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Challenges leading to
the development of SRD
Conflicting
requirements pose challenges to the radar designer
1.0 Waveform
Fundamentals:
- 1.1
Range Resolution is inversely
proportional to pulse bandwidth such that increased ability to resolve
closely space targets in range requires increased pulse bandwidth.
- 1.2
Doppler Resolution is inversely
proportional to pulse duration such that increased ability to resolve
small variations in target velocity (Doppler) requires increased pulse
duration.
- 1.3 Probability of
Detection (Pd)
and Probability of False Alarm
(Pfa) are functions of
the amount of energy bounced off of the target and collected back at
the radar receiver. The energy needed to
meet Pd and Pfa requirements can be delivered at higher peak power in a
short pulse, or at lower peak power in a long pulse.
A
short pulse, by definition is Doppler tolerant meaning
that a single matched filter
will produce
good output even with significant Doppler shift in the target echo. With Doppler tolerant pulses, typically only
a single matched filter is needed for detection, rather than a bank of
matched
filters each tuned for a different Doppler shift. However,
the resulting detections provide
only limited Doppler resolution.
Conversely,
a long pulse will
produce reduced matched filter
output as Doppler shift increases. If a
radar pulse has a significant reduction in matched filter output as a
function
of Doppler shift, it is said to be Doppler
fragile. Long Phase Modulated (PM)
pulses
are typically Doppler fragile pulses. On
the other hand, long Linear FM (LFM) pulses are designed to be more
Doppler tolerant. For Doppler fragile
pulses, a bank of matched
filters is often required to meet detection and Doppler resolution
requirements. The resulting detections
provide improved Doppler resolution.
Coherent pulse integration is a very popular
technique which produces excellent Doppler Resolution while working
with short, Doppler Tolerant waveforms. But
this is a pulse train technique, forcing a design trade-off between
achieving unambiguous Range and unambiguous Doppler. Low PRFs can
be utilized to get unambiguous range. Higher PRFs often utilized
to get more energy on target and to achieve unambiguous
Doppler. In trying to "have it all", multiple PRFs are
often used to "unwind" the range ambiguities. But the
multiple PRFs result in an increased Pfa, forcing an increased
detection threshold to push Pfa back down, thus mandating an increase
in SNR to achieve the desired Pd.
Since
Pd and Pfa requirements
fix the total amount of energy required
for the radar waveform in a given application, a radar transmitter's
peak
power requirement is
determined by the selected pulse duration and duty cycle. It
becomes apparent then that significant
drivers in the design of a radar waveform are the peak power
requirements
imposed
by shorter pulses, the matched filter bank processing requirements
imposed
by longer Doppler fragile pulses, and the Range/Doppler Ambiguity
trade-offs imposed by pulse trains.
2.0 Shorter Doppler
Tolerant Pulses
Short
Doppler tolerant pulses
can be used to avoid the
computational complexities required with a bank of matched filters. However,
a serious limitation to achieving long range surveillance goals with
short-duration Doppler tolerant pulses is the high peak power required
to
achieve adequate pulse energy to obtain target echo with reasonable
probability
of detection.
2.1
EXAMPLE
1 - Impact of reducing Doppler Resolution
Consider
an S-Band air surveillance
radar using a 100 microsecond pulse and 10 kW peak power to produce 1
Joule of
energy per pulse. To achieve Vmax =
+/-1000 m/s and velocity resolution = 100 m/s, a bank of 20 matched
filters is
required.
Now
consider the same radar without
the velocity resolution requirement. By
reducing
the pulse duration to 5 microsecond, we can detect targets within the
+/- 1000
m/s range with only one matched filter. However
the peak power requirement is increased 20 fold to 200 kW to maintain
the same
pulse energy of one joule.
Unfortunately
peak power can not
be increased indefinitely. In newer
radars, solid-state microwave
sources and amplifiers are replacing vacuum tube devices.
Solid-state devices can easily be damaged by
high temperatures. Therefore solid-state
devices typically need to operate with longer, low peak power, high
duty cycle
pulses to prevent failure.
Peak
power limits can stem from
power supply limitations,
inability of the cooling system to extract heat from T/R modules fast
enough,
or even transmission line voltage breakdown (arc discharge),
particularly at
higher carrier frequencies where waveguide dimensions are small. To the extent that peak power limitations
constrain the total available pulse energy, they
constrain the radar's detection
sensitivity.
3.0
Long Pulses
Long
pulses offer a solution to
the peak power problem. However, since
range resolution is inversely
proportional to pulse bandwidth, simply extending pulse duration would
have an
adverse effect on range resolution.
Pulse
compression was developed
as a solution to create long
pulses which address the peak power challenge while preserving the
spectral
bandwidth of short pulses. Pulse
compression imposes high bandwidth modulation onto the long transmitted
pulse
and then demodulates the pulse back to an effectively short
(compressed) pulse
at the receiver. Pulse compression
enables a waveform that simultaneously achieves the high energy
benefits of a
long pulse and the range resolution of a short pulse without the high
peak power
requirements of a high-energy, short pulse.
