CN107135023B - Three-dimensional training codebook design method and beam alignment method for millimeter wave communication system - Google Patents

Three-dimensional training codebook design method and beam alignment method for millimeter wave communication system Download PDF

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CN107135023B
CN107135023B CN201710293707.XA CN201710293707A CN107135023B CN 107135023 B CN107135023 B CN 107135023B CN 201710293707 A CN201710293707 A CN 201710293707A CN 107135023 B CN107135023 B CN 107135023B
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codebook
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CN107135023A (en
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黄永明
苏敏华
章建军
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Southeast University
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    • 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
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • 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
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • 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
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0619—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
    • H04B7/0621—Feedback content
    • H04B7/0632—Channel quality parameters, e.g. channel quality indicator [CQI]

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Abstract

The invention disclosesA three-dimensional training codebook design method and a beam alignment method for a millimeter wave communication system are disclosed, wherein the three-dimensional training codebook design method comprises the following steps: 1. according to resolution and beam space
Figure DDA0001282519760000011
Establishing a three-dimensional training codebook tree structure with the depth of S and the degree of N; 2. will be provided with
Figure DDA0001282519760000012
Equally divided into N rectangular regions
Figure DDA0001282519760000013
Is recorded as a set
Figure DDA0001282519760000014
Figure DDA0001282519760000015
Having a set of beams
Figure DDA0001282519760000016
Corresponding to it; the root node of the tree structure is
Figure DDA0001282519760000017
And
Figure DDA0001282519760000018
a combination of (1); 3. determining the b-th node C of the s-th layers,b，Cs,bIs composed of
Figure DDA0001282519760000019
And beam set
Figure DDA00012825197600000110
A combination of (1); determining each node in 2 to S layers in turn
Figure DDA00012825197600000111
4. Solving the beam forming vector contained in the corresponding beam set of each node
Figure DDA00012825197600000112
A three-dimensional training codebook is obtained, where q is 1, …, N. The three-dimensional training codebook generated by the method can be used for realizing high-precision beam alignment and channel estimation, and can remarkably reduce the training overhead of the system.

Description

Three-dimensional training codebook design method and beam alignment method for millimeter wave communication system
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a three-dimensional training codebook design method for a millimeter wave communication system with uniform planar array arrangement of receiving and transmitting end antennas.
Background
With the continuous development of wireless communication technology, high-speed data services and ubiquitous access demands are exhibiting an explosive increase. The next generation of 5G mobile communication technology will have higher and higher demands for capacity, energy consumption and bandwidth. Millimeter wave communication technology operating in the 30-300GHz relatively idle band is considered as one of the key technologies for next generation wireless local area networks and mobile communications due to the large amount of unauthorized bandwidth contained in the operating band, because direct spread spectrum bandwidth is simple and effective for increasing system capacity. Research has shown that millimeter wave communication can achieve peak transmission rates of 10 Gbps.
However, compared to the conventional microwave band, the millimeter wave transmission suffers from larger path loss, so the communication distance and coverage are very limited. The millimeter wave signal has extremely short wavelength, a large number of antennas can be packaged in a small size, and then a large-scale array antenna is combined with a digital-analog hybrid beam forming technology, and the array gain and the space division multiplexing gain provided by the millimeter wave signal can make up for partial attenuation of a system, so that the transmission rate and the transmission quality of the system are improved. In addition, in order to obtain the array gain better, it is necessary to perform beam alignment on the transmitting and receiving beams at the beginning of communication, and the high-precision beam alignment plays a key role in establishing a reliable millimeter wave communication link, obtaining required transmission data, and enlarging the communication coverage of the area. Accurate beam alignment can also be used for improving the channel estimation performance of the millimeter wave system by estimating relevant parameters including an arrival angle (AoA), a departure angle (AoD), path gain and the like.
In practical millimeter wave communication systems, there is a certain difficulty in achieving accurate beam alignment. First, the high frequency band in the millimeter wave band means that the channel may change rapidly in a short time, and beam alignment needs to be done in a very short channel coherence time, so an exhaustive beam search algorithm is not suitable here. Secondly, to fully utilize the array gain of a large antenna array, the training beam should be narrow enough, which will undoubtedly increase the complexity of beam alignment, and therefore it is necessary to provide an efficient beam codebook design method and a beam search algorithm. To reduce the training overhead of beam alignment, an effective approach is to use a tree search algorithm based on a hierarchical multiresolution training codebook. The layered training codebook generally consists of sub codebooks of different levels, wherein on a high level, the sub codebooks contain a small number of training beams with low resolution to cover a preset angle range; on a low level, the number of training beams included in the subcode book is increased, and the resolution is improved to a certain extent.
