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2810 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 5, MAY 2015
Optimizing Radiation Patterns of a Cylindrical
Radar for Multimissions
Shaya Karimkashi, Member, IEEE, and Guifu Zhang, Senior Member, IEEE
Abstract—Accurate radar remote sensing requires a radar sys-
tem with high cross-polarization isolation, highly matched dual-
polarization patterns, and low sidelobes. A cylindrical polarimetric
phased-array radar (CPPAR), which has polarization purity and
scan-invariant beam properties, has recently been introduced to
the weather and air surveillance communities. To achieve low
sidelobes and matched beams, pattern synthesis using an opti-
mization method is presented. Results reported herein support the
idea that CPPARs can be designed and implemented for accurate
weather measurements. Furthermore, some uncertainty analysis
is performed to show the effects of the amplitude and phase errors
on the radiation patterns of the PAR.
Index Terms—Antenna arrays, optimization, phased arrays,
ADAR surveillance for weather, air-trafﬁc control, and
target detection and recognition all share the same princi-
ples of electromagnetic scattering and propagation, comparable
radar systems, and similar signal processing and information
extraction. It is cost-effective and operationally efﬁcient to
perform all of these missions and functions within a single
radar network. It is desirable to use one radar network equipped
with multifunction phased-array radars (MPAR) to replace
four networks of the following: 1) National Weather Surveil-
lance Radars (WSR-88D or NEXRAD); 2) Terminal Doppler
Weather Radars; 3) Airport Surveillance Radars; and 4) Air
Route Surveillance Radars. The idea was initiated by a joint
effort between the National Oceanic Atmospheric Administra-
tion (NOAA) and the Federal Aviation Agency (FAA) , and
it has been receiving great attention in the last few years.
Research activities for MPAR have begun in academia, in-
dustry, and government laboratories to identify technical chal-
lenges, mitigate risk, and demonstrate technologies from both
the weather and the airport surveillance points of views (e.g.,
see  and . The nation’s ﬁrst S-band phased-array r adar
(PAR) f or weather observations, the National Weather Radar
Testbed, was developed in Norman, OK, USA, and its interfer-
Manuscript received January 30, 2014; revised July 17, 2014 and
September 19, 2014; accepted October 23, 2014. This work was sup-
ported by the National Oceanic and Atmospheric Administration under Grant
S. Karimkashi is with the Advanced Radar Research Center, University of
Oklahoma, Norman, OK 73019 USA.
G. Zhang is with the School of Meteorology, University of Oklahoma,
Norman, OK 73019 USA.
Color versions of one or more of the ﬁgures in this paper are available online
Digital Object Identiﬁer 10.1109/TGRS.2014.2365362
ometry  and electronic scan capabilities to allow for faster
data updates and thus the observation of detailed evolutions of
severe storm phenomena have been demonstrated in , ,
and . Several other PARs including Umass-MIRSL Phase-
Tilt Weather Radar , , MIRSL X-band PAR , and
Toshiba Phased Array Weather Radar  have recently been
designed and developed for weather sensing application.
While PAR technology has recently received widespread
attention in the weather community, radar polarimetry has
matured to the point that it has just been implemented on
the national network of WSR-88D Doppler radars , .
Therefore, the weather community and the nation expect that
the f uture MPAR will retain all of the capabilities of the polari-
metric WSR-88D . Furthermore, this polarimetric capabil-
ity is also beneﬁcial to the FAA ,  and the Department
of Homeland Security by providing more information for better
air surveillance and target detection and identiﬁcation.
Polarimetric PAR (PPAR) technology is well established in
NASA and military missions—it can be pursued for the MPAR
project as well. The Spaceborne Imaging Radar at C-band and
the X-band Synthetic Aperture Radar missions are conducted
by a joint U.S./German/Italian Space Agency effort, where
phased-array radars with full polarization capabilities are built
by JPL and the Ball Communication Systems Division . An
Airborne Synthetic Aperture Radar mission is also conducted
by NASA/JPL for all-weather imaging with full-polarization
radars. In addition, Japan has a Phased-Array type L-band
Synthetic Aperture Radar with polarimetric capabilities, and
Canada continues to operate the RADARSAR-2 with full-
polarization capabilities. NAVY/P-3 has the Foliage Penetra-
tion (FOPEN) Radar with full polarization capabilities onboard
for better detection of objects.
