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Journal
1
Time-varying Clutter Suppression in CP-OFDM
Based Passive Radar for Slowly Moving Targets
Detection
Yuqi Liu, Jianxin Yi*, Member, IEEE, Xianrong Wan*, Xun Zhang, Hengyu Ke
Abstract—Time-varying
clutter
suppression
is
challenging in passive radar. Although some existed
methods are robust against the time-varying clutter, they
bear heavy computational burden and memory load. In
this study, we propose two advanced versions of the
average channel response filter on subcarrier (ACRF-C)
for time-varying clutter suppression. The methods take
advantage of the orthogonal frequency division multiplex
(OFDM) modulation with cyclic prefix (CP-OFDM) of the
third-party radio sources, and are implemented in the
subcarrier domain. The proposed batch version of ACRFC (ACRF-CB) can effectively suppress time-varying
clutter but modulates targets with small Doppler
frequency. To detect slowly moving targets, a sliding
version of ACRF-C (ACRF-CS) is presented to partially
overlap the channel frequency response for filter
coefficients estimation. The ACRF-CS yields a good
trade-off between time-varying clutter suppression and
slowly moving targets detection. Simulation and
experimental results following the theoretical analysis
validate that the proposed methods can obtain
comparable performance to that of the existed methods
but possess remarkable computational and memory
advantages.
Index Terms—Passive radar, time-varying clutter,
slowly moving targets, CP-OFDM, subcarrier domain.
I.
INTRODUCTION
Passive radar, which exploits noncooperative illuminators
of opportunity (IOs) to perform target detection and tracking,
has received growing interest in recent years [1-4]. As there
is no need for the deployment and operation of dedicated
transmitters, passive radar systems are significantly cost
This work was supported in part by the National Natural Science
Foundation of China under grants (61931015, 61701350), in part by the
National Key Research and Development Plan of China (2016YFB0502403),
in part by the Technological Innovation Project of Hubei Province of China
(2019AAA061), in part by the Postdoctoral Innovative Talent Support
Program of China (BX201600117), and in part by the Fundamental Research
Funds for the Central Universities (2042019kf1001).
Yuqi Liu, Jianxin Yi, Xianrong Wan, Xun Zhang, and Hengyu Ke are
with the School of Electronic Information, Wuhan University, Wuhan, China,
and also with the Collaborative Innovation Center for Geospatial Technology,
Wuhan, China. Corresponding authors: Jianxin Yi (e-mail:
jxyi@whu.edu.cn), Xianrong Wan (e-mail: xrwan@whu.edu.cn).
effective and covert, and are immune to anti-radiation
missiles inherently. At present, with the development of
passive radar technology, passive radar systems can be
applied to detect multiple types of targets [5]. One of the
important applications is slowly moving targets detection.
The slowly moving targets, such as drones, boats, and birds,
own the salient features of low altitude and slow speed.
These features pose great challenges for slowly moving
targets detection using conventional radar, but make the
passive radar a potential alternative.
Nowadays, digital broadcasting signals, like digital audio
broadcasting (DAB) [6], digital video broadcasting-terrestrial
(DVB-T) [7], China mobile multimedia broadcasting
(CMMB) [8] and so on, are the mostly widely used IOs in
passive radars. Most of these digital broadcasting signals
adopt orthogonal frequency division multiplex (OFDM)
modulation with cyclic prefix (CP-OFDM). The high radiated
power and omnidirectional low altitude coverage of these
signals make them easy to detect low altitude targets. Besides,
the continuous radiation and relatively wide bandwidth of
these signals enable them possible to continuously detect
slow-speed and small targets. Thus, it is practicable to utilize
the digital broadcasting signals as the IOs for slowly moving
targets detection.
So far, the feasibility of CP-OFDM based passive radar for
slowly moving targets detection has been demonstrated by
many researchers [9-13]. In practice, the passive radar may
be deployed to detect slowly moving targets in several
specific scenarios such as jungle, lake, or sea. In these
scenarios, the clutter environments are usually non-stationary
and the targets are obscured by the time-varying clutter with
a spread Doppler spectrum. In this case, it is technically
challenging to suppress the time-varying clutter in the
presence of slowly moving targets.
In passive radar, the clutter suppression methods can be
classified by two primary categories, adaptive filtering and
fixed coefficient filtering [14]. The fixed coefficient filtering
techniques, such as least square (LS) method [15] and
extensive cancellation algorithm (ECA) [16], require the
filter weights to be estimated by averaging over the whole
coherent processing interval (CPI). These filters assume that
the received signals are wide-sense-stationary over the CPI,
which may not hold in practice due to the time-varying
clutter environments. The adaptive filtering methods, in
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contrast, can automatically adjust to the signal statistics and
make the system more robust to the time-varying clutter
environments. Specifically, the adaptive filtering methods
can be divided into two groups: fully and block adaptive
methods. The fully adaptive methods, such as recursive LS
(RLS) and normalized least mean square (NLMS) filters [17],
update the filter coefficients for each sample throughout the
processed CPI. The block adaptive methods, such as the
batch version of ECA (ECA-B) [18] and fast block least
mean square (FBLMS) algorithm [19], update the filter
coefficients in each batch duration. Although the fully
adaptive methods are robust to time-varying clutter, they
exist the problem of slow convergence speed and high
filtering order. The block adaptive methods, which can
reduce the computational and memory complexities in each
block, but may periodically modulate the slowly moving
targets and clutters along the Doppler dimension [20, 21].
Up to now, two methods, i.e. the sliding version of ECA
(ECA-S) [21] and the multi-channel NLMS (MC-NLMS)
filter [22, 23], have been proposed to deal with the timevarying clutter in the presence of slowly moving targets. The
ECA-S method is proposed to counteract the Doppler
modulation caused by the ECA-B in slowly moving targets
detection. It operates over partially overlapped portions of the
received signals, thus paying more computational and
memory loads. The MC-NLMS filter is proposed to suppress
sea clutter in the presence of low-velocity sea-surface targets.
It is implemented through the exploitation of multiple
reference channels that modulate the original reference signal
with different Doppler frequencies within the sea clutter
spectrum band. Its structure also requires high computational
and memory complexities as a result of the exploitation of
multiple channels.
In order to balance the computational cost and timevarying clutter suppression in the presence of slowly moving
targets, we propose two clutter suppression methods in the
subcarrier domain. The methods are inspired by the average
channel response filter on subcarrier (ACRF-C) [24]. In our
previous work, we have evaluated the ACRF-C and
confirmed that it is sensitive to the time-varying clutter [25].
