Belcher, M.L., Nessmith, J.T., Wiltse, J.C. “Radar”
The Electrical Engineering Handbook
Ed. Richard C. Dorf
Boca Raton: CRC Press LLC, 2000
41
Radar
41.1Pulse Radar
Overview of Pulsed Radars?Critical Subsystem Design and
Technology?Radar Performance Prediction?Radar
Waveforms?Detection and Search?Estimation and Tracking
41.2Continuous Wave Radar
CW Doppler Radar?FM/CW Radar?Interrupted Frequency-
Modulated CW (IFM/CW)?Applications?Summary Comments
41.1 Pulse Radar
Melvin L. Belcher and Josh T. Nessmith
Overview of Pulsed Radars
Basic Concept of Pulse Radar Operation
The basic operation of a pulse radar is depicted in Fig. 41.1. The radar transmits a pulse of RF energy and then
receives returns (reflections) from desired and undesired targets. Desired targets may include space, airborne,
and sea- and/or surface-based vehicles. They can also include the earth’s surface and the atmosphere, depending
on the application. Undesired targets are termed clutter. Clutter sources include the ground, natural and man-
made objects, sea, atmospheric phenomena, and birds. Short-range/low-altitude radar operation is often con-
strained by clutter since the multitude of undesired returns masks returns from targets of interest such as aircraft.
The range, azimuth angle, elevation angle, and range rate can be directly measured from a return to estimate
target position and velocity. Signature data can be extracted by measuring the amplitude, phase, and polarization
of the return.
Pulse radar affords a great deal of design and operational flexibility. Pulse duration and pulse rate can be
tailored to specific applications to provide optimal performance. Modern computer-controlled multiple-func-
tion radars exploit this capability by choosing the best waveform from a repertoire for a given operational mode
and interference environment automatically.
Radar Applications
The breadth of pulse radar applications is summarized in Table 41.1. Radar applications can be grouped into
search, track, and signature measurement applications. Search radars are used for tracking but have relatively
large range and angle errors. The search functions favor broad beam-widths and low bandwidths in order to
efficiently search over a large spatial volume. As indicated in Table 41.1, search is preferably performed in the
lower frequency bands. The antenna pattern is narrow in azimuth and has a cosecant pattern in elevation to
provide acceptable coverage from the horizon to the zenith.
Tracking radars are typically characterized by a narrow beamwidth and moderate bandwidth in order to
provide accurate range and angle measurements on a given target. The antenna pattern is a pencil beam with
approximately the same dimensions in azimuth and elevation. Track is usually conducted at the higher frequency
bands in order to minimize the beamwidth for a given antenna aperture area. After each return from a target
Melvin L. Belcher
Georgia Tech Research Institute
Josh T. Nessmith
Georgia Tech Research Institute
James C. Wiltse
Georgia Tech Research Institute
? 2000 by CRC Press LLC
is received, the range and angle are measured and input into a track filter. Track filtering smooths the data to
refine the estimate of target position and velocity. It also predicts the target’s flight path to provide range gating
and antenna pointing control to the radar system.
Signature measurement applications include remote sensing of the environment as well as the measurement
of target characteristics. In some applications, synthetic aperture radar (SAR) imaging is conducted from aircraft
or satellites to characterize land usage over broad areas. Moving targets that present changing aspect to the
radar can be imaged from airborne or ground-based radars via inverse synthetic aperture radar (ISAR) tech-
niques. As defined in the subsection “Resolution and Accuracy,” cross-range resolution improves with increasing
antenna extent. SAR/ISAR effectively substitutes an extended observation interval over which coherent returns
are collected from different target aspect angles for a large antenna structure that would not be physically
realizable in many instances.
In general, characterization performance improves with increasing frequency because of the associated
improvement in range, range rate, and cross-range resolution. However, phenomenological characterization to
support environmental remote sensing may require data collected across a broad swath of frequencies.
A multiple-function phased array radar generally integrates these functions to some degree. Its design is
usually driven by the track function. Its operational frequency is generally a compromise between the lower
FIGURE 41.1 Pulse radar.
TABLE 41.1 Radar Bands
Band
Frequency
Range Principal Applications
HF 3–30 MHz Over-the-horizon radar
VHF 30–300 MHz Long-range search
UHF 300–1000 MHz Long-range surveillance
L 1000–2000 MHz Long-range surveillance
S 2000–4000 MHz Surveillance
Long-range weather characterization
Terminal air traffic control
C 4000–8000 MHz Fire control
Instrumentation tracking
X 8–12 GHz Fire control
Air-to-air missile seeker
Marine radar
Airborne weather characterization
Ku 12–18 GHz Short-range fire control
Remote sensing
Ka 27–40 GHz Remote sensing
Weapon guidance
V 40–75 GHz Remote sensing
Weapon guidance
W 75–110 GHz Remote sensing
Weapon guidance
? 2000 by CRC Press LLC
frequency of the search radar and the higher frequency desired for the tracking radar. The degree of signature
measurement implemented to support such functions as noncooperative target identification depends on the
resolution capability of the radar as well as the operational user requirements. Multiple-function radar design
represents a compromise among these different requirements. However, implementation constraints, multiple-
target handling requirements, and reaction time requirements often dictate the use of phased array radar systems
integrating search, track, and characterization functions.
Critical Subsystem Design and Technology
The major subsystems making up a pulse radar system are depicted in Fig. 41.2. The associated interaction
between function and technology is summarized in this subsection.
Antenna
The radar antenna function is to first provide spatial directivity to the transmitted EM wave and then to intercept
the scattering of that wave from a target. Most radar antennas may be categorized as mechanically scanning or
electronically scanning. Mechanically scanned reflector antennas are used in applications where rapid beam
scanning is not required. Electronic scanning antennas include phased arrays and frequency scanned antennas.
Phased array beams can be steered to any point in their field-of-view, typically within 10 to 100 ms, depending
on the latency of the beam steering subsystem and the switching time of the phase shifters. Phased arrays are
desirable in multiple function radars since they can interleave search operations with multiple target tracks.
There is a Fourier transform relationship between the antenna illumination function and the far-field antenna
pattern. Hence, tapering the illumination to concentrate power near the center of the antenna suppresses
sidelobes while reducing the effective antenna aperture area. The phase and amplitude control of the antenna
illumination determines the achievable sidelobe suppression and angle measurement accuracy.
Perturbations in the illumination due to the mechanical and electrical sources distort the illumination
function and constrain performance in these areas. Mechanical illumination error sources include antenna
shape deformation due to sag and thermal effects as well as manufacturing defects. Electrical illumination error
is of particular concern in phased arrays where sources include beam steering computational error and phase
shifter quantization. Control of both the mechanical and electrical perturbation errors is the key to both low
sidelobes and highly accurate angle measurements. Control denotes that either tolerances are closely held and
maintained or that there must be some means for monitoring and correction. Phased arrays are attractive for
low sidelobe applications since they can provide element-level phase and amplitude control.
FIGURE 41.2 Radar system architecture.
? 2000 by CRC Press LLC
TABLE 41.2
Pulse Radar Transmitter Technology
Transmitter
The transmitter function is to amplify waveforms to a power level sufficient for target detection and estimation.
There is a general trend away from tube-based transmitters toward solid-state transmitters. In particular, solid-
state transmit/receive modules appear attractive for constructing phased array radar systems. In this case, each
radiating element is driven by a module that contains a solid-state transmitter, phase shifter, low-noise amplifier,
and associated control components. Active arrays built from such modules appear to offer significant reliability
advantages over radar systems driven from a single transmitter. However, microwave tube technology continues
to offer substantial advantages in power output over solid-state technology. Transmitter technologies are
summarized in Table 41.2.
Receiver and Exciter
This subsystem contains the precision timing and frequency reference source or sources used to derive the
master oscillator and local oscillator reference frequencies. These reference frequencies are used to downconvert
received signals in a multiple-stage superheterodyne architecture to accommodate signal amplification and
interference rejection. The receiver front end is typically protected from overload during transmission through
the combination of a circulator and a transmit/receive switch.
The exciter generates the waveforms for subsequent transmission. As in signal processing, the trend is toward
programmable digital signal synthesis because of the associated flexibility and performance stability.
Signal and Data Processing
Digital processing is generally divided between two processing subsystems, i.e., signals and data, according to
the algorithm structure and throughput demands. Signal processing includes pulse compression, Doppler
filtering, and detection threshold estimation and testing. Data processing includes track filtering, user interface
support, and such specialized functions as electronic counter-counter measures (ECCM) and built-in test (BIT),
as well as the resource management process required to control the radar system.
