CN110932765B - Omnidirectional beam forming method for uniform rectangular array - Google Patents

Omnidirectional beam forming method for uniform rectangular array Download PDF

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CN110932765B
CN110932765B CN201911056190.8A CN201911056190A CN110932765B CN 110932765 B CN110932765 B CN 110932765B CN 201911056190 A CN201911056190 A CN 201911056190A CN 110932765 B CN110932765 B CN 110932765B
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matrix
beam forming
beamforming
equation
uniform rectangular
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CN110932765A (en
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蒋轶
李峰杰
王昕�
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Fudan 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
    • H04B7/06—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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention belongs to the technical field of public signal transmission, and particularly relates to an omnidirectional beam forming design method based on a complementary sequence under a uniform rectangular array. The method comprises the following steps: for a base station end composed of a uniform rectangular large-scale antenna array composed of M antennas, space-time block coding is carried out on data streams to be sent flowing in, beamforming is carried out on the space-time block coding by utilizing 4 beamforming vectors W, a sending signal X = WB is obtained, the sending signal is a common signal to be broadcasted and sent to each user by the base station end, and each beamforming vector is
Figure DEST_PATH_IMAGE001
A vector of length Q that can be grouped into P corresponding rectangular array P rows of antennas: and finally determining a beam forming matrix design scheme. The invention can achieve completely smooth beam patterns in all directions and has the excellent characteristics of low complexity and closed-form solution; and the code word in the design scheme has the constant modulus characteristic, so that the whole beam forming scheme can be efficiently realized only by using an analog domain beam forming framework, and the hardware efficiency is effectively improved.

Description

Omnidirectional beam forming method for uniform rectangular array
Technical Field
The invention belongs to the technical field of public signal transmission, and particularly relates to an omnidirectional beam forming design method.
Background
The large-scale antenna is one of the key technologies for realizing 5G commercial use, and the realization of the antenna is more inclined to use a uniform rectangular array for the convenience of commercialization after the antenna is increased in size. For a base station end with a uniform rectangular array, realizing omnidirectional transmission and full cell coverage of a public signal is one of key factors for improving the performance of the whole network.
Disclosure of Invention
The invention aims to provide an omnidirectional beam forming design method capable of realizing omnidirectional transmission of public signals for a uniform rectangular array.
The invention provides an omnidirectional beam forming design method under a uniform rectangular array, which comprises the following specific steps:
firstly, for a base station end composed of a uniform rectangular large-scale antenna array composed of M antennas, performing space-time block coding on a data stream to be transmitted, wherein a matrix used by the space-time block coding is 4 × N, and the specific steps are as follows:
Figure SMS_1
m = P × Q, P, Q being the rows and columns of the antenna array; as shown in fig. 1;
second, using 4 beamforming vectors W = [ W = 1 ,w 2 ,…,w 4 ](i.e. a M × 4-dimensional beamforming matrix) performs beamforming on the obtained space-time block code to obtain a transmission signal as follows:
X＝WB (2)
wherein the content of the first and second substances,
Figure SMS_2
is a common signal to be broadcast and sent to each user at a base station end, and each beam forming vector w k The Q-long vectors can be grouped into P vectors corresponding to P rows of antennas of the array: w is a k ＝[w k,1 T ,w k,2 T ,…,w k,P T ] T K =1,2,3,4, wherein w k,p ＝[w k,p1 ,w k,p2 ,…,w k,pQ ] T ；
Thirdly, the uniform rectangular array guide vector matrix in the first step
Figure SMS_3
And vectorized steering vector thereof>
Figure SMS_4
The definition is as follows:
