2.2) if
Figure 952801DEST_PATH_IMAGE002
The strongest beam numbers corresponding to other users are all not consistent, then user k belongs to non-interfering packets, i.e.
Figure 152838DEST_PATH_IMAGE004
And for aggregation of non-interfering users
Figure 942940DEST_PATH_IMAGE005
Means that, for a non-interfering user, the strongest beam of the user is directly selected
Figure 228428DEST_PATH_IMAGE006
；
(2.3) if the strongest beam of user k is coincident with other users, then user k belongs to the interfered user, i.e. user k is a user with interference
Figure 762177DEST_PATH_IMAGE007
And for sets of interfering users
Figure 816721DEST_PATH_IMAGE008
Indicating that, for users with interference, selection is made
Figure 777724DEST_PATH_IMAGE009
A beam to serve them, wherein
Figure 816087DEST_PATH_IMAGE010
Representation collection
Figure 622369DEST_PATH_IMAGE011
The number of medium beams and assembling the beams from the set
Figure 62577DEST_PATH_IMAGE012
Are selected one by one, wherein
Figure 928902DEST_PATH_IMAGE013
Show that
Figure 454562DEST_PATH_IMAGE014
From a collection of elements
Figure 64534DEST_PATH_IMAGE015
And (4) removing.
5. The method of claim 1, wherein the method further comprises: the system parameter in the step (3) is variable
Figure 93670DEST_PATH_IMAGE016
And auxiliary variables
Figure 662055DEST_PATH_IMAGE017
To make
Figure 143852DEST_PATH_IMAGE018
Satisfy the requirement of
Figure 823095DEST_PATH_IMAGE019
Wherein P represents the all-digital precoding matrix at the base station side,
Figure 706737DEST_PATH_IMAGE020
and
Figure 446023DEST_PATH_IMAGE021
weight factors and receiver gains for the k-th user, respectively, while initializing auxiliary variables
Figure 415116DEST_PATH_IMAGE022
Wherein
Figure 632471DEST_PATH_IMAGE023
Is used to measure the upper bound of the variation value of the objective function of the optimization problem.
6. The method of claim 1, wherein the method further comprises: the step (4) specifically comprises the following substeps:
(4.1) fixing other variables, solving separately
Figure 636199DEST_PATH_IMAGE024
By checking its first-order optimum condition, obtain
Figure 280807DEST_PATH_IMAGE025
Closed-form solution of (c):
Figure 2775DEST_PATH_IMAGE026
wherein
Figure 758242DEST_PATH_IMAGE027
，
Figure 616476DEST_PATH_IMAGE028
Representation matrix
Figure 431985DEST_PATH_IMAGE029
The ith column;
(4.2) fixing other variables and solving separately
Figure 641250DEST_PATH_IMAGE030
By checking its first-order optimum condition, obtain
Figure 200407DEST_PATH_IMAGE030
Closed-form solution of (c):
Figure 178728DEST_PATH_IMAGE031
(4.3) fixing other variables, solving P independently, and obtaining the following by checking first-order optimal conditions:
Figure 899559DEST_PATH_IMAGE032
wherein the content of the first and second substances,
Figure 330540DEST_PATH_IMAGE033
for lagrange multipliers, the need is satisfied
Figure 693388DEST_PATH_IMAGE034
If, if
Figure 526215DEST_PATH_IMAGE035
The solution corresponding to P satisfies the constraint of the problem, that is, the solution of the problem, if the constraint is not satisfied, the solution can be determined according to the relaxation condition
Figure 683527DEST_PATH_IMAGE036
To obtain
Figure 601805DEST_PATH_IMAGE037
To obtain a solution of P;
(4.4) enter the next cycle until
Figure 768344DEST_PATH_IMAGE038
At this time, the values of the beam selection matrix F and the baseband precoding matrix P are the optimization problemThe solution of (1).
7. The method of claim 6, wherein the beam selection matrix design method based on lens array comprises: the condition of the algorithm loop ending is
Figure 190098DEST_PATH_IMAGE039
。
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