HFSWR based on synthetic impulse and aperture processing
ABSTRACT A novel high-frequency surface wave radar (HFSWR) has been proposed, which is based on the principles of synthetic impulse and aperture processing. It uses multiple omnidirectional transmit antennae to simultaneously transmit a set of orthogonal waveforms, and the echoed signals are received and processed by one or multiple reception arrays. Although the transmit beam pattern is omnidirectional, by proper processing, the received signal multiple equivalent directional transmit beam patterns can be simultaneously formed. The signal processing scheme to obtain equivalent directional transmit beam pattern is investigated in detail. Considerations for system parameter selection to achieve an overall best system performance are proposed and discussed. In particular, for the novel HFSWR, target range and angle estimates are coupled together due to the orthogonality of the transmitted waveforms. A necessary and sufficient condition on the transmit antenna array geometry and transmit frequencies, which ensures that target range and angle estimates are uncoupled, is presented
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ABSTRACT: Intense co-channel interference (CCI) severely depresses the target detection in high-frequency surface wave radar (HFSWR). In this study, the CCI cancellation algorithm by time and range adaptive processing is proposed for a novel HFSWR - bistatic HF surface wave synthesis impulse and aperture radar. With the real data, the interference is firstly modelled and then its features are investigated. The analyses show that the same interference prevails over a few but different bins through different channels, whereas the echoes are relatively weak and exist in all bins; in range domain, however, the interference takes over all the bins including positive and negative bins and will spread over the same and considerable Doppler area through different channels, whereas the echoes appear only in partially positive bins. On the basis of the features, the interference covariance matrix can be obtained by selecting the samples whose average power is much higher than that of the others in time domain and in range domain; the samples from either or both of beyond the detectable bins and negative bins can be selected for training. The interference can be cancelled by projecting the polluted data into the orthogonal subspace, constructing the projecting matrix with the eigenvectors associated with large eigenvalues of the covariance matrix. Finally, the segment handling and samples requirement are also discussed for reducing the computation burden. The experimental results are provided to demonstrate the performance of the method.IET Radar Sonar ? Navigation 01/2010; · 1.03 Impact Factor
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HFSWR based on synthetic impulse and
aperture processing
H. Su, H. Liu, P. Shui, S. Zhang and Z. Bao
Abstract: A novel high-frequency surface wave radar (HFSWR) has been proposed, which is
based on the principles of synthetic impulse and aperture processing. It uses multiple omnidirec-
tional transmit antennae to simultaneously transmit a set of orthogonal waveforms, and the
echoed signals are received and processed by one or multiple reception arrays. Although the trans-
mit beam pattern is omnidirectional, by proper processing, the received signal multiple equivalent
directional transmit beam patterns can be simultaneously formed. The signal processing scheme to
obtain equivalent directional transmit beam pattern is investigated in detail. Considerations for
system parameter selection to achieve an overall best system performance are proposed and dis-
cussed. In particular, for the novel HFSWR, target range and angle estimates are coupled together
due to the orthogonality of the transmitted waveforms. A necessary and sufficient condition on the
transmit antenna array geometry and transmit frequencies, which ensures that target range and
angle estimates are uncoupled, is presented.
1 Introduction
High-frequency surface wave radar (HFSWR) operates in
HF band (3–30 MHz). In HF band, the electromagnetic
waves can propagate by following the curvature of the
earth along the air–water interface. Owing to the very
low propagation losses of the highly conductive ocean
surface, HF radiation can easily propagate beyond the
line-of-sight. Therefore, HFSWR can provide over the
horizon detection of targets on large oceanic area, which
is widely used in both military surveillance and civilian
applications [1–4]. As the wavelength of HFSWR is gener-
ally of 10–100 m, which approximates to the physical size
of ships and large aircrafts, the radar cross-section (RCS) of
these targets is more dependent on their gross dimension
than that of shape details. Therefore HFSWR has the poten-
tial to detect stealth targets to which RCS reduction tech-
nique has been used by proper shape design. Besides, the
observed Doppler spectrum of sea echoes with a HFSWR
has peculiar and unique dominant peaks, which are gener-
ated by the Bragg scatter from ocean waves with wave-
length exactly half the radar wavelength [5, 6]. Therefore
sea surface currents as well as other sea-state information
can be extracted from the sea echoes’ spectrum, because
sea surface currents always cause the first-order Bragg res-
onant frequencies to be shifted by a small amount from their
predicted positions, and the second-order sea echoes contain
much information about wave properties. In conclusion,
HFSWR offers the capability of inexpensive surveillance
of a large area as well as monitoring of exclusive economic
zone, with the ability to track targets and protect environ-
ments continuously and in all weathers.
