VME 2100 Apr 02 PDF - VITA Technologies

Broadband FIR Moving-Target Indicator
Radar Filters for Low-PRF Applications
By Christopher Repesh
Simple, feed-forward, multi-pulse cancellers are typical in
Doppler processing Moving Target Indicator (MTI) radars for
suppression of fixed targets. Doppler shift allows detection of
targets that have a radial velocity component relative to the
background return. Coherent pulsed radars that preserve transmitted
pulse phase in the receiver demodulation reference signal
allow for recovery of both phase and amplitude effects of
propagation and Doppler shift. Using low pulse repetition frequencies,
unambiguous range measurements with narrowband
static clutter rejection can be achieved with simple binomial,
weighted high-pass Finite Impulse Response (FIR) filters. In
conditions of weather and chaff, the predominant clutter returns
may have Doppler shifts that allow ineffective canceling with
such filters. By using the phase recovery of coherent pulsed
radars, these filters can become broadband cancellers.
Introduction
The analysis described in this article is used in the Peregrine
Coastal Surveillance Radar developed by Metric Systems Inc.
This system is being deployed as part of the Adriatic Coastal
Surveillance Project in the Republic of Croatia. It is a signal processing
and C3 modernization and upgrade of the original ITT
Gilfillan FALCON design. Peregrine has an instrumented MTI
range of 100 km, providing airborne and coastal maritime surveillance
in low-coverage, gap-filler applications.
Transmitted radar pulses can be described using the Binary Phase
Shift Key (BPSK) complex envelope representation for demodulation
purposes. The pulse width determines the frequency width
of the power spectral density. The complex envelope, g(t), is
described in Equations 1-3, where x(t) and y(t) are the quadrature
components, m(t) is the binary code waveform, and A c is the
carrier amplitude.
g(t)=x(t) + jy(t) = R(t)e jθ(t) (1)
m(t) = + 1 (2)
g(t) = jA c m(t) (3)
Code-modulated waveforms used in pulse compression allow for
increased range resolution for a fixed peak transmission power.
The bit duration interval has an inverse effect on the complex
envelope power spectral density. Increased receiver bandwidth
degrades the receiver sensitivity to noise, limiting the effectiveness
of longer code words. If the pulse duration to be code modulated
is shorter than the period of the Doppler modulation, then
the code waveform’s phase information will be preserved for the
matched filter for a given target return.
Figure 1 shows the synchronous detection of the complex envelope
during the coherent local oscillator demodulation stage in
the receiver. Quadrature demodulation avoids loss of signal due
to blind phase effects of a single demodulator as well as resolves
the phase function of the complex envelope. Once the synchronous
detection of the complex envelope is complete, it is
processed in two stages: high-pass FIR filters with sampling at
the pulse repetition rate, and a matched correlator for return code
(target) detection with video A/D sampling at the bit duration
interval. This data forms a 2D array of long time scale range line
rows and short time scale range gate (code bit) columns.
Equations 4-7 define the Doppler modulated complex envelope.
R d (t) = R(t) = y(t) = A c m(t) (4)
θ d (t) = ω d t+θ(t) = w d t+
2
π (5)
I(t) = x d (t) = R d (t) cos (θ d (t)) = A c m(t) cos (ω d t+θ Rx ) (6)
Q(t) = y d (t) = R d (t) sin (θ d (t)) = A c m(t) sin (ω d t+θ Rx ) (7)
The superheterodyne receiver must meet certain MTI stability
requirements. The receiver frequency synthesizer is designed with
an MTI improvement factor that is affected by equipment instabilities.
This factor describes clutter cancellation performance of
MTI relative to average signal gain and is not uniquely determined
by the MTI system itself. The first contribution to phase instabilities
is the synthesizer outputs (stable local oscillator, coherent
oscillator, or STALO, COHO) used in generating and receiving
Re[g d (t)e j cohot ]
LPF
x d (t)
2 cos( coho t )
-2 sin( coho t )
LPF
y d (t)
Figure 1. Synchronous detection of Doppler-shifted pulse return
Reprinted from VMEbus Systems / April 2002
Copyright 2002 / VMEbus Systems

the signal. Phase jitter in the video A/D sampling clock also
causes imperfect clutter cancellation. Sensitivity time control
attenuation for range normalization of nearby small targets contributes
to amplitude and phase distortion. The phase, amplitude,
and timing of the pulse code transmitter driver must also be considered.
