CN115833887A - Antenna selection and beam forming method for dynamic super-surface antenna array - Google Patents

Antenna selection and beam forming method for dynamic super-surface antenna array Download PDF

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CN115833887A
CN115833887A CN202211389903.4A CN202211389903A CN115833887A CN 115833887 A CN115833887 A CN 115833887A CN 202211389903 A CN202211389903 A CN 202211389903A CN 115833887 A CN115833887 A CN 115833887A
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array
vector
beam forming
weight
dma
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陈胜垚
曾庆康
冉龙瑶
席峰
刘中
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Nanjing University of Science and Technology
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Nanjing University of Science and Technology
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Abstract

The invention discloses a dynamic super-surface antenna array antenna selection and beam forming method, which belongs to the field of array signal processing in signal processing and comprises the steps of determining the guide vector and mixed emission weight value representation of a one-dimensional DMA (direct memory access) uniform linear array; then, establishing an antenna selection and transmission beam forming problem model based on the DMA array; then, a problem effective solving method based on the alternative direction multiplier technology is provided, the original problem can be disassembled into a plurality of sub-problems to be solved alternately, and each sub-problem has a closed solution; and finally, analyzing the antenna selection and the transmitted beam forming performance of the DMA array in different beam scenes, and proving that the DMA array has the advantage of saving the number of antennas in the field of mixed beam forming.

Description

Antenna selection and beam forming method for dynamic super-surface antenna array
Technical Field
The invention belongs to the field of array signal processing, and particularly relates to a method for selecting and beamforming a dynamic super-surface antenna array antenna.
Background
With the wide application of antenna arrays in communication, radar, radio interference, electronic reconnaissance and other systems, beamforming technology plays an increasingly important role in these fields nowadays. The beam forming technology can be divided into digital beam forming and analog beam forming, and an analog beam forming system has a simple structure and low hardware cost, but has the problems of incapability of spatial multiplexing of beams, incapability of improving spectrum efficiency and the like. The digital beam forming system has high degree of freedom and can provide better beam forming performance, but the method is mostly realized in a baseband, and each antenna needs a special radio frequency hardware. Unfortunately, this results in very high costs when considering a large number of antennas, since radio frequency components are very expensive and have high power consumption, especially in millimeter wave technology. It is therefore desirable to design economical hardware using a large number of inexpensive antenna elements using the potential gain of a small number of expensive radio frequency chains. To better trade off performance and cost, analog-Digital Hybrid Beamforming (Analog-Digital Hybrid Beamforming) technology has attracted a lot of attention and research. Foad Sohrabi et al consider a two-stage hybrid beamforming architecture in which the beamformer is formed by a low-dimensional digital beamformer in series with an analog beamformer implemented using phase shifters. However, in the existing analog-digital hybrid beamforming technology, analog beamforming is usually implemented by using phase shifters and amplifiers, so that each array element is independent of phase and amplitude modulation. This approach is equivalent to sacrificing the beamforming gain to reduce hardware complexity, cost and power consumption, but since the analog domain still adopts the structure of a transposer and an amplifier, it is still a not small challenge to solve the power consumption and complexity of the whole rf link.
On the other hand, in a communication system, since signals of multiple frequency bands usually occupy a large amount of antenna resources, a common sparse antenna array for multiple frequency bands is often used as a base station. Nested arrays and co-prime arrays are often used in radar and sonar as structured sparse arrays, providing both high resolution DOA estimation and handling more sources than physical sensors. In 2010, nai Siew Eng et al will iterate l 1 The norm optimization method is applied to the problem of array element sparsity and achieves a good effect. In recent years, talents and others have been based on unmanned aerial vehiclesThe radar has the requirement of self-adaptive beam forming adjustment aiming at targets and interference in different directions, and a novel phase-only (phase-only) based sparse array synthesis method is proposed. The wang et al studied the problem of implementing sparse array design by antenna selection under the framework of dual-function radar communications (DFRC) system, and utilized the extra spatial freedom and configuration flexibility provided by the sparse array to suppress cross interference and promote coexistence of the two functions. However, these array models using antenna selection for beamforming almost start from the perspective of all-digital beamforming, and the digital beamforming itself requires very large power consumption and cost of the radio frequency link, so that the implementation scenarios are limited, and especially in a large-scale Multiple Input Multiple Output (MIMO) system, further optimization is required.
Disclosure of Invention
The invention aims to provide a dynamic super-surface antenna array antenna selection and beam forming method.