In this paper, we further develop it to deal with time-varying
clutter for slowly moving target detection. The proposed
methods first estimate the frequency response of the
propagation channel at each OFDM symbol. The batch
version of ACRF-C (ACRF-CB) divides the total OFDM
symbols into small fragments to estimate the average channel
response on each effective subcarrier. In this way, the ACRFCB is robust against the highly time-varying clutter
environments. Whereas, theoretical analysis indicates that the
ACRF-CB will periodically modulate the slowly moving
targets and clutters in Doppler dimension. To solve this
problem, we then propose a sliding version of ACRF-C
(ACRF-CS). The ACRF-CS method allows to estimate the
average channel response and suppress the time-varying
clutter in each batch with two additional sliding windows. It
makes a trade-off between the capability of effectively
remove the time-varying clutter and the possibility to
2
eliminate the Doppler modulation in ACRF-CB. The
effectiveness of the proposed methods is verified by the
simulation and experimental data. For comparison, the
proposed subcarrier-domain methods can obtain comparable
performance to that of the ECA methods but possess
remarkable computational and memory advantages. Besides,
compared with the ECA methods, the proposed methods are
easier to be implemented in real time due to the lack of
matrix inversion.
The rest of this paper is organised as follows. Section II
describes the passive radar signal model and 2-dimensional
range-Doppler
cross-correlation
function
(2D-CCF)
calculation in the subcarrier domain. The proposed methods
are elaborated in Section III. Section IV investigates the
computational and memory complexities of the proposed
methods. In Section V and VI, the proposed methods are
demonstrated on simulation and experimental data,
respectively. Finally, Section VII concludes the paper.
II.
SIGNAL MODEL AND 2D-CCF CALCULATION
In this section, we establish the subcarrier-domain signal
model in passive radar by combining the CP-OFDM
characteristic of IOs first. Then a brief introduction of the
CP-OFDM based 2D-CCF calculation is given.
A.
Signal model
A typical passive radar consists of two channels: a
reference channel and a surveillance channel. In practice, the
surveillance channel is usually contaminated by the directpath signal and multipath clutter. For simplicity, we assume
that the surveillance channel contains a single moving target
echo. The complex envelop of the baseband surveillance
signal can be modelled as
Nc
y (t ) =  ci d (t − τic ) + α0 d (t − τ 0 )e j 2πf0t + nsurv (t ),
(1)
i =0
where d (t ) is the complex envelop of direct-path signal (i.e.
the transmitted signal) and c0 is the corresponding complex
amplitude. τ 0c = 0 represents the delay of direct-path signal.
ci and τ ic are the complex amplitude and the delay (with
respect to the direct-path signal) of the ith clutter component,
respectively. N c is the number of clutter components. α0 , τ 0
and f 0 are the complex amplitude, the delay, and the
Doppler frequency of the target echo, respectively. nsurv (t ) is
the white Gaussian noise in the surveillance channel.
In the reference channel, the purified reference signal can
be extracted via the reconstruction methods [26, 27] thanks to
the digital modulation of OFDM signals. Since the influence
of reconstruction quality on the proposed methods is outside
the scope of this paper, we assume that the reference signal
can be reconstructed accurately. Without loss of generality,
the purified reference signal with CP-OFDM modulation can
be modelled as
L
d (t ) =  dl (t − lTe ),
(2)
l =0
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where Te = Tu + Tg is the duration of a CP-OFDM symbol. Tu
dl (t ) =
Nu −1
C
l ,k
k =0
e j 2πfk t , − Tg  t  Tu ,
(3)
where k indicates the subcarrier index and N u denotes the
total subcarrier number in each OFDM symbol. Cl , k is the
complex modulation data at the kth subcarrier in symbol l.
f k is the carrier frequency of the kth subcarrier.
Assuming that the largest possible delay in both clutter and
targets is smaller than the duration of CP. After decomposing
the reference and surveillance signals into OFDM symbols
and performing discrete Fourier transform (DFT) on each
symbol without CPs, we can convert the signals from the
temporal domain to the subcarrier domain. Referring to [25],
in the surveillance signal, the complex modulation data at the
kth subcarrier in symbol l can be expressed as
Yl , k = H l , k Cl , k + γk e j 2 πf0lTe Cl , k + Nl , k ,
(4)
with
Nc
H l , k =  ci e − j 2πfk τi and γk = α0 e− j 2πfk τ0 e
c
j 2 πf0 (Tg + τ0 )
,
(5)
i =0
where H l , k represents the channel frequency response of
clutter components at the kth subcarrier in symbol l and N l , k
is the corresponding thermal noise. Besides, since the phase
j 2 πf (T + τ )
e 0 g 0 in γk has no effect on the derivation of the
proposed methods in the following section, we ignore it and
define γk = α0 e − j 2 πfk τ0 for simplification.
B.
2D-CCF calculation
In the CP-OFDM based passive radar, the integration time
Tint is usually chosen as an integer multiple of Te , which
means L = Tint Te OFDM blocks are involved to implement
the 2D-CCF. As such, we can adopt the well-known 2D DFT
approach in [28] to approximate the 2D-CCF. After dividing
d (t ) and y (t ) into L OFDM blocks and omitting the phase
rotation by the Doppler shift within one OFDM block [29],
we can calculate the 2D-CCF as
L −1
χ[ τ , f ] =  e− j 2πflTe  yl (t )dl (t − τ )e− j 2πft dt ,
Tu
0
l =0
(6)
L −1
Nu −1
l =0
k =0
C

l ,k l ,k
Y e j 2πfk τ .
l =0
k =0
2
(8)
III. ALGORITHM DESCRIPTION
In the CP-OFDM based passive radar, the ACRF-C
method extracts the target echo from mixture received signal
by the channel estimation [24, 25]. Here we first summarize
the core idea and procedures of the ACRF-C. Then the
modified versions of the ACRF-C for time-varying clutter
suppression are given in the following subsection.
In the ACRF-C method, the frequency response of the
propagation channel at the kth subcarrier in symbol l is
estimated from Yl ,k and Cl ,k . That is
H l ,k =
Yl , k
Cl , k
= H l , k +  k e j 2 f0lTe +
Nl , k
Cl , k
(9)
,
where H l ,k is a channel response estimate on subcarrier
which includes clutter, target echo and thermal noise.