The synthetic impulse and aperture radar (SIAR) is a 4-D
radar, namely, it can measure target range, azimuth angle,
elevation angle and Doppler frequency. It uses multiple
omnidirectionaltransmit antennae
radiate a set of orthogonal waveforms, and a reception
array to receive target-echoed signals of all the transmit
antennae [7–9]. As each transmit antenna is omnidirec-
tional, and their transmitted waveforms are orthogonal to
each other, the overall transmit beam pattern is omnidirec-
tional. However, multiple equivalent directional transmit
beam patterns can be obtained by performing digital time-
space beamforming on received signals, which is also
called as synthetic impulse and aperture processing
(SIAP). This gives rise to increased dwell time and
improved target detection performance of SIAR compared
with the conventional radar. Besides, SIAR has many
other advantages, such as, low probability of interception,
flexible system construction, high reliability and so on.
By using pulse compression technique, frequency modu-
lated interrupted continuous waveform (FMICW) can
achieve good range resolution and large maximum range
with a relatively high duty cycle [10, 11]. It can also
provide good isolation between the transmitter and the
receiver, thus allowing a relative higher power monostatic
operation of HFSWR. Therefore FMICW is an ideal wave-
form for HFSWR.
The traditional HFSWR generally works in a monostatic
mode. By applying the SIAP to HFSWR, we propose a
novel HFSWR, which uses multiple omnidirectional trans-
mit antennae to transmit FMICWs with different carrier
frequencies, namely, the transmitted signals are orthogonal
to each other. The target echoed signal is received and pro-
cessed by one or multiple reception antennae. In theory, the
directional transmit antenna array beam pattern can be
formed by proper processing of the received signals. In
addition, the external interference can be suppressed via
adaptive beamforming based on a reception antenna array.
The system construction of the proposed HFSWR is flex-
ible, it can operate in monostatic, bistatic or multistatic
mode, and the reception antenna can be installed on
to simultaneously
# The Institution of Engineering and Technology 2006
IEE Proceedings online no. 20050069
doi:10.1049/ip-rsn:20050069
Paper first received 13th July and in revised form 13th December 2005
The authors are with the National Laboratory of Radar Signal Processing,
Xidian University, Xi’an, Shaanxi, 710071, People’s Republic of China
E-mail: suht@xidian.edu.cn
IEE Proc.-Radar Sonar Navig., Vol. 153, No. 5, October 2006
445
Page 2
ground, ground vehicles or other moving platforms. In
addition to the advantages of the conventional HFSWR
and SIAR, as mentioned earlier, the HFSWR proposed in
this paper also has the advantages of good electronic
counter-countermeasures(ECCM)
agility and manoeuvrability and good survivability. In
this paper, the signal processing scheme and the system
parameters selection issues of the proposed HFSWR are
concerned in detail.
performance,high
2 System overview
2.1 System description
The HFSWR proposed in this paper uses multiple transmit
antennae to simultaneously radiate a set of orthogonal
waveforms, respectively, as mentioned earlier, the radiation
pattern is omnidirectional, target range, azimuth angle and
Doppler can be estimated from the target echoed signal
via particular signal processing algorithm. As the transmit
pattern is omnidirectional, the large transmit array can be
established along the coast, and the small reception array
can be installed on the ship or the ground vehicle. In
addition, multiple reception arrays can be employed to con-
struct a multistatic radar system with the transmit antennae
serving as illuminator. Furthermore, the system may be
operated as passive coherent location system, for example,
utilises a single transmit antenna as illuminator and a recep-
tion antenna as a passive receiver.
For each reception antenna, the received signal is ampli-
fied by low-noise amplifier, coherent demodulated and
sampled by A/D converter to generate high-quality I, Q
components. The complex signal is then band-pass filtered
digitally to generate multichannel signals (each channel cor-
responds to a transmit antenna). The signal of each channel
is range transformed separately, and the multiple channel
range transformed signals are used as the input of time-
space beamforming. At this stage, the system has deter-
mined the ranges and azimuths of a number of targets. In
order to determine the Doppler of each target, it is necessary
to further process the data by coherent integration, which
will be described in detail in Section 3.