The signal processor is often optimized to perform the repetitive complex multiply-and-add operations
associated with the fast Fourier transform (FFT). FFT processing is used for implementing pulse compression
via fast convolution and for Doppler filtering. Fast convolution consists of taking the FFT of the digitized
receiver output, multiplying it by the stored FFT of the desired filter function, and then taking the inverse FFT
Mode of Maximum Demonstrated Peak/ Typical Typical
Technology Operation Frequency (GHz) Average Power (kW) Gain Bandwidth
Thermionic
Magnetron Oscillator 95 1 MW/500 W @ X-band n/a Fixed–10%
Helix traveling Amplifier 95 4 kW/400 W @ X-band 40–60 dB Octave/multioctave
wave tube (TWT)
Ring-loop TWT Amplifier 18 8 kW/200 W @ X-band 40–60 dB 5–15%
Coupled-cavity TWT Amplifier 95 100 kW/25 kW @ X-band 40–60 dB 5–15%
Extended interaction Oscillator 220 1 kW/10 W @ 95 GHz n/a 0.2% (elec.)
oscillator (EIO) 4% (mech.)
Extended interaction
Klystron (EIK) Amplifier 140 1 kW/10 W @ 95 GHz 40–50 dB 0.5–1%
Klystron Amplifier 35 50 kW/5 kW @ X-band 30–60 dB 0.1–2% (inst.)
1–10% (mech.)
Crossed-field Amplifier 18 500 kW/1 kW @ X-band 10–20 dB 5–15%
amplifier (CFA)
Solid state
Silicon BJT Amplifier 5 300 W/30 W @1 GHz 5–10 dB 10–25%
GaAs FET Amplifier 30 15 W/5 W @ X-band 5–10 dB 5–20%
Impatt diode Oscillator 140 30 W/10 W @ X-band n/a Fixed–5%
Source: Tracy V. Wallace, Georgia Tech Research Institute, Atlanta, Georgia.
? 2000 by CRC Press LLC
of the resulting product. Fast convolution results in significant computational saving over performing the time-
domain convolution of returns with the filter function corresponding to the matched filter. The signal processor
output can be characterized in terms of range gates and Doppler filters corresponding approximately to the
range and Doppler resolution, respectively.
In contrast, the radar data processor typically consists of a general-purpose computer with a real-time
operating system. Fielded radar data processors range from microcomputers to mainframe computers, depend-
ing on the requirements of the radar system. Data processor software and hardware requirements are signifi-
cantly mitigated by off loading timing and control functions to specialized hardware. This timing and control
subsystem typically functions as the two-way interface between the data processor and the other radar sub-
systems. The increasing inclusion of BIT (built-in-test) and built-in calibration capability in timing and control
subsystem designs promises to result in significant improvement in fielded system performance.
Radar Performance Prediction
Radar Line-of-Sight
With the exception of over-the-horizon (OTH) radar systems, which exploit either sky-wave bounce or ground-
wave propagation modes and sporadic ducting effects at higher frequencies, surface and airborne platform
radar operation is limited to the refraction-constrained line of sight. Atmospheric refraction effects can be
closely approximated by setting the earth’s radius to 4/3 its nominal value in estimating horizon-limited range.
The resulting line-of-sight range is depicted in Fig. 41.3 for a surface-based radar, an airborne surveillance
radar, and a space-based radar.
FIGURE 41.3 Maximum line-of-sight range for surface-based radar, an airborne surveillance radar, and a space-based
radar.
? 2000 by CRC Press LLC
As evident in the plot, airborne and space-based surveillance radar systems offer significant advantages in
the detection of low-altitude targets that would otherwise be masked by earth curvature and terrain features
from surface-based radars. However, efficient clutter rejection techniques must be used in order to detect targets
since surface clutter returns will be present at almost all ranges of interest.
Radar Range Equation
The radar range equation is commonly used to estimate radar system performance, given that line-of-sight
conditions are satisfied. This formulation essentially computes the signal-to-noise ratio (S/N) at the output of
the radar signal processor. In turn, S/N is used to provide estimates of radar detection and position measurement
performance as described in the subsections “Detection and Search” and “Estimation and Tracking.” S/N can
be calculated in terms of the number of pulses coherently integrated over a single coherent processing interval
(CPI) using the radar range equation such that
(41.1)
where P is peak transmitter power output, D is directivity of the transmit antenna, A is effective aperture area
of the receive antenna in meters squared, T
p
is pulse duration, s is radar cross section in square meters, N
p
is
the number of coherently integrated pulses within the coherent processing interval, R is range to target in
meters, L
t
is system ohmic and nonohmic transmit losses, L
rn
is system nonohmic receive losses, L
sp
is signal
processing losses, k is Boltzmann’s constant (1.38 ′ 10
–23
K), and T
s
is system noise temperature, including
receive ohmic losses (kelvin).
At X-band and above it may also be necessary to include propagation loss due to atmospheric absorption
[Blake, 1986]. This form of the radar range equation is applicable to radar systems using pulse compression or
pulse Doppler waveforms as well as the unmodulated single-pulse case. In many applications, average power
is a better measure of system performance than peak power since it indicates the S/N improvement achievable
with pulse integration over a given interval of time. Hence, the radar range equation can be modified such that
(41.2)
where P
a
is average transmitter power and T
c
is coherent processing interval (CPI).
The portion of time over which the transmitter is in operation is referred to as the radar duty cycle. The
average transmitter power is the product of duty cycle and peak transmitter power. Duty cycle ranges from less
than 1% for typical noncoherent pulse radars to somewhat less than 50% for high pulse repetition frequency
(PRF) pulse Doppler radar systems. High PRF systems are sometimes referred to as interrupted continuous
wave (ICW) systems because they operate essentially as a CW radar system with transmitter and receiver
alternately turned on and off.
The CPI is the period over which returns are collected for coherent processing functions such as integration
and Doppler filtering. The CPI can be estimated as the product of the number of coherently integrated pulses
and the interval between pulses. Noncoherent integration is less efficient and alters the statistical character of
the signal and interference.
Antenna Directivity and Aperture Area
The directivity of the antenna is
(41.3)
SN
PDATN
RLLLkT
pp
trnsps
/ =
s
p()4
24
SN
PDAT
RLLLkT
ac
trnsps
/ =
s
p()4
24
D
A
=
4
2
ph
l
? 2000 by CRC Press LLC
where h is aperture efficiency and l is radar carrier wavelength. Aperture inefficiency is due to the antenna
illumination factor.
The common form of the radar range equation uses power gain rather than directivity. Antenna gain is equal
to the directivity divided by the antenna losses. In the design and analysis of modern radars, directivity is a
more convenient measure of performance because it permits designs with distributed active elements, such as
solid-state phased arrays, to be assessed to permit direct comparison with passive antenna systems. Beamwidth
and directivity are inversely related; a highly directive antenna will have a narrow beamwidth. For typical design
parameters,
(41.4)
where q
az
and q
el
are the radar azimuth and elevation beamwidths, respectively, in milliradians.
Radar Cross Section
In practice, the radar cross section (RCS) of a realistic target must be considered a random variable with an
associated correlation interval. Targets are composed of multiple interacting scatters so that the composite
return varies in magnitude with the constructive and destructive interference of the contributing returns. The
target RCS is typically estimated as the mean or median of the target RCS distribution. The associated correlation
interval indicates the rate at which the target RCS varies over time. RCS fluctuation degrades target detection
performance at moderate to high probability of detection.
The median RCS of typical targets is given in Table 41.3. The composite RCS measured by a radar system
may be composed of multiple individual targets in the case of closely spaced targets such as a bird flock.
Loss and System Temperature Estimation
Sources of S/N loss include ohmic and nonohmic (mismatch) loss in the antenna and other radio frequency
components, propagation effects, signal processing deviations from matched filter operation, detection thresh-
olding, and search losses. Scan loss in phased array radars is due to the combined effects of the decrease in
projected antenna area and element mismatch with increasing scan angle.
TABLE 41.3 Median Target RCS (m
2
)
Carrier Frequency, GHz 1–2 3 5 10 17
Aircraft (nose/tail avg.)