The technical scheme for realizing the purpose of the invention is as follows: a method for antenna selection and beam forming of a dynamic super-surface antenna array comprises the following steps:
step 1: obtaining a comprehensive guide vector and a mixed weight vector of a uniform linear array formed by DMA;
step 2: establishing an optimization problem model for minimizing the DMA quantity under the condition of meeting the given beam shape and simulation weight constraints;
and step 3: by introducing auxiliary variables and dual variables, an augmented Lagrangian function of an optimization problem is obtained, the problem is decomposed into a plurality of subproblems, and the problems are alternately solved by utilizing a framework of an alternating direction multiplier method, wherein each subproblem has a closed solution.
Preferably, the uniform linear array is composed of M one-dimensional DMAs, the distance between the DMAs is D, each super-surface antenna is composed of N uniform linearly arranged metamaterial array elements integrated on one waveguide, the distance between the array elements is D, and the interval between the last array element of the previous DMA and the first array element of the next DMA is D.
Preferably, the integrated steering vector of the uniform linear array is:
Figure BDA0003931582690000021
wherein b (theta) is a guide vector of the M DMAs in the direction theta, a (theta) is a guide vector of the N metamaterial array elements in the direction theta,
Figure BDA0003931582690000022
is a complex vector representing MN × 1.
Preferably, the steering vectors of the M DMAs in the direction θ are specifically:
Figure BDA0003931582690000023
where k =2 π/λ is the wave number in free space, λ represents the wavelength of the signal, M is the number of DMAs, D is the pitch of the DMAs,
Figure BDA0003931582690000024
representing an M x 1 complex vector.
Preferably, the steering vectors of the N metamaterial array elements in the direction θ are specifically:
Figure BDA0003931582690000025
wherein gamma is the guided wave attenuation ratio along the waveguide, d is the distance between the metamaterial array elements,
Figure BDA0003931582690000026
representing an N x 1 complex vector.
Preferably, the mixing weight vector is specifically:
Figure BDA0003931582690000027
in the formula (I), the compound is shown in the specification,
Figure BDA0003931582690000028
is a vector composed of the number weights of the M DMAs,
Figure BDA0003931582690000029
is a vector formed by simulation weights of MN metamaterial array elements, 1 N Is an N × 1 full 1 vector.
Preferably, the established optimization problem model for minimizing the DMA number under the condition of satisfying the given beam shape and simulation weight constraints is specifically:
Figure BDA0003931582690000031
Figure BDA0003931582690000032
Figure BDA0003931582690000033
|x m,n -j/2|＝1/2,m＝1,...,M；n＝1,...,N,
Figure BDA0003931582690000034
wherein the main lobe region comprises
Figure BDA0003931582690000035
At equally spaced discrete angles, i.e.
Figure BDA0003931582690000036
U 0 For the desired main lobe power, e ∈ [0,1 ∈ ∈ ∈ ∈ ∈]Is the main lobe ripple ratio; the side lobe region contains S equally spaced discrete angles, i.e.
Figure BDA0003931582690000037
U 1 The allowable maximum side lobe power, M is the number of DMA, N is the number of metamaterial array elements, c H Representing the conjugate transpose of matrix c.
Preferably, the main lobe, the side lobe level and the analog weight value introduction auxiliary variables are as follows:
Figure BDA0003931582690000038
Figure BDA0003931582690000039
z＝x
the equivalent mixed emission weight value is represented by analog and digital weight values, and the optimization problem is converted into:
Figure BDA00039315826900000310
Figure BDA00039315826900000311
Figure BDA00039315826900000312
z＝x,
Figure BDA00039315826900000313
Figure BDA00039315826900000314
|z m,n -j/2|＝1/2,m＝1,...,M；n＝1,...,N.
wherein
Figure BDA00039315826900000315
The augmented Lagrangian function using the objective function and linear constraint construction problem is expressed as
Figure BDA00039315826900000316
Wherein the content of the first and second substances,
Figure BDA00039315826900000317
is a self-defined penalty factor and is a self-defined penalty factor,
Figure BDA0003931582690000041
dual vectors corresponding to the three groups of auxiliary variables;
all variables in the formula are solved in sequence according to the framework of ADMM, namely:
4) Initializing variables: let i =0, set the random starting point x (0) ,g (0) Let eta (0) ,
Figure BDA0003931582690000042
μ (0) Is a zero vector;
5) Starting iteration:
h) In the prior art are known
Figure BDA0003931582690000043
Updating y in the case of (1);
i) In the prior art are known
Figure BDA0003931582690000044
Is updated in the case of
Figure BDA0003931582690000045
j) In the prior art are known
Figure BDA0003931582690000046
Updating z in case of (1);
k) In the prior art are known
Figure BDA0003931582690000047
Updating x in the case of (1);
l) in the known
Figure BDA0003931582690000048
Updating g in case of (1);
m) updating dual variables
Figure BDA00039315826900000422
n)i＝i+1；
6) And repeating the iteration until a termination condition is met to obtain a digital weight g and an analog weight x.