The MTI improvement factor has a direct effect on the
stability of the constant receiver phase shift θ Rx in Equations 6-7.
A steadily moving target moving at v d will Doppler shift by ω d
the carrier frequency ω c , thereby altering the complex envelope of
the radar waveform. This is defined in Equation 8, where ω c is the
speed of light. The Doppler frequency is simply the time derivative
of the complex envelope’s phase function, thus the emphasis
on constant receiver phase offset. This Doppler shift is found by
sampling the quadrature phase angle at the pulse repetition frequency.
It is this angle α, defined in Equation 9 and illustrated in
Figure 2, that is measured using consecutive IQ samples at the
pulse repetition interval. This is averaged over many continuous
Q
(I 0 , Q 0 )
d
(I 1 , Q 1 )
Figure 2. Quadrature Doppler phase angle
measurement
I
range bins. The measured α, pulse repetition interval at the time of
measurement, and carrier frequency determine a Doppler velocity
that, combined with any other pulse repetition interval, determines
the weights of the broadband filter when used at that pulse repetition
sampling. Log detection in the IF stage with wide instantaneous
dynamic range (80 dB) can be used to determine range bin
phase samples for appropriate measurement of the Doppler phase
angle over many samples using averaging.
c
v d = 2fc
f d (8)
2πfd 4π f
α d = fpr
= . c
. c f
v pr d (9)
Static Clutter Pulse Cancellers
The fundamental MTI filter component is the high-pass FIR
feed-forward pulse canceller. These filters are guaranteed to be
stable, i.e., all zeroes and no poles in the transfer function. They
are easy to implement in direct form using a tapped delay line.
The binomial weights, given in Equation 10, provide a symmetric
or anti-symmetric unit sample response, depending on the
order of the weights being odd or even. This symmetry guarantees
a linear phase transformation and constant group delay,
which is essential for presenting the filtered pulse compressed
signal to the matched correlator. The nth power of two in the
denominator of Equation 10 normalizes the maximum filter gain
to unity. This is normalized for fixed-point DSP mapping to
avoid accumulative overflow, where the inputs are normalized to
Reprinted from VMEbus Systems / April 2002
Copyright 2002 / VMEbus Systems

avoid multiplicative overflow. Equation 11 gives the time domain
response of the filter, where the order of the filter is q+1. Figure
3 shows the unity gain frequency response of the filter.
Given a pulse repetition frequency, only a small range of Doppler
frequencies can be resolved at that sampling rate. Aliasing in the
MTI filter will periodically stopband at integer multiples of the
sample rate any incoming Doppler signal at that frequency. These
periodic ambiguous rejection stopbands are known as blind
speeds. Pulse-to-pulse staggering eliminates use of feedback to
improve the blind speed response, thereby avoiding the stability
issues of IIR filters. Staggering can be described as cascaded
interpolation and decimation filter stages. Sample rate conversion
maintains detection of targets by scaling the frequency domain
spectrum envelope into the passband of the MTI filter. Low frequency
components are not significantly scaled, so they always
fall in the stopband of the MTI filter. Figure 4 illustrates a fourthorder
response with varying stagger schedules compared to the
uniform sampled filter response. Many stagger ratios have been
described by other researchers on this topic, and they are dependent
on the order of the filter. Those shown in Figure 4 use 10-
20 percent increases in subsequent sampling intervals. A good
stagger ratio can result in only a 10 dB loss of signal in the blind
speed zones while maintaining the low-frequency stopband.