2.2 Characteristics
With above system structure, the proposed HFSWR has
several merits.
(i) The fact that the reception is passive makes it far less
vulnerable to electronic counter measures.
(ii) Operation in HF band makes it a good means to detect
stealth targets.
(iii) Simultaneous multiple equivalent transmit beams can
be formed by time-space beamforming on the received
signal, which enables it to increase the dwell time for long-
time coherent integration, thus improving the detection
performance for weak targets.
(iv) Space synchronisation can be automatically achieved
by time-space beamforming at reception, thus the system
control complexity can be decreased.
(v) Reception array on moving platform provides it with
high agility, manoeuvrability and good survivability.
(vi) The target location information estimated by multiple
reception arrays can be combined together to provide
enhanced target location estimation.
(vii) Extendedsurveillance
line-of-sight target detectability.
(viii) The potential for environmental monitoring.
areaand beyondthe
3 Signal processing scheme
The signal processing scheme at the receiving side plays an
important role in the system described in this paper. The
targets of interest to an HFSWR are low-flying aircrafts,
missiles and ships. So, we only consider target azimuth
angle in this paper. Assuming a transmit antenna array of
N isotropic elements, and FMICWs with different carrier
frequencies are employed as transmit waveforms. As
shown in Fig. 1, the location of the nth transmit antenna
is given by the position vector rn¼ jrnj(cos fn, sin fn)T,
T denotes transpose operator, jrnj is the distance between
the nth transmit antenna and the origin of the Cartesian
coordinate system, which is selected as reference point
and fnis the azimuth angle of the nth transmit antenna
measured counterclockwise from the X-axis.
3.1Transmit signal
The system utilises an antenna array to transmit orthogonal
waveforms, the transmit signal of the nth transmit antenna is
snðtÞ ¼ gðtÞej2pððf0þDfnÞt?ðm=2Þt2Þ
where g(t) is the gate signal which controls on and off of the
FMCW signal to produce FMICW waveform, f0is the radar
carrier frequency, Dfnis the frequency deviation of the nth
transmit antenna relative to f0, m is the frequency sweep
rate, N is the number of transmit antenna.
n ¼ 1;...;N
ð1Þ
3.2Multi-channel signals separation
For simplicity, we suppose the HFSWR discussed in this
paper operating in monostatic mode and only a single iso-
tropic reception antenna located at the origin of the
Cartesian coordinate system. We also suppose there is
only one target moving with constant radial velocity. The
results for this case can be extended to the cases of multiple
targets at various distances and radial velocities and the
HFSWRoperating inbistatic
Suppose the target is initially located at distance R0and is
moving with constant radial velocity v, the reflected
signal from this target will essentially be a delayed and
Doppler shifted version of the original transmit signal.
Without loss of generality, the signal decay factors corre-
sponding to target RCS and propagation distance of each
transmitted signal are assumed equal to each other, and
they are omitted in the following deduction. As the transmit
signals are orthogonal to each other, the signal received by
the reception antenna is vector sum of the reflected signals
that are transmitted by the transmit antenna array and
reflected by the target. Hence the received signal is
ormultistaticmode.
rðtÞ ¼
X
N
n¼1
gðt ? tnÞej2pðfnðt?tnÞ?ðu=2Þðt?tnÞ2Þ
ð2Þ
θ
n
φ
n r
Antenna
Y
X
u
Target
0
R
Fig. 1
X-Y plane
Transmit antenna array geometry on two dimensional
IEE Proc.-Radar Sonar Navig., Vol. 153, No. 5, October 2006
446
Page 3
where fn¼ f0þ Dfn, tnis the delay time introduced by the
target distance, target motion and the distance between
the nth transmit antenna and reference point, which is
given by
tn¼ t0? Dtn?2vt0
c
n ¼ 1;...;N
ð3Þ
where t0¼ mTrþ t, (0 ? t , Tr), t is the fast time, Tris the
frequency sweep repetition period, m is the transmitted
sweep number index, c is the velocity of the light,
t0¼ 2R0/c, Dtn¼ rn
unit direction vector as shown in Fig. 1.