While hierarchical searching can significantly reduce the training overhead of the system, its performance depends largely on the hierarchical training codebook used. There have been many studies on hierarchical codebook design methods, but these studies have focused mainly on Uniform Linear Array (ULA) structures, while very few studies have been made on Uniform Planar Array (UPA) structures. In order to realize variable-precision three-dimensional beam coverage and obtain larger beam forming gain, the invention provides a three-dimensional training codebook design method suitable for a millimeter wave communication system. In the present invention, the overshoot of the training beam pattern and the ripple of the main side lobe are properly constrained so that each training beam has a relatively flat amplitude response and a more desirable transition band. The three-dimensional training codebook designed by the invention can realize high-precision beam alignment and channel estimation in a millimeter wave communication system even under the condition of low signal-to-noise ratio.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention discloses a three-dimensional training codebook design method for a millimeter wave communication system, wherein the three-dimensional training codebook generated by the method can be used for realizing high-precision beam alignment and channel estimation and can obviously reduce the training overhead of the system.
The technical scheme is as follows: the invention discloses a three-dimensional training codebook design method for a millimeter wave communication system, which comprises the following steps:
(1) establishing a three-dimensional training codebook tree structure with the depth of S and the degree of N according to the resolution rs and the range of the beam space B;
let resolution rs ═ ve×vaThe width of the beam space B in the e direction is WeA width in the a direction of WaI.e. B is We×WaThe degree of the tree structure N is Ne×NaThe depth S and the degree N satisfy the condition:
Figure GDA0002371391930000021
each node in layers 1 to S-1 in the three-dimensional training codebook tree structure is provided with N sub-nodes;
(2) taking beam space B in e direction by NeAliquoting, N in the a directionaEqually dividing, i.e. equally dividing B into N rectangular areas
Figure GDA0002371391930000022
N＝Ne×NaIs recorded as a set
Figure GDA0002371391930000023
Each rectangular region
Figure GDA0002371391930000024
With beamforming vectors
Figure GDA0002371391930000025
Correspondingly, i is 1, …, and N, N beamforming vectors form a beam set
Figure GDA0002371391930000026
Namely, it is
Figure GDA0002371391930000027
Root node C of three-dimensional training codebook tree structure1,1Is a set of rectangular regions
Figure GDA0002371391930000031
And beam set
Figure GDA0002371391930000032
In combination with (1)
Figure GDA0002371391930000033
(3) Determining the (b) th node C of the s layer of the three-dimensional training codebook tree structures,b，Cs,bIs a set of rectangular regions
Figure GDA0002371391930000034
And beam set
Figure GDA0002371391930000035
In combination with (1)
Figure GDA0002371391930000036
Wherein
Figure GDA0002371391930000037
Node with s-1 th layer
Figure GDA0002371391930000038
Has the following relationship:
Figure GDA0002371391930000039
wherein S is 2, …, S, b is 1, …, Ns-1，
Figure GDA00023713919300000310
Is the rounding up operation,% is the remainder operation;
to pair
Figure GDA00023713919300000311
In the e direction by NeAliquoting, N in the a directionaEqually dividing to obtain N sub-rectangular areas
Figure GDA00023713919300000312
Each sub-rectangular region
Figure GDA00023713919300000313
With beamforming vectors
Figure GDA00023713919300000314
Correspondingly, i is 1, …, and N, N beamforming vectors form a beam set
Figure GDA00023713919300000315
Namely, it is
Figure GDA00023713919300000316
Sequentially determining each node in 2 to S layers according to the steps
Figure GDA00023713919300000317
(4) Solving the beamforming vector contained in each node in the three-dimensional training codebook tree structure
Figure GDA00023713919300000318
A three-dimensional training codebook is obtained, where q is 1, …, N.
Preferably, each node in the three-dimensional training codebook tree structure contains a beamforming vector
Figure GDA00023713919300000319
Having constant but not identical amplitude response values in the main and side lobes, i.e.
Figure GDA00023713919300000320
Wherein psi ═ psie,ψa)＝(sin(θe),sin(θa) Is a pitch angleθeAnd azimuth angle thetaaThe combination of the sine values of (a) and (b),
Figure GDA00023713919300000321
for antenna array response vector a in horizontal directionh(2π/λdhsin(θe)cos(θa) Antenna array response vector a in the vertical directionv(2π/λdvsin(θa) The Kronecker product of (c),
Figure GDA00023713919300000322
is a beamforming vector
Figure GDA00023713919300000323
The amplitude response value of (a); wherein q is 1, …, N.
Preferably, the beamforming vector is solved in step (4)
Figure GDA0002371391930000041
To solve the optimization problem:
Figure GDA0002371391930000042
wherein epsilon is the ripple of the main and side lobes of the training beam and is a very small positive real number,
Figure GDA0002371391930000043
respectively, main side lobe corresponding regions.