Small propeller 2 3 2.5
Small jet (Lear) 1 1.5 1 1.2
T38-twin jet, F5 2 2–3 2 1–2/6
T39-Sabreliner 2.5 10/8 9
F4, large fighter 5–8/5 4–20/10 4 4
737, DC9, MD80 10 10 10 10 10
727, 707, DC8-type 22–40/15 40 30 30
DC-10-type, 747 70 70 70 70
Ryan drone 2/1
Standing man (180 lb) 0.3 0.5 0.6 0.7 0.7
Automobiles 100 100 100 100 100
Ships-incoming (′10
4
m
2
)
4K tons 1.6 2.3 3.0 4.0 5.4
16K tons 13 18 24 32 43
Birds
Sea birds 0.002 0.001–0.004 0.004
Sparrow, starling, etc. 0.001 0.001 0.001 0.001 0.001
Slash marks indicate different set.
D
azel
=
10
7
qq
? 2000 by CRC Press LLC
Search operations impose additional losses due to target position uncertainty. Because the target position is
unknown before detection, the beam, range gate, and Doppler filter will not be centered on the target return.
Hence, straddling loss will occur as the target effectively straddles adjacent resolution cells in range and Doppler.
Beamshape loss is a consequence of the radar beam not being pointed directly at the target so that there is a
loss in both transmit and receive antenna gain. In addition, detection threshold loss associated with radar
system adaptation to interference must be included [Nathanson, 1991]).
System noise temperature estimation corresponds to assessing the system thermal noise floor referenced to
the antenna output. Assuming the receiver hardware is at ambient temperature, the system noise temperature
can be estimated as
T
s
= T
a
+ 290 (L
ro
F – 1) (41.5)
where T
a
is the antenna noise temperature, L
ro
is receive ohmic losses, and F is the receiver noise figure.
In phased array radars, the thermodynamic temperature of the antenna receive beam-former may be signif-
icantly higher than ambient, so a more complete analysis is required. The antenna noise temperature is
determined by the external noise received by the antenna from solar, atmospheric, earth surface, and other
sources.
Table 41.4 provides typical loss and noise temperature budgets for several major radar classes. In general,
loss increases with the complexity of the radar hardware between the transmitter/receiver and the antenna
radiator. Reflector antennas and active phased arrays impose relatively low loss, while passive array antennas
impose relatively high loss.
Resolution and Accuracy
The fundamental resolution capabilities of a radar system are summarized in Table 41.5. In general, there is a
trade-off between mainlobe resolution corresponding to the nominal range, Doppler, and angle resolution, and
effective dynamic range corresponding to suppression of sidelobe components. This is evident in the use of
weighting to suppress Doppler sidebands and angle sidelobes at the expense of broadening the mainlobe and
S/N loss.
Cross range denotes either of the two dimensions orthogonal to the radar line of sight. Cross-range resolution
in real-aperture antenna systems is closely approximated by the product of target range and radar beamwidth
in radians. Attainment of the nominal ISAR/SAR cross-range resolution generally requires complex signal
processing to generate a focused image, including correction for scatterer change in range over the CPI.
The best accuracy performance occurs for the case of thermal noise-limited error. The resulting accuracy is
the resolution of the radar divided by the square root of the S/N and an appropriate monopulse or interpolation
factor. In this formulation, the single-pulse S/N has been multiplied by the number of pulses integrated within
the CPI as indicated in Eqs. (41.1) and (41.2).
TABLE 41.4 Typical Microwave Loss and System Temperature Budgets
Mechanically Scanned Electronically Scanned
Reflector Slotted Solid-State
Antenna Array Phased Array
Nominal losses
Transmit loss, L
t
(dB) 1 1.5 0.5
Nonohmic receiver loss, L
r
(dB) 0.5 0.5 0.1
Signal processing loss, L
sp
(dB) 1.4 1.4 1.4
Scan loss (dB) N/A N/A 30 log
[cos (scan angle)]
Search losses, L
DS
Beam shape (dB) 3 3 3
Range gate straddle (dB) 0.5 0.5 0.5
Doppler filter straddle (dB) 0.5 0.5 0.5
Detection thresholding (dB) 1 1 1
System noise temperature (kelvin) 500 600 400
? 2000 by CRC Press LLC
In practice, accuracy is also constrained by environmental effects, target characteristics, and instrumentation
error as well as the available S/N. Environmental effects include multipath and refraction. Target glint is
characterized by an apparent wandering of the target position because of coherent interference effects associated
with the composite return from the individual scattering centers on the target. Instrumentation error is
minimized with alignment and calibration but may significantly constrain track filter performance as a result
of the relatively long correlation interval of some error sources.
Radar Range Equation for Search and Track
The radar range equation can be modified to directly address performance in the two primary radar missions:
search and track.
Search performance is basically determined by the capability of the radar system to detect a target of specific
RCS at a given maximum detection range while scanning a given solid angle extent within a specified period
of time. S/N can be set equal to the minimum value required for a given detection performance, S/N*r, while
R can be set to the maximum required target detection range, R
max
. Manipulation of the radar range equation
results in the following expression:
(41.6)
where W is the solid angle over which search must be performed (steradians), T
fs
is the time allowed to search
W by operational requirements, and L
os
is the composite incremental loss associated with search.
The left-hand side of the equation contains radar design parameters, while the right-hand side is determined
by target characteristics and operational requirements. The right-hand side of the equation is evaluated to
determine radar requirements. The left-hand side of the equation is evaluated to determine if the radar design
meets the requirements.
The track radar range equation is conditioned on noise-limited angle accuracy as this measure stresses radar
capabilities significantly more than range accuracy in almost all cases of interest. The operational requirement
is to maintain a given data rate track providing a specified single-measurement angle accuracy for a given number
of targets with specified RCS and range. Antenna beamwidth, which is proportional to the radar carrier wave-
length divided by antenna extent, impacts track performance since the degree of S/N required for a given
measurement accuracy decreases as the beamwidth decreases. Track performance requirements can be bounded as
TABLE 41.5 Resolution and Accuracy
Dimension Nominal Resolution Noise-Limited Accuracy
Angle
Range
Doppler
SAR/ISAR
a, taper broadening factor, typically ranging from 0.89
(unweighted) to 1.3 (Hamming); d, antenna extent in azi-
muth/elevation; B, waveform bandwidth; K
m
, monopulse slope
factor, typically on the order of 1.5; K
i
, interpolation factor, typ-
ically on the order of 1.8; Dq, line-of-sight rotation of target
relative to radar over CPI.
al
d
-------
al
dK
m
2SN¤
------------------------------
aC
2B
--------
aC
2BK
i
2SN¤
---------------------------------
a
CPI
----------
a
CPIK
i
2SN¤
------------------------------------
al
2Dq
----------
al
2DqK
i
2SN¤
------------------------------------
PA
LLL L T
S
N
R
T
a
trsposs
r
fs
3
?
è
?
?
?
÷
×
max
k
4
16
W
s
? 2000 by CRC Press LLC
(41.7)
where r is the single-target track rate, N
t
is the number of targets under track in different beams, s
q
is the
required angle accuracy standard deviation (radians), and s is the RCS. In general, a phased array radar antenna
is required to support multiple target tracking when N
t
> 1.
Incremental search losses are suppressed during single-target-per-beam tracking. The beam is pointed as
closely as possible to the target to suppress beamshape loss. The tracking loop centers the range gate and
Doppler filter on the return. Detection thresholding loss is minimal since the track range window is small.
Radar Waveforms
Pulse Compression
Typical pulse radar waveforms are summarized in Table 41.6. In most cases, the signal processor is designed
to closely approximate a matched filter. As indicated in Table 41.5, the range and Doppler resolution of any
match-filtered waveform are inversely proportional to the waveform bandwidth and duration, respectively.
Pulse compression, using modulated waveforms, is attractive since S/N is proportional to pulse duration rather
than bandwidth in matched filter implementations. Ideally, the intrapulse modulation is chosen to attain
adequate range resolution and range sidelobe suppression performance while the pulse duration is chosen to
provide the required sensitivity. Pulse compression waveforms are characterized as having a time bandwidth
product (TBP) significantly greater than unity, in contrast to an unmodulated pulse, which has a TBP of
approximately unity.
Pulse Repetition Frequency
The radar system pulse repetition frequency (PRF) determines its ability to unambiguously measure target
range and range rate in a single CPI as well as determining the inherent clutter rejection capabilities of the
radar system. In order to obtain an unambiguous measurement of target range, the interval between radar
pulses (1/PRF) must be greater than the time required for a single pulse to propagate to a target at a given
range and back. The maximum unambiguous range is then given by C/(2 · PRF) where C is the velocity of
electromagnetic propagation.