The received signal is demodulated by multiplying it with
an ungated version of the transmit signal ej2p( f0t2(m/2)t2),
and then sampled by an A/D converter. In order to separate
the reflected signals with different carrier frequencies, with
each carrier frequency corresponding to different transmit
antenna, the sampled signal is passed through multiple
channels, and multiplied by e2j2pDfntin each channel
separately, and then low-pass filtered individually, as illus-
trated in Fig. 2. By neglecting the gate signal, the output
signal of the nth channel is given by
Tu/c, u ¼ (cos u, sin u)Tis the target
rnðtÞ ¼ ej2pðmtnt?fntn?ðm=2Þt2
As t0? Dtn, t0? 2vt0/c, the instantaneous frequency of
the above signal is approximately related to target delay
time t0by fT¼ mt0.
nÞ
n ¼ 1;...;N
ð4Þ
3.3Range transform
As shown in (4), the range of the specific targets can be esti-
mated from the frequency of demodulated and separated
signals. This can be done by performing the fast Fourier
transform (FFT) of a single sweep, which is also known
as range transform. As demonstrated in Fig. 2, the range
transformed signal of the range cell R0at the mth repetition
interval is given as
rnðR0;mTrÞ ¼ Aej2pfnð2v=cÞmTre?j2pfnðt0?DtnÞ
n ¼ 1;...;N; m ¼ 0;...;M ? 1 ð5Þ
where A is the signal amplitude, M is the number of pulses
used for coherent integration, and MTr is the coherent
integration time. The target velocity is involved in the
first exponential term in (5). When certain limitation (11)
is satisfied, the Doppler frequency corresponding to radar
carrier frequency f0, which is denoted by f¯d, is equal to
2vfn/c approximately. Consequently, the range transformed
signal in (5) can be written as
rnðR0;mTrÞ ¼ Aej2p?fdmTre?j2pfnðt0?DtnÞ
n ¼ 1;...;N; m ¼ 0;...;M ? 1 ð6Þ
Letr(R0,mTr) ¼ [r1(R0,mTr),r2(R0,mTr), ... , rN(R0,mTr)]T,
denote the multichannel signals after range transform, then
we have
rðR0;mTrÞ ¼ sðmTrÞaðR0;uÞ
where s(mTr) ¼ Aej2pf¯dmTrcan be viewed as the complex
envelope of the range transformed signal, a(R0, u) ¼
[e2j2pf1(t02Dt1), e2j2pf2(t02Dt2), ... , e2j2pfN(t02DtN)]Tis the
equivalent steering vector of the system. Unlike the steering
vector of the conventional array, which is a function of
target azimuth angle, the steering vector here is a function
of both target range and target azimuth angle.
The effect of noise is neglected in the above analysis. At
the transmit antenna, the signal-to-noise ratio (SNR) is so
high that the effect of transmitter noise can be neglected.
At HF band, the external noise due to atmospherics,
cosmic noise and man-made noise can be significantly
greater that the internal receiver noise generated within
the receiver itself. Consequently in a HFSWR, the receiver
sensitivity is usually determined by the external noise.
Therefore noise effect must be considered at the reception
antenna. So, the range transformed multichannel signals
may be modified as
m ¼ 1;...;M
ð7Þ
rðR0;mTrÞ ¼ sðmTrÞaðR0;uÞ þ n
where n is the noise vector with covariance of s2I.
m ¼ 1;...;M
ð8Þ
3.4Time-space beamforming
By far, we only use the receiver output multichannel
signals independently to determine target range (with
range resolution of c/2mTrfor each channel, the overall
range resolution of the system will be discussed in detail
in Section 4.3) The range transformed multichannel
signals can be further processed to improve target range
estimation accuracy and to obtain the estimate of target
azimuth angle. As shown in Fig. 2, the range transformed
multichannel signals, which is given by (8), is further pro-
cessed by SIAP which is also called time-space beamform-
ing or synthesis processing in this paper. The time-space
beamforming weight vector is given by
wðR;uÞ ¼ ½e?j2pf1ðt?Dt1Þ;e?j2pf2ðt?Dt2Þ;...;e?j2pfNðt?DtNÞ?T
ð9Þ
Fig. 2
Signal processing diagram
IEE Proc.-Radar Sonar Navig., Vol. 153, No. 5, October 2006
447
Page 4
where t ¼ 2R/c, Dtn¼ [rn
range cell R0, R [ [R02 (DR/2), R0þ (DR/2)], where
DR ¼ (c/2mTr) is the range resolution determined by the
bandwidth of each transmitted FMICW. Obviously, the
output of time-space beamforming is a function of target
range and azimuth angle, which can be represented by an
amplitude–range–azimuth (ARA) surface therefore for
each range cell, the synthesised output is given by
T.(cos u, sin u)T]/c, for a certain
yðR;u;mTrÞ ¼ wHðR;uÞ ? rðR0;mTrÞ
where H denotes complex conjugate. Target range with
improved accuracy and azimuth angle can be simul-
taneously determined by examining the ARA surface.