Preferably, the specific process of solving all variables in turn according to the frame of ADMM is as follows:
4) Initializing variables: let i =0, set the random starting point x (0) ,g (0) ,η (0) ,
Figure BDA0003931582690000049
μ (0) Setting as a zero vector;
5) Starting iteration:
h) In the prior art are known
Figure BDA00039315826900000410
Update y:
Figure BDA00039315826900000411
Figure BDA00039315826900000412
wherein
Figure BDA00039315826900000413
The above formula is further decomposed into
Figure BDA00039315826900000414
Sub-problems, the solution of each sub-problem being:
Figure BDA00039315826900000415
the updated y can be represented as
Figure BDA00039315826900000416
i) In the prior art are known
Figure BDA00039315826900000417
Is updated in case of
Figure BDA00039315826900000418
Figure BDA00039315826900000419
Figure BDA00039315826900000420
Wherein
Figure BDA00039315826900000421
The above equation is decomposed into S sub-problems and the solution for each sub-problem is solved:
Figure BDA0003931582690000051
j) In the prior art are known
Figure BDA0003931582690000052
Update z:
Figure BDA0003931582690000053
s.t.|z m,n -j/2|＝1/2,m＝1,...,M；n＝1,...,N.
let p be (i) ＝x (i) -μ (i) Will beThe above problem is broken down into a total of MN sub-problems:
Figure BDA0003931582690000054
Figure BDA0003931582690000055
is provided with
Figure BDA0003931582690000056
And
Figure BDA0003931582690000057
are respectively
Figure BDA0003931582690000058
Real and imaginary part of z nR And z nI Are each z n The real and imaginary parts of each sub-problem are solved as follows:
Figure BDA0003931582690000059
then:
Figure BDA00039315826900000510
the final solution to the vector is:
Figure BDA00039315826900000511
k) In the prior art are known
Figure BDA00039315826900000512
Update x:
Figure BDA00039315826900000513
in the formula:
Figure BDA00039315826900000514
least squares are used for the above equation:
Figure BDA00039315826900000515
l) in the known
Figure BDA00039315826900000516
Update g:
Figure BDA0003931582690000061
warping the mixing weights h, i.e.
Figure BDA0003931582690000062
Wherein X = diag (X),
Figure BDA0003931582690000063
setting an auxiliary matrix
Figure BDA0003931582690000064
And an auxiliary vector
Figure BDA0003931582690000065
At this time, the problem becomes
Figure BDA0003931582690000066
For minimizing l 1 Solving the problem by using a fibsta algorithm;
m) updating dual variables
Figure BDA0003931582690000067
Figure BDA0003931582690000068
Figure BDA0003931582690000069
μ (i+1) ＝μ (i) +z (i+1) -x (i+1)
n) updating the iteration value, i = i +1;
repeating the iteration step in the 2) till the iteration step is satisfied
Figure BDA00039315826900000610
And | z (i+1) -x (i +1) ‖ ∞ And delta is less than or equal to delta or the preset maximum iteration times are reached, and a digital weight g and an analog weight x are obtained.
Compared with the prior art, the invention has the following remarkable advantages: the invention uses the array with higher degree of freedom, namely the dynamic super-surface antenna array, combines the antenna selection to carry out the transmission beam forming, can use a smaller number of antennas, lower transmitting end cost and power consumption to complete the expected beam pattern, and provides a complete algorithm for solving the problems.
Drawings
FIG. 1 is a diagram of a one-dimensional DMA array of the present invention.
FIG. 2 is an equivalent model diagram of the present invention.
Fig. 3 is a flowchart of an algorithm for implementing antenna selection and beamforming of a dynamic super-surface antenna array according to the present invention.
Fig. 4 is a broad beam forming diagram of the present invention.
Fig. 5 is a diagram showing the antenna selection results of different arrays in the case of a wide beam according to the present invention.
Fig. 6 is a single beamforming diagram with null steering according to the present invention.