Dynamic Clutter Pulse Cancellers
Clutter-locked MTI uses a measured average Doppler shift of a
given volume of clutter that is used to control an offset frequency
oscillator that shifts clutter into the rejection notch. The first stage of
the process is to take the complex conjugate of the synchronous
detected signal to obtain a symmetric weight distribution in the
completed derivation. Both h 1 and h 2 in Figure 5 are high-pass FIR
transfer functions as defined by Equations 10 and 11 and can have
any order as needed. The frequency oscillator performs a down con-
dB
0
-10
Order
2
3
4
5
-20
-30
-40
0 0.1 0.2 0.3 0.4 0.5
Figure 3. MTI high-pass filter response vs. normalized frequency
f
f
pr
dB
0
Stagger Ratio 1
Stagger Ratio 2
Stagger Ratio 3
Stagger Ratio 4
No Stagger
-20
-40
-60 0 0.5 1 1.5 2 2.5 3
Figure 4. MTI fourth-order HPF response with stagger vs. normalized frequency
f
f
pr
Reprinted from VMEbus Systems / April 2002
Copyright 2002 / VMEbus Systems

version role that shifts the mean moving clutter component into the
rejection notch of h 2 . The purpose of h 1 is to remove any static clutter
component before the frequency translation stage, preventing
upconverting it into the passband of h 2 . The resulting complex signal
r(n) will be filtered in both the in-phase and quadrature-phase
components and is defined in Equation 12.
The order of h 1 is q+1, and the order of h 2 is p+1. Expanding the
complex exponential term using Euler’s identity and multiplying
it across the responses of the first stage filter, the r(n) response
can then be expanded into its in-phase and quadrature components.
Doppler cross-modulation terms are defined for each component
by Equations 13-16, where t pr is the reciprocal of the
pulse repetition frequency.
b(k) =
(–1) k (q)!
2 q .
(q – k)!(k)!
(10)
q
out(n) = Σb(k)in(n – k) (11)
k =0
x d (n) - jy d (n) h 1 (n) h 2 (n) r(n)
The filter response shown in Figure 7 illustrates the stopband
improvement of Equation 12. This response is computed using a
C-band carrier of 5.4 GHz, Doppler velocity-tuned weighting at
8.5 meters/sec, and a pulse repetition frequency of 1538 Hz. A
third-order filter is used on the input stage, and a fourth-order filter
is used on the output stage. For comparison, a third- and
fourth-order static filter response highlights the significant rejection
capability of the broadband filter. The filter sidelobe
centered around 0.1 on the normalized scale is the Doppler component
that passed the input stage filter and is not fully downconverted
into the rejection notch of the output stage filter. This
sidelobe will increase as the notch frequency is increased. Pulseto-pulse
stagger degrades the low frequency stopband of the
broadband filter and is not recommended for dynamic clutter
cancellation. Rather, a group-to-group pulse stagger is recommended
to alleviate the blind zone cancellations.
IpI(n) = cos (2π f d
. nt pr ) (13)
IpQ(n) = sin (2π f d
. nt pr ) (14)
QpI(n) = sin (2π f d
. nt pr ) (15)
QpQ(n) = cos (2π f d
. nt pr ) (16)
e jn d
Figure 5. Doppler clutter-locked MTI transfer
function
The expansion and collection of Equation 12 will result in two
real terms and two imaginary summation terms. Each term will
have the same weight distribution as shown in Figure 6 except
for the replacement of the Doppler cross-modulation term. The
subscript naming identifies how the weight vector contributes to
r(n). The letter on the left indicates to which component the
weight dot product contributes, and the letter on the right indicates
the input component with which to be dot product.
Equations 17 and 18 give the real and imaginary responses of
r(n), respectively.
Conclusion
Metric System’s Peregrine is operated in a dynamic MTI mode
configuration. It has an instrumented 100km range in a normal
MTI mode using four-pulse static filtering with pulse-to-pulse
staggering in favorable weather conditions. Log video is monitored
for threshold switching into a 70km range special MTI
mode when inclement weather, high seas, or chaff conditions are
detected. Six-pulse dynamic clutter MTI suppression against
moving volumetric clutter simultaneous with low velocity ground
and heavy sea clutter is performed in special MTI mode. The
adaptive broadband weights are computed and applied in an openloop
fashion based on an accumulated log video clutter map that
directs phase video sampling in appropriate sectors. Dynamic
clutter characteristics typically have a velocity mean around ±20
r(n) =
p
Σb 2 (k)
l = 0
q
q
Σ b 1 (k)x d (n – l – k) – j Σ b 1 (k)y d (n – l – k) e j(n – l) ω d (12)
k = 0
k = 0
b 1 (q)b 2 (p)IpI(0)
b 1 (q – 1)b 2 (p)IpI(0) + b 1 (q)b 2 (p – 1) IpI(1)
.