TABLE 41.6Selected Waveform Characteristics
Time Range
Bandwidth Sidelobes S/N Loss Range/Doppler ECM/EMI
Comments Product (dB) (dB) Coupling Robustness
Unmodulated No pulse ~1 Not applicable 0 No Poor
compression
Linear Linearly swept >10 Unweighted: –13.5 0 Yes Poor
frequency over bandwidth Weighted: >–40
a
0.7–1.4
modulation
Nonlinear FM Multiple variants Waveform Waveform 0 Waveform Fair
specific specific specific
Barker N-bit biphase ￡ 13 (N) –20 log(N) 0 No Fair
LRS N-bit biphase ~N; >64/pulse
a
~–10 log (N) 0 No Good
Frank N-bit polyphase ~N ~–10 log (p
2
N) 0 Limited Good
(N = integer
2
)
Frequency N subpulses ~N
2
Waveform Waveform Good
coding noncoincidental specific specific
in time and ? Periodic 0.7–1.40
frequency ? Pseudorandom 0
a
Constraint due to typical technology limitations rather than fundamental waveform characteristics.
PA
LLLT
kk
rNR
a
trsps
m
t
3
4
22
4
2
5
l
h
ss
q
3
? 2000 by CRC Press LLC
Returns from moving targets and clutter sources are offset from the radar carrier frequency by the associated
Doppler frequency. As a function of range rate, R·, the Doppler frequency, f
D
, is given by 2R· /l. A coherent
pulse train samples the returns’ Doppler modulation at the PRF. Most radar systems employ parallel sampling
in the in-phase and quadrature baseband channels so that the effective sampling rate is twice the PRF. The
target’s return is folded in frequency if the PRF is less than the target Doppler.
Clutter returns are primarily from stationary or near-stationary surfaces such as terrain. In contrast, targets
of interest often have a significant range rate relative to the radar clutter. Doppler filtering can suppress returns
from clutter. With the exception of frequency ambiguity, the Doppler filtering techniques used to implement
pulse Doppler filtering are quite similar to those described for CW radar in Section 41.2. Ambiguous measure-
ments can be resolved over multiple CPIs by using a sequence of slightly different PRFs and correlating
detections among the CPIs [Morris, 1988].
Detection and Search
Detection processing consists of comparing the amplitude of each range gate/Doppler filter output with a
threshold. A detection is reported if the amplitude exceeds that threshold. A false alarm occurs when noise or
other interference produces an output of sufficient magnitude to exceed the detection threshold. As the detection
threshold is decreased, both the detection probability and the false alarm probability increase. S/N must be
increased to enhance detection probability while maintaining a constant false alarm probability.
As noted in the subsection “Radar Cross Section,” RCS fluctuation effects must be considered in assessing
detection performance. The Swerling models which use chi-square probability density functions (PDFs) of 2
and 4 degrees of freedom (DOF) are commonly used for this purpose [Nathanson, 1991]. The Swerling 1 and
2 models are based on the 2 DOF PDF and can be derived by modeling the target as an ensemble of independent
scatterers of comparable magnitude. This model is considered representative of complex targets such as aircraft.
The Swerling 3 and 4 models use the 4 DOF PDF and correspond to a target with a single dominant scatterer
and an ensemble of lesser scatterers. Missiles are sometimes represented by Swerling 2 and 4 models. The
Swerling 1 and 3 models presuppose slow fluctuation such that the target RCS is constant from pulse to pulse
within a scan. In contrast, the RCS of Swerling 2 and 4 targets is modeled as independent on a pulse to pulse basis.
Single-pulse detection probabilities for nonfluctuating, Swerling 1/2, and Swerling 3/4 targets are depicted
in Fig. 41.4. This curve is based on a typical false alarm number corresponding approximately to a false alarm
probability of 10
–6
. The difference in S/N required for a given detection probability for a fluctuating target
relative to the nonfluctuating case is termed the fluctuation loss.
The detection curves presented here and in most other references presuppose noise-limited operation. In
many cases, the composite interference present at the radar system output will be dominated by clutter returns
or electromagnetic interference such as that imposed by hostile electronic countermeasures. The standard
textbook detection curves cannot be applied in these situations unless the composite interference is statistically
similar to thermal noise with a Gaussian PDF and a white power spectral density. The presence of non-Gaussian
interference is generally characterized by an elevated false alarm probability. Adaptive detection threshold
estimation techniques are often required to search for targets in environments characterized by such
interference.
Estimation and Tracking
Measurement Error Sources
Radars measure target range and angle position and, potentially, Doppler frequency. Angle measurement
performance is emphasized here since the corresponding cross-range error dominates range error for most
practical applications. Target returns are generally smoothed in a tracking filter, but tracking performance is
largely determined by the measurement accuracy of the subject radar system. Radar measurement error can be
characterized as indicated in Table 41.7.
The radar design and the alignment and calibration process development must consider the characteristics
and interaction of these error components. Integration of automated techniques to support alignment and
? 2000 by CRC Press LLC
calibration is an area of strong effort in modern radar design that can lead to significant performance improve-
ment in fielded systems.
As indicated previously, angle measurement generally is the limiting factor in measurement accuracy. Target
azimuth and elevation position is primarily measured by a monopulse technique in modern radars though
early systems used sequential lobing and conical scanning. Specialized monopulse tracking radars utilizing
FIGURE 41.4Detection probabilities for various target fluctuation models.
TABLE 41.7Radar Measurement Error
Random errors Those errors that cannot be predicted except on a statistical basis. The magnitude of the random error
can be termed the precision and is an indication of the repeatability of a measurement.
Bias errors A systematic error whether due to instrumentation or propagation conditions. A nonzero mean value of
a random error.
Systematic error An error whose quantity can be measured and reduced by calibration.
Residual systematic Those errors remaining after measurement and calibration. A function of
error the systematic and random errors in the calibration process.
Accuracy The magnitude of the rms value of the residual systematic and random errors.
False Alarm Number = 10
6
Swerling Cases
1 & 2
Swerling Cases
3 & 4
Steady Target
Probability of Detection, P
D
Signal-to-Noise Ratio Per Pulse, dB
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 +5 +10 +15 +20 +25 +30
? 2000 by CRC Press LLC
reflectors have achieved instrumentation and S/N angle residual systematic error as low as 50 mrad. Phased
array antennas have achieved a random error of less than 60 mrad, but the composite systematic residual errors
remain to be measured. The limitations are primarily in the tolerance on the phase and amplitude of the
antenna illumination function.
Figure 41.5 shows the monopulse beam patterns. The first is the received sum pattern that is generated by
a feed that provides the energy from the reflector or phased array antenna through two ports in equal amounts
and summed in phase in a monopulse comparator shown in Fig. 41.6. The second is the difference pattern
generated by providing the energy through the same two ports in equal amounts but taken out with a phase
difference of p radians, giving a null at the center. A target located at the center of the same beam would receive
a strong signal from the sum pattern with which the target could be detected and ranged. The received difference
pattern would produce a null return, indicating the target was at the center of the beam. If the target were off
the null, the signal output or difference voltage would be almost linear proportional to the distance off the
center (off-axis), as shown in the figure. This output of the monopulse processor is the real part of the dot
product of the complex sums and the difference signals divided by the absolute magnitude of the sum signal
squared, i.e.,
(41.8)
The random instrumentation measurement errors in the angle estimator are caused by phase and amplitude
errors of the antenna illumination function. In reflector systems, such errors occur because of the position of
the feedhorn, differences in electrical length between the feed and the monopulse comparator, mechanical
precision of the reflector, and its mechanical rotation. In phased array radars, these errors are a function of the
phase shifters, time delay units, and combiners between the antenna elements and the monopulse comparator
as well as the precision of the array. Although these errors are random, they may have correlation intervals
considerably longer than the white noise considered in the thermal-noise random error and may depend upon
FIGURE 41.5Monopulse beam patterns and difference voltage: (a) sum (S); (b) difference (D); (c) difference voltage.
FIGURE 41.6Monopulse comparator.
E
1
E
2
S
D
l/2
l/2
e
d
=
×
é
?
ê
ù
?
ú
Re
SD
S**
2
? 2000 by CRC Press LLC
the flight path of the target. For a target headed radially from or toward the radar, the correlation period of
angle-measurement instrumental errors is essentially the tracking period. For crossing targets, the correlation
interval may be pulse to pulse.