Preferably, for
Figure GDA0002371391930000044
Sampling discretization is carried out to obtain discrete wave beam main and side lobe corresponding areas
Figure GDA0002371391930000045
Figure GDA0002371391930000046
And (4) a region.
To avoid overshoot after discrete sampling, constraint bars are introducedPiece
Figure GDA0002371391930000047
Solving the beamforming vector in step (4)
Figure GDA0002371391930000048
To solve the optimization problem:
Figure GDA0002371391930000049
wherein epsilon is the ripple of the main and side lobes of the training beam and is a small positive real number; esIs constant, the value decreases with increasing s;
Figure GDA00023713919300000410
respectively, the main and side lobe corresponding areas of the discrete wave beam.
Preferably, the constraint condition is relaxed, and an optimization problem is solved by using a constraint concave-convex process iterative algorithm, wherein the steps are as follows:
(6.1) determining an iteration initial value f0The following constraint optimization problem is constructed:
Figure GDA00023713919300000411
wherein
Figure GDA00023713919300000413
The real part of the number in parentheses is taken,
Figure GDA00023713919300000412
respectively representing discretized main and side lobe corresponding regions;
(6.2) iteratively solving the optimization problem in the step (6.1), checking whether the r value obtained by the iteration meets the convergence standard, and if so, obtaining the optimal solution f of the iterationnI.e. the final solution
Figure GDA00023713919300000511
If not, according to the optimal solution f of the iterationnSolving the optimization problem in the step (6.1) again;
(6.3) outputting the final solution
Figure GDA00023713919300000512
The desired three-dimensional training beam is obtained.
Preferably, the initial value f in step (6.1)0Determined by solving the following optimization problem:
Figure GDA0002371391930000051
the invention also discloses a beam alignment method, which comprises the following steps:
(8.1) parameter configuration and initialization: the receiving and transmitting end designs the three-dimensional training codebook according to any one of the three-dimensional training codebook design methods;
the designed three-dimensional training code book is designed to contain S training sub code books
Figure GDA0002371391930000052
Respectively corresponding to S training stages; the degree of the designed three-dimensional training codebook tree structure is N; beamforming vectors
Figure GDA0002371391930000053
The subscript values in (1) are initialized as: s is 1, bf＝1；
(8.2) the transmitting end continuously uses the low resolution training beam vector in the first layer sub-codebook
Figure GDA0002371391930000054
To transmit a training signal z, and repeat training M for each training beamsTo increase the received signal-to-noise ratio of the system;
(8.3) the receiving end receives the signal according to the corresponding
Figure GDA0002371391930000055
Selecting the beamforming vector that yields the highest received energy, i.e.
Figure GDA0002371391930000056
Wherein
Figure GDA0002371391930000057
p is the transmit power, h is the channel matrix, hHIs a conjugate transpose of h and,
Figure GDA0002371391930000058
additive Gaussian noise;
the receiving end indexes the value
Figure GDA00023713919300000513
Is fed back to the transmitting end, whereby the transmitting end is based on
Figure GDA0002371391930000059
And its corresponding rectangular area
Figure GDA00023713919300000510
Preliminarily determining the area of the departure angle AoD corresponding to the strongest wave beam;
(8.4) transmitting end according to index value
Figure GDA0002371391930000063
Selecting a set of beamforming vectors with higher resolution in a sub-codebook of a next layer of a three-dimensional codebook
Figure GDA0002371391930000061
To transmit training signals to further more accurately determine the area where the AoD is located;
wherein
Figure GDA0002371391930000064
And (8.5) repeating the steps (8.3) to (8.4) until the beamforming vector meeting the highest resolution requirement is found, wherein the rectangular domain corresponding to the beamforming vector is the area where the AoD is located.
Has the advantages that: the three-dimensional training codebook design method suitable for the millimeter wave communication system can be used for realizing high-precision beam alignment and channel estimation, and has the advantages that:
(1) the existing research mainly aims at a millimeter wave system with antennae arranged in an ULA mode, the UPA structure is fully considered, and the defects of the existing research are overcome. Under the UPA structure, more transmission antennas can be configured in a limited two-dimensional space, so that a wider geographical area can be detected and intercepted, three-dimensional beam coverage with variable precision is realized, and a larger beam forming gain is obtained.
(2) The invention processes the overshoot phenomenon which may occur on the non-sampling point in the training beam pattern, and properly restricts the ripple of the main and side lobes, so that each training beam has relatively flat amplitude response and ideal transition frequency band, which is beneficial to improving the beam alignment precision.
(3) The three-dimensional training codebook generated by the invention is suitable for a beam alignment algorithm based on a tree search algorithm, can obviously reduce the training overhead of the system, and can realize high-precision beam alignment and channel estimation performance in a millimeter wave communication system based on a UPA structure.