Fig. 7 is a diagram showing the antenna selection results of different arrays in the case of the single beam with nulls according to the present invention.
Fig. 8 is a multi-beam forming diagram of the present invention.
Fig. 9 is a diagram showing the antenna selection results of different arrays in the multi-beam case according to the present invention.
Detailed Description
The antenna selection and beam forming method of the dynamic super-surface antenna array of the present invention is further described with reference to the accompanying drawings and examples.
A Dynamic super surface Antenna array Antenna selection and beam forming method includes obtaining a transmitting signal model by a one-dimensional Dynamic super surface Antenna (DMA) array structure, and further obtaining an equivalent transmitting structure chart; then, constructing an optimization problem by utilizing signal models such as a steering vector, a mixed weight and the like, namely selecting a sparse antenna as a target function and controlling the shape of a wave beam as a constraint condition; then, introducing an auxiliary variable to obtain an augmented Lagrangian function of the problem; and finally, based on the frame of the ADMM algorithm, an optimization algorithm is provided, and the original problem is decomposed into sub-problems to be solved alternately.
According to the dynamic super-surface antenna array antenna selection and beam forming, firstly, an ULA (ultra wideband array) formed by one-dimensional DMA (direct memory access) is considered, and an analog weight, a digital weight and a guide vector of the hybrid array are obtained; subsequently, a problem model is proposed that minimizes the number of DMAs given the beam shape; and finally, setting an auxiliary variable and a dual variable to obtain an augmented Lagrangian function of the optimization problem, decomposing the problem into a plurality of subproblems and performing alternate solution by using a framework of an Alternate Direction Multiplier Method (ADMM). The flow chart of the invention is shown in fig. 1, and the specific implementation steps are as follows:
step 1, considering an ULA formed by M one-dimensional DMAs, wherein the distance between the DMAs is D, each super-surface antenna is formed by N uniform and linearly arranged metamaterial array elements integrated on one waveguide, the distance between the array elements is D, and the interval between the last array element of the previous DMA and the first array element of the next DMA is also D, so that the DMA distance satisfies D = Nd. Each metamaterial array element is generally regarded as a point dipole, and weak coupling between the array elements is assumed, so that coupling between the array elements in the waveguide is ignored. The guiding vector a (theta) of the N metamaterial array elements at the direction theta is as follows:
Figure BDA0003931582690000071
where k =2 pi/λ is the wave number of free space, λ represents the wavelength of the signal; gamma (f) =2 pi fn g C is the guided wave attenuation ratio along the waveguide, f denotes the signal frequency, n g Denotes the waveguide index and c denotes the speed of light. At a central frequency f 0 In the narrow band of (2), γ (f) is approximated by a constant γ (f) 0 ) And will be referred to as gamma. The steering vectors b (θ) of the M DMAs in the direction θ are:
Figure BDA0003931582690000089
the integrated steering vector c (θ) for the entire DMA array is:
Figure BDA0003931582690000081
step 2, defining the digital weight value of the mth DMA as g m Wherein M =1, 2.. Multidot.m, then the vector of the numerical weights of all M DMAs is
Figure BDA0003931582690000082
Defining the simulation weight of the nth array element on the mth DMA as x m,n Wherein N =1, 2.. And N, and the vector formed by the simulation weights of all MN metamaterial array elements is
Figure BDA0003931582690000083
Different from the phase of the traditional phased array adopting a phase shifter to regulate and control the simulation weight, the DMA array element regulates and controls the simulation weight by controlling the working state of the PIN diode, and the phase and the amplitude of the simulation weight can be changed simultaneously.However, the amplitude and the phase of the analog weight need to satisfy a certain constraint relation, and are not independently regulated. Typical DMA analog weight constraint forms are: amplitude only constraints, binary amplitude constraints and lorentz phase constraints. The invention starts from the perspective of Lorentz phase constraint, namely, the simulation weight needs to satisfy | x m,n -j/2| =1/2 (M =1, 2.. Multidot., M; N =1, 2.. Multidot., N). The equivalent hybrid transmission weight vector is
Figure BDA0003931582690000084
And 3, in order to further reduce the system hardware overhead, the invention mainly researches an antenna selection and transmission beam forming method of the DMA array so as to use DMA as little as possible on the basis of not reducing the performance of a transmission direction diagram. Essentially, the transmit beamforming of the sparse DMA array belongs to the antenna selection category and can be expressed as a digital weight l under the constraint of a given beam shape and an analog weight 0 Norm minimization problem, namely:
Figure BDA0003931582690000085
wherein the main lobe region comprises
Figure BDA0003931582690000086
At equally spaced discrete angles, i.e.