Then we obtain the average channel response on each
subcarrier by averaging the channel response along the slowtime dimension, namely across index l. That is
1 L -1
1 L -1
1 L -1 N
(10)
H k =  H l ,k +  k  e j 2 f0lTe +  l ,k .
L l =0
L l =0
L l = 0 Cl ,k
When f 0 is much larger than the frequency resolution (i.e.
f 0 LTe
1 ), the second term in (10) satisfies
T ( L) ( f0 ) =
sin(πf 0 LTe )
1 L −1 j 2πf0lTe
= e jπf ( L −1)Te
 0. (11)
e
L l =0
L sin(πf 0Te )
For slowly moving targets detection, the CPI is often
chosen large enough to achieve high velocity resolution,
which eventually makes the frequency resolution much
smaller than the target Doppler shift f 0 . Thus, the average
response of the target echo satisfies T ( L ) ( f 0 )  0 for slowly
moving targets detection. Besides, the uncorrelated property
of N l , k and Cl , k makes the average response of the thermal
noise approximately equal to zero. Thus, H l ,k can be
simplified as
1 L −1
 H l ,k . The clutter in surveillance channel is
L l =0
removed by
Yl , k = Yl , k − H k Cl , k = γk e j 2 πf0lTe Cl , k + N l , k ,
(12)
where Yl , k is the surveillance signal after clutter suppression.
N l , k is the sum of the residual clutter and the thermal noise.
where d l (t ) and yl (t ) are the lth OFDM symbols of the
reference and surveillance signals, respectively. Substituting
(3) into (6) and simplifying, we can get
χ[ τ , f ] =  e− j 2πflTe
Nu −1
χtar [ τ , f ] = α0  e− j 2πlT（e f − f0 )  Cl , k e j 2πfk ( τ − τ0 ) .
and Tg are the duration of the useful part and CP of a symbol,
respectively. l is the temporally consecutive index of OFDM
symbol. L denotes the number of OFDM symbols and d l (t )
denotes the lth OFDM symbol with
L −1
(7)
Substituting (4) into (7), χ[ τ , f ] can be represented by the
sum of clutter, target echo and thermal noise. Thus, we can
describe the 2D-CCF of target echo as
Substituting the first term in (12) into (8) we can obtain the
2D-CCF of target echo after clutter suppression. Specifically,
we focus on the range bin containing the target echo, i.e.,
τ = τ 0 . To simplify the mathematical notation, we define

χtar [ τ 0 , f ] = χtar
[ f ] . That is
Nu −1
L −1

χ tar
[ f ] = α0  e − j 2 πlT（e f − f0 )  Cl , k
l =0
= α0 LN u T
k =0
( L)
2
(13)
( f 0 − f ).
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In (13), we have utilized the prior knowledge that
Nu −1
C
k =0
A.
l ,k
2
 1 in the CP-OFDM modulation [25].
Batch version of the ACRF-C
Yk
Batch b-1
LB
Batch b
Batch b+1
Ck
Yl , k
H k(b ) =
Cl , k
1
LB
Yl , k
C
l I b
l ,k
Yl , k − H k(b ) Cl , k
Yk
Fig. 1. Block diagram of ACRF-CB at kth subcarrier
From the implementation of ACRF-C, we can see that the
average channel response on each subcarrier is estimated by
averaging over the whole CPI. It means that the clutter is
suppressed based on the hypothesis of the block fading
propagation channel in one observation time. In practice, the
clutter environments are usually non-stationary since the
passive radar may be deployed to monitor several specific
scenarios such as jungle, lake, or sea. In these scenarios, the
performance of the ACRF-C cannot be guaranteed due to its
single set of filtering factor for the entire CPI.
Inspired by the block adaptive filters in the temporal
domain such as the ECA-B, we develop a batch version of
ACRF-C (ACRF-CB) in the subcarrier domain to deal with
the time-varying clutter in passive radar. The block diagram
of ACRF-CB at kth subcarrier is shown in Fig. 1. In the
ACRF-CB, we divide the channel response in (9) into a set of
consecutive smaller portions of duration LB along the slow-
where Yl , k is the suppressed surveillance signal in bth batch
at kth subcarrier. Similarly, the clutter in other batches and
subcarriers can be suppressed by repeating the above steps.
To present the effectiveness and limitations of the ACRFCB, we consider an experimental data for drone detection
employing a CMMB-based passive radar. The detailed
experimental scenario, which is omitted here, will be
described in Section VI. Fig. 2 shows the range-Doppler (RD)
map after clutter suppression by the ACRF-CB. In Fig. 2, the
CPI is 0.8 s and the batch duration is set to be 25 ms. In this
paper, all RD maps are normalized to the thermal noise
power level so that the value at the maps represents the
estimated signal-to-noise ratio (SNR).
As shown in Fig. 2, although the ACRF-CB can achieve a
wide Doppler notch to suppress the time-varying clutter, it
yields same limitations as the temporal block adaptive filters
in the presence of slowly moving targets such as drones.
Specifically, to deal with the highly varying environments,
we shorten the batch duration to ensure that the propagation
channel in each batch is almost block fading. Whereas the
short batches widen the Doppler notch which yields to a
partial suppression of the detected drone. Besides, the batch
operation in the ACRF-CB introduces modulated side peaks
on the drone at the output of the RD map, as shown in Fig. 2.
time dimension. LB is the number of OFDM symbols in each
batch and B = L LB is the number of the batches. Since the
total OFDM symbols is divided into smaller portions, we can
assume that the propagation channel is block fading in each
batch.
Without loss of generality, we discuss the implementation
of ACRF-CB in the bth batch at kth subcarrier in the
subcarrier domain. After defining the index set I b as
I b = bLB , bLB + 1,
, (b + 1) LB − 1 ,
(14)
we can obtain the average channel response in bth batch at
kth subcarrier as follow:
N l ,k
1
1
1
(15)
H k(b ,LB ) =
e j 2 f0lTe +
.
