US 11,909,564 B1 · Angular domain channel estimation method based on matrix reconstruction for symmetrical nonuniform array

Abstract

An angular domain channel estimation method based on matrix reconstruction for a symmetrical nonuniform array is a combined two-stage channel estimation and channel equalization scheme provided based on an SNLA model. In a first stage, a matrix reconstruction method is used to estimate a path AOA, and compared with traditional channel estimation based on ULA, the matrix reconstruction method achieves a higher resolution ratio. In a second stage, an LS method is used to obtain a path gain. According to the angular domain channel estimation method, a mean square error of channel estimation, a bit error of data transmission and complexity of a traditional scheme are significantly reduced. A simulation result indicates that compared with the traditional method, the angular domain channel estimation method can achieve a lower MSE and BER.

An angular domain channel estimation method based on matrix reconstruction for a symmetrical nonuniform array, defining that a system comprises a base station with M antennas and a user with a single antenna, wherein the M antennas form a symmetrical nonuniform linear array and the symmetrical nonuniform linear array is divided into a dense symmetrical uniform linear subarray, a first sparse uniform linear subarray and a second sparse uniform linear subarray;

the dense symmetrical uniform linear subarray has 2M1+1 array elements;
each of the array elements has a spacing d, and d=λ/2, λ being a half of a wavelength;
each of the first sparse uniform linear subarray and the second sparse uniform linear subarray comprises M2 array elements, each of the array elements has a spacing (M1+1)d, and M=2(M1+M2)+1;
the first sparse uniform linear subarray and the second sparse uniform linear subarray are respectively deployed on two sides of the dense symmetrical uniform linear subarray;
an array element in a middle of the dense symmetrical uniform linear subarray is selected as a reference array element, and rest array elements are symmetrically distributed by taking the reference array element as a center;
since a wireless channel experiences limited scattering propagation, the channel has a sparse multi-path structure and the user is defined to have L scattering paths;
and the channel estimation method comprises:
performing path angle estimation based on a matrix reconstruction method, specifically as follows:
enabling a user side to send a training signal s t at a time t, and in all snapshots, enabling |st|=1, then a receiving signal at a position of a base station antenna being:
yt=htst+nt=Agtst+nt
wherein ht is a user uplink channel, nt is an additive white Gaussian noise obeying complex Gaussian distribution CN(0,σ2I), σ2I is a variance of the additive white Gaussian noise, and Agt is a form of matrix multiplication of the channel ht:
gt=[g1,t, . . . ,gl,t]TϵCL×1
A=[a(θ1), . . . ,a(θL))]ϵCM×L
gl,t being a channel gain of the user at the time t and at an lth scattering path and obeying complex Gaussian distribution gi,t˜CN(0,1), θl representing an angle-of-arrivals of an lth path of the user, and a vector a(θl)ϵCM×1 representing an array manifold vector, l=1, . . . L;
enabling xt=gtstϵCL×1 to obtain a receiving signal covariance matrix:
Ry=EytytH=Rh+σ2I=ARxAH+σ2I
wherein Rh=EhthtH and Rx=ExtxtH;
vectorizing the covariance matrix Ry to obtain a vector z:
z=vec(Ry)=Ãp+σm2
wherein Ã=A*⊙AϵC|M|2×L, p=[g12σ12, . . . , gL2σL2]T, gl2 and σl2 respectively represent a transmission signal power and a path gain power, 1≤l≤L, σm2 is a noise power, =[e1T, e2T, . . . , eMT]T, ei is a column vector, except that the ith position is 1, the rest are 0, the vector z is equivalent to receiving data with an array manifold matrix (A*⊙A), and array element positions of the vector z are given by a set D=di−dj, i,j=1, 2, . . . , M, di represents a distance from an ith array element to the reference array element, repeated elements in the set D are deleted to obtain a set B, integer elements of the set B correspond to positions of virtual array elements, the repeated data in the receiving data z are removed and corresponding rows are rearranged to cause the rows to correspond to the positions of the virtual array to obtain a new vector:
{tilde over (z)}=ABp+σm2e0
wherein {tilde over (z)}ϵC|B|×1 is a receiving signal of the virtual array, and ABϵC|B|×L is an array manifold matrix corresponding to the virtual array, |B|=M+2(M1+(M1+1)M2), e0ϵC|B|×1, and except that a central term is 1, the rest are 0;
reconstructing the received data {tilde over (z)} into a covariance matrix
R
~
y
∈
ℂ
(
❘
"\[LeftBracketingBar]"
B
❘
"\[RightBracketingBar]"
+
1
2
)
×
(
❘
"\[LeftBracketingBar]"
B
❘
"\[RightBracketingBar]"
+
1
2
)
of the virtual array, the matrix {tilde over (R)}y having a toeplitz matrix property, that is, elements on the same diagonal line being the same, so during construction of the matrix {tilde over (R)}y, only constructing data in a first column and a first row, constructing previous
❘
"\[LeftBracketingBar]"
B
❘
"\[RightBracketingBar]"
+
1
2
data in the vector {tilde over (z)} into a first column of the matrix {tilde over (R)}y, constructing last
❘
"\[LeftBracketingBar]"
B
❘
"\[RightBracketingBar]"
-
1
2
data in me vector {tilde over (z)} into a first row of the matrix {tilde over (R)}y, and then complementing {tilde over (R)}y according to the property that the elements on the same diagonal line of {tilde over (R)}y are the same;
based on feature value decomposition of {tilde over (R)}y, representing:
R
~
y
=
[
U
S
U
N
]
[
∑
S
0
0
∑
N
]
[
U
S
H
U
N
H
]
wherein US is a signal subspace formed by a feature vector corresponding to a large feature value, and UN is a noise subspace formed by a feature vector corresponding to a small feature value;
multiplying both sides of the matrix by UN to obtain:
{tilde over (R)}yUN=(A1RxA1H+σm2I)UN=σm2Un,
wherein A1ϵC(|B|+1)/2×L represents an array manifold matrix corresponding to the virtual array and meets:
A1RxA1HUN=0
since a column vector of A1 corresponds to a signal transmitting direction, a direction of a signal source is estimated by the characteristic;
based on a multiple signal classification algorithm, defining a spatial spectrum signal Pmusic({circumflex over (θ)}1) as:
P
music
(
θ
ˆ
l
)
=
1
a
~
(
θ
l
)
H
⁢
U
N
⁢
U
N
H
⁢
a
˜
(
θ
l
)
wherein in a case that a denominator ã({circumflex over (θ)}l)HUNUNHã({circumflex over (θ)}l) reaches a minimum value, ã({circumflex over (θ)}l) is an lth column vector of the matrix A1, Pmusic({circumflex over (θ)}l) reaches a maximum value, a direction-of-arrivals l is estimated according to a peak value of Pmusic({circumflex over (θ)}l), thereby obtaining all path angle information {circumflex over (θ)}=[{circumflex over (θ)}1, {circumflex over (θ)}2, . . . , {circumflex over (θ)}L];
and
performing path gain estimation, specifically as follows:
obtaining an array manifold matrix Â based on the obtained {tilde over (θ)}, sending a pilot signal ut, estimating path gains in different time blocks based on the obtained Â, and constructing a cost function:
J
⁡
(
g
ˆ
t
)
=