Drawings
FIG. 1 is a schematic diagram of a Uniform Planar Array (UPA) architecture;
FIG. 2 is a schematic structural diagram of a three-dimensional training codebook generated in the embodiment;
FIG. 3 is a schematic diagram of main side lobe amplitude fluctuation;
FIG. 4 is a diagram of 4 training beam vectors generated in an embodiment
Figure GDA0002371391930000062
An amplitude response map of (a);
FIG. 5 is a training beam diagram under two codebook design methods (BPSA, LSA);
fig. 6 is a detailed flowchart of the three-dimensional training codebook design method and a flowchart for beam training after codebook generation according to the present invention;
fig. 7 is a graph showing the variation trend of the average beam alignment error rate with the signal-to-noise ratio under two codebook design methods (BPSA, LSA).
Detailed Description
The invention is further elucidated with reference to the drawings and the detailed description.
As shown in fig. 1, the three-dimensional training codebook design method disclosed in the present invention is suitable for a millimeter wave system with antennas arranged in a uniform area array, taking a transmitting end as an example, N in the figureh、NvRespectively, the number of antennas in the horizontal direction and the vertical direction, so that the total number of transmitting antennas NT＝NhNv，dhAnd dvThe distance between two adjacent antennas in the horizontal direction and the vertical direction is respectively.
The beam space B is a rectangular area, the e direction and the a direction are vertical to each other, and the width of B in the e direction is WeA width in the a direction of WaI.e. B is We×WaA rectangular area of (a).
In this embodiment, the millimeter wave communication system with the transmitting antennas arranged in a uniform area array is considered, where N ish＝Nv32, the distance d between two adjacent antennash＝dvλ is the wavelength of the millimeter wave signal, 3 λ/8. For simplicity, it is assumed that the receiving end is equipped with only a single antenna. It should be noted that, although the three-dimensional training codebook design at the transmitting end is taken as an example in this embodiment, this method is also applicable to codebook design at the receiving end.
A three-dimensional training codebook design method for a millimeter wave communication system comprises the following steps:
step 1, establishing a three-dimensional training codebook tree structure with the depth of S and the degree of N according to the resolution rs and the range of a beam space B;
let resolution rs ═ ve×va(ii) a Pitch angle theta of the transmitted beameAzimuth angle thetaaAre respectively located in an angle range
Figure GDA0002371391930000073
In the embodiment, the beam space B can be defined as sin (θ) by the independent and uncorrelated variations of the pitch angle and the azimuth angle, which can be expressed by the variations of the two perpendicular directions e and ae)、sin(θa) The product of the corresponding ranges, i.e. B ═ sin (θ)e),sin(θe)]×[-sin(θa),sin(θa)]＝[-0.64,0.64)]×[-0.64,0.64)]In (sin (theta))e),sin(θa) Plane is a rectangular field, i.e., We＝2sin(θe)，Wa＝2sin(θa)。
Degree N-N of three-dimensional training codebook tree structuree×NaThe depth S and the degree N satisfy the condition:
Figure GDA0002371391930000071
Figure GDA0002371391930000072
i.e. equally dividing the beam space B into NSAnd after the small rectangular areas, each small rectangular area is less than or equal to the resolution.
Each node in layers 1 to S-1 in the three-dimensional training codebook tree structure is provided with N sub-nodes;
step 2, carrying out N on the beam space B in the e directioneAliquoting, N in the a directionaEqually dividing, i.e. equally dividing B into N rectangular areas
Figure GDA0002371391930000081
N＝Ne×NaIs recorded as a set
Figure GDA0002371391930000082
Each rectangular region
Figure GDA0002371391930000083
With beamforming vectors
Figure GDA0002371391930000084
Correspondingly, i is 1, …, and N, N beamforming vectors form a beam set
Figure GDA0002371391930000085
Namely, it is
Figure GDA0002371391930000086
Root node C of three-dimensional training codebook tree structure1,1Is a set of rectangular regions
Figure GDA0002371391930000087
And beam set
Figure GDA0002371391930000088
In combination with (1)
Figure GDA0002371391930000089
Step 3, determining the b-th node C of the s-th layer of the three-dimensional training codebook tree structures,b，Cs,bIs a set of rectangular regions
Figure GDA00023713919300000810
And beam set
Figure GDA00023713919300000811
In combination with (1)
Figure GDA00023713919300000812
Wherein
Figure GDA00023713919300000813
Node with s-1 th layer
Figure GDA00023713919300000814
Has the following relationship:
Figure GDA00023713919300000815
wherein S is 2, …, S, b is 1, …, Ns-1，
Figure GDA00023713919300000816
Is the rounding up operation,% is the remainder operation;
to pair
Figure GDA00023713919300000817
In the e direction by NeAliquoting, N in the a directionaEqually dividing to obtain N sub-rectangular areas
Figure GDA00023713919300000818
Each sub-rectangular region
Figure GDA00023713919300000819
With beamforming vectors
Figure GDA00023713919300000820
Correspondingly, i is 1, …, and N, N beamforming vectors form a beam set
Figure GDA00023713919300000821
Namely, it is
Figure GDA00023713919300000822
And is
Figure GDA00023713919300000823
Corresponding;
sequentially determining each node in 2 to S layers according to the steps
Figure GDA00023713919300000824
Step 4, solving the beam forming vector contained in each node in the three-dimensional training codebook tree structure
Figure GDA00023713919300000825
A three-dimensional training codebook is obtained, where q is 1, …, N.