 H l ,k + L  k l

LB lIb
L
C
Ib
B
B lIb
l ,k
Eventually, the clutter can be suppressed as
Yl , k = Yl , k − H k(b, LB ) Cl , k , l  I b ,
(16)
Fig. 2. RD map after clutter suppression by the ACRF-CB in the
experimental data
Now, we conduct theoretical analysis of the modulations
yielded by the ACRF-CB. After replacing Yl , k and H k(b , LB ) in
(16) by (4) and (15), we can rewrite the supressed
surveillance signal in bth batch at kth subcarrier as
Yl , k = γk [e j 2 πf0lTe − Tb( LB ) ( f 0 )]Cl , k + Nˆ l , k , l  I b ,
(17)
where Nˆ l , k is the sum of the residual clutter and the thermal
noise after clutter suppression. The parameter Tb( L ) ( f 0 ) in
(17) can be expressed as
1
Tb( LB ) ( f 0 ) =
 e j 2πf0lTe = e j 2πf0bLBTe T ( LB ) ( f 0 ). (18)
LB lIb
B
Substituting the target echo in Yl , k into (7) and focusing on
the range bin containing the target return, we get
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L −1
Nu −1
l =0
k =0
χ tar [ f ] = α0  e − j 2 πflTe  [e j 2 πf0lTe − Tb( LB ) ( f 0 )] Cl , k
2
(19)
І
П
= χtar
[ f ] − χtar
[ f ],
І
П
[ f ] is same as (13). After simplification, χ tar
[f]
where χ tar
can be expressed as
LB −1
B −1
l =0
b =0
П
χtar
[ f ] = α0 N u T ( LB ) ( f 0 )  e − j 2 πflTe  e j 2 π ( f0 − f ) bLBTe
(20)
= α0 LN u T ( LB ) ( f 0 )[T ( LB ) ( f )]  ( B ) ( f 0 − f ),
where
1 B −1 j 2 π ( f0 − f )bLBTe
e
B b=0
sin[π ( f 0 − f ) BLBTe ]
= e jπ ( f0 − f )( B −1) LBTe
.
B sin[π ( f 0 − f ) LBTe ]
( B ) ( f0 − f ) =
(21)
5
ignored while the amplitude of the second fraction decreases
as p increases. That is, the target response at the output of
the RD map shows modulated peaks at either side of the
target echo. Besides, the side peaks are separated by 1 ( LBTe )
with amplitudes attenuation at high Doppler frequencies. In
fact, any slowly moving reflected echo, whether the target or
clutter, will be periodically modulated by the ACRF-CB as
long as its Doppler frequency is smaller than 1 ( LBTe ) . As
shown in Fig. 2, the drone is surrounded by the modulated
side peaks in the Doppler dimension since its Doppler
frequency is smaller than 40 Hz. Besides, these side peaks are
separated by 40 Hz, which consistent with the theoretical
analysis.
B.
Sliding version of the ACRF-C
LA
LS
As is apparent, χ [ f ] is shaped by  ( f 0 − f ) and its
peak amplitude is modulated by the product
І
[ f ] and
between T ( LB ) ( f 0 ) and [T ( LB ) ( f )] . That is, both χ tar
П
tar
(B)
Yk
Batch b
Ck
П
χ tar
[ f ] are centered in f = f 0 with mainlobe width 1 ( LTe ) .
І
[ f ] is 1 Te and that
The difference is that the period of χ tar
П
[ f ] is 1 ( LBTe ) . It is this difference that makes the
of χ tar
ACRF-CB has nonnegligible impacts on the slowly moving
targets whose Doppler frequency f 0  1 ( LBTe ) .
In order to present the impacts, we first set f = f 0 and
substitute (13) and (20) into (19). The peak amplitude of the
target after clutter suppression can be written as
2

sin(πf 0 LBTe ) 
.
χtar [ f 0 ] = α0 LNu 1 −
(22)
LB sin(πf 0Te ) 


From (22) we can note that the Doppler notch yielded by
the ACRF-CB is approximately equal to 1 ( LBTe ) . That is,
the target with Doppler frequency f 0  1 ( LBTe ) will lead to
a SNR loss by the batch operation of the ACRF-CB. As
shown in Fig. 2, the Doppler notch is about 40 Hz since the
batch duration is set to be 25 ms. In this case, the detected
drone, whose Doppler frequency is about -16.25 Hz, may
bear SNR loss by the batch operation.
In addition, to investigate the modulated side peaks caused
by the ACRF-CB on the slowly moving targets, we set
f = f 0 + p ( LBTe ) ( p  N , p  0) . Substituting it into (19)
we can get
χtar  f 0 + p ( LBTe ) 
= α0 LN u
sin  πf 0 LBTe  sin π ( f 0 + p ( LBTe ) ) LBTe 
.
LB sin  πf 0Te  LB sin π ( f 0 + p ( LBTe ) ) Te 
(23)
In general, the target Doppler frequency f 0 is not a
multiple of 1 ( LBTe ) , so that the value of (23) is not equal to
zero. In this case, the modulated side peaks aside the target
echo will clearly appear in the RD map. Specifically, as far as
the Doppler frequency of a slowly moving target is smaller
than 1 ( LBTe ) , the value of the first fraction in (23) cannot be
Yl , k
(b , LA ,S )
Hk
=
Cl , k
1
LA
Yl ,k − H k

lIbA ,S
(b , LA ,S )
Yl ,k
Cl ,k
Cl ,k
Yk
Fig. 3. Block diagram of ACRF-CS in kth subcarrier
From subsection III-A we know that the limitations of
ACRF-CB lie in two aspects: partial suppression of slowly
moving targets and Doppler modulation of reflected echoes
with small Doppler frequencies. In essence, the performance
of ACRF-CB depends on the selection of LB , i.e. the number
of OFDM symbols in each batch. Long LB should be
selected to preserve the slowly moving target echoes by
narrowing the Doppler notch after clutter suppression. In
contrast, short LB is preferred to be effective against the
time-varying clutter and to move the modulated side peaks
out of the Doppler range of interest.
To decouple the selection of LB in the presence of slowly
moving targets, we propose a sliding version of ACRF-C
(ACRF-CS), which follows a similar principle as the ECA-S
but is implemented in the subcarrier domain. As shown in Fig.
3, the number of OFDM symbols in each batch for average
channel response estimation is set to be L A . In addition, a
new parameter LS is introduced to represent the update rate
of the response estimation. The corresponding number of
consecutive fragments for the estimation of the average
channel response is BS =  L LS  . Similarly, we discuss the
implementation of the ACRF-CS in the bth batch at kth
subcarrier. First of all, we define two index sets as follows:
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6
L + LA 
 L − LA LS − LA
I bA, S = bLS +  S
,
+ 1, , S
− 1
2
2
2


S
I b = bLS , bLS + 1, , (b + 1) LS − 1 .