For weather applications, however, it i s difﬁcult to use PPAR
technology because of the requirement for highly accurate
polarimetric radar measurements, given that there are limited
resources for antenna technology development. The technical
requirements include the following: 1) 2-D wide-angle scan
versus 1-D narrow angle scan in NASA missions (2D wide
angle means each face covers 90
in azimuth and 20
elevation, and 1-D narrow angle scan means < 20
in azimuth and zero elevation/zenith) and 2) high accuracy in
polarimetric radar measurements that exceeds requirements for
satellite remote sensing or for detection of traditional airborne
targets. For example, it is desirable that the measurement error
for differential reﬂectivity (Z
) be on the order of 0.2 dB
since the intrinsic Z
values range only from about 0.2 dB
for drizzle and dry snow to 3–4 dB for heavy rain and large
0196-2892 © 2014
IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
KARIMKASHI AND ZHANG: OPTIMIZING RADIATION PATTERNS OF A CPPAR FOR MULTIMISSIONS 2811
drops –. In addition, the error of the copolar correlation
) must be less than 0.01 so that rain and melting
snow can be distinguished.
To achieve the highly accurate polarimetric measurements,
a high-performance radar/antenna system is required, includ-
ing high polarization purity and pattern characteristics. The
0.2-dB accuracy for Z
requires the high cross-polarization
isolation (CPI) of 40 dB for the simultaneous transmission
and simultaneous reception mode and a CPI of 20 dB for the
alternate transmission and simultaneous reception. The 0.01
accuracy for ρ
means that the horizontal polarization and
vertical polarization antenna patterns match with an accuracy
as high as 99%. These accuracies have been achieved with dish
antenna radar systems through a few decades of research and
development; however, this is not an easy task for the PPAR. It
is this PPAR task that the 2nd MPAR symposium  identiﬁed
as the most challenging technical issue that the community
For a planar PPAR (PPPAR), four faces are normally used to
cover the 360
in azimuth. Because the antenna faces and their
broadside directions are ﬁxed, the beam and polarization char-
acteristics change depending on the electronic beam direction.
The scan-dependent beam characteristics and polarization cou-
pling are not desirable f eatures. As shown in  and , there
are sensitivity losses and measurement bias errors when the
PPPAR beam points off broadside. The Z
bias is correctable
,  through the calibration, but calibrating thousands of
beams is extremely challenging from an operational perspec-
tive. Furthermore, it would be costly to compensate for the
sensitivity loss by increasing the antenna aperture and the trans-
mitting power. Using the slot-dipole radiating elements, which
have better isolation compared to the microstrip patch elements,
we can simplify t he calibration procedure; however, design and
fabrication of new antenna elements would be costly. Although
the PPPAR is feasible for MPAR, it is not necessarily the
best choice for weather measurements because of its inherent
limitations in making accurate weather measurements .
The cylindrical PPAR (CPPAR) has recently been introduced
for MPAR to overcome the deﬁciencies encountered with the
PPPAR . The CPPAR has several advantages such as polar-
ization purity and azimuthal scan-invariant beam characteristics
, ; however, there is a concern as how to achieve
the desired performance in making accurate polarimetric
The Advanced Radar Research Center (ARRC) at the Uni-
versity of Oklahoma (OU) in collaboration with the National
Severe Storm Laboratory (NSSL) has recently been designing
and developing a cylindrical PAR to demonstrate the polari-
metric performance of such a system , . Although
cylindrical array antennas have been designed and implemented
for many years –, their polarimetric characteristics have
not been studied. The main challenges in designing the CPPAR
are achieving low cross-polarization patterns, high isolation
between the vertical and horizontal polarizations, and matched
beams between the horizontal and vertical radiation patterns
. It should be noted that, for accurate polarimetric mea-
surements, high port isolation and low cross-polar pattern are
needed. The cross-polarized isolation is the difference of re-
ceived signal level at the receiver when, in turn, the transmitter
has the same and different polarization with the receiver. In
addition, designing an antenna with low cross-polarization pat-
tern results in high port isolation, which is the isolation between
the horizontal and vertical polarization excitation ports.