The tree structure of the three-dimensional training CodeBook (CodeBook) has S layers, each layer is a Sub-CodeBook (Sub-CodeBook) and corresponds to a training stage; the sub-code book at the s-th layer has Ns-1Nodes, each node comprising N code words (CodeWord), each node being assembled by beams
Figure GDA00023713919300000826
And its corresponding rectangular area
Figure GDA0002371391930000091
To represent;
Figure GDA0002371391930000092
and its corresponding rectangular area
Figure GDA0002371391930000093
In combination with (1)
Figure GDA0002371391930000094
Is a code word.
As shown in fig. 2, the three-dimensional training codebook generated in this embodiment has a quadtree structure, i.e., the degree N of the tree structure of the three-dimensional training codebook is equal to Ne×Na2 × 2. The training device consists of S sub code books corresponding to S training stages; subcode book for the s-th training phase
Figure GDA0002371391930000095
In total, contains 4sA beamforming vector having the same main lobe width, and these vectors constitute 4s-1A set of beams
Figure GDA0002371391930000096
Wherein the b-th set
Figure GDA0002371391930000097
Including beamforming vectors
Figure GDA0002371391930000098
Zi code book
Figure GDA0002371391930000099
The number of the beam forming vectors in (1) is the sub-codebook of the previous layer
Figure GDA00023713919300000910
4 times of the number of middle training beams. In the s-th training phase, the beam space is partitioned into 4s-1Rectangular fields of the same size
Figure GDA00023713919300000911
Wherein the b-th rectangular field
Figure GDA00023713919300000912
And beam set
Figure GDA00023713919300000913
Are related to, and
Figure GDA00023713919300000914
simultaneous beamforming vectors
Figure GDA00023713919300000915
Are respectively connected with
Figure GDA00023713919300000916
One-to-one correspondence is realized; in the next training phase, the rectangular field
Figure GDA00023713919300000917
And equally divided into 4 smaller sub-regions, j ∈ { LL, LR, RL, RR }, i.e., the
Figure GDA00023713919300000918
Figure GDA00023713919300000919
Beamforming vectors designed to improve beam alignment performance for millimeter wave communications
Figure GDA00023713919300000920
Have constant but not identical amplitude response values on the main and side lobes, respectively, i.e.:
Figure GDA00023713919300000921
wherein psi ═ psie,ψa)＝(sin(θe),sin(θa) Is a pitch angle θeAnd azimuth angle thetaaThe combination of the sine values of (a) and (b),
Figure GDA00023713919300000922
is an antenna array response vector a in the horizontal direction and the vertical directionh(2π/λdhsin(θe)cos(θa) A and av(2π/λdvsin(θa) Kronecker product of d)hAnd dvThe distance between two adjacent antennas in the horizontal direction and the vertical direction respectively, lambda is the wavelength of the millimeter wave signal,
Figure GDA00023713919300000923
is a beam vector
Figure GDA00023713919300000924
The amplitude response value of (a).
If the ripple epsilon of the main and side lobes of the training beam is strictly limited to 0, it is difficult to successfully design the three-dimensional codebook, and to avoid this infeasibility and ensure high-precision beam alignment performance, as shown in fig. 3, the main and side lobes of the beam pattern may be allowed to have small amplitude fluctuation, and the amplitude response value of the main lobe should be as large as possible under the condition that the value of the ripple epsilon is fixed, so the design of the training beam can be expressed as the following optimization problem:
Figure GDA0002371391930000101
where epsilon is a very small positive real number,
Figure GDA0002371391930000102
are respectively a main area and a side lobe corresponding area,
Figure GDA0002371391930000103
is a rectangular area
Figure GDA0002371391930000104
In the interior of said container body,
Figure GDA0002371391930000105
is composed of
Figure GDA0002371391930000106
And (3) outside. Due to the fact that
Figure GDA0002371391930000107
Continuous and countless, so the corresponding area of the main and side lobes of the wave beam must be sampled or discretized; and because the number of sampling points is limited, overshoot phenomenon possibly exists in an area which is not sampled, and in order to avoid the overshoot phenomenon after discrete sampling, a constraint condition of | | | f | | < E | is introduceds，EsThe value of (c) is reduced along with the increase of s, i | · | | is 2 norms of the vector, namely the optimization problem is as follows:
Figure GDA0002371391930000108
the present embodiment employs the following finite scattering channel model:
Figure GDA0002371391930000109
where L is the total number of channels, αlIs the complex gain of the ith path, β is the average path loss,
Figure GDA00023713919300001010
is an antenna array response vector, and ab(b ∈ { h, v }) has the following form:
Figure GDA00023713919300001011
Figure GDA00023713919300001012
is the Kronecker product operator.
