CSBASED OMNIDIRECTIONAL BEAMFORMING DESIGN METHOD IN UNIFORM RECTANGULAR ARRAYS

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First Claim
1. A CSbased omnidirectional beamforming design method in a uniform rectangular array, comprising:
 a first step of, on a base station side consisting of a uniform rectangular largesize antenna array including M antennas, spacetime block coding an incoming data flow to be sent, a matrix B used for the spacetime block coding having K×
N dimensions, specifically;
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Abstract
The present invention belongs to the technical field of common signal transmission, and specifically relates to a CSbased omnidirectional beamforming design method in a uniform rectangular array. The main purpose of the present invention is to handle the beamforming design for realizing celllevel coverage in downlink transmission of common signals. For a largesize antenna base station with a uniform rectangular array, the present invention provides two omnidirectional beamforming design schemes: beamforming design based on complementary sequence sets and CCCbased beamforming design. Both schemes can obtain a completely smooth beam pattern in each direction, with low complexity and closedform solution. Furthermore, most complementary sequence sets and code words of the complete complementary codes show a constant modulus, so that the whole beamforming scheme can be efficiently realized only by using the simulationdomain beamforming architecture. The hardware efficiency is effectively improved.
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1 Claim
 1. A CSbased omnidirectional beamforming design method in a uniform rectangular array, comprising:
a first step of, on a base station side consisting of a uniform rectangular largesize antenna array including M antennas, spacetime block coding an incoming data flow to be sent, a matrix B used for the spacetime block coding having K×
N dimensions, specifically;
1 Specification
This application claims the benefit of priority from Chinese Patent Application No. CN201811262310.5, filed on Oct. 27, 2018. The content of the aforementioned application, including any intervening amendments thereto, is incorporated herein by reference in its entirety.
The present invention belongs to the technical field of common signal transmission, and specifically relates to a CSbased omnidirectional beamforming design method.
Largescale antennas are one of the key technologies for commercialization of 5G. With the increase in the scale of antennas, it is tended to use a uniform rectangular array for implementation in order to facilitate productization. For a base station side with a uniform rectangular array, realizing omnidirectional transmission of common signals and celllevel coverage is one of key factors to improve overall network performance.
An objective of the present invention is to provide a CSbased omnidirectional beamforming design method in a uniform rectangular array.
The CSbased omnidirectional beamforming design method, as provided in the present invention, is divided into two similar and independent design schemes: beamforming design based on complementary sequence sets and CCCbased beamforming design.
The CSbased omnidirectional beamforming design method in a uniform rectangular array, as provided in the present invention, comprises:
a first step of, on a base station side consisting of a uniform rectangular largesize antenna array including M antennas, spacetime block coding an incoming data flow to be sent, a matrix used for the spacetime block coding having K x N dimensions, specifically:
M=P×Q, where P and Q represent a row and column of the antenna array, as shown in
a second step of performing beamforming on the obtained spacetime block codes by K beamforming vectors W=[w_{1}, w_{2}, . . . , w_{K}], the vector being a beamforming matrix having M×K dimensions, to obtain following a signal to be sent:
X=WB (2)
where X∈^{M×N }is a common signal to be broadcasted and sent by the base station side to each user, and each beamforming vector w_{k }can be divided into P vectors each corresponding to an antenna in a row of the rectangular array and having a length of Q: w_{k}=[w_{k,1}^{T},w_{k,2}^{T}, . . . , w_{k,P}^{T}]^{T}, k=1,2 . . . , K, where w_{k,p}=[w_{k,p1},w_{k,p2}, . . . , w_{k,pQ}]^{T};
a third step of defining a steering vector matrix [A(φ,θ)] in the uniform rectangular array in the first step, and a steering vector a(φ,θ) after vectorization of the uniform rectangular array, specifically:
where φ and θ are an angle between a certain emission direction in a space and an xaxis and an angle between the emission direction and a zaxis, respectively, in the uniform rectangular array of
h_{eff}(φ,θ)=W^{H}a(φ,θ) (5)
further in combination with the spacetime block codes, according to the reference document [1], the obtained signal to noise ratio (SNR) of a received signal, which has been processed, on a user side being:
where E_{S }represents the energy of the sent signal, σ^{2 }represents the energy of noise, and
represents the SNR of the input; and
a fourth step of, in order to obtain a completely smooth beam pattern, designing a beamforming matrix by the following standard:
∥h_{eff}(φ,θ)∥^{2}=∥W^{H}a(φ,θ)^{2}=a(φ,θ)^{H}WW^{H}a(φ,θ)=const (7)
wherein, let SWW^{H}, the matrix is divided into P×P submatrices, specifically:
where S_{i,j}=Σ_{k=1}^{K}w_{k,i}w_{k,j}^{H}∈^{Q×Q};