І
tar
coincides with that of χ [ f ] in (29). However, compared
(24)
Then the average channel response is obtained as follows:
N l ,k
1
1
1
(b , L )
H k A ,S =
H l ,k +  k  e j 2 f0lTe +
. (25)


LA lIbA ,S
LA lIbA ,S
LA lIbA ,S Cl ,k
Obviously, the difference between (25) and (15) is the
index set of the parameter l. The output of the surveillance
signal suppressed by the ACRF-CS can be written as
Yl , k = Yl , k − H k
( b , LA , S )
Cl ,k , l  I bS .
(26)
In (26), the average channel response is estimated by L A
continuous OFDM symbols and the surveillance signal to be
(b, L )
suppressed by H k A ,S lasts for LS continuous OFDM
symbols.
Based on the implementation of the ACRF-CS method, we
give the theoretical derivation of its decoupling effect.
Similar to (17), we rewrite the suppressed surveillance signal
(b, L )
by substituting Yl , k and H k A ,S into (26). That is
Yl , k = γk [e j 2 πf0lTe − Tb
( LA , S )
( f 0 )]Cl , k + N l , k , l  I bS ,
(27)
where N l , k is the sum of the residual clutter and the thermal
(L
)
noise after clutter suppression. The parameter Tb A ,S ( f 0 ) can
be written as
L −L
j 2 πf0 ( bLS + S A )Te
1
(L )
2
Tb A,S ( f 0 ) =
e j 2πf0lTe = e
T ( LA ) ( f 0 ). (28)

LA lIbA,S
Similarly, substituting the target echo in Yl , k into (7), we
can obtain the Doppler dimension of the target response at
the output of the 2D-CCF after setting τ = τ 0 . That is
L −1
Nu −1
χ tar [ f ] = α0  e − j 2 πflTe  [e j 2 πf0lTe − Tb
l =0
( LA , S )
k =0
( f 0 )] Cl , k
2
(29)
= χ [ f ] − χ [ f ],
І
tar
П
tar
І
І
[ f ] is equal to χ tar
[ f ] in (13). The second term in
where χ tar
(29) can be expressed as
LS −1
BS −1
l =0
b=0
П
χtar
[ f ] = e jπf0 ( LS − LA )Te α0 N u T ( LA ) ( f 0 )  e − j 2 πflTe
e
j 2 π ( f 0 − f ) bLS Te
= e jπf0 ( LS − LA )Te α0 LN u T ( LA ) ( f 0 )[T ( LS ) ( f )]  ( BS ) ( f 0 − f ),
(30)
where
 ( BS ) ( f 0 − f ) =
1
BS
BS −1
e
j 2 π ( f0 − f ) bLS Te
b =0
= e jπ ( f0 − f )( BS −1) LS Te
sin[π ( f 0 − f ) BS LS Te ]
.
BS sin[π ( f 0 − f ) LS Te ]
П
П
[ f ] in the ACRF-CB, the period of χ tar
[ f ] in the
with χ tar
ACRF-CS is now 1 ( LS Te ) . That is, the expected Doppler
separation of the modulated side peaks associated to the
detected slowly moving targets is equal to 1 ( LS Te ) instead
of 1 ( LBTe ) . It indicates that to remove the side peaks out of
the Doppler range of interest for all the targets belonging to
the cancellation notch area, we can modestly select the filter
update rate LS without restriction of the batch duration L A .
In this way, a good cancellation capability against timevarying clutter can still be guaranteed by adjusting the
independent parameter L A .
In addition, it is of interest to consider the Doppler notch
yielded by the ACRF-CS. By setting f = f 0 in (29), we can
write the output of the target response as

χtar [ f 0 ] = α0 LN u 1 − e jπf0 ( LS − LA )Te T ( LA ) ( f 0 )[T ( LS ) ( f 0 )]

(32)
 sin(πf 0 LATe ) sin(πf 0 LS Te ) 
= α0 LN u 1 −
.
 LA sin(πf 0Te ) LS sin(πf 0Te ) 
Notice that the SNR loss of the detected target, or the
Doppler notch width, depends on both L A and LS . In
practice, the batch duration for average channel response
estimation in the ACRF-CS is selected as LA = LB to
guarantee effective cancellation against the time-varying
clutter. In this case, a wider Doppler notch is yielded by the
ACRF-CS with respect to the ACRF-CB since the sliding
operation makes LS much smaller than L A . On the other
hand, if we set LA = LB , the wider notch yielded by the
ACRF-CS will lead to a SNR loss of the slowly moving
targets. Actually, we can also select L A to be larger than LB
to achieve approximate Doppler notch between ACRF-CB
and ACRF-CS. In this way, we can obtain comparable peak
amplitude of the detected target, but the suppression
performance of the ACRF-CS cannot be guaranteed.
In conclusion, the ACRF-CS allows a trade-off between
time-varying clutter suppression and modulated side peaks
removal in the presence of slowly moving targets. The
decoupling effect of the ACRF-CS is achieved by separately
selecting the parameters L A and LS . In practice, the
parameter L A is first determined according to the clutter
environments to maximize the cancellation capability. Then
LS is set based on the Doppler notch width and observation
region to exclude the side peaks from the Doppler of interest.
(31)
П
[ f ] is determined by
Similar to (21), the shape of χ tar
 ( BS ) ( f 0 − f ) and its peak amplitude is modulated by the
П
[ f ] is
product between T ( LA ) ( f 0 ) and [T ( LS ) ( f )] . Thus, χ tar
centered in f = f 0 with mainlobe width 1 ( LS Te ) , which
IV. COMPUTATIONAL AND MEMORY COMPLEXITIES
In Section III, we have proposed the ACRF-CB and
ACRF-CS methods in the subcarrier domain for time-varying
clutter suppression. Essentially, the ACRF-CB and ECA-B,
or the ACRF-CS and ECA-S, follow the similar suppression
principle. In this section, we investigate the computational
complexity and required memory space of the proposed
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methods. For comparison, the computational and memory
complexities of the ECA-B and ECA-S are also presented.
One should note that the temporal domain methods will also
experience the process of reference signal reconstruction
before clutter suppression to improve the clutter suppression
performance [15]. Thus, when comparing the complexities of
the aforementioned methods, the process of reference signal
reconstruction is not taken into consideration.
