# 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; · 0.92 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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