Figure BDA0003931582690000087
U 0 For the desired main lobe power, e ∈ [0,1 ∈ ∈ ∈ ∈ ∈]Is the main lobe ripple ratio; the side lobe region contains S equally spaced discrete angles, i.e.
Figure BDA0003931582690000088
U 1 The maximum allowable sidelobe power.
Step 4, in the above problem,/ 0 The norm minimization problem is an NP problem which is difficult to solve effectively, and convex relaxation treatment is carried out on the NP problem by usingl 1 Norm replacement l 0 And (4) norm. In order to effectively solve the problem, the invention provides a solution algorithm based on ADMM based on an alternative optimization thought. Firstly, introducing auxiliary variables on the amplitude to convert high-dimensional quadratic constraints into univariate quadratic constraints, then introducing the auxiliary variables to split Lorentz phase constraints of the simulated weight to solve, and aiming at the minimum l in the objective function 1 And solving the norm problem by using a classical fista algorithm numerical weight. Thus, the reconstructed problem can be solved alternately under the ADMM framework, with each sub-problem having a closed-form solution.
The main lobe, the side lobe level and the analog weight value lead-in auxiliary variables as follows:
Figure BDA0003931582690000091
Figure BDA0003931582690000092
z＝x (10)
the equivalent mixed emission weight value is represented by analog and digital weight values, and the optimization problem can be converted into
Figure BDA0003931582690000093
Wherein
Figure BDA0003931582690000094
The augmented Lagrangian function using the objective function and the linear constraint construction problem is then expressed as
Figure BDA0003931582690000095
Wherein the content of the first and second substances,
Figure BDA0003931582690000096
ρ＝[ρ 1 ,ρ 2 ,ρ 3 ] T is a self-defined penalty factor and is a self-defined penalty factor,
Figure BDA0003931582690000097
and the dual vectors corresponding to the three groups of auxiliary variables. All variables in the equation can then be solved in turn according to the framework of ADMM.
6) Initializing variables: let i =0, set the random starting point x (0) ,g (0) ,η (0) ,
Figure BDA0003931582690000098
μ (0) Setting as a zero vector;
7) Starting iteration:
o) in a known manner
Figure BDA0003931582690000099
Update y:
Figure BDA00039315826900000910
wherein
Figure BDA00039315826900000911
The above formula can be further decomposed into
Figure BDA00039315826900000912
Sub-problems, the solution of each sub-problem being:
Figure BDA0003931582690000101
the updated y can be represented as
Figure BDA0003931582690000102
p) in the known
Figure BDA0003931582690000103
Is updated in case of
Figure BDA0003931582690000104
Figure BDA0003931582690000105
Wherein
Figure BDA0003931582690000106
The same can decompose the above equation into S subproblems and solve each subproblem:
Figure BDA0003931582690000107
q) in the known state of the art
Figure BDA0003931582690000108
Update z:
Figure BDA0003931582690000109
let p be (i) ＝x (i) -μ (i) The above problem is broken down into MN sub-problems:
Figure BDA00039315826900001010
is provided with
Figure BDA00039315826900001011
And
Figure BDA00039315826900001012
are respectively
Figure BDA00039315826900001013
Real and imaginary parts of, z nR And z nI Are each z n The real and imaginary parts of each sub-problem can be solved as:
Figure BDA00039315826900001014
then:
Figure BDA0003931582690000111
the final solution to the vector can be found as:
Figure BDA0003931582690000112
r) in a known manner
Figure BDA0003931582690000113
Update x:
Figure BDA0003931582690000114
in the formula:
Figure BDA0003931582690000115
using least squares on the above equation:
Figure BDA0003931582690000116
s) in the known
Figure BDA0003931582690000117
Update g:
Figure BDA0003931582690000118
first, the mixed weight valueh is deformed to a certain extent, i.e.
Figure BDA0003931582690000119
Wherein X = diag (X),
Figure BDA00039315826900001110
setting an auxiliary matrix
Figure BDA00039315826900001111
And an auxiliary vector
Figure BDA00039315826900001112
At this time, the problem becomes
Figure BDA00039315826900001113
For this classical minimization l 1 The problem, referred to herein as the classic fista algorithm, is solved.
t) updating the dual variable
Figure BDA00039315826900001114
Figure BDA00039315826900001115
Figure BDA00039315826900001116
μ (i+1) ＝μ (i) +z (i+1) -x (i+1) . (30)
u) update the iteration value, i = i +1;
8) Repeating the iteration step in 2) until the condition is met
Figure BDA0003931582690000121
And | z (i+1) -x (i+1) ‖ ∞ And delta is less than or equal to delta or the preset maximum iteration times are reached, and a digital weight g and an analog weight x are obtained.
