IEEE - Aerospace and Electronic Systems - August 2023 - 52

An Overview of Radar Operation in the Presence of Diminishing Spectrum
radar, such as rain or ground reflections, are targets of
interest in another. Manmade targets exhibit complexity
in RCS not seen in the more uniform characteristics of
naturally occurring objects. The target voltage return is
approximately the coherent summation of the response
of many subscatters [1].Asaresult,manmade targets
tend to show much greater variability in target RCS
over angle with increasing frequency, or conversely, the
response becomes more uniform at decreasing frequency
[17]. To accommodate target RCS variability
with angle and frequency, many radar systems frequency
hop. Frequency hopping forces the target
response out of a fade, making the target behavior better
approximate a Swerling II model [1], [2], [17].The
radar system then noncoherently processes the response
over the frequency hops to substantially improve radar
detection and estimation performance. For example, at
a detection rate of 0.9 and a false alarm rate of 1E-6,
noncoherently combining four, frequency-hopped,
coherent processing intervals (CPIs) for a fluctuating,
Swerling II target leads to a reduction of 11.5 dB in
average required input SINR for each CPI [2].
In light of the prior discussion, a number of factors
influence frequency selection when designing a radar
mode. As is already evident, a FOPEN radar will not be
effective operating at X-band (8-12 GHz), nor will a
weather radar work at VHF (30-300 MHz). Beyond our
discussion thus far, we highlight several additional considerations
affecting radar mode development. A search version
of the RRE readily follows from (1) by noting the
following relationships: processing gain is ideally the
product of temporal integration gain (which is the number
of pulses) N times the pulse compression gain, which is
the ratio of uncompressed pulse width tu to compressed
pulse width tc giving Gp ¼ Nðtu=tcÞ; average power is
the peak power times the duty factor Pavg ¼ PTðtu=TpriÞ,
where Tpri is the pulse repetition interval, or PRI; and the
antenna solid beam angle is approximately the product of
beamwidths in azimuth and elevation, or usb ¼2
c=Ae
steradians. Using these relationships, a search version
of the RRE gives search rate Sr
(sr/s)
Sr ¼
PavgAesTFp
4pkBT0FnLsysR4
1
M SNRo
:
(3)
Both SNRo and RM are given as requirements in
(3). Two factors in particular stand out in this expression:
all other factors equal, ensuring Fp
is near unity
(i.e., minimal propagation loss) and increasing Ae
improves search rate. It is easier to build larger area
antennas for ground and large ship deployment at
lower frequency, a choice that also minimizes propagation
loss (Fp ' 1). These are two considerations
strongly supporting the selection of L-band and S-band
52
in steradians per second
for surveillance radar systems used for air traffic control
and military applications.
In contrast, target assessment and engagement scenarios
benefit from higher resolution, favoring higher
frequencies such as X-band, whose nomenclature is
believed to originate from the thought that, at higher
resolution, " X marks the spot. " Antenna beamwidth in a
given dimension is proportional toc=Lx,where Lx
is
the corresponding antenna length, thus favoring shorter
wavelengths (higher frequencies) for fixed antenna size.
Additionally, the Doppler frequency is fd ¼ 2vr=c,
where vr
is the radial velocity between the radar and
the object of interest, and the Doppler resolution is the
inverse of the coherent dwell, or dD ¼ 1=ðNTpriÞ [1],
[2], [3]. This indicates that the radar's ability to
resolve radial velocity for a fixed dwell linearly
improves as wavelength gets shorter, or frequency
increases, where radial velocity resolution is
dV ¼c=ð2NTpriÞ¼ c=ð2fcNTpriÞ.
Imaging radars similarly take advantage of higher
frequency operation to reduce cross-range resolution.
Specifically, the cross-range resolution is dCR ¼
c=ð2uint sin csqnÞ, where uint is known as integration
angle (the angle the platform subtends with respect to the
target between the start and end of the coherent dwell),
and csqn
is squint angle relative to the radar-carrying
platform's velocity vector at the antenna reference point
[3], [16]. As a rule of thumb, one degree of integration
angle at X-band yields cross-range resolution of approximately
one meter; for the same integration angle at Lband,
the cross-range resolution is an order of magnitude
coarser, as shown in Figure 4. Conversely, to achieve the
same cross-range resolution, the L-band radar must traverse
ten times the integration angle, an endeavor that substantially
reduces the radar's ability to image other points
as it must take additional time to service a given request.
In practice, both Doppler and cross-range resolution
worsen with commonly used, Fourier weighting functions,
but the trend is clear: high frequency operation yields much
improved Doppler resolution and image cross-range resolution.
It is for this reason that engagement and imaging radars
often favor X-band and Ku-band frequency selection.
Many radar applications must contend with payload
limits. Examples include satellite-borne radar, where the
launch vehicle faring limits deployable payload [21], radar
systems on unmanned aerial vehicles (UAVs), and automotive
radar. Such applications favor higher frequency
operation, from C-band (4-8 GHz) through Ka-band (26-
40 GHz), and into W-band for automotive use, since
antenna gain is inversely proportional to the square of
wavelength-or, proportional to the square of operating
frequency-with antenna area fixed. Similarly, antenna
beamwidth is important for resolving target location and,
for fixed antenna dimension, is inversely proportional to
operating frequency.
IEEE A&E SYSTEMS MAGAZINE
AUGUST 2023
IEEE - Aerospace and Electronic Systems - August 2023

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