1
u
t
⁢
y
t
-
A
^
⁢
g
^
t

2
=
(
1
u
t
⁢
y
t
-
A
^
⁢
g
^
t
)
H
⁢
(
1
u
t
⁢
y
t
-
A
^
⁢
g
^
t
)
=
(
1
u
t
)
2
⁢
y
t
H
⁢
y
t
-
1
u
t
⁢
y
t
H
⁢
A
^
⁢
g
^
t
-
1
u
t
⁢
g
ˆ
t
H
⁢
A
^
H
⁢
y
t
+
g
ˆ
t
H
⁢
A
^
H
⁢
A
^
⁢
g
^
t
minimizing the cost function to obtain a channel gain estimation ĝt, specifically, by calculating a partial derivative of the cost function relative to ĝt, obtaining:
∂
J
⁡
(
g
ˆ
t
)
∂
g
ˆ
t
=
-
1
u
t
⁢
y
t
H
⁢
A
^
+
g
^
t
H
⁢
A
^
H
⁢
A
^
in a case that
g
ˆ
t
H
⁢
A
^
H
⁢
A
^
=
1
u
t
⁢
y
t
H
⁢
A
^
,
a solution of the channel gain being:
g
ˆ
t
=
1
u
t
⁢
(
A
^
H
⁢
A
^
)
-
1
⁢
A
^
H
⁢
y
t
,
t
=
1
,
…
,
T
wherein T is a time block, then within one time block, the whole channel estimation result expression is:
t=t,t=1, . . . ,T.

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Angular domain channel estimation method based on matrix reconstruction for symmetrical nonuniform array

Life of this patent

Angular domain channel estimation method based on matrix reconstruction for symmetrical nonuniform array

Life of this patent

Abstract

Claims1