超视距雷达多模杂波抑制：基于盲源分离的新方法
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"这篇研究论文探讨了如何在多输入多输出（MIMO）超视距雷达系统中利用盲源分离（Blind Source Separation, BSS）技术来抑制多模式杂波，以提升对慢速船只等目标的检测性能。传统处理算法依赖于目标方向的先验信息，而这种信息往往难以获取。文中提出了一种新颖的基于第二阶盲识别（Second-Order Blind Identification, SOBI）技术的多模式杂波抑制算法，该算法无需目标方向的先验信息，能有效地进行杂波抑制。"
正文:
多输入多输出（MIMO）超视距雷达是一种先进的雷达系统，其利用多个发射和接收天线来提高探测性能和分辨率。超视距雷达能够探测到地平线之外的目标，但同时也面临着特定的挑战，如由多模式传播引起的扩散多普勒杂波。这种杂波严重干扰了对慢速移动目标，如船只的探测，降低了雷达系统的性能。
传统的杂波抑制方法通常依赖于对目标方向的精确先验知识，这对于实际应用来说可能并不现实或难以获取。针对这一问题，本研究论文提出了一种创新的解决方案，即利用BSS技术来抑制多模式杂波。BSS是一种统计信号处理方法，能够在没有完整先验信息的情况下，从混合信号中恢复出原始独立信号源。它主要适用于非线性、非高斯噪声环境，对于雷达系统中的复杂信号环境尤为适用。
本文提出的算法基于SOBI技术，这是一种特殊的BSS方法，通过分析信号的第二阶统计特性来实现源分离。SOBI通过构造一个协方差矩阵的阵列，来估计不同信号源之间的相关性和独立性。在MIMO超视距雷达系统中，每个天线接收到的信号是多个信号源的线性混合，这些信号源包括目标回波和各种类型的杂波。通过SOBI算法，可以估计并分离这些混合信号，从而有效地抑制多模式杂波。
在实际应用中，该算法的优势在于其不需要目标方向的先验信息。这使得它具有更高的适应性和实用性，尤其是在无法精确预知目标位置或杂波环境变化较大的情况下。此外，SOBI算法还具有计算效率相对较高和鲁棒性强的特点，这使得它在实时雷达系统中具有潜在的应用价值。
该研究论文提出了一种基于SOBI的多模式杂波抑制算法，为MIMO超视距雷达提供了一种有效的杂波管理策略。通过这种方法，可以显著提高雷达的检测能力和抗干扰性能，对于提升超视距雷达系统的整体性能具有重要的理论与实践意义。
From the data format in (3), we construct the received data matrix
X (MN × K), where MN is the product that the number of
transmitting array element M multiplied by the number of
receiving array element N. In the case of the transmitter unit plus a
rectangular window, the mathematical expression of X is given
by [25]
X = (a
r
(
f
rx
) ⊗ a
t
(
f
tx
))(C ⊙ b
T
(f
t
T
r
)) (4)
where ⊗ and ʘ denote Kronecker product and Hadamard product, a
and b are spatial and temporal steering vectors of the target,
respectively, and C =
j
[c
1
, c
2
, …, c
K
] is the product that the vector
of slow time random scattering coefficient multiplied by the
complex coefficient
j
. Subscripts ‘r’ and ‘t’ on the steering vectors
differentiate receive and transmit directions
a
r
(
f
) = [1, e
j2
p
d sin (
f
)/
l
0
, ...,e
j2
p
(N−1)d sin (
f
)/
l
0
]
T
(5)
a
t
(
f
) = [1, e
j2
p
d sin (
f
)/
l
0
, ...,e
j2
p
(M−1)d sin (
f
)/
l
0
]
T
(6)
b(f
t
T
r
) = [1, e
j2
p
f
t
T
r
, ...,e
j2
p
(K−1)f
t
T
r
]
T
(7)
Equation (4) gives the case of single frequency component. When
there are multiple frequencies ingredient (number is P + 1) in the
multi-mode propagation conditions, which contain the target to be
detected (number is 1) and sea clutter (number is P), expression of
the received data matrix X is
X = (a
r
(
f
rx
target
) ⊗ a
t
(
f
tx
target
))(C
1
⊙ b
T
(f
d
T
r
))
+ (a
r
(
f
rx
clutter1
) ⊗ a
t
(
f
tx
clutter1
))(C
2
⊙ b
T
(f
c1
T
r
))
+···+(a
r
(
f
rx
clutterP
) ⊗ a
t
(
f
tx
clutterP
))(C
P+1
⊙ b
T
(f
cP
T
r
))
(8)
where a
r
(
f
rx
target
) ⊗ a
t
(
f
tx
target
) denotes transmit–receive
comprehensive direction steering vector of the target, f
d
is Doppler
frequency of the target and a
r
(
f
rx
clutter1
) ⊗ a
t
(
f
tx
clutter1
) denotes
transmit–receive comprehensive direction steering vector of clutter
1st, f
c1
is Doppler frequency of clutter 1st and a
r
(
f
rx
clutterP
) ⊗
a
t
(
f
tx
clutterP
) denotes transmit–receive comprehensive direction
steering vector of clutter Pth and f
cP
is Doppler frequency of
clutter Pth.