It should be noted that the above synthesis processing can
be accomplished on the basis of single omnidirectional
receiver. The spatial gain of the received signal equals to
the equivalent (or synthesised) transmitted beam gain. In
order to further improve the spatial gain of the system,
one can adopt multiple receiver antennae, the time-space
beamforming output signals of each receiver antenna can
be coherent integrated via beamforming, and thus the detec-
tion performance can be further improved. In addition, the
external interference can be suppressed via adaptive beam-
forming if multiple receiver antennae is adopted.
m ¼ 1;...;M
ð10Þ
3.5Coherent integration
For weak target or long distance target, the power of its
echoed signal after the above processing is generally not
strong enough compared with noise power for reliable
detection, the SNR should be improved by coherent inte-
grating multiple echoed signals. The coherent integration
over a number of sweeps, which is also known as Doppler
transform, can be implemented by FFT. This transform
gives a good first-order estimate of target radial velocity.
In real-time implementation, overall computation complex-
ity can be greatly reduced by using some efficient algor-
ithms [11, 12] to implement range and Doppler transform.
For the convenience of state, we perform synthesis pro-
cessing followed by coherent integration as illustrated in
Fig. 2, however, their orders are actually interchangeable.
To put the coherent integration before the synthesis proces-
sing may be helpful in reducing the computational load for
target parameters estimation especially under moderate or
low SNR circumstances.
4System parameter selection considerations
In order to achieve an overall best system performance,
system parameters should be deliberately selected. Some
system parameter selection principles, such as frequency
sweep repetition period, on and off time of gating sequence
and so on are familiar to radar researchers. Thus, in this
section, we will mainly discuss the selection of system
parameters with respect to the proposed particular radar
regime, including operating frequency and transmit array
geometry, which play an important role in the proposed
system and affects system performance in many respects.
4.1 Transmit waveform orthogonality
In order to keep the orthogonality of the transmit wave-
forms, transmit frequencies can be selected as a set of
orthogonal basis. For example, fn¼ f0þ cnDf, Df is fre-
quency separation, cnis the transmit frequency code of
the nth transmit antenna, cn[ f0, N 2 1g, ci= cj(i = j).
448
4.2Avoiding Doppler spread
In (6), we have used a constant to represent the Doppler
frequency corresponding to different frequency fn, approxi-
mately. In fact, as each transmit antenna has different carrier
frequency, the Doppler frequency of target corresponding to
each transmit antenna is different too. If the bandwidth
of the Doppler filter is too narrow, these different Doppler
frequency components will fall into different Doppler fre-
quency bin, which is called as Doppler spread in this
paper. Obviously, the presence of Doppler spread will
degrade the performance of target detection. In order to
avoid Doppler spread, the maximum frequency deviation
relative to radar carrier frequency f0must satisfy the follow-
ing limitation
max jcnDfj
n¼0;...;N?1
,
c
4MTrv
ð11Þ
4.3Effects on range resolution
From the discussion in Section 3, we know that both
frequency sweep bandwidth mTrand the whole frequency
deviation of the transmit antenna NDf will affect the range
resolution of the system. In this sub-section, the ambiguity
function (AF) is utilised to show how these two parameters
affecttherangeresolutionofthesystem.TheAFrepresented
in terms of radar measurement delay and Doppler, provides
the radar signal designer a means to qualitatively assess
different waveforms in meeting system requirements for a
radar system. The AF of a signal r(t) is defined as
Aðt;fdÞ ¼
ðþ1
?1
rðtÞr?ðt þ tÞej2pfdtdt
ð12Þ
By substituting (2) into (12), we have
Aðt;fdÞ ¼
ðþ1
?1
X
N
N
n¼1
gðt ? tnÞej2pðfnðt?tnÞ?ðu=2Þðt?tnÞ2Þ
!
?
X
k¼1
gðt þ t ? tkÞej2pðfkðtþt?tkÞ?ðu=2Þðtþt?tkÞ2Þ
!?