The invention adopts the one-dimensional mixed DMA array, the DMA array element regulates and controls the analog weight by controlling the working state of the PIN diode, and the phase and the amplitude of the analog weight can be changed simultaneously. By using the minimized number of antennas as an objective function, the method has better sparse selection effect compared with the conventional hybrid array, and can meet the requirements of transmitting beams in different scenes
Examples
The specific implementation of the antenna selection and transmit beam forming method based on the dynamic super-surface antenna array is further explained by Matlab simulation.
1) Simulation system parameter setting
The array scale is M =16, N =8, the wavelength is lambda =1cm, the array element interval is d = lambda/5, the spatial angle sampling interval is 1 DEG, and the sampling interval is [ -90 DEG, 90 DEG]Wave guide index n g =2.5, error term of termination condition Δ =10 -3 . Setting the mainlobe power U of a desired beam 0 ＝128 2 The main lobe ripple value e =0.01, and the peak-to-side lobe ratio is set to-20 dB.
2) Simulation scenario design
The scene is wide beam forming, and aiming at the situation that a wide main lobe beam needs to be synthesized, the main lobe area is set to be [ -10 degrees and 10 degrees ], and other directions in a sampling interval are side lobe areas.
And the second scenario is single-beam forming with null, and the null is formed by corrugated constraint to reduce the interference amplitude under the condition that the interference direction exists, and the solution method is the same as the main lobe. In this case, the main lobe region is set to-5 °, 40 °, 35 °, the ratio of the power in the interference direction to the main lobe power is set to-50 dB, and the remaining regions are set to the side lobe ranges.
Scene three is multi-beam forming, main lobe areas are set as [ -40 °, -35 ° ] and [5 °,10 ° ], and the rest areas are set as side lobe ranges.
3) Measurement index
In the invention, the DMA array is used for antenna selection and transmitting beam forming, the result is compared with a method for using a full digital array and a phase-only mixed array for antenna selection and transmitting beam forming, and the value of the invention is verified from two results of a beam pattern and an antenna selection result respectively.
4) Analysis of results
The invention carries out example simulation under three scenes. Fig. 4 and 5 are diagrams of beam patterns and antenna selection in a wide beam forming scene; fig. 6 and 7 are beam patterns and antenna selection diagrams in a single beamforming scene with nulls; fig. 8 and 9 are beam patterns and antenna selection diagrams in a multi-beam forming scene (in the antenna selection diagrams, circles represent selected ones, and crosses represent unselected ones).
By observing and comparing, it is easy to find that, when different scenes are satisfied, as shown in fig. 4, fig. 6, and fig. 8, the beam patterns of the DMA array, the all-digital array, and the phase-only hybrid array all satisfy the constraint that the main lobe, the side lobe, or the interference direction forms the null, but have a difference in the effect of antenna selection. As shown in fig. 5, in a wide beam forming scenario, the phase-only hybrid method screens out 9 antennas from 16 antennas, while the DMA array uses 8 antennas, and the full digital array only uses 7 antennas. In a single beamforming scenario with nulls, as shown in fig. 7, the phase-only hybrid approach screens out 10 antennas, while DMA arrays and all-digital arrays use only 9 antennas. As shown in fig. 9, in the multi-beam forming scenario, the hybrid phase-only array needs to select 14 antennas, at this time, the DMA array selects 12 antennas, and the full digital array selects 11 antennas. In the three scenes, the full-digital array, the DMA array and the hybrid phase-only array with the least number of antennas are selected. Considering the relatively high hardware cost of all-digital arrays, DMA arrays have better performance than classical phase-only hybrids in terms of saving antenna cost in hybrid arrays.
In conclusion, the method of the invention has good performance. The method and the system can greatly reduce the cost of the antenna array radio frequency link and have higher practical value.