3 MIMO-OTH radar multi-mode clutter
suppression based on BSS
Traditional clutter suppression methods filter the clutter out to
improve the signal-to-noise ratio (SNR). At the same time,
information of clutter is removed. In many cases, the clutter
contains a lot of useful information. The BSS algorithm suppresses
clutter by separating the signal to clutters, that is, the algorithm
preserves the information of clutter. The BSS algorithm is more
practical compared with the traditional clutter suppression
algorithms [26].
3.1 SOBI algorithm
Consider the following signal model
x(t) = y( t) + n(t) = As(t) + n(t) (9)
where x(t) is the observation vector, vector y(t)=As(t) contains the
array output sampled at time t, signal vector s(t)=[s
1
(t), …, s
n
(t)]
T
and A(m × n) is referred to as the array matrix or the mixing
matrix. The additive noise n(t)(m × 1) is modelled as a stationary,
temporally white, zero-mean complex random process independent
of the source signals, that is
E[n(t +
t
)n
H
(t)] =
s
2
d
(
t
)I (10)
where δ(
t
) is the Kronecker delta and I denotes the identity matrix.
Superscript ‘H’ denotes conjugate transpose operation.
Furthermore, we can obtain
R(0) = E[x(t)x
H
(t)] = AR
s
(0)A
H
+
s
2
I (11)
R(
t
) = E[x(t +
t
)x
H
(t)] = AR
s
(
t
)A
H
(
t
= 0) (12)
x(t) = As(t) + n(t) =
n
p=1
b
p
a
p
a
p
s
p
(t) + n(t) (13)
whereas a
p
is an arbitrary complex factor and β
p
denotes the pth
column of A. Under the premise of that the signal source is not
relevant, according to (13), there is no loss of generality: R
s
(0) = I.
Therefore
R
y
(0) = E[y(t)y
H
(t)] = AA
H
(14)
Specific steps of the algorithm are summarised as follows:
(1) Whitening: This is achieved by applying to y(t) a whitening
matrix W(n × m)
E[Wy(t)y
H
(t)W
H
] = WR
y
(0)W
H
= WAA
H
W
H
= I
(15)
Equation (15) shows that if W is a whitening matrix, then WA = U
and U is a n × n unitary matrix. As a consequence, matrix A can
be factored as
A = W
−
U (16)
where superscript ‘−’ denotes the Moore–Penrose pseudoinverse.
Using (11), R
s
(0) = I and (15), W can be determined.
(2) Determining the unitary factor: z(t)isdefined as
z(t)
=
def
Wx(t) = W [As(t) + n(t)] = Us(t) + Wn(t) (17)
The covariance matrices
R(
t
) of the process z(t) are defined as
∀
t
= 0 ...R(
t
) = WR(
t
)W
H
(18)
Then we obtain the key relation
∀
t
= 0 ...R(
t
) = UR
s
(
t
)U
H
(19)
Since U is unitary and R
s
(
t
) is diagonal, the unitary factor U may be
obtained as a unitary diagonalising matrix of a whitened covariance
matrix
R(
t
) for some lag
t
.
(3) Joint diagonalisation: In numerical analysis, the ‘off’ of a n × n
matrix M with entries M
ij
is defined as
off (M) =
1≤i=j≤n
M
ij
2
(20)
C(M, V)
=
def
k=1, ..., K
off (V
H
M
k
V ) (21)
If equation off (V
H
MV) = 0 holds, where M denotes R(
t
), then V is
the matrix U that we want to obtain. In practice, however, we
estimate V according to (21), minimising C(M, V), which is a
statistical optimum. An important feature of joint diagonalisation is
that it is not required that the matrix set under consideration can
be exactly simultaneously diagonalised by a single unitary matrix.
IET Radar Sonar Navig., 2015, Vol. 9, Iss. 8, pp. 956–966
958
&
The Institution of Engineering and Technology 2015
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