in the fourth step, there are following existing sequences to be used to complete the omnidirectional beamforming design:
considering two sequences c_{1 }and c_{2 }having a length of L:
c_{1}=(c_{1.1}, . . . , c_{1.L}), c_{1}=(c_{1.1}, . . . , c_{2.L}) (9)
the aperiodic correlation function R_{c}_{1,}_{c}_{2 }(τ) is defined as follows:
for c, the autocorrelation function is the same as (9), as long as c=c_{1}=c_{2}; a sequence set {c_{n}}_{n=1}^{N }is called a (N,L) complementary sequence set if it meets the following equation:
where δ(τ) is a Kroneckerdelta function and EΣ_{n=1}^{N}Σ_{t=1}^{L}c_{n,l}^{2};
if M sequence sets consisting of N sequences having a length of L meet the following two equations:
then, the M sequence sets are called (M,N,L)—complete complementary codes; now, the found complete complementary codes are required as follows: M≤N, and the common divisor of M and L is the greatest factor of L; the (M,N,L)—complete complementary codes consist of M(N,L) complementary sequence sets meeting the equation (12);
the sequences are expressed, in the form of vectors, by c∈^{L}, then the equations (10), (11) and (12) are expressed by:
where E_{L}^{−τ} represents a Toeplitz matrix that is 1 on the (−τ)^{th }auxiliary diagonal and 0 on all other diagonals, where the diagonal is a superdiagonal when −τ is greater than 0 and a subdiagonal when −τ is less than 0;
in the fourth step, the omnidirectional beamforming matrix needs to meet the following requirements in order to realize omnidirectional coverage:
let the sum of submatrices on the diagonals of the S matrix in the equation (8):
the equation (3) is rewritten by
and the equation (3) is substituted into the equation (7) to obtain:
where E_{Q}^{−n }represents a Toeplitz matrix that is 1 on the (−n)^{th }auxiliary diagonal and 0 on all other diagonals, where the diagonal is a superdiagonal when −n is greater than 0 and a subdiagonal when −n is less than 0; it can be found in the equation (18) that the signal energy obtained in each direction is the twodimensional Fourier transform of tr(E_{Q}^{−n}S_{l}), and therefore, if tr(E_{Q}^{−n}S_{l}) meets the following condition:
tr(E_{Q}^{−n}S_{l})=Eδ(n)δ(l) (19).
then, the obtained value of ∥W^{H}a(φ,θ)∥^{2 }is independent of the direction (θ,φ);
in the fourth step, there are following two beamforming matrix design schemes:
first scheme: beamforming matrix design based on complementary sequence sets
it is assumed that {c_{1}, c_{2}, . . . , c_{P}} is a (P,Q) complementary sequence set, then a beamforming matrix having a rank of K=P to realize omnidirectional coverage is designed as follows:
from the equation (20), then:
it can be known that:
according to the definition of S_{1 }in the equation (17), S_{l}=0, ∀l≠0;
according to the equation (11) for the property of the complementary sequence set and S_{0}=Σ_{p=1}^{P}c_{p}c_{p}^{H}, then:
tr(E_{Q}^{τ}S_{0})=Eδ(τ) (22)
thus, the omnidirectional beamforming matrix based on complementary sequence sets, constructed according to the equation (21), realizes omnidirectional coverage, i.e., meets the equation (19);
second scheme: beamforming matrix design based on complete complementary codes:
it is assumed that {c_{11}, . . . , c_{1K}}, {c_{21}, . . . , c_{2K}}, . . . , {c_{P1}, . . . , c_{PK}} are (P,K,Q)—complete complementary codes, then a beamforming matrix having a rank of K to realize omnidirectional coverage is designed as follows:
from the equation (20) and the equation (8), then:
S_{i,j}=Σ_{p=1}^{P}c_{i,k}c_{j,k}^{H} (24)
and according to the equations (15) and (16), then:
tr(E_{Q}^{τ}S_{i,j})=Eδ(τ)(i−j) (25)
thus, the CCCbased omnidirectional beamforming design, constructed according to the equation (25), realizes omnidirectional coverage, i.e., meets the equation (19).
The present invention has the following advantages:
(1) two beamforming designs that can, theoretically, completely realize omnidirectional transmission of common signals are obtained, and same array response is found in any point in a space;
(2) both omnidirectional beamforming designs in the present invention are extremely low in complexity and have a closedform solution, and the implementation is simple without consumption of computing resources;
(3) the nonzero elements in the obtained beamforming matrix show a constant modulus, which may be implemented by the fullyconnected RF beamforming structure of
The present invention will be further described below by specific embodiments.
As an embodiment, in the present invention, the beam pattern of the beamforming matrix based on complementary sequence sets in a 8×16 uniform rectangular array is simulated by a computer, as shown in
In the present invention, the BER performance of the system is also stimulated in the case where Alamouti codes are used as the spacetime block codes. For a 2×16 uniform rectangular array, both beamforming matrices obtained in the equations (20) and (23) have a rank of 2. There are other two comparison methods: ZCbased scheme (two ZadoffChu sequences are used to produce a kronecker product to obtain a beamforming matrix) and BGM (broadbeam generation method, with reference to [2]). In this stimulation, 10^{5 }Monte Carlo experiments have been carried out. The final BER result is shown in
 [1] Ganesan G, Stoica P. Spacetime block codes: a maximum SNR approach. IEEE Transactions on Information Theory, vol. 47, no. 4, pp. 16501656, May 2001
 [2] Qiao, Deli, H. Qian, and G. Y. Li. Broadbeam for Massive MIMO Systems. IEEE Transactions on Signal Processing, vol. 64, no. 9, pp. 23652374, May 2016