A.
Computational complexity
The computational complexities of the ECA-B and ECA-S
have been analysed in [21]. Similar to [21], we assume that a
complex addition and a complex multiplication involve 2 and
6 floating-point operations (FLOPs), respectively. Notice that
the computational complexities of the proposed methods
stem from the following four stages: signals conversion from
temporal domain to subcarrier domain, the OFDM channel
response estimation, the average channel response estimation,
and clutter suppression. The first two stages of the proposed
two methods are exactly the same, whereas the difference lies
in the third and fourth stages.
In order to figure out the computational complexity of the
first stage, we should note that the N-point fast Fourier
transform (FFT) butterfly algorithm includes 0.5 N log 2 ( N )
complex multiplications and N log 2 ( N ) complex additions.
Thus, the computational complexity of the first stage requires
10 LN u log 2 ( N u ) FLOPs. In addition, note that a complex
division involves 11 FLOPs. Consequently, the
computational complexity of the OFDM channel estimation
requires 11LN u FLOPs. In the ARCF-CB method, the L
OFDM symbols in one CPI are divided into B fragments.
The dimension of each fragment is LB . In each fragment, the
average channel response estimation at one subcarrier
requires 2 LB FLOPs. Hence, the computational complexity
TABLE I
COMPARISON OF THE COMPUTATIONAL COMPLEXITIES OF DIFFERENT
SUPPRESSION METHODS
Methods
Number of FLOPs
ECA-B
B  27.5 N B log 2 ( N B ) + 17 N B + 16 K 2 
ECA-S
BS 17.5 N A log 2 ( N A ) + 15 N S log 2 ( N S ) +16 K 2 + 9 N A + 8 N S 
ACRF-CB
LN u 10 log 2 ( N u ) + 21
ACRF-CS
LN u 10 log 2 ( N u ) + 19 + 2 BS LA N u
Assuming that the parameters of the OFDM symbol are
consistent with that of the CMMB signal [8]. The relevant
parameters for clutter suppression are set as follow:
K = 1000 , N A = N B = 2.5  105 , N S = 1 105 , LA = LB = 53 ,
and LS = 21 . Fig. 4 reports the computational complexities as
a function of the CPI for different suppression methods. It is
obvious that the proposed methods are one order of
magnitude lower than the temporal methods in terms of
computational complexity. In contrast to the notable
difference of computational complexity in the temporal
domain methods, the number of required FLOPs for the
ACRF-CS is comparable to that of the ACRF-CB. It indicates
that the sliding operation in the ACRF-CS yields a limited
increase in the computational burden, but achieves significant
performance improvement.
of the third stage requires 2 LN u FLOPs. We can also work
out that the clutter suppression in the ACRF-CB requires
8 LN u FLOPs. Similarly, the third and fourth stages of the
ACRF-CS method require 2 BS LA N u and 8 LN u FLOPs,
respectively.
The overall computational complexities of the different
suppression methods are concluded in TABLE I. Notice that
the modified versions of the ECA have been appropriately
optimized in [21]. Comparing the proposed subcarrierdomain methods with the different ECA versions reveals that
the subcarrier-domain methods are more efficient in terms of
computational complexity. Besides, the computational
complexities of the subcarrier-domain methods are mainly
proportional to the number of integrated samples (i.e. LN u ).
Whereas, the number of FLOPs required for the temporal
methods is not only related to the integrated number, but also
to the suppressed range bins K and the number of fragments
(i.e. B and BS ). It is also worth noting that, since there is no
matrix multiplication and inversion in the proposed methods,
they are more attractive in parallel processing.
Fig. 4. Computational complexities as a function of the CPI for different
suppression methods
B.
Memory complexity
In this subsection, we study the memory complexities of
the mentioned four suppression methods. The total complex
number required by these methods is defined to measure the
memory complexity. The memory complexities of different
methods are listed in TABLE II. Compared with the temporal
methods, the proposed methods can significantly save the
memory space. In the temporal methods, the increased
memory spaces are mainly caused by the construction of the
clutter subspace. The total memory space occupied by the
clutter subspace is determined both by the parameter K and
the number of fragments such as B or BS . In contrast, the
proposed methods can dramatically reduce the required
memory space since they do not need to construct the clutter
subspace.
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TABLE II
COMPARISON OF THE MEMORY COMPLEXITIES OF DIFFERENT SUPPRESSION
METHODS
Methods
Memory Complexity
ECA-B
7N + BK 2 + BK
ECA-S
5 N + 4 BS N A + BS K 2 + BS K
ACRF-CB
2 N + BN u
ACRF-CS
2 N + BS N u
The comparison of memory complexities for different
suppression methods as a function of the CPI are shown in
Fig. 5. The clutter suppression parameters are consistent with
those in subsection IV-A. As is apparent, the memory spaces
required for the subcarrier-domain methods are one order of
magnitude lower than for the temporal methods. Besides,
although the ACRF-CS produces more fragments for its
sliding operation, it generates a comparable memory
complexity to that of the ACRF-CB. This result indicates that
the sliding operation in subcarrier domain occupies less
memory space than that in temporal domain.
In sum, the performance improvement of ECA-S is at the
price of significant increase in computational and memory
complexities. On the contrary, the sliding operation in
ACRF-CS hardly lead to increased computational and
memory complexities. Moreover, the proposed subcarrierdomain methods are about 10 times lower than the ECA-S
method from both aspects of required memory space and
computational complexity. All these indicate that the
proposed subcarrier-domain methods are more attractive in
the CP-OFDM based passive radar for time-varying clutter
suppression.
Fig. 5. Memory complexities as a function of the CPI for different
suppression methods
V.
SIMULATION RESULTS
To evaluate the time-varying clutter suppression
performance of the proposed methods in the presence of
slowly moving targets, a simulated scenario is considered in
this section. In the simulation, the purify reference signal is
reconstructed from the reference channel which has recorded
a typical CP-OFDM waveform, i.e. CMMB signal. The
CMMB frame structure is similar to that of DVB-T, but with
additional beacons [8]. Specifically, one frame of a CMMB
8
signal lasts 1 s and consists of 40 time slots. Each time slot is
made up of one beacon and 53 OFDM symbols. The beacon
can be divided into one transmitter identifier signal and two
identical synchronization signals. The main body of an
OFDM symbol consists of the useful symbol ( Tu = 409.6 μs )
and the CP ( Tg = 51.2 μs ).