As in the estimate of range, the propagation effects of refraction and multipath also enter into the tracking
error. The bias error in range and elevation angle by refraction can be estimated as
D R = 0.007 N
s
cosecant E
o
(meters) (41.9)
D E
o
= N
s
cot E
o
(mrad)
where N
s
is the surface refractivity and E
o
is the elevation angle [Barton and Ward, 1984].
One can calculate the average error in multipath. However, one cannot correct for it as in refraction since
the direction of the error cannot be known in advance unless there are controlled conditions such as in a
carefully controlled experiment. Hence, the general approach is to design the antenna sidelobes to be as low
as feasible and accept the multipath error that occurs when tracking close to the horizon. There has been
considerable research to find means to reduce the impact, including using very wide bandwidths to separate
the direct path from the multipath return.
Tracking Filter Performance
Target tracking based on processing returns from multiple CPIs generally provides a target position and velocity
estimate of greater accuracy than the single-CPI measurement accuracy delineated in Table 41.5. In principle,
the error variance of the estimated target position with the target moving at a constant velocity is approximately
4/n · s
2
m
where n is the number of independent measurements processed by the track filter and s
m
is the single
measurement accuracy. In practice, the variance reduction factor afforded by a track filter is often limited to
about an order of magnitude because of the reasons summarized in the following paragraphs.
Track filtering generally provides smoothing and prediction of target position and velocity via a recursive
prediction-correction process. The filter predicts the target’s position at the time of the next measurement based
on the current smoothed estimates of position, velocity, and possibly acceleration. The subsequent difference
between the measured position at this time and the predicted position is used to update the smoothed estimates.
The update process incorporates a weighting vector that determines the relative significance given the track
filter prediction versus the new measurement in updating the smoothed estimate.
Target model fidelity and adaptivity are fundamental issues in track filter mechanization. Independent one-
dimensional tracking loops may be implemented to control pulse-to-pulse range gate positioning and antenna
pointing. The performance of one-dimensional polynomial algorithms, such as the alpha-beta filter, to track
targets from one pulse to the next and provide modest smoothing is generally adequate. However, one-
dimensional closed-loop tracking ignores knowledge of the equations of motion governing the target so that
their smoothing and long-term prediction performance is relatively poor for targets with known equations of
motion. In addition, simple one-dimensional tracking-loop filters do not incorporate any adaptivity or measure
of estimation quality.
Kalman filtering addresses these shortcomings at the cost of significantly greater computational complexity.
Target equations of motion are modeled explicitly such that the position, velocity, and potentially higher-order
derivatives of each measurement dimension are estimated by the track filter as a state vector. The error associated
with the estimated state vector is modeled via a covariance matrix that is also updated with each iteration of
the track filter. The covariance matrix determines the weight vector used to update the smoothed state vector
in order to incorporate such factors as measurement S/N and dynamic target maneuvering.
Smoothing performance is constrained by the degree of a priori knowledge of the target’s kinematic motion
characteristics. For example, Kalman filtering can achieve significantly better error reduction against ballistic
or orbital targets than against maneuvering aircraft. In the former case the equations of motion are explicitly
known, while the latter case imposes motion model error because of the presence of unpredictable pilot or
guidance system commands. Similar considerations apply to the fidelity of the track filter’s model of radar
measurement error. Failure to consider the impact of correlated measurement errors may result in underesti-
mating track error when designing the system.
? 2000 by CRC Press LLC
Defining Terms
Coherent:Integration where magnitude and phase of received signals are preserved in summation.
Noncoherent:Integration where only the magnitude of received signals is summed.
Phased array:Antenna composed of an aperture of individual radiating elements. Beam scanning is imple-
mented by imposing a phase taper across the aperture to collimate signals received from a given angle
of arrival.
Pulse compression: The processing of a wideband, coded signal pulse, of initially long time duration and
low-range resolution, to result in an output pulse of time duration corresponding to the reciprocal of
the bandwidth.
Radar cross section (RCS): A measure of the reflective strength of a radar target; usually represented by the
symbol s, measured in square meters, and defined as 4p times the ratio of the power per unit solid angle
scattered in a specified direction of the power unit area in a plane wave incident on the scatterer from a
specified direction.
Related Topics
35.1 Maxwell Equations?69.1 Modulation and Demodulation
References
D.K. Barton and H.R. Ward, Handbook of Radar Measurement, Dedham, Mass.: Artech, 1984.
L.V. Blake, Radar Range-Performance Analysis, Dedham, Mass.: Artech, 1986.
J.L. Eaves and E.K. Reedy, Eds., Principles of Modern Radar, New York: Van Nostrand, 1987.
G.V. Morris, Airborne Pulsed Doppler Radar, Dedham, Mass.: Artech, 1988.
F.E. Nathanson, Radar Design Principles, 2nd ed., New York: McGraw-Hill, 1991.
Further Information
M.I. Skolnik, Ed., Radar Handbook, 2nd ed., New York: McGraw-Hill, 1990.
IEEE Standard Radar Definitions, IEEE Standard 686-1990, April 20, 1990.
41.2 Continuous Wave Radar
James C. Wiltse
Continuous wave (CW) radar employs a transmitter which is on all or most of the time. Unmodulated CW
radar is very simple and is able to detect the Doppler-frequency shift in the return signal from a target which
has a component of motion toward or away from the transmitter. While such a radar cannot measure range,
it is used widely in applications such as police radars, motion detectors, burglar alarms, proximity fuzes for
projectiles or missiles, illuminators for semiactive missile guidance systems (such as the Hawk surface-to-air
missile), and scatterometers (used to measure the scattering properties of targets or clutter such as terrain
surfaces) [Nathanson, 1991; Saunders, 1990; Ulaby and Elachi, 1990].
Modulated versions include frequency-modulated (FM/CW), interrupted frequency-modulated (IFM/CW),
and phase-modulated. Typical waveforms are indicated in Fig. 41.7. Such systems are used in altimeters, Doppler
navigators, proximity fuzes, over-the-horizon radar, and active seekers for terminal guidance of air-to-surface
missiles. The term continuous is often used to indicate a relatively long waveform (as contrasted to pulse radar
using short pulses) or a radar with a high duty cycle (for instance, 50% or greater, as contrasted with the typical
duty cycle of less than 1% for the usual pulse radar). As an example of a long waveform, planetary radars may
transmit for up to 10 hours and are thus considered to be CW [Freiley et al., 1992]. Another example is
interrupted CW (or pulse-Doppler) radar, where the transmitter is pulsed at a high rate for 10 to 60% of the
total time [Nathanson, 1991]. All of these modulated CW radars are able to measure range.
? 2000 by CRC Press LLC
The first portion of this section discusses concepts, principles of operation, and limitations. The latter portion
describes various applications. In general, CW radars have several potential advantages over pulse radars. Advan-
tages include simplicity and the facts that the transmitter leakage is used as the local oscillator, transmitter spectral
spread is minimal (not true for wide-deviation FM/CW), and peak power is the same as (or only a little greater
than) the average power. This latter situation means that the radar is less detectable by intercepting equipment.
The largest disadvantage for CW radars is the need to provide antenna isolation (reduce spillover) so that
the transmitted signal does not interfere with the receiver. In a pulse radar, the transmitter is off before the
receiver is enabled (by means of a duplexer and/or receiver-protector switch). Isolation is frequently obtained
in the CW case by employing two antennas, one for transmit and one for reception. When this is done, there
is also a reduction of close-in clutter return from rain or terrain. A second disadvantage is the existence of
noise sidebands on the transmitter signal which reduce sensitivity because the Doppler frequencies are relatively
close to the carrier. This is considered in more detail below.
CW Doppler Radar
If a sine wave signal were transmitted, the return from a moving target would be Doppler-shifted in frequency
by an amount given by the following equation:
(41.10)
where f
T
= transmitted frequency; c = velocity of propagation, 3210
8
m/s; and v
r
= radial component of velocity
between radar and target.
FIGURE 41.7 Waveforms for the general class of CW radar: (a) continuous sine wave CW; (b) frequency modulated CW;
(c) interrupted CW; (d) binary phase-coded CW.
f
vf
c
d
rT
==
2
Doppler frequency
? 2000 by CRC Press LLC
RADIO ENGINEERING DURING
WORLD WAR II
o single event had a greater effect on electrical engineering than the Second World War. The
years from 1939 to 1945 saw a radical change in the field of electrical engineering as it was
transformed from a specialty with well-defined applications, primarily in power and commu-
nications, into the source for the most powerful and pervasive technologies of the 20th century.
