US 2022/0179031 A1 · METHOD FOR ESTIMATING THE DIRECTION-OF-ARRIVAL OF A COPRIME ARRAY BASED ON VIRTUAL DOMAIN STATISTICS RECONSTRUCTION OF SINGLE-BIT QUANTIZED SIGNAL

Abstract

The invention discloses a method for estimating the direction-of-arrival of a coprime array based on virtual domain statistics reconstruction of single-bit quantized signal, which mainly solves the problems of difficult realization of software and hardware, limited degree of freedom and the like in the prior art. The realization steps are as follows: arranging a coprime array and a single-bit analog-to-digital converter at a receiving end; calculating equivalent virtual signal corresponding to a single-bit receipt signal of the coprime array; constructing a virtual domain augmented covariance matrix of an initialized single-bit quantized signal; designing, based on statistical correlation analysis between statistics of the single-bit quantized signal and the original unquantized signal, an optimization problem based on virtual domain statistics reconstruction of quantized signal; and performing direction-of-arrival estimation by utilizing the virtual domain augmented covariance matrix corresponding to the optimized single-bit quantized signal.

A method for estimating the direction-of-arrival of a coprime array based on virtual domain statistics reconstruction of single-bit quantized signal, comprising the following steps:

(1) arranging a coprime array at a receiving end using M+N−1 antennas, each array element of the coprime array being connected with a single-bit analog-to-digital converter for single-bit quantization of receipt signal, wherein M and N are coprime integers;
(2) modeling a single-bit receipt signal of the coprime array:
assuming that there are K far-field narrowband incoherent signal sources from directions θ1, θ2, . . . , θK, receiving an incident signal by adopting the coprime array and the single-bit analog-to-digital converter constructed in step (1), and obtaining the single-bit receipt signal y(l)∈M+N−1 of the coprime array at the lth time, wherein the modeling is
y
⁡
(
l
)
=
𝒬
⁡
(
x
⁡
(
l
)
)
=
𝒬
⁡
(
∑
k
=
1
K
⁢
⁢
a
S
⁡
(
θ
k
)
⁢
s
k
⁡
(
l
)
+
n
S
⁡
(
l
)
)
,
wherein, (·) is a single-bit quantization operator, x(l) is an unquantized original receipt signal of the coprime array, sk(l) is a waveform of a kth signal, (l) is a noise item independent of each signal source, and (θk) is a steering vector of the coprime array corresponding to the direction θk, expressed as
(θk)=┌1,e−jπu2sin(θk), . . . ,e−jπuM+N−1sin(θk)┐T,
wherein, u1, i=1, 2, . . . , M+N−1 represents an actual position of the ith physical antenna element in the coprime array, and u1=0, j=√{square root over (−1)}, [·]T represents a transposition operation, and a sampling covariance matrix of the single-bit receipt signal of the coprime array is obtained by using collected L sampling snapshots, expressed as
Q
^
S
=
1
L
⁢
∑
l
=
1
L
⁢
⁢
y
⁡
(
l
)
⁢
y
H
⁡
(
l
)
,
wherein (·)H represents conjugate transpose;
(3) calculating an equivalent virtual signal corresponding to the single-bit receipt signal of the coprime array:
vectorizing the sampling covariance matrix of the single-bit receipt signal of the coprime array, and obtaining the equivalent receipt signal of a virtual array corresponding to the single-bit quantized signal, expressed as
q
^
𝔻
=
vec
⁡
(
Q
^
𝕊
)
=
2
π
⁢
(
arcsin
⁡
(
(
∑
-
1
2
⁢
⊗
∑
-
1
2
)
⁢
ℜ
⁡
(
r
𝔻
)
)
+
j
·
arcsin
⁡
(
(
∑
-
1
2
⁢
⊗
∑
-
1
2
)
⁢
𝔍
⁡
(
r
𝔻
)
)
)
,
corresponding to a non-uniform virtual array,
={v1−vD|vDv1∈},
wherein, vec(·) represents a vectorization operation, that is, columns in the matrix are stacked in sequence to form a new vector, Σ=diag(), =E[x(l)xH(l)] is the covariance matrix of the receipt signal of a unquantized original coprime array, diag(·) represents an operation of taking diagonal elements to form a diagonal matrix, E[·] represents taking expectation operation, ⊗ represents Kronecker product, (·) represents taking real part operation, (·) represents taking imaginary part operation,
r
D
=
∑
k
=
1
K
⁢
⁢
σ
k
2
⁢
a
D
⁡
(
θ
k
)
+
σ
n
2
⁢
vec
⁡
(
I
)
,
