CN110932765A - Omnidirectional beam forming design method under uniform rectangular array - Google Patents

Omnidirectional beam forming design method under uniform rectangular array Download PDF

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CN110932765A
CN110932765A CN201911056190.8A CN201911056190A CN110932765A CN 110932765 A CN110932765 A CN 110932765A CN 201911056190 A CN201911056190 A CN 201911056190A CN 110932765 A CN110932765 A CN 110932765A
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matrix
beam forming
beamforming
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uniform rectangular
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CN110932765B (en
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蒋轶
李峰杰
王昕�
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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

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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 in the design schemeThe code word has 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 design method under 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 BDA0002256610730000011
m × Q, P, Q are rows and columns of the antenna array; as shown in fig. 1;
second, using 4 beamforming vectors W ═ W1,w2,…,w4](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 BDA0002256610730000012
is a common signal to be broadcast and sent to each user at a base station end, and each beam forming vector wkThe Q-long vectors can be grouped into P vectors corresponding to P rows of antennas of the array: w is ak＝[wk,1 T,wk,2 T,…,wk,P T]TK is 1,2,3,4, wherein wk,p＝[wk,p1,wk,p2,…,wk,pQ]T；
Thirdly, the uniform rectangular array guide vector matrix in the first step
Figure BDA0002256610730000013
And vectorized steering vector thereof
Figure BDA0002256610730000014
The definition is as follows:
Figure BDA0002256610730000015
Figure BDA0002256610730000021
wherein the content of the first and second substances,
Figure BDA0002256610730000022
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, dyAnd dxThe 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 BDA0002256610730000023
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 BDA0002256610730000024
wherein E isSIs the energy of the transmitted signal, σ2Is the energy of the noise, and is,
Figure BDA0002256610730000025
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 BDA0002256610730000026
the definition of the method is that,
Figure BDA0002256610730000027
it is divided into P × P sub-matrices as follows:
Figure BDA0002256610730000028
wherein:
Figure BDA0002256610730000029
in the fourth step, the design of omnidirectional beam forming is completed, and the existing sequences required to be used are as follows:
consider two long L sequences c1And c2The following were used:
c1＝(c1,1,…,c1,L)，c2＝(c2,1,…,c2,L) (9)
its non-periodic correlation function
Figure BDA00022566107300000210
Is defined as:
Figure BDA00022566107300000211
the autocorrelation function for c is the same as in equation (9) provided that c is set to c1＝c2(ii) a A sequence set
Figure BDA00022566107300000212
If the following formula is satisfied:
Figure BDA00022566107300000213
then called the (N, L) complementary sequence set; wherein δ (τ) is a kronecker-delta function, and
Figure BDA00022566107300000214
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 BDA0002256610730000031
and are provided with
Figure BDA0002256610730000032
And
Figure BDA0002256610730000033
rewriting formula (3), and substituting formula (7) to obtain:
Figure BDA0002256610730000034
wherein the content of the first and second substances,
Figure BDA0002256610730000035
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), it can be seen that the signal energy obtained in each direction is
Figure BDA0002256610730000036
So long as it is a two-dimensional Fourier transform of
Figure BDA0002256610730000037
The following conditions are satisfied:
Figure BDA0002256610730000038
then obtained
Figure BDA0002256610730000039
Value and direction of
Figure BDA00022566107300000310
(contained in (u, v)) is not relevant.
In the fourth step, the beamforming matrix design scheme is as follows:
let b be1,b2Is a complementary sequence of length P, c1,c2If 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 BDA00022566107300000311
wherein the content of the first and second substances,
Figure BDA00022566107300000312
operation of
Figure BDA00022566107300000313
Representing the kronecker product. (in practice, if the columns are spread into a matrix, four matrices are obtained
Figure BDA00022566107300000314
)
From equation (15) and equation (8), we can obtain:
Figure BDA00022566107300000315
wherein, b1＝[b11,b12,…,b1P]T，b2＝[b21,b22,…,b2P]T，c1＝[c11,c12,…,c1Q]T，c2＝[c21,c22,…,c2Q]T。
Then, the following formula (13) is obtained:
Figure BDA00022566107300000316
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 and closed solution, and is simple to realize and does not consume 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 uniform rectangular array representation.
Fig. 2 is a diagram of a system for omni-directional transmission of common signals.
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 81＝[1 1 1 1 1 -1 -1 1],b2＝[-1 1 -1 1 -1 -1 11]And a CS sequence pair c of length 161＝[1 1 1 -1 1 1 1 -1 1 1 -1 1 -1 -1 1 -1],c2＝[1 -1 11 1 -1 1 1 1 -1 -1 -1 -1 1 1 1]. According to the above matrix configuration
Figure BDA0002256610730000041
We generate four 8 x 16 phase shift matrices,
Figure BDA0002256610730000042
Figure BDA0002256610730000051
Figure BDA0002256610730000052
Figure BDA0002256610730000053
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 to the literature
[1]Ganesan G,Stoica P.Space-time block codes:a maximum SNRapproach.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 Codingfrom Orthogonal Designs,"IEEE Transactions on Information Theory,July 1999.
[3]H.Jafarkhani,"A Quasi-Orthogonal Space-Time Block Code,"IEEETransactions on Communications,Jan.2001.。