In the heat of war, radio engineering was transformed into electronics. Electronics became a technology
to harness the most advanced and subtle knowledge of the very parts of matter itself, manipulating
N
? 2000 by CRC Press LLC
Using Eq. (41.10) the Doppler frequencies have been calculated for several speeds and are given in Table 41.8.
As may be seen, the Doppler frequencies at 10 GHz (X-band) range from 30 Hz to about 18 kHz for a speed
range between 1 and 600 mph. The spectral width of these Doppler frequencies will depend on target fluctuation
and acceleration, antenna scanning effects, frequency variation in oscillators or components (for example, due
TABLE 41.8Doppler Frequencies for Several Transmitted
Frequencies and Various Relative Speeds
Microwave
Relative Speed
Frequency—f
T
1 m/s 300 m/s 1 mph 600 mph
3 GHz 20 Hz 6 kHz 8.9 Hz 5.4 kHz
10 GHz 67 Hz 20 kHz 30 Hz 17.9 kHz
35 GHz 233 Hz 70 kHz 104 Hz 63 kHz
95 GHz 633 Hz 190 kHz 283 Hz 170 kHz
electrons and electromagnetic waves in an effort not simply to communicate, but to detect, control, and
even as some saw it, think. The tremendous pressures of wartime development forged a new relationship
between engineers and physical scientists. More and more the realms and tasks of both overlapped and
advances in electronics made use of the latest findings, theories, and techniques of physicists and chemists,
while scientific discovery came to rely progressively more on the instrumentation created by engineers.
This merging of science and technology was one of the war’s greatest legacies and has continued to shape
our times.
The enormous demands that the war put on the world also marked the indispensable and strategic
place of electric power. Electric power rose to the status of necessity, not only increasing the general
industrial consumption of power, but also highlighting specialized uses of electricity, such as the pro-
duction of aluminum and explosives, that were critical to the pursuit of the war. In Europe, the targeting
of power plants and dams by both allied and axis bombers provided proof of electricity’s central place
in modern warfare.
The postwar years were ones of growth and change, accompanied by tensions and conflicts both within
the engineering community and in society at large. The war was, again, followed by unprecedented
prosperity, but at this time it was in a world where the dangers and possible consequences of international
conflict were distressingly obvious. The efforts of engineers were, therefore, divided between the creation
of a consumer society, powered by electricity and tuned by electronics, and the demands of national and
international security. Alongside this division was another division of the engineering community. The
split between the AIEE and the IRE became less and less justifiable and in the coming decades, this
problem was solved, as engineers everywhere recognized their common interests. (Courtesy of the IEEE
Center for the History of Electrical Engineering.)
to microphonism from vibrations), but most significantly, by the spectrum of the transmitter, which inevitably
will have noise sidebands that extend much higher than these Doppler frequencies, probably by orders of
magnitude. At higher microwave frequencies the Doppler frequencies are also higher and more widely spread.
In addition, the spectra of higher frequency transmitters are also wider, and, in fact, the transmitter noise-
sideband problem is usually worse at higher frequencies, particularly at millimeter wavelengths (i.e., above
30 GHz). These characteristics may necessitate frequency stabilization or phase locking of transmitters to
improve the spectra.
Simplified block diagrams for CW Doppler radars are shown in Fig. 41.8. The transmitter is a single-frequency
source, and leakage (or coupling) of a small amount of transmitter power serves as a local oscillator signal in
the mixer. The transmitted signal will produce a Doppler-shifted return from a moving target. In the case of
scatterometer measurements, where, for example, terrain reflectivity is to be measured, the relative motion may
be produced by moving the radar (perhaps on a vehicle) with respect to the stationary target [Wiltse et al.,
1957]. The return signal is collected by the antenna and then also fed to the mixer. After mixing with the
transmitter leakage, a difference frequency will be produced which is the Doppler shift. As indicated in
Table 41.8, this difference is apt to range from low audio to over 100 kHz, depending on relative speeds and
choice of microwave frequency. The Doppler amplifier and filters are chosen based on the information to be
obtained, and this determines the amplifier bandwidth and gain, as well as the filter bandwidth and spacing.
The transmitter leakage may include reflections from the antenna and/or nearby clutter in front of the antenna,
as well as mutual coupling between antennas in the two-antenna case.
The detection range for such a radar can be obtained from the following [Nathanson, 1991]:
(41.11)
where R=the detection range of the desired target.
–P
T
=the average power during the pulse.
G
T
=the transmit power gain of the antenna with respect to an omnidirectional radiator.
FIGURE 41.8Block diagrams of CW-Doppler radar systems: (a) single antenna type; (b) double antenna type.
R
PGLALLLL
kTbSN
TTTeRpasT
s
4
2
4
=
d
p()()/
? 2000 by CRC Press LLC
L
T
=the losses between the transmitter output and free space including power dividers, waveguide
or coax, radomes, and any other losses not included in A
e
.
A
e
=the effective aperture of the antenna, which is equal to the projected area in the direction of
the target times the efficiency.
L
R
=the receive antenna losses defined in a manner similar to the transmit losses.
L
p
=the beam shape and scanning and pattern factor losses.
L
a
=the two-way-pattern propagation losses of the medium; often expressed as exp(–2μR), where
μ is the attenuation constant of the medium and the factor 2 is for a two-way path.
L
s
=signal-processing losses that occur for virtually every waveform and implementation.
d
T
=the radar cross-sectional area of the object that is being detected.
k=Boltzmann’s constant (1.38210
–23
W-s/K).
T
s
=system noise temperature.
b=Doppler filter or speedgate bandwidth.
S/N=signal-to-noise ratio.
S
min
=the minimum detectable target-signal power that, with a given probability of success, the radar
can be said to detect, acquire, or track in the presence of its own thermal noise or some external
interference. Since all these factors (including the target return itself) are generally noiselike,
the criterion for a detection can be described only by some form of probability distribution
with an associated probability of detection P
D
and a probability that, in the absence of a target
signal, one or more noise or interference samples will be mistaken for the target of interest.
While the Doppler filter should be a matched filter, it usually is wider because it must include the target
spectral width. There is usually some compensation for the loss in detectability by the use of postdetection
filtering or integration. The S/N ratio for a CW radar must be at least 6 dB, compared with the value of 13 dB
required with pulse radars when detecting steady targets [Nathanson, 1991, p. 449].
The Doppler system discussed above has a maximum detection range based on signal strength and other
factors, but it cannot measure range. The rate of change in signal strength as a function of range has sometimes
been used in fuzes to estimate range closure and firing point, but this is a relative measure.
FM/CW Radar
The most common technique for determining target range is the use of frequency modulation. Typical mod-
ulation waveforms include sinusoidal, linear sawtooth, or triangular, as illustrated in Fig. 41.9. For a linear
sawtooth, a frequency increasing with time may be transmitted. Upon being reflected from a stationary point
target, the same linear frequency change is reflected back to the receiver, except it has a time delay which is
related to the range to the target. The time is T = (2R)/c, where R is the range. The received signal is mixed
with the transmit signal, and the difference or beat frequency (F
b
) is obtained. (The sum frequency is much
higher and is rejected by filtering.) For a stationary target this is given by
(41.12)
where DF = frequency deviation and F
m
= modulation rate.
The beat frequency is constant except near the turn-around region of the sawtooth, but, of course, it is
different for targets at different ranges. (If it is desired to have a constant intermediate frequency for different
ranges, which is a convenience in receiver design, then the modulation rate or the frequency deviation must
be adjusted.) Multiple targets at a variety of ranges will produce multiple-frequency outputs from the mixer
and frequently are handled in the receiver by using multiple range-bin filters.
If the target is moving with a component of velocity toward (or away) from the radar, then there will be a
Doppler frequency component added to (or subtracted from) the difference frequency (F
b
), and the Doppler
will be slightly higher at the upper end of the sweep range than at the lower end. This will introduce an
F
R
c
FF
bm
=××
4
D
? 2000 by CRC Press LLC
uncertainty or ambiguity in the measurement of range, which may or may not be significant, depending on
the parameters chosen and the application. For example, if the Doppler frequency is low (as in an altimeter)
and/or the difference frequency is high, the error in range measurement may be tolerable. For the symmetrical
triangular waveform, a Doppler less than F
b
averages out, since it is higher on one-half of a cycle and lower on
the other half. With a sawtooth modulation, only a decrease or increase is noted, since the frequencies produced
in the transient during a rapid flyback are out of the receiver passband. Exact analyses of triangular, sawtooth,
dual triangular, dual sawtooth, and combinations of these with noise have been carried out by Tozzi [1972].