TABLE III
CLUTTER AND TARGET PARAMETERS OF THE SIMULATION
Bistatic range bin
Doppler shift (Hz)
CNR/SNR (dB)
Clutter
0:5:70
v
30:-2:2
Target 1
23
-10
-35
Target 2
52
65
-45
The values of the simulation parameters are listed in
TABLE III. In the surveillance channel, 15 slowly moving
scatterers with Doppler spread are used to emulate the timevarying clutter. The clutter-to-noise ratios (CNR) of the
clutter at zero-Doppler frequency takes value (30:-2:2) dB,
where (30:-2:2) denotes the sequence from 30 to 2 with step 2. The corresponding bistatic range bin is (0:5:70). Besides,
we assume that the Doppler spread of the simulated clutter is
caused by the windblown trees [30]. In this case, the
amplitude of each simulated clutter has an exponential power
spectrum density (PSD) over the integration time [20]. The
exponential PSD P (ν) is modelled as
r
1 βλ − βλ2 ν
(33)
δ (ν ) +
e
,
r +1
r +1 4
where ν is the Doppler spread of the clutter. λ is the radar
wavelength and β is the exponential shape parameter which
P (ν ) =
is a function of the wind speed. The parameter r is the ratio
of dc power to ac power in the spectrum which is dependent
on the radar frequency and wind speed. The exponential PSD
can be divided into two components: the dc component in the
spectrum, namely the stationary component in the clutter
PSD, is shaped by the Dirac delta function δ (ν) ; the ac
component in the spectrum, namely the varying component
in the clutter PSD, is determined by the second term in (33).
In the simulation, two targets are synthesized in the
surveillance signal. One slowly moving target at the vicinity
of bistatic range bin 23 and Doppler shift -10 Hz is
synthesized with SNR of -35 dB. Another relatively fastmoving target at the vicinity of bistatic range bin 52 and
Doppler shift 65 Hz is synthesized with SNR of -45 dB.
Additionally, thermal noise is modelled as complex white
Gaussian noise. We consider the exponential PSD of clutter
with the parameters β = 12 and r = 30 (i.e. the wind speed
is set to be about 5.4 m/s). The Doppler frequencies in (33)
are expanded from -0.5 Hz to 0.5 Hz with step of 0.1 Hz. The
carrier frequency is 658 MHz. Besides, 32 time slots (i.e. 0.8
s) at the sampling rate of 10 MHz are chosen as a typical CPI,
which means that the integrated number N = 8  106 . Thus, in
the ECA methods, the integration gain is approximately 69
dB, while the integration gain of the proposed subcarrierdomain methods is about 68.4 dB since the beacons and CPs
are discarded for 2D-CCF calculation.
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9
(a)
(b)
(c)
(d)
Fig. 7 RD maps after clutter suppression by different methods in the simulation. (a) ECA-B, (b) ECA-S, (c) ACRF-CB, (d) ACRF-CS
coefficient filtering method, i.e. the ECA, has its limitation in
time-varying clutter suppression.
In our simulation, the filter parameters of the temporal and
subcarrier-domain methods are set to be consistent with those
in Section IV. Specifically, the temporal batch duration and
OFDM block used for each method are listed in TABLE IV.
Actually, one should note that in practical application it is
necessary to select the value of filter parameters according to
the clutter environment. The optimal filter parameters can be
achieved by a large number of experimental data statistics
results. Since the selection of optimal filter parameters is
outside the scope of this paper, we do not discuss it here.
Fig. 6. RD map after clutter suppression by the ECA method in the
simulation
To highlight the masking effect of the time-varying clutter
in passive radar, Fig. 6 gives the RD map after clutter
suppression by the ECA method. As shown in Fig. 6, the
simulated clutter at zero-Doppler frequency is suppressed.
Whereas, a lot of strong residual clutter components appear
around the zero-Doppler frequency, whose sidelobes have
already masked the targets. It indicates that the fixed
TABLE IV
THE VALUE OF FILTER PARAMETERS IN TEMPORAL AND SUBCARRIERDOMAIN METHODS
(TB , LB )
(TA , LA )
(TS , LS )
ECA-B
ECA-S
ACRF-CB
ACRF-CS
(25ms, 53)
~
(25ms, 53)
~
~
(25ms, 53)
~
(25ms, 53)
~
(9.73ms, 21)
~
(9.73ms, 21)
The RD maps after clutter suppression by different
methods are compared in Fig. 7. As is apparent, all methods
can effectively suppress the time-varying clutter and the two
simulated targets are observed after suppression. However,
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similar Doppler side peaks around the slowly moving target
echo are observed in Fig. 7 (a) and (c) after filtering with
ECA-B and ACRF-CB. Obviously, the side peaks are
separated by 40 Hz. It is consistent with the theoretical
analysis since the batch durations exploited for filter
estimation in EAC-B and ACRF-CB are 25 ms. Besides, the
batch operation in ECA-B and ACRF-CB also modulate the
slowly moving clutters, and cause the residual clutter in Fig.
7 (a) and (c) to be separated by 40 Hz.
For comparison, the sliding operations in ECA-S and
ACRF-CS remove the side peaks out of the Doppler range of
interest, as shown in Fig. 7 (b) and (d). In our simulation, we
suppose the slowly moving target is a drone such as DJI
Phantom 4 and the maximum observed velocity of the drone
can be limited to be 18 m/s. Thus, the observed Doppler area
is about 80 Hz. In the sliding methods, the batch durations
exploited for the update rate of the filter coefficients are
about 10 ms, which allow to remove the first Doppler
modulated side peak of the drone out of the observed area.
Thus, no side peaks but only the two simulated targets exist
in the observed area, as shown in Fig. 7 (b) and (d).
Furthermore, we compare the target SNR after clutter
suppression by different methods. In our simulation, the
SNRs of the slowly moving target after clutter suppression by
ECA-B, ECA-S, ACRF-CB, and ACRF-CS are about 20.45
dB, 16.07 dB, 19.73 dB, and 15.73 dB, respectively. As is
apparent, the sliding operation causes the target SNR loss.
This is consistent with the theoretical analysis since we set
N A = N B and LA = LB in the simulation. In this condition,
the sliding methods in both temporal and subcarrier domain
yield a wider Doppler notch with respect to the batch
methods, as shown in Fig. 7. We can also note that the
ACRF-CS can obtain comparable target SNR to that of ECAS. The slight difference is caused by the different integration
gain between the temporal and subcarrier-domain methods.