Claims (9)

1. A method for antenna selection and beam forming of a dynamic super-surface antenna array is characterized by comprising the following steps:
step 1: obtaining a comprehensive guide vector and a mixed weight vector of a uniform linear array formed by DMA;
step 2: establishing an optimization problem model for minimizing the DMA quantity under the condition of meeting the given beam shape and simulation weight constraints;
and 3, step 3: by introducing auxiliary variables and dual variables, an augmented Lagrangian function of an optimization problem is obtained, the problem is decomposed into a plurality of subproblems, and the problems are alternately solved by utilizing a framework of an alternating direction multiplier method, wherein each subproblem has a closed solution.
2. The method for antenna selection and beam forming for a dynamic super-surface antenna array according to claim 1, wherein the uniform linear array is composed of M one-dimensional DMAs, the distance between the DMAs is D, each super-surface antenna is composed of N uniform linearly arranged metamaterial array elements integrated on one waveguide, the distance between the array elements is D, and the interval between the last array element of the previous DMA and the first array element of the next DMA is D.
3. The method for dynamic super-surface antenna array antenna selection and beamforming according to claim 1, wherein the integrated steering vector of the uniform linear array is:
Figure FDA0003931582680000011
wherein b (theta) is the guide vector of M DMAs in the direction theta, a (delta) is the guide vector of N metamaterial array elements in the direction delta,
Figure FDA0003931582680000012
representing an MN × 1 complex vector.
4. The method for antenna selection and beamforming for a dynamic super-surface antenna array according to claim 3, wherein the steering vectors of the M DMAs in the direction Δ are specifically:
Figure FDA0003931582680000013
where k =2 π/λ is the wave number in free space, λ represents the wavelength of the signal, M is the number of DMAs, D is the pitch of the DMAs,
Figure FDA0003931582680000014
representing an M x 1 complex vector.
5. The method for antenna selection and beam forming of a dynamic super-surface antenna array according to claim 3, wherein the steering vectors of the N metamaterial array elements in the direction θ are specifically as follows:
Figure FDA0003931582680000015
wherein gamma is the guided wave attenuation ratio along the waveguide, d is the distance between the metamaterial array elements,
Figure FDA0003931582680000016
representing an N x 1 complex vector.
6. The method for antenna selection and beamforming for a dynamic super-surface antenna array according to claim 3, wherein the hybrid weight vector specifically comprises:
Figure FDA0003931582680000017
in the formula (I), the compound is shown in the specification,
Figure FDA0003931582680000018
as a number of M DMAsA vector composed of the word weights is calculated,
Figure FDA0003931582680000019
is a vector formed by simulation weights of MN metamaterial array elements, 1 N Is an N × 1 full 1 vector.
7. The method for antenna selection and beam forming for a dynamic super-surface antenna array according to claim 1, wherein the established optimization problem model for minimizing the number of DMAs under the constraint of satisfying the given beam shape and the simulation weight is specifically:
Figure FDA0003931582680000021
||g|| 0
Figure FDA0003931582680000022
Figure FDA0003931582680000023
|x m,n -j/2|＝1/2,m＝1,...,M；n＝1,...,N,
Figure FDA0003931582680000024
wherein the main lobe region comprises
Figure FDA0003931582680000025
At equally spaced discrete angles, i.e.
Figure FDA0003931582680000026
U 0 For the desired main lobe power, e ∈ [0,1 ∈ ∈ ∈ ∈ ∈]Is the main lobe ripple ratio; the side lobe region contains S equally spaced discrete angles, i.e.
Figure FDA0003931582680000027
U 1 The allowable maximum side lobe power, M is the number of DMA, N is the number of metamaterial array elements, c H Representing the conjugate transpose of matrix c.
8. The method for antenna selection and beam forming of a dynamic super-surface antenna array according to claim 7, wherein the main lobe, the side lobe level and the analog weight introduce auxiliary variables as follows:
Figure FDA0003931582680000028
Figure FDA0003931582680000029
z＝x
the equivalent mixed emission weight value is represented by analog and digital weight values, and the optimization problem is converted into:
Figure FDA00039315826800000210
||g|| 1
Figure FDA00039315826800000211
Figure FDA00039315826800000212
z＝x,
Figure FDA00039315826800000213
Figure FDA00039315826800000214
|z m,n -j/2|＝1/2,m＝1,...,M；n＝1,...,N.