wherein, σk2 represents power of the kth signal source, σn2 represents noise power, I is an identity matrix, (θk) is a steering vector of a non-uniform virtual array corresponding to the direction θk, and is calculated as (θk)=(θk)⊗(θk), wherein (·)* is a conjugate operation;
(4) constructing a virtual domain augmented covariance matrix of an initialized single-bit quantized signal:
in order to overcome a signal model mismatch problem caused by the non-uniform virtual array of the coprime array, constructing a virtual domain uniform linear array with a same aperture as a positive half axis of the non-uniform virtual array and a spacing d, wherein the unit spacing d is half of the wavelength of incident narrowband signal, expressed as
={ud|u=0,1,2, . . . ,max()/d},
wherein, max(·) represents an operation of taking the set maximum, correspondingly, the equivalent virtual signal ∈ corresponding to the virtual domain uniform linear array is obtained by the following method:
for the equivalent virtual signal corresponding virtual array element position corresponding to , if the virtual array element position is included in the non-uniform virtual array , the equivalent virtual signal at this position is the same as a virtual signal corresponding to the corresponding virtual array element position in ;
the equivalent virtual signal corresponding to discontinuous virtual array elements in the remaining non-uniform virtual arrays are set to zero, and then a virtual domain augmented covariance matrix of the initialized single-bit quantized signal can be constructed as
=Toep(),
wherein, Toep(·) represents that a vector taken is the first column of a Hermitian Toeplitz matrix;
(5) designing, based on statistical correlation analysis between statistics of the single-bit quantized signal and the original unquantized signal, an optimization problem based on virtual domain statistics reconstruction of quantized signal to obtain a single-bit quantized signal covariance matrix corresponding to a virtual uniform array ;
according to statistical characteristic analysis, based on the characteristic that the single-bit quantized signal covariance matrix =E[y(l)yH(l)] is the same as a maximum linear independent set of an original unquantized signal covariance matrix , indicating that a rank of covariance matrix does not change in a single-bit quantization process, and the virtual domain augmented covariance matrix corresponding to the single-bit quantized signal derived from can be regarded as a sampling covariance matrix calculated from the single-bit receipt signal of the virtual uniform array , but some elements are missing;
under an ideal condition that all elements are known, the covariance matrix will still retain the matrix rank information related to the incident signal source;
based on statistical correlation analysis among the above statistics, the reconstruction problem of augmented covariance matrix can be constrained and optimized by using low rank characteristics of the covariance matrix, and then the following optimization problem for virtual domain statistics reconstruction of single-bit quantized signal is constructed taking as an optimization target:
q
U
★
=
arg
⁢
⁢
min
q
U
∈
C
[
U
]
⁢

𝒫
Ω
⁡
(
Toep
⁡
(
q
U
)
)
-
Q
^
U

F
+
λ
·
rank
⁡
(
Toep
⁡
(
q
U
)
)
subject
⁢
⁢
to
⁢
⁢
Toep
⁡
(
q
U
)
≽
0
,
wherein, Ω(·) represents a projection operation used to select the element in Toep() corresponding to the position of non-zero elements for fitting, λ is a user adjustment parameter, Toep()0 is a positive semi-definite matrix constraint item, ∥·∥F represents a Frobenius norm, rank(·) represents the rank of the matrix;
the single-bit quantized signal covariance matrix Toep() corresponding to the virtual uniform array can be obtained by solving the above optimization problem;
and
(6) performing direction-of-arrival estimation by utilizing the optimized single-bit quantized signal covariance matrix Toep() corresponding to the virtual uniform array .

263 more elements

Method for estimating the direction-of-arrival of a coprime array based on virtual domain statistics reconstruction of single-bit quantized signal

Life of this patent

Method for estimating the direction-of-arrival of a coprime array based on virtual domain statistics reconstruction of single-bit quantized signal

Life of this patent

Abstract

Claims6