? ej2pfdtdt
ð13Þ
The AF given by the above equation is not only depen-
dent on time delay t and Doppler frequency fd, but also
on target range. The dependence of AF on target range is
introduced by the gating sequence for generating FMICW
waveform. The AFs of various gating schemes were first
examined by Khan and Mitchell [10]. Design procedures
were also developed for FMICW waveforms to realise a
desired AF [10]. Although the AF is dependent on target
range, the range resolution is independent on it. Thus, by
neglecting the effects of gating sequence and assuming
the time delay introduced by the distance between transmit
antennae has been well compensated, (13) is modified as
Aðt;fdÞ ¼
ðþ1
?1
X
N
N
n¼1
ej2pðfnðt?t0Þ?ðu=2Þðt?t0Þ2Þ
!
?
X
k¼1
ej2pðfkðtþt?t0Þ?ðu=2Þðtþt?t0Þ2Þ
!?
ej2pfdtdt
ð14Þ
IEE Proc.-Radar Sonar Navig., Vol. 153, No. 5, October 2006
Page 5
Substituting fd¼ 0 into (14), we have
Aðt;0Þ ¼
ðþ1
?1
X
N
N
n¼1
ej2pðfnðt?t0Þ?ðu=2Þðt?t0Þ2Þ
!
?
X
k¼1
ej2pðfkðtþt?t0Þ?ðu=2Þðtþt?t0Þ2Þ
!?
dt
¼ A1ðt;0Þ þ A2ðt;0Þð15Þ
where
A1ðt;0Þ ¼ ej2pððmt2=2Þ?mtt0ÞX
XN
n=k
?
The first term A1(t, 0) in (15) dominates the mainlobe
characteristics of the AF, and the second term A2(t, 0) in
(15) mainly contributes to the sidelobe characteristics of
the AF. Thus, the range resolution is mainly determined
by A1(t, 0). After some derivations and manipulations,
A1(t, 0) can be written as
N
n¼1
e?j2pfnt
ðþ1
?1
ej2pmttdt
A2ðt;0Þ ¼
n;k¼1
Xðþ1
?1
ej2pðfnðt?t0Þ?ðu=2Þðt?t0Þ2
??
? ej2pðfkðtþt?t0Þ?ðu=2Þðtþt?t0Þ2Þ
??
dt
A1ðt;0Þ ¼ ej2pððmt2=2Þ?mtt0?f0t0?ððN?1ÞDf t=2ÞÞðTr? jtjÞ
?sinðpmtðTr? jtjÞ
pmtðTr? jtjÞ
sinðpNDftÞ
sinðpDftÞ
jtj ? Tr
ð16Þ
where fn¼ f0þ (n 2 1)Df, n ¼ 1, ... , N has been used.
Let
A1
A1
range resolution is determined by both A1
The range resolution determined by A1
is DR1¼ c/2B1¼ c/2mTr) and DR2¼ c/2B2¼ c/2NDf,
respectively. B1¼ mTrdenotes the frequency sweep band-
width of the transmit waveform, and B2¼ NDf denotes
the whole frequency deviation of the transmit antenna rela-
tive to f0. The effects of B1and B2on range resolution of the
system can be divided into three cases.
1(t) ¼ (sin(pmt(Tr2 jtj)))/(pmt(Tr2 jtj))
2(t) ¼ sin (pNDft)/(sin(pDft)). As (16) suggests, the
and
1(t) and A1
1(t) and A1
2(t).
2(t)
Case 1: B1? B2, the range resolution is more dependent on
B1than on B2. In other words, if targets can be resolved by
range transform processing (with range resolution DR1) but
cannot be resolved by DR2, then the range resolution of the
system is approximate to DR1. This conclusion is reason-
able. As illustrated in Fig. 2, the synthesis processing is per-
formed on the received signals of the same range bin with a
width of DR1. Thus in this case DR1 limits the range
resolution.
Case 2: B1? B2, the range resolution is more dependent on
B2than on B1.
Case 3: B1’ B2, they have approximately the same effects
on the range resolution.
In order to effectively utilise the signal bandwidth and
alleviate the requirement of larger receiver bandwidth, a
reasonable choice is B1’ B2.