With beamforming vectors in a training codeword in a three-dimensional training codebook
Figure GDA00023713919300001013
For example, the code word is in a discrete beam region
Figure GDA00023713919300001014
Has a large amplitude response value, and is in other regions
Figure GDA00023713919300001015
The amplitude response of the training beam is extremely small, the design problem of the training beam is a non-convex optimization problem, and the solution is difficult. By relaxing the partially non-convex constraint, the non-convex optimization problem can be transformed into a convex optimization problem and solved using a constrained concave-convex process (CCCP) iterative algorithm. If fnThe optimal solution f of the next iteration is shown if the optimal solution obtained by the nth iteration is representedn+1This can be obtained by solving the following problem:
Figure GDA0002371391930000111
wherein
Figure GDA0002371391930000112
The real part of the number in parentheses is taken,
Figure GDA0002371391930000113
respectively representing discretized main and side lobe corresponding regions.
Since initialization has a large influence on the convergence performance of the CCCP algorithm, to obtain a good initial value, the following optimization problem can be solved:
Figure GDA0002371391930000114
this problem is a second order cone programming problem (SOCP) that can be solved by the CVX toolkit in the MATLAB simulation platform.
Obtaining good initial value f0Then, the three-dimensional training beam design method based on the CCCP algorithm specifically comprises the following steps:
(6.1) constructing and solving the following constraint optimization problem:
Figure GDA0002371391930000115
wherein
Figure GDA0002371391930000116
The real part of the number in parentheses is taken,
Figure GDA0002371391930000117
respectively representing discretized main and side lobe corresponding regions;
(6.2) iteratively solving the optimization problem in the step (6.1), checking whether the r value obtained by the iteration meets the convergence standard, and if so, obtaining the optimal solution f of the iterationnI.e. the final solution f＊(ii) a If not, according to the optimal solution f of the iterationnSolving the optimization problem in the step (6.1) again;
(6.3) outputting the final solution f＊And obtaining the required three-dimensional training beam.
FIG. 4 shows 4 training codewords generated by the design method of the present invention, taking the first layer of sub-codebook in the three-dimensional codebook as an example
Figure GDA0002371391930000121
The amplitude response map of (a). It can be seen that the beam patterns of these several codewords have relatively flat amplitude responses and ideal transition bands, and no overshoot occurs at the unsampled points. Fig. 5 also compares the present invention with a Least Squares (LS) based beam design method, where BPSA represents the three-dimensional codebook design algorithm proposed by the present invention and LSA represents the least squares beam design algorithm. It can be seen from the figure that the side lobes of the training beams generated by the LS method have relatively large fluctuation, and in addition, the width of the transition band is also large, which further embodies the superiority of the three-dimensional training codebook design method provided by the present invention.
The three-dimensional training codebook generated by the invention can be used for realizing beam alignment based on a tree search algorithm, detecting the strongest beam of a single-path millimeter wave channel, and estimating related parameters of a millimeter wave communication channel, such as an angle of departure (AoD) and an angle of arrival (AoA), and specifically comprises the following steps:
(8.1) parameter configuration and initialization: the transceiving end designs a three-dimensional training codebook according to the method of any one of claims 1 to 7;
setting S layer of the three-dimensional training codebook tree structure, namely S training subcodebooks
Figure GDA0002371391930000122
Respectively corresponding to S training stages; the degree of the designed three-dimensional training codebook tree structure is N; beamforming vectors
Figure GDA0002371391930000123
The subscript values in (1) are initialized as: s is 1, bf＝1；
(8.2) the transmitting end continuously uses the low resolution training beam vector in the first layer sub-codebook
Figure GDA0002371391930000124
To transmit a training signal z, and repeat training M for each training beamsTo increase the received signal-to-noise ratio of the system;
(8.3) the receiving end receives the signal according to the corresponding
Figure GDA0002371391930000125
Selecting the beamforming vector that yields the highest received energy, i.e.