Specific design parameters are given later in this chapter for an application utilizing sawtooth modulation in
a missile terminal guidance seeker.
FIGURE 41.9Frequency vs. time waveforms for FM/CW radar: (a) sinusoidal, (b) linear sawtooth, (c) triangular
modulations.
? 2000 by CRC Press LLC
For the case of sinusoidal frequency modulation the spectrum consists of a series of lines spaced away from
the carrier by the modulating frequency or its harmonics. The amplitudes of the carrier and these sidebands
are proportional to the values of the Bessel functions of the first kind (J
n
, n = 0, … 1, … 2, … 3, …), whose
argument is a function of the modulating frequency and range. By choosing a particular modulating frequency,
the values of the Bessel functions and thus the characteristics of the spectral components can be influenced.
For instance, the signal variation with range at selected ranges can be optimized, which is important in fuzes.
A short-range dependence that produces a rapid increase in signal, greater than that corresponding to the
normal range variation, is beneficial in producing well-defined firing signals. This can be accomplished by
proper choice of modulating frequency and filtering to obtain the signal spectral components corresponding
to the appropriate order of the Bessel function. In a similar fashion, spillover and/or reflections from close-in
objects can be reduced by filtering to pass only certain harmonics of the modulating frequency (F
m
). Receiving
only frequencies near 3F
m
results in considerable spillover rejection, but at a penalty of 4 to 10 dB in signal-
to-noise [Nathanson, 1991].
For the sinusoidal modulation case, Doppler frequency contributions complicate the analysis considerably.
For details of this analysis the reader is referred to Saunders [1990] or Nathanson [1991].
Interrupted Frequency-Modulated CW (IFM/CW)
To improve isolation during reception, the IFM/CW format involves preventing transmission for a portion of
the time during the frequency change. Thus, there are frequency gaps, or interruptions, as illustrated in
Fig. 41.10. This shows a case where the transmit time equals the round-trip propagation time, followed by an
equal time for reception. This duty factor of 0.5 for the waveform reduces the average transmitted power by
3 dB relative to using an interrupted transmitter. However, the improvement in the isolation should reduce the
system noise by more than 3 dB, thus improving the signal-to-noise ratio [Piper, 1987]. For operation at short
range, Piper points out that a high-speed switch is required [1987]. He also points out that the ratio of frequency
deviation to beat frequency should be an even integer and that the minimum ratio is typically 6, which produces
an out-of-band loss of 0.8 dB.
IFM/CW may be compared with pulse compression radar if both use a wide bandwidth. Pulse compression
employs a “long” pulse (i.e., relatively long for a pulse radar) with a large frequency deviation or “chirp.” A
long pulse is often used when a transmitter is peak-power limited, because the longer pulse produces more
FIGURE 41.10 Interrupted FM/CW waveform. (Source: S.O. Piper, “MMW seekers,” in Principles and Applications of
Millimeter Wave Radar, N. Currie and C. E. Brown, Eds., Norwood, Mass.: Artech House, 1987, p. 683. With permission.)
? 2000 by CRC Press LLC
energy and gives more range to targets. The frequency deviation is controlled in a predetermined way (frequently
a linear sweep) so that a matched filter can be used in the receiver. The large time-bandwidth product permits
the received pulse to be compressed in time to a short pulse in order to make an accurate range measurement.
A linear-sawtooth IFM/CW having similar pulse length, frequency deviation, and pulse repetition rate would
thus appear similar, although arrived at from different points of view.
Applications
Space does not permit giving a full description of the many applications mentioned at the beginning of this
chapter, but several will be discussed.
Radar Proximity Fuzes
Projectiles or missiles designed to be aimed at ships or surface land targets often need a height-of-burst (HOB)
sensor (or target detection device) to fire or fuze the warhead at a height of a few meters. There are two primary
generic methods of sensing or measuring height to generate the warhead fire signal. The most obvious, and
potentially the most accurate, is to measure target round trip propagation delay employing conventional radar
ranging techniques. The second method employs a simple CW Doppler radar or variation thereof, with loop
gain calibrated in a manner that permits sensing the desired burst height by measurement of target return
signal amplitude and/or rate of change. Often the mission requirements do not justify the complexity and cost
of the radar ranging approach. Viable candidates are thus narrowed down to variations on the CW doppler fuze.
In its simplest form, the CW Doppler fuze consists of a fractional watt RF oscillator, homodyne detector, Doppler
amplifier, Doppler envelope detector, and threshold circuit. When the Doppler envelope amplitude derived from
the returned signal reaches the preset threshold, a fire signal is generated. The height at which the fire signal occurs
depends on the radar loop gain, threshold level, and target reflectivity. Fuze gain is designed to produce the desired
height of burst under nominal trajectory angle and target reflectivity conditions, which may have large fluctuations
due to glint effects, and deviations from the desired height due to antenna gain variations with angle, target
reflectivity, and fuze gain tolerances are accepted. A loop gain change of 6 dB (2 to 1 in voltage), whether due to
a change in target reflection coefficient, antenna gain, or whatever, will result in a 2 to 1 HOB change.
HOB sensitivity to loop gain factors can be reduced by utilizing the slope of the increasing return signal, or
so-called rate-of-rise. Deriving HOB solely from the rate-of-rise has the disadvantage of rendering the fuze
sensitive to fluctuating signal levels such as might result from a scintillating target. The use of logarithmic
amplifiers decreases the HOB sensitivity to the reflectivity range. An early (excessively high) fire signal can
occur if the slope of the signal fluctuations equals the rate-of-rise threshold of the fuze. In practice a compromise
is generally made in which Doppler envelope amplitude and rate-of-rise contribute in some proportion of HOB.
Another method sometimes employed to reduce HOB sensitivity to fuze loop gain factors and angle of fall
is the use of FM sinusoidal modulation of suitable deviation to produce a range correlation function comprising
the zero order of a Bessel function of the first kind. The subject of sinusoidal modulation is quite complex, but
has been treated in detail by Saunders [1990, pp. 1422–1446 and 144.41]. The most important aspects of fuze
design have to do with practical problems such as low cost, small size, ability to stand very high-g accelerations,
long life in storage, and countermeasures susceptibility.
Police Radars
Down-the-road police radars, which are of the CW Doppler type, operate at 10.525, 24.150, or in the 33.4 to
36.0 GHz range, frequencies approved in the United States by the Federal Communications Commission. Half-
power beamwidths are typically in the 0.21 to 0.31 radian range. The sensitivity is usually good enough to
provide a range exceeding 800 meters. Target size has a dynamic range of 30 dB (from smallest cars or
motorcycles to large trucks). This means that a large target can be seen well outside the antenna 3-dB point at
a range exceeding the range of a smaller target near the center of the beam. Thus there can be uncertainty
about which vehicle is the target. Fisher [1992] has given a discussion of a number of the limitations of these
systems, but in spite of these factors probably a hundred thousand have been built.
The designs typically have three amplifier gains for detection of short, medium, or maximum range targets,
plus a squelch circuit so that sudden spurious signals will not be counted. The Doppler signal is integrated and
this direct current provides a speed readout. Provision is made for calibration to assure the accuracy of the readings.
? 2000 by CRC Press LLC
Altimeters
A very detailed discussion of FM/CW altimeters has been given by Saunders [1990, pp. 14.34–14.36], in which
he has described modern commercial products built by Bendix and Collins. The parameters will be summarized
below and if more information is needed, the reader may want to turn to other references [Saunders, 1990;
Bendix Corp., 1982; and Maoz et al., 1991]. In his material, Saunders gives a general overview of modern
altimeters, all of which use wide-deviation FM at a low modulation frequency. He discusses the limitations on
narrowing the antenna pattern, which must be wide enough to accommodate attitude changes of the aircraft.
Triangular modulation is used, since for this waveform the Doppler averages out, and dual antennas are
employed. There may be a step error or quantization in height (which could be a problem at low altitudes),
due to the limitation of counting zero crossings. A difference of one zero crossing (i.e., 1/2 Hz) corresponds
to 3/4 meter for a frequency deviation of 100 MHz. Irregularities are not often seen, however, since meter
response is slow. Also, if terrain is rough, there will be actual physical altitude fluctuations. Table 41.9 shows
some of the altimeters’ parameters. These altimeters are not acceptable for military aircraft, because their
relatively wide-open front ends make them potentially vulnerable to electronic countermeasures. A French
design has some advantages in this respect by using a variable frequency deviation, a difference frequency that
is essentially constant with altitude, and a narrowband front-end amplifier [Saunders, 1990].