It is the purpose of this paper to show a method to optimize the
radiation pattern of the CPPAR with the desired characteristics
of the cylindrical phased-array antenna for polarimetric weather
measurements. Section II presents the CPPAR antenna and its
characteristics. The characteristics of the antenna patterns are
discussed in Section III. Optimization of the CPPAR antenna pat-
terns is discussed in Section IV. The uncertainty analysis is pre-
sented in Section V. The conclusion is presented in Section VI.
II. CPPAR A
The frequency chosen, the S-Band, is appropriate for atmo-
spheric measurements and is the same as that of WSR-88D.
It is appropriate because most hydrometer scattering at the
S-band frequency is in the Rayleigh scattering regime where
there is very little attenuation and which allows for easy data
interpretation. A 3-dB beamwidth of 5
is needed to obtain
accurate short-distance polarimetric weather measurements.
These requirements yield a cylinder diameter of 2 m. It should
be noted that, for weather sensing, a 3-dB beamwidth of 1
is needed to achieve accurate weather measurements; however,
for the CPPAR demonstrator, a beamwidth of 5
is chosen for
short-range weather measurements. Having a beamwidth of 1
means a much larger antenna, ﬁve times larger in diameter
and height, which would be costly. The CPPAR demonstrator
beamwidth is ﬁve times that for the WSR-88D due to its smaller
antenna aperture. Considering the difference in aperture size,
transmitter power, and waveform, the CPPAR demonstrator’s
sensitivity is ∼20 dB lower than that of WSR-88D. It should
be noted that the purpose of the CPPAR demonstrator is to
demonstrate the concept, while the future CPPAR for MPAR
should have the same sensitivity as WSR-88D.
In order to simplify the radar design and reduce costs by
avoiding element-level phase shifters, a frequency scanning
array has been suggested. The frequency scanning array an-
tenna is a special case of linear phased-array antennas, where
beam steering occurs by changing the frequency of the exciter
–. Therefore, elevation steering for the CPPAR antenna
is achieved using a frequency scan. The maximum elevation
scan angle needed for weather measurements is about 20
while the limited frequency range is 2.7–3.0 GHz. In the case of
the CPPAR demonstrator, a large number of frequency scanning
vertical arrays are mounted on a cylindrical surface, forming a
fully operational large array antenna suitable for short-range
weather measurements. Therefore, the azimuth scanning is
achieved either by changing the phase between the adjacent
antenna columns or by commutating the active sector, and
the elevation scanning is achieved by changing the operating
frequency. It should be emphasized that the future operational
CPPAR suitable for long-range weather measurements will not
be based on the frequency scanning array since the radar’s
performance would be the most important driver.
A. Antenna Column
The1.53m× 0.065 m dual-polarized antenna column having
19 radiating patches, parasitic patches, two main transmission
lines, and two ground planes is shown in Fig. 1. The antenna
2812 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 5, MAY 2015
Fig. 1. Nineteen-element series-fed antenna column measured at Federal
Aviations Administrator (FAA) anechoic chamber .
Fig. 2. OU/NSSL CPPAR antenna array designed and fabricated at The
University of Oklahoma.
design is presented in . The antenna column, shown in
Fig. 1, was measured in an anechoic chamber, and the measured
results showed satisfactory agreements between the simulation
and the measured results. Low cross-polar patterns, high port
isolation, and moderate sidelobe levels are achieved. The re-
turn loss is better than 10 dB for both polarizations, and the
isolation is higher than 40 dB for the entire frequency band. A
beamwidth of 5
is achieved at the frequency of 2.76 GHz. As
the frequency is increased from 2.76 to 3.0 GHz, the main beam
is steered from the broadside to approximately 20
B. CPPAR Antenna Design
The fully populated CPPAR demonstrator with a diameter
of 2 m and a height of 2 m has the capacity for 96 antenna
columns. However, 52 antenna columns are mounted currently
covering more than half of the cylinder. Here, 46 unplated holes
are designed on each antenna column to mount the antenna on
the desired surface using nonmetallic screws. The column-to-
column spacing is 65 mm. Having such a spacing between ele-
ments, a 3.72
of beam commutating is achieved. Fig. 2 shows
a photograph of the cylindrical antenna array radar mounted
on a trailer. The elevation scan is achieved by increasing the
operational frequency of the radar, while the azimuth scan can
be implemented through either commutation or beam steering
by controlling phases. The signal amplitude and phase for each
column are controlled by using digital beam-formers to achieve
the desired radiation patterns.