Figure SMS_5
Figure SMS_6
wherein the content of the first and second substances,
Figure SMS_7
and θ is the angle formed by a certain emission direction in space with the x-axis and z-axis under the uniform rectangular array as shown in FIG. 1, d y And d x The spacing of adjacent antennas of the uniform rectangular array on the y-axis and the x-axis is respectively represented, lambda represents the wavelength of a transmitted signal, and the operation vec represents matrix column vectorization; this results in a system-efficient array response:
Figure SMS_8
further, in combination with space-time block coding, according to reference [1], the signal-to-noise ratio (SNR) after the ue receives the signal processing is obtained as:
Figure SMS_9
wherein E is S Is the energy of the transmitted signal, σ 2 Is the energy of the noise(s),
Figure SMS_10
representing the input signal-to-noise ratio;
fourthly, in order to enable the transmission beam pattern to be completely flat, a beam forming matrix is designed to achieve the following purposes:
Figure SMS_11
the definition of the method is that,
Figure SMS_12
it is divided into P × P sub-matrices as follows:
Figure SMS_13
wherein:
Figure SMS_14
in the fourth step, the omnidirectional beam forming design is completed, and the existing sequences required to be used are as follows:
consider two long L sequences c 1 And c 2 The following were used:
c 1 ＝(c 1,1 ,…,c 1,L )，c 2 ＝(c 2,1 ,…,c 2,L ) (9)
its non-periodic correlation function
Figure SMS_15
Is defined as:
Figure SMS_16
the autocorrelation function for c is the same as equation (9) as long as c = c is set 1 ＝c 2 (ii) a A sequence set
Figure SMS_17
If the following formula is satisfied:
Figure SMS_18
then called the (N, L) complementary sequence set; wherein δ (τ) is a kronecker-delta function, and
Figure SMS_19
in the fourth step, the requirements that the omnidirectional beam forming matrix needs to meet to achieve omnidirectional coverage are as follows:
the sum of the sub-matrix blocks on each diagonal of the S matrix in equation (8) is defined as follows:
Figure SMS_20
and are provided with
Figure SMS_21
And &>
Figure SMS_22
Rewriting formula (3), and substituting formula (7) to obtain: />
Figure SMS_23
Wherein the content of the first and second substances,
Figure SMS_24
represents Toplitz matrix with all zeros on the other diagonals being 1 on the (-n) th pair of diagonals (-n is greater than 0 for the upper diagonal and less than 0 for the lower diagonal); from equation (13), the signal energy obtained in each direction is
Figure SMS_25
So long as ∑ is greater than ∑ and greater than ∑ is greater than { (r) }>
Figure SMS_26
The following conditions are satisfied:
Figure SMS_27
then obtained
Figure SMS_28
In a value and direction>
Figure SMS_29
(contained in (u, v)) is not relevant.
In the fourth step, the beamforming matrix design scheme is as follows:
let b be 1 ,b 2 Is a complementary sequence of length P, c 1 ,c 2 If the length of the beamforming matrix is Q, the beamforming matrix with rank of 4 that can satisfy the omni-directional coverage can be designed as follows:
Figure SMS_30
wherein the content of the first and second substances,
Figure SMS_31
operated>
Figure SMS_32
Representing the kronecker product. (in fact, if the columns are expanded into a matrix, four matrices result->
Figure SMS_33
)
From equation (15) and equation (8), we can obtain:
Figure SMS_34
wherein, b 1 ＝[b 11 ,b 12 ,…,b 1P ] T ，b 2 ＝[b 21 ,b 22 ,…,b 2P ] T ，c 1 ＝[c 11 ,c 12 ,…,c 1Q ] T ，c 2 ＝[c 21 ,c 22 ,…,c 2Q ] T 。
Then, the following formula (13) is obtained:
Figure SMS_35
therefore, the omni-directional beamforming matrix constructed by equation (15) satisfies the omni-directional coverage condition (i.e., equation (14)).
The invention mainly aims to solve the problems of common signal downlink transmission and cell full-coverage beam forming design. For a large-scale antenna base station equipped with a uniform rectangular array, the beam forming design scheme provided by the invention can achieve a completely smooth beam pattern in all directions, and has the excellent characteristics of low complexity and closed-form solution. And the code word in the design scheme has the constant modulus characteristic, so that the whole beam forming scheme can be efficiently realized only by using an analog domain beam forming framework, and the hardware efficiency is effectively improved.