Figure GDA0002371391930000126
Wherein
Figure GDA0002371391930000127
p is the transmit power, h is the channel matrix, hHIs a conjugate transpose of h and,
Figure GDA0002371391930000128
additive Gaussian noise;
the receiving end indexes the value q＊Is fed back to the transmitting end, whereby the transmitting end is based on
Figure GDA0002371391930000129
And its corresponding rectangular area
Figure GDA0002371391930000131
Preliminarily determining the area of the departure angle AoD corresponding to the strongest wave beam;
(8.4) transmitting end according to index value q＊Selecting a set of beamforming vectors with higher resolution in a sub-codebook of a layer below the three-dimensional codebook
Figure GDA0002371391930000132
To transmit training signals to further more accurately determine the area where the AoD is located;
wherein b isf+1＝bf*N-N+q＊；
For the quad-tree structure in this embodiment, bfThe updating of (1) follows the following principle:
a) if q is＊LL, then bf+1＝4bf-3；
b) If q is＊If it is LR, then bf+1＝4bf-2；
c) If q is＊RL, then bf+1＝4bf-1；
d) If q is＊RR, then bf+1＝4bf；
And (8.5) repeating the steps (8.3) to (8.4) until the beamforming vector meeting the highest resolution requirement is found, wherein the rectangular domain corresponding to the beamforming vector is the area where the AoD is located.
Fig. 6 shows a specific flow of the three-dimensional training codebook design method (BPSA) proposed by the present invention, and besides, fig. 6 also shows a specific process for beam training after codebook generation. As shown in fig. 7, this figure shows the variation trend of the average beam alignment error probability (BAER) with the signal-to-noise ratio (SNR) generated by the beam training using the codebooks generated by the LS method and the method of the present invention when the path gain of the millimeter wave communication channel is fixed to 1. It can be seen from the figure that the performance of the codebook generated by the method of the present invention is obviously superior to that of the LSA codebook, and more accurate beam alignment and channel estimation performance can be realized. As the SNR increases, BAER corresponding to two codebooks decreases, but the error probability corresponding to the BPSA codebook decays significantly, while the error probability corresponding to the LSA codebook decays slowly.

Claims (2)

1. A three-dimensional training codebook design method for a millimeter wave communication system is characterized by comprising the following steps:
(1) according to resolution rs and beam space
Figure FDA0002371391920000011
Establishing a three-dimensional training codebook tree structure with the depth of S and the degree of N;
let resolution rs ═ ve×vaSpace of wave beam
Figure FDA0002371391920000012
The e direction and the a direction are two vertical directions;
Figure FDA0002371391920000013
width in e direction is WeA width in the a direction of WaI.e. by
Figure FDA0002371391920000014
Is We×WaThe degree of the tree structure N is Ne×NaThe depth S and the degree N satisfy the condition:
Figure FDA0002371391920000015
and is
Figure FDA0002371391920000016
Each node in layers 1 to S-1 in the three-dimensional training codebook tree structure is provided with N sub-nodes;
(2) space beam
Figure FDA0002371391920000017
In the e direction by NeAliquoting, N in the a directionaIs divided equally, i.e. about
Figure FDA0002371391920000018
Equally divided into N rectangular regions
Figure FDA0002371391920000019
N＝Ne×NaIs recorded as a set
Figure FDA00023713919200000110
Each rectangular region
Figure FDA00023713919200000111
With beamforming vectors
Figure FDA00023713919200000112
Correspondingly, i is 1, …, and N, N beamforming vectors form a beam set
Figure FDA00023713919200000113
Namely, it is
Figure FDA00023713919200000114
Root node C of three-dimensional training codebook tree structure1，1Is a set of rectangular regions
Figure FDA00023713919200000115
And beam set
Figure FDA00023713919200000116
In combination with (1)
Figure FDA00023713919200000117
(3) Determining the (b) th node C of the s layer of the three-dimensional training codebook tree structures，b，Cs，bIs a set of rectangular regions
Figure FDA00023713919200000118
And beam set
Figure FDA00023713919200000119
In combination with (1)
Figure FDA00023713919200000120
Wherein
Figure FDA00023713919200000121
Node with s-1 th layer
Figure FDA00023713919200000122
Has the following relationship:
Figure FDA00023713919200000123
wherein S is 2, …, S, b is 1, …, Ns-1，
Figure FDA00023713919200000124
Is the rounding up operation,% is the remainder operation;
to pair
Figure FDA00023713919200000125
In the c direction by NeAliquoting, N in the a directionaEqually dividing to obtain N sub-rectangular areas
Figure FDA00023713919200000126
Each sub-rectangular region
Figure FDA00023713919200000127
With beamforming vectors
Figure FDA00023713919200000128
Correspondingly, i is 1, …, and N, N beamforming vectors form a beam set
Figure FDA0002371391920000021
Namely, it is
Figure FDA0002371391920000022
Sequentially determining each node in 2 to S layers according to the steps
Figure FDA0002371391920000023
(4) Solving the beamforming vector contained in each node in the three-dimensional training codebook tree structure
Figure FDA0002371391920000024
Obtaining a three-dimensional training codebook, wherein q is 1, …, N; a beamforming vector contained by each node in the three-dimensional training codebook tree structure
Figure FDA0002371391920000025
Having constant but not identical amplitude response values in the main and side lobes, i.e.