C. Radar System
Each frequency scanning antenna column is controlled by
its own radar. Since the system has the capability of 96 dual-
Fig. 3. Simulation results of the CPPAR antenna at the frequency of 2.76 GHz
when one antenna column is excited. (a) Horizontal polarization. (b) Vertical
polarized antenna columns, 192 radar channels are needed. The
radar system for each channel consists of RF and digital trans-
verse systems. The RF transverse system consists of up-down
converters, transmitters, and radar front end. It is responsible
for translating between the IF and RF frequencies, translating
between the intermediate and operating frequency of the radar,
and all of the other functionalities between the antenna and
the digital transceiver. The digital transceiver consists of a
transceiver, a data link module, and a control computer. Each
digital transceiver module has eight channels corresponding
to the eight-channel RF transceiver subassembly. Analog IF
transmits pulses, and digital IQ data are produced using the
digital transceiver card. The waveform generator is DDS based
with ﬁne control of phase and frequency .
A. Element Pattern
In order to include the effect of mutual coupling between the
elements, the frequency scanning antenna column is modeled
within neighboring elements. In other words, one antenna col-
umn is excited, while the other antenna columns are terminated
to the matched loads. To include the effect of the mutual
coupling, 23 antenna columns on a cylindrical conﬁguration
are chosen, while the center element is excited, and the others
are terminated to matched loads. It was shown that having
23 antenna columns could fully model the effect of mutual
coupling. Both the horizontal- and vertical-polarized element
patterns, called embedded patterns, are modeled using the
High Frequency Simulator Software . Fig. 3 shows the
simulation results of the antenna at the frequency of 2.76 GHz,
KARIMKASHI AND ZHANG: OPTIMIZING RADIATION PATTERNS OF A CPPAR FOR MULTIMISSIONS 2813
where the main beam is scanned around 4
off broadside in
elevation. The ripples on the main beam of the H-polarized
beam are due to the ﬁniteness of the curved array and the
higher level of coupling for H-polarized pattern compared to the
V-polarized pattern. The embedded-element pattern is given by
a superposition of the isolated-element patterns of all elements
when excited through mutual coupling. When added together,
the interference between the different contributions will result
in an oscillating behavior. The ripples on the main beam of the
H-polarized beam are due to the higher level of coupling for
the H-polarized pattern compared to the V-polarized pattern
. The reason for the higher coupling of the H-polarized
pattern at the azimuth plane is that the electric ﬁeld vector is
along this plane. It should be noted that the cross-polarization
is also affected for the H-polarized pattern due to the high level
of coupling. In addition, the simulation results for the isolated
antenna column with no mutual coupling effect are presented.
Similar behavior of embedded patterns is observed at higher
frequencies; however, the ripple levels increase since electrical
spacing between the columns increases.