The method has the advantages that:
(1) The beam forming design which completely meets the omnidirectional transmission of the public signals theoretically is obtained, and the same array response is provided at any point in space;
(2) The omnidirectional beam forming design has extremely low complexity, closed solution, simple realization and no consumption of computing resources;
(3) The obtained beam forming matrix nonzero element has constant modulus property, the full-connection radio frequency beam forming structure in the figure 3 can be used, and the power efficiency of a radio frequency end can be greatly improved.
Drawings
FIG. 1 is a schematic representation of a uniform rectangular array.
Fig. 2 is a diagram of a system for omni-directional transmission of a common signal.
Fig. 3 is a fully connected rf beamforming structure.
Fig. 4 is a spatial beam pattern of a beamforming design based on a complementary sequence set.
Detailed Description
The invention is further described below by means of specific examples.
As an example, the present invention simulates with a computer the beam pattern of a beamforming matrix under an 8 × 16 uniform rectangular antenna array. Using CS sequence pairs b of length 8 1 ＝[1 1 1 1 1 -1 -1 1],b 2 ＝[-1 1 -1 1 -1 -1 1 1]And a CS sequence pair c of length 16 1 ＝[1 1 1 -1 1 1 1 -1 1 1 -1 1 -1 -1 1 -1],c 2 ＝[1 -1 1 1 1 -1 1 1 1 -1 -1 -1 -1 1 1 1]. According to the above matrix configuration
Figure SMS_36
We generate four 8 x 16 phase shift matrices,
Figure SMS_37
Figure SMS_38
Figure SMS_39
Figure SMS_40
they correspond to the phase shifts of the four radio frequencies each connected to an 8 x 16 uniform rectangular antenna array (1 for 0 phase rotation, -1 for 180 phase rotation).
As shown in FIG. 2, with 4 × 4 STBC coding, (which can be Orthogonal STBC [2] or semi-Orthogonal code Quasi-Orthogonal STBC [3 ]), and based on the 4 phase shift matrices, spatial omnidirectional signal energy transmission can be realized, as shown in FIG. 4.
Reference documents
[1]Ganesan G,Stoica P.Space-time block codes:a maximum SNR approach.IEEE Transactions on Information Theory,vol.47,no.4,pp.1650-1656,May.2001
[2]V.Tarokh,H.Jafarkhani,and A.R.Calderbank,"Space-Time Block Coding from Orthogonal Designs,"IEEE Transactions on Information Theory,July 1999.
[3]H.Jafarkhani,"A Quasi-Orthogonal Space-Time Block Code,"IEEE Transactions on Communications,Jan.2001.。

Claims (1)

1. An omnidirectional beam forming method for a uniform rectangular array is characterized by comprising the following specific steps:
firstly, for a base station end composed of a uniform rectangular large-scale antenna array composed of M antennas, performing space-time block coding on a data stream to be transmitted, wherein a matrix used by the space-time block coding is 4 × N, and the specific steps are as follows:
Figure FDA0004054093710000011
m = P × Q, P, Q being the rows and columns of the antenna array;
second, using 4 beamforming vectors W = [ W = 1 ,w 2 ,…,w 4 ]That is, an M × 4-dimensional beamforming matrix, performs beamforming on the obtained space-time block code to obtain a transmission signal as follows:
X＝WB (2)
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0004054093710000012
is a common signal to be broadcast and sent to each user at a base station end, and each beam forming vector w k A vector of length Q that can be grouped into P corresponding rectangular array P rows of antennas: w is a k ＝[w k,1 T ,w k,2 T ,…,w k,P T ] T ,k＝1,2,…,4，w k,p ＝[w k,p1 ,w k,p2 ,…,w k,pQ ] T ；
Thirdly, defining a guide vector matrix of the uniform rectangular array in the first step
Figure FDA00040540937100000110
And vectorized steering vector thereof>
Figure FDA0004054093710000013
The following were used:
Figure FDA0004054093710000014
Figure FDA0004054093710000015
wherein the content of the first and second substances,