Two
types of waveforms which are
often used for pulse
compression in surveillance applications are Linear FM (LFM) and
Phase-Modulated (PM) pulses. The
waveform type is selected to optimize the ambiguity function response
and in so
doing affects; detection sensitivity, Doppler resolution, range
resolution, and
clutter discrimination. By selecting a
proper waveform within the scope of the application requirements, the
designer
is provided the opportunity to balance performance with peak power
requirements
and computational complexity.
4.0 Longer Doppler
Tolerant Pulses
To
avoid the performance
penalties imposed by peak power
limitations, and to simultaneously preserve low processing loads, radar
systems
often opt for long Doppler tolerant pulses. Linear
FM (LFM) pulse compression satisfy the
Doppler tolerance
requirement.
LFM
radars typically provide
good detection sensitivity for
long range coverage. They also offer low
processing loads for more practical computational implementations. However these benefits come at the expense of
Doppler resolution. As mentioned earlier, coherent pulse
integration is often implemented to buy back Doppler resolution.
But this comes at the expense of increased computational load, Range /
Doppler Ambiguity trade-offs, and multi the PRF impact to Pfa vs Pd.
5.0 Longer Doppler Fragile
Pulses
To
simultaneously achieve the
benefits of reduced peak power
and high Doppler resolution, radar designers can implement long pulse
durations with Phase-Modulated (PM) pulse compression. PM
pulses can be designed to have highly
localized ambiguity functions which, unlike LFM pulses, provide for
high
resolution in both range and Doppler.
The
ideal analysis of a radar
return utilizes the cross-ambiguity
function. The cross-ambiguity function
presents radar returns in a three dimensional Time, Frequency,
Amplitude space and
is "tuned" for optimal detection sensitivity to the transmitted pulse
waveform. Radars
that employ a PM waveform approximate
the cross-ambiguity function in the receiver by implementing a matched
filter
bank. Each matched filter provides a time
slice of a portion of the cross-ambiguity function.
Multiple matched filters are used to span the
cross-ambiguity function across all Doppler shifts of interest.
The
number of matched filters
needed to approximate the
cross-ambiguity function, is proportional to the maximum target speed,
Doppler resolution
and radar operating frequency. Doppler
fragile waveforms that demand a large number of filters in the matched
filter bank
are often eliminated from consideration due to processing load
practicality
issues.
5.1 EXAMPLE
2 - Impact of Increasing Fc and Vmax
Consider
a radar operating at 2 GHz,
providing surveillance for a maximum target velocity of +/-1700 m/s
by using
a Doppler fragile waveform. This radar
requires
14 filters to provide 250 m/s velocity resolution.
A comparable radar operating at 9.8 GHz,
using the same pulse waveform, tracking targets with maximum Doppler
velocity
of +/-7500 m/s would require 300 filters.
Unfortunately,
the waveforms
that provide the highest
Doppler resolution to meet the most challenging surveillance
requirements
result in the highest computational complexity. At
some point the designer has to trade-off
Doppler resolution
performance for matched filter bank computational practicality.
6.0
Electronic Countermeasures Immunity
Electronic Countermeasures (ECM) present additional challenges to the
design of an effective radar system. Any technique that makes it
difficult for an adversary to anticipate, detect, record or emulate the
radar waveform is going to have an advantage in the Electronic Warfare
(EW) arena. In this regard, long PM waveforms, with their
spread spectrum nature and virtually infinite codes offers advantages
over shorter waveforms and/or over long predictable LFM
waveforms.
7.0 Challenges force
trade-offs
Historically,
radar design has
involved painful trade-offs. Short Doppler
tolerant pulses offer design simplicity, but ultimately incur peak
power limitations
which lead to reduced detection sensitivity. Long
Doppler fragile pulses
provide
target velocity detail but demand extreme computational horsepower
which drives
radar size, weight, power and cost. As a
compromise solution, long Doppler tolerant
pulses enable efficient and practical radar designs, but at the expense
of accurate
target velocity knowledge.
Coherent
Pulse Integration utilized in Pulsed Doppler Radar has become the
standard for achieving good Doppler Resolution while preserving a
shorter Doppler Tolerant Waveform. However this too is a
compromise solution with the Pulse
Train Implementation resulting in a conflict between unambiguous
Range and unambiguous Doppler. Various techniques, such as
multiple PRFs, try to reduce this conflict. But as Werner
Heisenberg might have been wont to say, "you can't have your cake and
eat it too".
8.0 SRD Addresses the
Challenges
SRD
offers an alternative signal
processing platform to provide
accurate range and Doppler data simultaneously while avoiding many of
painful trade-offs typically encountered with conventional radar design. The
processing efficiencies of SRD enable the practical use of long
Doppler fragile
application-matched PM and FM waveforms. By
matching waveform cross ambiguity response
to detection, accuracy,
and resolution goals, SRD provides the detection performance
required for long-range
surveillance and tracking of high-speed, uncooperative targets. Additionally, the ability to utilize long PM waveforms
offers advantages in the area of ECM immunity. Fundamentally,
SRD provides the radar system
designer with a new tool for achieving the most challenging goals
of long
range missile defense surveillance, enabling simultaneous range and
Doppler
extraction, increased detection sensitivity, reduced peak power, and
reduced processing
load.
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