B. Array Patterns for V and H
The beam is formed from a nominal 90
sector with 24 active
antenna columns, and the simulated azimuthal radiation pat-
terns of the antenna are calculated. The embedded element
pattern is used to calculate the far ﬁeld r adiation pattern of the
antenna array, and it is assumed to be the same for all of the ex-
cited elements. It should be noted that the 24 antenna columns
are located at the center of the cylindrical array with 52 antenna
columns. Therefore, each excited antenna column has a mini-
mum of 14 parasitic elements next to itself. Applying a −30-dB
Taylor amplitude distribution to the antenna columns results in
relatively low sidelobe levels; however, the main beams for the
horizontal- and vertical-polarized beams are not matched. For
polarimetric weather sensing, it is required to have the same
beam directions between the H- and V-polarized beams and the
mismatch as low as 0.1 dB for 10-dB beamwidth. Fig. 4(a)
shows the simulated results for the normalized radiation pat-
terns of the array. The mismatch error is deﬁned as
ME =20∗ log 10
where N is the number of the observation points around the
main beam and ah
are ﬁeld values at the nth observa-
tion point for the horizontal and vertical polarization beams,
respectively. The mismatch error for the radiation patterns
shown in Fig. 4 is −1.69 dB, while a mismatch error better than
−20 dB is required. A zoom-in view of the patterns around the
main beams is shown in Fig. 4(b).
In this section, an evolutionary optimization algorithm, inva-
sive weed optimization (IWO) , is applied to the excitation
coefﬁcients of the antenna columns to achieve low sidelobe lev-
els and matched main beams for the H- and V-polarized patterns.
The IWO is a numerical stochastic optimization algorithm in-
spired from the phenomenon of colonization of invasive weeds
Fig. 4. Co- and cross-polar radiation patterns of 24-element cylindrical array
with −30-dB Taylor amplitude distribution.
in nature , . This IWO has been successfully applied to
several antenna problems proved to be a powerful optimization
algorithm. Before considering the algorithm process, some key
terms used to describe the algorithm are introduced:
1) agent/seed: each individual in the colony;
2) plant: one agent/seed after evaluating its ﬁtness;
3) ﬁtness: the goodness of the solution for each seed;
4) colony: the entire agents or seeds.
To simulate the colonizing behavior of weeds, the following
steps are considered.
1) First of all, N, the number of optimization parameters
(variables), should be chosen. For each of these vari-
ables in the N-dimensional solution space, maximum and
minimum values should be assigned (deﬁne the solution
2) Each seed takes a random position over the
N-dimensional problem. That simply means assigning
initial random values to each optimization parameter
(initialize a population).
3) Each initialized seed grows to a ﬂowering plant. In
other words, the ﬁtness function, deﬁned to represent the
goodness of the solution, returns a ﬁtness value to be
assigned to each plant, and then, these plants are ranked
based on their assigned ﬁtness values. In other words, the
antenna problem is solved using the assigned values for
the variables, and the error, deﬁned as difference between
the desired and obtained patterns, is reported (ﬁtness
evaluation and ranking).
4) Each plant is allowed to produce seeds depending on its
ranking in the colony. In other words, the number of seeds
each plant produces depends on the ranking of that plant
and increases from its minimum possible seed production
) to its maximum (S
). Those seeds that solve
2814 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 5, MAY 2015
ARAMETER VALUES FOR THE CPPAR OPTIMIZATION
the problem better correspond to the plants which are
more adapted to the colony and consequently produce
more seeds (reproduction).
5) The produced seeds in this step are being spread over
the search space by normally distributed random numbers
with mean equal to the location of producing plants and
varying standard deviations (SD). The SD at the present
time step can be expressed by , 
is the maximum number of iterations.
are deﬁned as the i nitial and ﬁnal SDs,
respectively, and n is the nonlinear modulation index
6) After all seeds have found their positions over the search
area, the new seeds grow to be ﬂowering plants, and
then, they are ranked together with their parents. Plants
with lower rankings are eliminated to arrive at the max-
imum number of plants in the colony P
7) Survived plants can produce new seeds based on their
ranking in the colony. The process is repeated at step 3
until either the maximum number of iteration is reached
or the ﬁtness criterion is met (repeat).