In addition, the SNRs of the relatively fast-moving target
after clutter suppression by ECA-B, ECA-S, ACRF-CB, and
ACRF-CS are about 23.53 dB, 23.54 dB, 23.06 dB, and
23.09 dB, respectively. This result indicates that neither the
batch nor sliding operation would weak the SNR of the
relatively fast-moving target.
Overall, both the proposed batch and sliding methods can
sufficiently suppress the time-varying clutter. Similar to the
ECA-B, the ACRF-CB will modulate the targets with small
Doppler shift as well as slowly moving clutters. Whereas, the
ACRF-CS could avoid this modulation due to its sliding
operation in the subcarrier domain. Besides, the ACRF-CS
can achieve comparable performance to that of the temporal
ECA-S method in the presence of slowly moving targets, but
has lower computational and memory complexities.
VI. EXPERIMENTAL RESULTS
In this section, we present the experimental data results
obtained from a passive radar system developed in Wuhan
University in China. The target is a drone (DJI Phantom 4)
operated in S mode with the velocity of less than 5 m/s. The
10
radar system and experimental scenario are depicted in Fig. 8.
Specifically, the system is capable of receiving ultra-high
frequency (UHF) band signals such as the CMMB and digital
terrestrial multimedia broadcast (DTMB) [31]. Two Yagi
antennas with gain of approximately 10 dB are used to form
the reference and surveillance channels. The transmitter is the
Wuhan Guishan tower, about 7.5 km northwest of the
receiver site. The receiver is deployed on the top of a
building (about 20 m height) in Wuhan University and its
observation area is the East Lake in Wuhan. In our
experiment, the utilized IO is the CMMB signal at the
sampling rate of 10 MHz.
Fig. 8. Scenario of drone detection experiment trial
Fig. 9. RD map after clutter suppression by the ECA method in the
experimental data
In the following experimental results, the effectiveness of
the proposed methods is presented using the experimental
data acquired in June 2017. The CPI is 0.8 s and the
maximum suppressed range bin is set to be 300 to save
computation time. Other filter parameters are consistent with
the simulation in Section V. The RD map after clutter
suppression by the ECA method is depicted in Fig. 9. Similar
to the simulation, residual clutter components appear after
filtering due to the time-varying clutter environment. The
sidelobes of these clutter components mask the detected
drone at the vicinity of bistatic range bin 36 and Doppler shift
-16.25 Hz.
Fig. 10 gives the experimental results after clutter
suppression by different methods. As is apparent, the timevarying clutter is effectively suppressed by the four methods.
The detected drone can be clearly distinguished in each RD
map. However, the peak of the detected drone is modulated
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in the Doppler dimension by the EAC-B and ACRF-CB
methods as shown in Fig. 10 (a) and (c). For comparison, the
ECA-S and ACRF-CS can remove the modulated side peaks
out of the Doppler range of interest. In Fig. 10 (b) and (d),
only the detected drone exists in the observation area after the
sliding operation. The SNRs of the drone are about 24.33 dB,
20.30 dB, 26.02 dB, and 22.11 dB after clutter suppression
by the ECA-B, ECA-S, ACRF-CB, and ACRF-CS,
respectively. Similar to the simulation, the effectiveness of
the sliding operation is obtained at the expense of SNR loss
11
10 may be attributed to the interior interference of the
receiver, which will be the focus of our future work.
In sum, the effectiveness of different ACRF-C methods
for time-varying clutter suppression has been verified by the
experimental data. For comparison, the ACRF-CB and
ACRF-CS can achieve comparable or even better clutter
suppression performance to that of the corresponding ECA
methods in the experimental data. In terms of the slowly
moving drone detection, the limitations of ACRF-CB are
presented in the experimental result. Besides, the trade-off
(a)
(b)
(c)
(d)
Fig. 10. RD maps after clutter suppression by different methods in the experimental data. (a) ECA-B, (b) ECA-S, (c) ACRF-CB, (d) ACRF-CS
since we set N A = N B and LA = LB in the experimental data.
It is interesting that the ACRF-C versions are more effective
compared with the corresponding ECA methods in term of
target SNR. This effectiveness may be caused by the clutter
components with fractional delays in the experimental data.
In fact, the suppression performance of the temporal methods
is degraded by the fractional delay [32]. Whereas, the
subcarrier-domain methods are robust to the fractional delay
since all the clutter components, regardless of fractional
delay, are correlated in the subcarrier domain, as shown in (5)
[33]. In addition, the residual clutter after suppression in Fig.
between time-varying clutter suppression and slowly moving
drone detection in ACRF-CS are also verified by the
experimental data.
VII. CONCLUSION
In this paper we investigate the time-varying clutter
suppression in the presence of slowly moving targets in the
CP-OFDM based passive radar. Two advanced versions of
ACRF-C have been presented in the subcarrier domain to
cope with the time-varying clutter. We first propose a batch
version of ACRF-C, i.e. ACRF-CB for time-varying clutter
suppression. However, the ACRF-CB modulates the targets
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Journal
12
with small Doppler frequency as well as slowly moving
clutters. To overcome this problem, a sliding version of
ACRF-C, i.e. ACRF-CS is presented. The ACRF-CS is
implemented by taking advantage of partially overlapped
portions of the channel frequency response for filter
coefficients estimation. Theoretical analysis indicates that the
ACRF-CS allows a trade-off between time-varying clutter
suppression and Doppler modulated side peaks removal in
the presence of slowly moving targets. Furthermore, the
proposed methods share similar suppression performance
with the corresponding ECA methods but possess remarkable
computational and memory advantages. Both simulation and
experimental data confirm the effectiveness of the proposed
methods, which provides a valuable basis for their practical
applications in the CP-OFDM based passive radar. Although
we focus on the use of a CMMB signal in this paper, it
should be noted that the proposed methods can be applied to
any CP-OFDM based passive radars. In future work, we will
try to apply the proposed methods to hardware platform to
realize the real-time processing. Besides, the influence of
reference signal reconstruction performance on the proposed
methods is another interesting topic.
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Authorized licensed use limited to: Auckland University of Technology. Downloaded on May 26,2020 at 21:42:19 UTC from IEEE Xplore. Restrictions apply.