wherein
Figure FDA00039315826800000215
The augmented Lagrangian function using an objective function and a linear constraint construction problem is expressed as
Figure FDA00039315826800000216
Wherein the content of the first and second substances,
Figure FDA0003931582680000031
ρ＝[ρ 1 ,ρ 2 ,ρ 3 ] T is a self-defined penalty factor and is used for the purpose of self-defining,
Figure FDA0003931582680000032
dual vectors corresponding to the three groups of auxiliary variables;
all variables in the formula are solved in sequence according to the frame of ADMM, namely:
1) Initializing variables: let i =0, set the random starting point x (0) ,g (0) Let eta (0) ,
Figure FDA0003931582680000033
μ (0) Is a zero vector;
2) Starting iteration:
a) In the prior art are known
Figure FDA0003931582680000034
Updating y in the case of (3);
b) In the prior art are known
Figure FDA0003931582680000035
Is updated in case of
Figure FDA0003931582680000036
c) In the prior art are known
Figure FDA0003931582680000037
Updating z in case of (1);
d) In the prior art are known
Figure FDA0003931582680000038
Updating x in the case of (1);
e) In the prior art are known
Figure FDA0003931582680000039
Updating g in case of (1);
f) Updating dual variables
Figure FDA00039315826800000310
g)i＝i+1；
3) And repeating the iteration until a termination condition is met to obtain a digital weight g and an analog weight x.
9. The method for antenna selection and transmit beamforming based on a dynamic super-surface antenna array according to claim 8, wherein the specific process of sequentially solving all variables according to the frame of the ADMM is as follows:
1) Initializing variables: let i =0, set the random starting point x (0) ,g (0) ,η (0) ,
Figure FDA00039315826800000311
μ (0) Is a zero vector;
2) Starting iteration:
a) In the prior art are known
Figure FDA00039315826800000312
Update y:
Figure FDA00039315826800000313
Figure FDA00039315826800000314
wherein
Figure FDA00039315826800000315
The above formula is further decomposed into
Figure FDA00039315826800000316
Sub-problems, the solution of each sub-problem being:
Figure FDA00039315826800000317
the updated y can be represented as
Figure FDA00039315826800000318
b) In the prior art are known
Figure FDA00039315826800000319
Is updated in case of
Figure FDA00039315826800000320
Figure FDA00039315826800000321
Figure FDA00039315826800000322
Wherein
Figure FDA0003931582680000041
The above equation is decomposed into S sub-problems and the solution for each sub-problem is solved:
Figure FDA0003931582680000042
c) In the prior art are known
Figure FDA0003931582680000043
Update z:
Figure FDA0003931582680000044
s.t.|z m,n -j/2|＝1/2,m＝1,...,M；n＝1,...,N.
let p be (i) ＝x (i) ＝μ (i) The above problem is broken down into MN sub-problems:
Figure FDA0003931582680000045
Figure FDA0003931582680000046
is provided with
Figure FDA0003931582680000047
And
Figure FDA0003931582680000048
are respectively
Figure FDA0003931582680000049
Real and imaginary parts of, z nR And z nI Are each z n The real and imaginary parts of each sub-problem are solved as follows:
Figure FDA00039315826800000410
then:
Figure FDA00039315826800000411
the final solution to the vector is:
Figure FDA00039315826800000412
d) In the prior art are known
Figure FDA00039315826800000413
Update x:
Figure FDA00039315826800000414
in the formula:
Figure FDA00039315826800000415
least squares are used for the above equation:
Figure FDA00039315826800000416
e) In the prior art are known
Figure FDA0003931582680000051
Update g:
Figure FDA0003931582680000052
the mixing weight h is deformed, i.e.
Figure FDA0003931582680000053
Wherein X = diag (X),
Figure FDA0003931582680000054
setting an auxiliary matrix
Figure FDA0003931582680000055
And an auxiliary vector
Figure FDA0003931582680000056
At this time, the problem becomes
Figure FDA0003931582680000057
For minimizing l 1 Solving the problem by using a fibsta algorithm;
f) Updating dual variables
Figure FDA0003931582680000058
Figure FDA0003931582680000059
Figure FDA00039315826800000510
μ (i+1) ＝μ (i) +z (i+1) -x (i+1)
g) Updating an iteration value, i = i +1;
3) Repeating the iteration step in the 2) till the iteration step is satisfied
Figure FDA00039315826800000511
And | z (i+1) -x (i+1) ‖ ∞ And delta is less than or equal to delta or the preset maximum iteration times are reached, and a digital weight g and an analog weight x are obtained.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116540172A (en) * 2023-07-05 2023-08-04 南京理工大学 Method and device for estimating incoming wave direction of incident signal, electronic equipment and medium
CN116540172B (en) * 2023-07-05 2023-09-22 南京理工大学 Method and device for estimating incoming wave direction of incident signal, electronic equipment and medium

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