B. CPPAR Array Pattern Synthesis
The IWO with restricted boundary conditions  is applied
to the problem of synthesizing the far ﬁeld radiation pattern of
the CPPAR antenna. The phase shifts are chosen to make a
phase front in the direction of the chosen scan angle. There-
fore, only the amplitude weights of elements are optimized
to achieve the desired sidelobe levels and main beams. The
objective is to obtain sidelobe levels less than a tapered sidelobe
mask decreasing linearly from −27 to −35 dB in the range of
, where ϕ is the observation angle, for both
H- and V-polarized patterns and to minimize the difference
between their main beams, which is required for accurate
weather measurements. A “do not exceed criterion” is utilized
in the objective function for the SLLs, i.e., an error will be
reported if the obtained radiation pattern exceeds the desired
sidelobe level. In order to achieve the minimum SLLs for H
and V polarizations while matching their main beams, ﬁrst, the
optimization is applied to the H-polarized patterns where the
mutual coupling is stronger to achieve only low SLLs. Then,
the IWO is applied to the V-polarized pattern to get the same
level of SLLs, and then, the main beam is matched with that
of the H-polarized pattern. As a matter of fact, there are 24
optimization variables for each run of the optimization s ince
we have 24 active antenna columns. The IWO parameters are
summarized in Table I. It should be noted that the beamwidth
of the CPPAR antenna could be reduced at the cost of increasing
the sidelobe levels. However, the goal of this CPPAR antenna
Fig. 5. (a) Optimized radiation pattern of the antenna at 2.76 GHz. (b) Zoom-
in view. (c) Optimized current distributions. (d) Convergence curves.
is to achieve relatively low SLL while having the main beams
matched. Achieving both lower SLLs and reduced beamwidth
can be obtained by increasing the antenna’s aperture.
C. Optimization Results
The optimized radiation patterns of the CPPAR antenna at
the frequency of 2.76 GHz are shown in Fig. 4. It can be
seen that the desired sidelobe levels for both polarizations are
achieved, while the main beams are very well matched. Fig. 5(a)
shows both the copolar and cross-polar patterns. A zoom-in
KARIMKASHI AND ZHANG: OPTIMIZING RADIATION PATTERNS OF A CPPAR FOR MULTIMISSIONS 2815
Fig. 6. Three-dimensional radiation patterns of the CPPAR antenna for
(a) H-polarized isolated beam, (b) V-polarized isolated beam, (c) H-polarized
embedded beam, and (d) V-polarized embedded beam.
view of the copolar patterns around the main beams is shown in
Fig. 5(b). The current distribution is shown in Fig. 4(c). It can
be seen that the current distribution is not symmetrical. This
is due to the element pattern of the single column not being
symmetrical since the patch on each column is not designed
Fig. 7. Optimized copolar and cross-polar radiation patterns of the antenna
(dash line: H-polarized and solid line: V-polarized) at (a) 2.8, (b) 2.9, and
(c) 3.0 GHz.
to be in the middle of the antenna column. In addition, the
current distribution is achieved using an evolutionary optimiza-
tion algorithm which does not provide a unique solution to
the problem. Getting all of the sidelobe levels below a certain
level and matching the main beams using the optimization
algorithm result in an asymmetrical current distribution. This
will not affect the practical implantation of the array since
any current value can be applied to the antenna column using
the ampliﬁers. Fig. 4(d) shows the convergence curve of the
IWO. The cost function is deﬁned as the difference between
the desired and obtained radiation patterns. It should be noted
that the convergence curve shows the normalized cost function
versus each ﬁtness value evaluated.
Three-dimensional radiation patterns of the array simulated
by using both the isolated and embedded beams, presented in
Fig. 3, are shown in Fig. 6. Fig. 6(a)–(d) shows the 3-D patterns
of the CPPAR antenna for both H- and V-polarized patterns.
For the case of the isolated beam, a −30-dB Taylor amplitude
distribution, shown in Fig. 5(c), is applied, and for the case of
the embedded beam, the optimized currents are used.
2816 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 5, MAY 2015
Fig. 8. Uncertainty analysis of amplitude excitation of the CPPAR antenna’s
radiation pattern at 2.76 GHz (dot line: SD =0; solid line: SD =0.1;dash
line: SD =0.2) for (a) vertical and (b) horizontal polarizations.
Fig. 9. Uncertainty analysis of phase excitation of the CPPAR antenna’s
radiation pattern at 2.76 GHz (dot line: SD =0; solid line: SD =0.01;dash
line: SD =0.02) for (a) vertical and (b) horizontal polarizations.