b 1 (0)b 2 (p)IpI(0) + b 1 (1)b 2 (p –1)IPI(1) + . . . +b 1 (q – 1)b 2 (1)IpI(p – 1) + b 1 (q)b 2 (0)IpI(p)
.
b 1 (0)b 2 (1)IpI(p – 1) +b 1 (1)b 2 (0)IpI(p)
b 1 (0)b 2 (0)IpI(p)
Figure 6. b IPI (k) weight vector, where k begins from top (0) to bottom (p+q)
Re[r(n)]=
Im[r(n)]=
p + q
p + q
Σ b IPI (k)x d (n – k) + Σb IPQ (k)y d (n – k) (17)
k = 0
k = 0
p + q
p + q
Σ b QPI (k)x d (n – k) + Σ b QPQ (k)y d (n – k) (18)
k = 0
k = 0
Reprinted from VMEbus Systems / April 2002
Copyright 2002 / VMEbus Systems

dB
0
-10
6th order
clutter-locked
3rd order static
4th order static
6th order
clutter-locked
stagger
-20
-30
-40
-50
-60 0 0.5 1 1.5 2 2.5 3
f
f
pr
Figure 7. Doppler clutter-locked MTI response
meters/sec with a spectrum width near 1 meter/sec. The filters are
applied independently on the in-phase and quadrature-phase components.
In addition, the Peregrine performs the matched correlation
on these channels independently before applying its modulus.
It uses hard-limited (binary), phase-coded pulse compression
on a 17.65 ms pulse transmission at 63-bit or 127-bit resolution.
Instrumented pulse repetition frequencies vary from 1200 Hz to
1600 Hz, depending on mode, range, and stagger.
The Peregrine signal processing cabinet consists of:
■ A VMEbus chassis using a VMIC VMIVME-7740 Pentium
III based single-board bus master
■ Two Pentek 4290 quad TMS320C6201 DSP boards
■ A Metric-designed, RAM-based trigger generator card
The VMIC board is clocked at 800 MHz running Windows2000
real-time acquisition of the DSP results and synchronization of
the triggers. Pentek’s 6211 12-bit A/D mezzanine modules sample
two three-channel video signals (I, Q, and log video). A highelevation
beam path and a low-elevation beam path provide
improved target detection. All DSP algorithms are optimized
using the Texas Instruments Code Composer Studio V1.20 and
loaded using Pentek’s Swiftnet product. The post-processing programs
for multiple clutter map classification, sliding window
correlation detection, and plot extractions for tracking filter are
compiled using Visual Studio 6.0.
In summary, coherent phase video processing using Doppler filtering
and pulse compression in dedicated DSP hardware is combined
with log-detected clutter mapping and mode control to provide constant
false alarm rate detections to non-coherent short-term detection
and long-term clutter residue censor processes.
References
Eaves, Jerry L., and Edward K. Reedy, Principles of Modern Radar,
Von Nostrand, 1987.
Couch, Leon W., Digital and Analog Communication Systems, Prentice
Hall, 1997.
Kehtarnavaz, Nasser, and Burc Simsek, C6x-Based Digital Signal
Processing, Prentice Hall, 2000.
Hayes, Monson H., Digital Signal Processing, Schaum’s Outline Series,
McGraw-Hill, 1999.
Christopher Repesh is a senior signal processing engineer
for Metric Systems, a specialized manufacturer of threatradar-simulator
systems, airborne instrumentation, RF datalink
communications, and tactical surveillance radar systems. He
has been instrumental in re-engineering and migrating legacy
video processing hardware in ITT Gilfillan’s FALCON to a
COTS software-based solution. Prior to joining Metric Systems,
Christopher was an associate research engineer with Mission
Research Corporation, developing and employing advanced
computational electromagnetic software to diagnose the effectiveness
of operationally viable antenna designs and the effects
of high-power EMP discharges. Christopher holds a BSEE
from the University of Texas at Arlington and an MSEE from
the University of Florida, Gainesville. He currently works in
Fort Walton Beach, FL.
For more information, contact:
Metric Systems
645 Anchors Street • Fort Walton Beach, FL 32548
Tel: 850-302-3000 • Fax: 850-302-3371
Web site: www.metricsys.com
Reprinted from VMEbus Systems / April 2002
Copyright 2002 / VMEbus Systems