IEE Proc.-Radar Sonar Navig., Vol. 153, No. 5, October 2006
4.4
estimation
Target range and azimuth angle uncoupled
As described earlier, the equivalent steering vector of the
received signal is
aðR0;uÞ ¼ ½e?j2pf1ðt0?Dt1Þ;e?j2pf2ðt0?Dt2Þ;...;e?j2pfNðt0?DtNÞ?T
ð17Þ
as (17) suggests, a(R0, u) depends on both target range and
azimuth angle. Thus target range and azimuth angle esti-
mation by synthesis processing, which is illustrated in
Fig. 2, may be coupling. The Cramer–Rao inequality pro-
vides a relatively simple lower bound on the variance of
unbiased estimators [13–15]. Coupled estimates cause the
Cramer–Rao lower bound (CRLB) for each estimate to be
degraded. In this sub-section, we will use CRLB to find
conditions for uncoupled target range and azimuth angle
estimates. For multiple parameter estimation, the CRLB’s
are diagonal elements of the inversed Fisher information
matrix F. In our case, the (i, j)th element of the 2?2
matrix F is defined by
(
½FðjÞ?i;j¼ E
@lnpðx;jÞ
@ji
@lnpðx;jÞ
@jj
)
ð18Þ
where x is the data vector, j ¼ [R0, u]Tis the parameter
vector and p(x; j) denotes conditional probability density
function. In our case for joint estimation of two parameters
varð^jiÞ ?
1
Fi;i
1 ?
F2
1;2
F1;1F2;2
"#?1
ð19Þ
The first factor of (19) is the lower bound for the estimate of
jiwhen only this parameter is unknown. The second term is
greater or equal to unity. When the second term is greater
than unity the uncertainty of one parameter increases the
minimum variance for the other parameter and the estimates
are coupled. If Fi,ji = j, equal zero, the second term is
equal to unity, the estimates are said to be uncoupled.
From (8) and (18), the individual expressions for Fi,jare
F1;1¼ 8SNR
2p
c
?
?
?2X
2p
c
N
n¼1
N
ðDfnÞ2
ð20Þ
F2;2¼ 2SNR
?2X
?
n¼1
2p
c
ðfnjrnjsinðu ? fnÞÞ2
?2X
ð21Þ
F1;2¼ F2;1¼ 4SNR
N
n¼1
fnDfnjrnjsinðu ? fnÞð22Þ
where SNR ¼ jAj2/s2denotes the SNR of the received
signal after range transform. A necessary and sufficient
condition for uncoupled estimation,namely F1,2, equals
zero is that
X
N
n¼1
fnDfnjrnjsinðu ? fnÞ ¼ 0
ð23Þ
It follows that
X
N
n¼1
fnDfnjrnj½cosfnsinu ? sinfncosu? ¼ 0
ð24Þ
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For (24) to hold for all u (target azimuth angle), we have
X
N
n¼1
fnDfnjrnjcosfn¼
X
N
n¼1
fnDfnjrnjsinfn¼ 0
or in complex notation
X
N
n¼1
fnDfnjrnjejfn¼ 0
ð25Þ
Let r0
n¼ fnDfnjrnj, then (25) can be written as
X
As (26) suggests, there are many transmit array geometries
that satisfy (26). A straightforward choice is pseudo-circular
array geometry. The name comes from that r0
distance between the nth transmit antenna and reference
point, the actual distance can be found by the relation
r0
antennae are evenly spaced on a ring of radius r centred
about the origin of the Cartesian coordinate system, which
N
n¼1
r0
nejfn¼ 0
ð26Þ
nis not the
n¼ fnDfnjrnj. For the pseudo-circular array geometry, N
is shown in Fig. 1. For this geometry, (26) can be written as
r
X
N
n¼1
ej2pððn?1Þ=NÞ¼ 0
ð27Þ
where r ¼ r01¼ r02¼ ??? ¼ r0N. The sum of the above
equation is a geometric series that equals zero for N ? 3.
Thus, uncoupled parameters estimation can be obtained.
4.5Summary
As discussed earlier, the transmit frequencies affect the per-
formance of the system in many respects. It is therefore
critical that the transmit frequencies should be deliberately
selected. In practice, by taking into account all the effects of
the transmit frequencies on system performance, a compro-
mise solution may be obtained to achieve an overall best
system performance.
5 Numerical examples
In this section, we present some examples to demonstrate
the signal processing scheme and the effects of various
Fig. 3
Synthesis processing output with target range of 120 km and azimuth angle of 858
a 3-D range–azimuth angle profile
b Contour plot of a
c Slice of a with u ¼ 858
d Slice of a with R0¼ 120 km
IEE Proc.-Radar Sonar Navig., Vol. 153, No. 5, October 2006
450
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combinations of B1 and B2 on range resolution of the
system. The following system parameters are used in simu-
lations, the transmit antenna array uses pseudo-circular
array geometry with element number N ¼ 12, the position
vector of each transmit antenna meets the requirement of
(27), f0¼ 7 MHz, Tr¼ 1 s, M ¼ 100, and a single reception
antenna located at the origin of the Cartesian coordinate
system as shown in Fig. 1.