Figure FDA0004054093710000016
theta is the angle formed by a certain emission direction in space under the uniform rectangular array and the x-axis and the z-axis, d y And d x Individual watchShowing the spacing of adjacent antennas of the uniform rectangular array on the y-axis and the x-axis, λ representing the transmitted signal wavelength, and the operation vec representing matrix column vectorization; this results in a system-efficient array response:
Figure FDA0004054093710000017
and further combining space-time block coding to obtain the SNR of the signal received by the user terminal after signal processing as:
Figure FDA0004054093710000018
wherein E is S Is the energy of the transmitted signal, σ 2 Is the energy of the noise, and is,
Figure FDA0004054093710000019
representing the input signal-to-noise ratio;
fourthly, in order to make the transmission beam pattern reach the full flatness, the beam forming matrix is designed to achieve the following goal:
Figure FDA0004054093710000021
definition of
Figure FDA0004054093710000022
It is divided into P × P sub-matrices as follows:
Figure FDA0004054093710000023
wherein:
Figure FDA0004054093710000024
in the fourth step, the omnidirectional beam forming design is completed, and the following existing sequences are used:
two sequences c of length L 1 And c 2 ：
c 1 ＝(c 1,1 ,…,c 1,L )，c 2 ＝(c 2,1 ,…,c 2,L ) (9)
Its non-periodic correlation function
Figure FDA0004054093710000025
Is defined as:
Figure FDA0004054093710000026
the autocorrelation function for c is the same as equation (9) as long as c = c is set 1 ＝c 2 (ii) a A sequence set
Figure FDA0004054093710000027
If the following formula is satisfied:
Figure FDA0004054093710000028
then called the (N, L) complementary sequence set; wherein δ (τ) is a kronecker-delta function, and
Figure FDA0004054093710000029
in order to achieve omnidirectional coverage, an omnidirectional beamforming matrix needs to satisfy the following requirements:
the sum of the sub-matrix blocks on each diagonal of the S matrix in equation (8) is defined as follows:
Figure FDA00040540937100000210
and are provided with
Figure FDA00040540937100000211
And &>
Figure FDA00040540937100000212
Rewriting formula (3), and substituting formula (7) to obtain:
Figure FDA00040540937100000213
wherein the content of the first and second substances,
Figure FDA00040540937100000214
represents a Topritz matrix with 1 on the (-n) th auxiliary diagonal and all zeros on the other diagonals; as can be seen from equation (13), the resulting signal energy in each direction is->
Figure FDA00040540937100000215
Is determined, whereupon>
Figure FDA00040540937100000216
The following conditions are satisfied:
Figure FDA0004054093710000031
then obtained
Figure FDA0004054093710000032
Is greater than or equal to>
Figure FDA0004054093710000033
Irrelevant;
in the fourth step, the beamforming matrix design scheme is as follows:
let b be 1 ,b 2 Is a complementary sequence of length P, c 1 ,c 2 Is a complementary sequence with the length of Q, the rank meeting the omnidirectional coverage is the setting of the beamforming matrix of 4The following are counted:
Figure FDA0004054093710000034
wherein the content of the first and second substances,
Figure FDA0004054093710000035
operated>
Figure FDA0004054093710000036
Represents the kronecker product; />
From equation (15) and equation (8):
Figure FDA0004054093710000037
wherein, b 1 ＝[b 11 ,b 12 ,…,b 1P ] T ，b 2 ＝[b 21 ,b 22 ,…,b 2P ] T ，c 1 ＝[c 11 ,c 12 ,…,c 1Q ] T ，c 2 ＝[c 21 ,c 22 ,…,c 2Q ] T ；
Then, according to the formula (13), the following results are obtained:
Figure FDA0004054093710000038
that is, the omni-directional beamforming matrix constructed by equation (15) satisfies the omni-directional coverage condition, that is, equation (14).
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