Doppler Navigators
These systems are mainly sinusoidally modulated FM/CW radars employing four separate downward looking
beams aimed at about 15 degrees off the vertical. Because commercial airlines have shifted to nonradar forms
of navigation, these units are designed principally for helicopters. Saunders [1990] cites a particular example
of a commercial unit operating at 13.3 GHz, employing a Gunn oscillator as the transmitter, with an output
power of 50 mW, and utilizing a 30-kHz modulation frequency. A single microstrip antenna is used. A low-
altitude equipment (below 15,000 feet), the unit weighs less than 12 pounds. A second unit cited has an output
power of 300 mW, dual antennas, dual modulating frequencies, and an altitude capability of 40,000 feet.
Millimeter-Wave Seeker for Terminal Guidance Missile
Terminal guidance for short-range (less than 2 km) air-to-surface missiles has seen extensive development in
the last decade. Targets such as tanks are frequently immersed in a clutter background which may give a radar
return that is comparable to that of the target. To reduce the clutter return in the antenna footprint, the antenna
beamwidth is reduced by going to millimeter wavelengths. For a variety of reasons the choice is usually a
frequency near 35 or 90 GHz. Antenna beamwidth is inversely proportional to frequency, so in order to get a
reduced beamwidth we would normally choose 90 GHz; however, more deleterious effects at 90 GHz due to
atmospheric absorption and scattering can modify that choice. In spite of small beamwidths, the clutter is a
significant problem, and in most cases signal-to-clutter is a more limiting condition than signal-to-noise in
determining range performance. Piper [1987] has done an excellent job of analyzing the situation for 35- and
90-GHz pulse radar seekers and comparing those with a 90-GHz FM/CW seeker. His FM/CW results will be
summarized below.
In his approach to the problem, Piper gives a summary of the advantages and disadvantages of a pulse system
compared to the FM/CW approach. Most of these have already been covered in earlier sections, but one difficulty
for the FM/CW can be emphasized again. That is the need for a highly linear sweep, and, because of the desire
for the wide bandwidth, this requirement is accentuated. The wide bandwidth is desired in order to average
the clutter return and to smooth the glint effects. In particular, glint occurs from a complex target because of
TABLE 41.9Parameters for Two Commercial Altimeters
Modulation Frequency Prime Weight Radiated
Frequency Deviation Power (pounds) Power
Bendix 150 Hz 130 MHz 30 W 11*
ALA-52A
Collins 100 kHz 100 MHz 8 350 mW
ALT-55
*Not including antenna and indicator.
? 2000 by CRC Press LLC
the vector addition of coherent signals scattered back to the receiver from various reflecting surfaces. At some
angles the vectors may add in phase (constructively) and at others they may cancel, and the effect is specifically
dependent on wavelength. For a narrowband system, glint may provide a very large signal change over a small
variation of angle, but, of course, at another wavelength it would be different. Thus, very wide bandwidth is
desirable from this smoothing point of view, and typical numbers used in millimeter-wave radars are in the
450- to 650-MHz range. Piper chose 480 MHz.
Another tradeoff involves the choice of FM waveform. Here the use of a triangular waveform is undesirable
because the Doppler frequency averages out and Doppler compensation is then required. Thus the sawtooth
version is chosen, but because of the large frequency deviation desired, the difficulty of linearizing the frequency
sweep is made greater. In fact many components must be extremely wideband, and this generally increases cost
and may adversely affect performance. On the other hand, the difference frequency (F
b
) and/or the intermediate
frequency (F
IF
) will be higher and thus further from the carrier, so the phase noise will be lower. After discussing
the other tradeoffs, Piper chose 60 MHz for the beat frequency.
With a linear FM/CW waveform, the inverse of the frequency deviation provides the theoretical time
resolution, which is 2.1 ns for 480 MHz (or range resolution of 0.3 meter). For an RF sweep linearity of 300 kHz,
the range resolution is actually 5 meters at the 1000-meter nominal search range. (The system has a mechanically
scanned antenna.) An average transmitting power of 25 mW was chosen, which was equal to the average power
of the 5-W peak IMPATT assumed for the pulse system. The antenna diameter was 15 cm. For a target radar
cross section of 20 m
2
and assumed weather conditions, the signal-to-clutter and signal-to-noise ratios were
calculated and plotted for ranges out to 2 km and for clear weather or 4 mm per hour rainfall. The results show
that for 1 km range the target-to-clutter ratios are higher for the FM/CW case than the pulse system in clear
weather or in rain, and target-to-clutter is the determining factor.
Summary Comments
From this brief review it is clear that there are many uses for CW radars, and various types (such as fuzes) have
been produced in large quantities. Because of their relative simplicity, today there are continuing trends toward
the use of digital processing and integrated circuits. In fact, this is exemplified in articles describing FM/CW
radars built on single microwave integrated circuit chips [Maoz et al., 1991; Chang et al., 1995].
Defining Terms
Doppler-frequency shift: The observed frequency change between the transmitted and received signal pro-
duced by motion along a line between the transmitter/receiver and the target. The frequency increases
if the two are closing and decreases if they are receding.
Missile terminal guidance seeker: Located in the nose of a missile, a small radar with short-range capability
which scans the area ahead of the missile and guides it during the terminal phase toward a target such
as a tank.
Pulse Doppler: A coherent radar, usually having high pulse repetition rate and duty cycle and capable of
measuring the Doppler frequency from a moving target. Has good clutter suppression and thus can see
a moving target in spite of background reflections.
Related Topic
69.1 Modulation and Demodulation
References
Bendix Corporation, Service Manual for ALA-52A Altimeter; Design Summary for the ALA-52A, Bendix
Corporation, Ft. Lauderdale, Fla., May 1982.
K.W. Chang, H. Wang, G. Shreve, J.G. Harrison, M. Core, A. Paxton, M. Yu, C.H. Chen, and G.S. Dow, “Forward-
looking automotive radar using a W-band single-chip transceiver,” IEEE Transactions on Microwave Theory
and Techniques, vol. 43, pp. 1659–1668, July, 1995.
? 2000 by CRC Press LLC
Collins (Rockwell International), ALT-55 Radio Altimeter System; Instruction Book, Cedar Rapids, Iowa,
October 1984.
P.D. Fisher, “Improving on police radar,” IEEE Spectrum, vol. 29, pp. 38–43, July 1992.
A.J. Freiley, B.L. Conroy, D.J. Hoppe, and A.M. Bhanji, “Design concepts of a 1-MW CW X-band trans-
mit/receive system for planetary radar,” IEEE Transactions on Microwave Theory and Techniques, vol. 40,
pp. 1047–1055, June 1992.
B. Maoz, L.R. Reynolds, A. Oki, and M. Kumar, “FM-CW radar on a single GaAs/AlGaAs HBT MMIC chip,”
IEEE Microwave and Millimeter-Wave Monolithic Circuits Symposium Digest, pp. 3–6, June 1991.
F.E. Nathanson, Radar Design Principles, New York: McGraw-Hill, 1991, pp. 448–467.
S.O. Piper, “MMW seekers,”in Principles and Applications of Millimeter Wave Radar, N. C. Currie and C. E.
Brown, Eds., Norwood, Mass.: Artech House, 1987, chap. 14.
W.K. Saunders, “CW and FM radar,” in Radar Handbook, M.I. Skolnik, Ed., New York: McGraw-Hill, 1990,
chap. 14.
L.M. Tozzi, “Resolution in frequency-modulated radars,” Ph.D. thesis, University of Maryland, College Park,
1972.
F.T. Ulaby and C. Elachi, Radar Polarimetry for Geoscience Applications, Norwood, Mass.: Artech House, 1990,
pp. 193–200.
J.C. Wiltse, S.P. Schlesinger, and C.M. Johnson, “Back-scattering characteristics of the sea in the region from
10 to 50 GHz,” Proceedings of the IRE, vol. 45, pp. 220–228, February 1957.
Further Information
For a general treatment, including analysis of clutter effects, Nathanson’s [1991] book is very good and generally
easy to read. For extensive detail and specific numbers in various actual cases, Saunders [1990] gives good
coverage. The treatment of millimeter-wave seekers by Piper [1987] is excellent, both comprehensive and easy
to read.
? 2000 by CRC Press LLC