The first example is chosen to demonstrate the synthesis
processing and the coherent integration output of a target
located at distance R0¼ 120 km, with azimuth angle
u ¼ 858, and radial velocity v ¼ 24 m/s. Fig. 3 shows the
output of the synthesis processing. As shown in Figs 3a
and b, a large peak exists at the position corresponding to
target range and azimuth angle, at 3-D range–azimuth
angle profile. Figs. 3c and d show a slice of the 3-D
range–azimuth angle profile with u ¼ 858 and R0¼
120 km, respectively. As illustrated in Fig. 3 target range
and azimuth angle can be estimated from the output of syn-
thesis processing. Fig. 4 shows the outputs of the coherent
integration, which is performed on the output of the syn-
thesis processing at range R0¼ 120 km. As illustrated in
Figs. 4a and b, a large peak also exists at the position corre-
sponding to target Doppler and azimuth angle, at 3-D
Doppler–azimuth angle profile. Fig. 4c shows a slice of
3-D Doppler–azimuth angle profile with u ¼ 858. As
demonstrated inFig.4,target Doppler frequency can beesti-
mated from the output of coherent integration.
The second example is to compare the range resolution
obtained by range transform only and that achieved after
synthesis processing, with various combinations of B1and
B2. Fig. 5a shows the range transformed (dashed line) and
the synthesis processing (solid line) results of a stationary
target located at distance R0¼ 45 km with B1¼ 30 kHz
and B2¼ 15 kHz. As demonstrated in Fig. 5a, the range res-
olution of the system is DR ’ 5 km which approximates to
that of DR1¼ 5 km. Fig. 5b shows the results of the same
target with B1¼ 30 kHz and B2¼ 60 kHz. As illustrated
in Fig. 5b, the range resolution of the system is
DR ’ 2.5 km
DR2¼ 2.5 km. Fig. 5c shows the results of the same target
with B1¼ 30 kHz and B2¼ 30 kHz. As illustrated in
Fig. 5c, the range resolution of the system is DR ’ 3.6 km,
which is determined by the product of two sinc functions
each having a range resolution of about 5 km. Namely,
both B1and B2have approximately the same effects on the
range resolution. The results shown in Fig. 5 well confirm
the analysis in Section 4.3.
which approximatesto that of
Fig. 4
24 m/s
a 3-D doppler–azimuth angle profile
b Contour plot of a
c Slice of a with u ¼ 858
Signal output after synthesis processing and coherent integration with target range of 120 km, azimuth angle of 858 and velocity
IEE Proc.-Radar Sonar Navig., Vol. 153, No. 5, October 2006
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6Conclusions and future work
A novel HFSWR based on SIAP is proposed in this paper.
The equivalent transmit beam patterns are formed by
proper processing the received signals. It has advantages
over the conventional HFSWR for both military and civil
applications, such as good ECCM performance, high
agility and manoeuvrability, good survivability, multiple
fix or moving receive platforms sharing one transmit
antenna array and so on. The signal processing scheme to
obtain equivalent transmit beam patterns is investigated in
detail. Considerations for system parameter selection to
achieve overall best system performance are proposed
and discussed. In particular, a necessary and sufficient con-
dition on choosing the transmit array geometry and transmit
frequencies, which ensures that target range and angle
estimates are uncoupled, is presented.
This paper mainly concerns the signal processing issues
of the proposed HFSWR. For practical implementation,
several problems should be further studied, such as (i) syn-
chronisation between transmit antenna array and receive
platforms, (ii) spatial–temporal super resolution algorithms
to improve target detection performance under multiple
targets environments, (iii) clutter cancellation schemes to
alleviate sea clutter spectrum spread effects introduced by
receive platforms motion, (iv) data fusion techniques to
further improve the detection performance and measure
accuracy by combining the data from multiple receive
platforms.
7 Acknowledgments
This work is supported in part by the National Defense Key
Lab Research Foundation under grant 51431030205ZS0105.
The authors would like to thank the referees for their helpful
comments and suggestions, which have enhanced the
quality and readability of this paper.
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