Figure FDA0002371391920000026
Wherein psi ═ psie，ψa)＝(sin(θe)，sin(θa) Is a pitch angle θeAnd azimuth angle thetaaThe combination of the sine values of (a) and (b),
Figure FDA0002371391920000027
for antenna array response vector a in horizontal directionh(2π/λdhsin(θe)cos(θa) Antenna array response vector a in the vertical directionv(2π/λdvsin(θa) The Kronecker product of (c),
Figure FDA0002371391920000028
is a beamforming vector
Figure FDA0002371391920000029
The amplitude response value of (a); wherein q is 1.., N; dnAnd dvThe distance between two adjacent antennas in the horizontal direction and the vertical direction is respectively;
for main and side lobe corresponding region
Figure FDA00023713919200000210
And
Figure FDA00023713919200000211
sampling discretization is carried out to obtain discrete wave beam main and side lobe corresponding areas
Figure FDA00023713919200000212
And
Figure FDA00023713919200000213
an area;
solving beamforming vectors
Figure FDA00023713919200000214
To solve the optimization problem:
Figure FDA00023713919200000215
wherein epsilon is the ripple of the main and side lobes of the training beam and is a small positive real number; esIs constant, the value decreases with increasing s;
Figure FDA00023713919200000216
and
Figure FDA00023713919200000217
respectively corresponding areas of the main and side lobes of the discrete wave beam;
relaxing the constraint condition, and solving the optimization problem by adopting a constraint concave-convex process iterative algorithm, wherein the steps are as follows:
(6.1) determining an iteration initial value f0：
Initial value f0Determined by solving the following optimization problem:
Figure FDA0002371391920000031
the following constraint optimization problem is constructed:
Figure FDA0002371391920000032
wherein
Figure FDA0002371391920000033
Figure FDA0002371391920000034
The real part of the number in parentheses is taken,
Figure FDA0002371391920000035
respectively representing discretized main and side lobe corresponding regions;
(6.2) iteratively solving the optimization problem in the step (6.1), checking whether the r value obtained by the iteration meets the convergence standard, and if so, obtaining the optimal solution f of the iterationnI.e. the final solution f＊(ii) a If not, according to the optimal solution f of the iterationnSolving the optimization problem in the step (6.1) again;
(6.3) outputting the final solution f＊And obtaining the required three-dimensional training beam.
2. A method of beam alignment, comprising the steps of:
(8.1) parameter configuration and initialization: the transceiving end designs a three-dimensional training codebook according to the method in claim 1;
the designed three-dimensional training code book is designed to contain S training sub code books
Figure FDA0002371391920000036
Respectively corresponding to S training stages; the degree of the designed three-dimensional training codebook tree structure is N; beamforming vectors
Figure FDA0002371391920000037
The subscript values in (1) are initialized as: s is 1, bf＝1；
(8.2) the transmitting end continuously uses the low resolution training beam vector in the first layer sub-codebook
Figure FDA0002371391920000038
To transmit a training signal z, and repeat training M for each training beamsTo increase the received signal-to-noise ratio of the system;
(8.3) the receiving end receives the signal according to the corresponding
Figure FDA0002371391920000039
Selecting the beamforming vector that yields the highest received energy, i.e.
Figure FDA0002371391920000041
Wherein
Figure FDA0002371391920000042
p is the transmit power, h is the channel matrix, hHIs a conjugate transpose of h and,
Figure FDA0002371391920000043
additive Gaussian noise;
the receiving end indexes the value q＊Is fed back to the transmitting end, whereby the transmitting end is based on
Figure FDA0002371391920000044
And its corresponding rectangular area
Figure FDA0002371391920000045
Preliminarily determining the area of the departure angle AoD corresponding to the strongest wave beam;
(8.4) transmitting end according to index value q＊Selecting a set of beamforming vectors with higher resolution in a sub-codebook of a layer below the three-dimensional codebook
Figure FDA0002371391920000046
To transmit training signals to further more accurately determine the area where the AoD is located;
wherein b isf+1＝bf*N-N+q＊；
And (8.5) repeating the steps (8.3) to (8.4) until the beamforming vector meeting the highest resolution requirement is found, wherein the rectangular domain corresponding to the beamforming vector is the area where the AoD is located.
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