Claims (2)

1. An omnidirectional beam forming design method under 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 FDA0002256610720000011
m × Q, P, Q are rows and columns of the antenna array;
second, using 4 beamforming vectors W ═ W1,w2,…,w4]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 content of the first and second substances,
Figure FDA0002256610720000012
is a common signal to be broadcast and sent to each user at a base station end, and each beam forming vector wkA vector of length Q that can be grouped into P corresponding rectangular array P rows of antennas: w is ak＝[wk,1 T,wk,2 T,…,wk,P T]T,k＝1,2,…,4，wk,p＝[wk,p1,wk,p2,…,wk,pQ]T；
Thirdly, defining a guide vector matrix of the uniform rectangular array in the first step
Figure FDA0002256610720000013
And vectorized steering vector thereof
Figure FDA0002256610720000014
The following were used:
Figure FDA0002256610720000015
Figure FDA0002256610720000016
wherein the content of the first and second substances,
Figure FDA0002256610720000017
and θ is the angle formed by a certain emission direction in the space under the uniform rectangular array and the x-axis and the z-axis, dyAnd dxThe 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 FDA0002256610720000018
and further combining space-time block coding to obtain the SNR of the signal received by the user terminal after signal processing as:
Figure FDA0002256610720000019
wherein E isSIs the energy of the transmitted signal, σ2Is the energy of the noise, and is,
Figure FDA00022566107200000110
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 FDA0002256610720000021
the definition of the method is that,
Figure FDA0002256610720000022
it is divided into P × P sub-matrices as follows:
Figure FDA0002256610720000023
wherein:
Figure FDA0002256610720000024
2. the method as claimed in claim 1, wherein in the fourth step, the omni-directional beamforming design is completed, and the following existing sequences are used:
two sequences c of length L1And c2：
c1＝(c1,1,…,c1,L)，c2＝(c2,1,…,c2,L) (9)
Its non-periodic correlation function
Figure FDA0002256610720000025
Is defined as:
Figure FDA0002256610720000026
the autocorrelation function for c is the same as in equation (9) provided that c is set to c1＝c2(ii) a A sequence set
Figure FDA0002256610720000027
If the following formula is satisfied:
Figure FDA0002256610720000028
then called the (N, L) complementary sequence set; wherein δ (τ) is a kronecker-delta function, and
Figure FDA0002256610720000029
in order to achieve omnidirectional coverage, the 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 FDA00022566107200000210
and are provided with
Figure FDA00022566107200000211
And
Figure FDA00022566107200000212
rewriting formula (3), and substituting formula (7) to obtain:
Figure FDA00022566107200000213
wherein the content of the first and second substances,
Figure FDA00022566107200000214
represents a Topritz matrix with 1 on the (-n) th auxiliary diagonal and all zeros on the other diagonals; from equation (13), the signal energy obtained in each direction is
Figure FDA00022566107200000215
Is generated, the two-dimensional fourier transform of (a) is, thus,
Figure FDA00022566107200000216
the following conditions are satisfied:
Figure FDA0002256610720000031
then obtained
Figure FDA0002256610720000032
Value and direction of
Figure FDA0002256610720000033
Irrelevant;
in the fourth step, the beamforming matrix design scheme is as follows:
let b be1,b2Is a complementary sequence of length P, c1,c2If the sequence is a complementary sequence with a length of Q, the beamforming matrix with a rank of 4 and satisfying the omni-directional coverage is designed as follows:
Figure FDA0002256610720000034
wherein the content of the first and second substances,
Figure FDA0002256610720000035
operation of
Figure FDA0002256610720000036
Represents the kronecker product;
the following equations (15) and (8) yield:
Figure FDA0002256610720000037
wherein, b1＝[b11,b12,…,b1P]T，b2＝[b21,b22,…,b2P]T，c1＝[c11,c12,…,c1Q]T，c2＝[c21,c22,…,c2Q]T；
Then, the following formula (13) is obtained:
Figure FDA0002256610720000038
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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CN112929061A (en) * 2021-01-21 2021-06-08 复旦大学 Omnidirectional beam forming design method based on autocorrelation complementary matrix
CN113328773A (en) * 2021-06-23 2021-08-31 复旦大学 Two-stage beam forming method

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