The IWO with the same objectives is applied to the antenna
patterns at higher frequencies as well. It should be noted that,
by increasing the frequency, the beam is steered off broad
FFECT OF AMPLITUDE EXCITATION ERROR ON −3-dB AND −10-dB
EAMWIDTHS AND THE BEAM MATC HIN G OF T H E CPPAR ANTENNA
FFECT OF PHASE EXCITATION ERROR ON −3-dB AND −10-dB
EAMWIDTHS AND THE BEAM MATC H ING
side, and the cross-polarization is increased. The radiation
patterns are observed at azimuth planes for different eleva-
tion angles at 6
, and 18
for 2.8, 2.9, and 3.0 GHz,
respectively. Fig. 7(a)–(c) shows the simulated radiation pat-
terns of the CPPAR demonstrator after optimizations at 2.8,
2.9, and 3.0 GHz, respectively. Both the copolar and cross-
polar patterns for the H and V polarization excitations are
shown. It can be seen that the desired sidelobe levels are
KARIMKASHI AND ZHANG: OPTIMIZING RADIATION PATTERNS OF A CPPAR FOR MULTIMISSIONS 2817
FFECT OF AMPLITUDE EXCITATION ERROR ON THE SLLS
FFECT OF PHASE EXCITATION ERROR ON THE SLLS
achieved, and the H and V main beams are matched in all of
NCERTAINTY ANA LYS IS
The sidelobe levels and the beamwidths of the antenna array
can be affected by both the amplitude and phase uncertainty of
the excitation coefﬁcients. Assuming that the amplitude or/and
phase excitation of each antenna column can be changed from
5% to 20% of its assigned value, the far ﬁeld radiation patterns
are calculated. Gaussian error functions with different SDs are
assumed to be applied to the excitation coefﬁcients of each
antenna column. For each SD, the array is modeled by applying
new excitation coefﬁcients, and the rms error is calculated .
For each SD, the CPPAR antenna is modeled by running the
simulation 40 times, and the effects of amplitude and phase un-
certainties on the sidelobe levels and beamwidth are calculated
. Fig. 8(a) and (b) shows the effect of different SDs (10%
and 20%) of amplitude excitations on the vertical-polarized and
horizontal-polarized radiation patterns, respectively. The effect
of the phase excitation error is shown in Fig. 9(a) and (b) for the
vertical and horizontal polarizations, respectively. It should be
noted that there are two lines in the plots for each SD, showing
the effect of uncertainties on decreasing or increasing the SLLs.
It can be observed that SLLs are more sensitive to the phase
error rather than to the amplitude error. The effects of the ampli-
tude and phase excitations on the −10-dB beamwidth and the
mismatch error of the CPPAR antenna are shown in Tables II
and III, respectively. It can be seen that the effect of the phase
error on the main beam is much more than that of the amplitude
excitation error. The effects of amplitude and phase distribution
on maximum SLLs are shown in Tables IV and V, respectively.
The simulation results of a CPPAR have been presented. The
radiation patterns of the antenna modeled using ﬁnite array
showed that there is a mismatch between the H- and V-polarized
beams, and the sidelobe levels are higher than what is de-
sired. The main beam mismatch between the two polarimetric
beams could result in inaccurate weather sensing. The reason
for obtaining different patterns is different element patterns
for horizontal- and vertical-polarized beams due to different
levels of coupling. The IWO algorithm was used to match the
main beams for all different frequencies while minimizing the
sidelobe levels. The pattern synthesis using an evolutionary
optimization algorithm shows that low sidelobe levels and
matched horizontal- and vertical-polarized main beams can be
achieved for accurate dual-polarization weather measurements.
Uncertainty analysis calculating the effect of amplitude and
phase excitations error on the radiation patterns of the antenna
was presented. It was shown that both amplitude and phase
error can affect the radiation patterns of the antenna. The
mismatch between the H and V main beams can be crucial for
weather polarimetric measurements. It was shown that the ef-
fect of phase uncertainty is much more critical than the effect of
amplitude uncertainty to the sidelobe levels and the beamwidth
of the CPPAR antenna.
The authors would like to thank the ARRC and NSSL
 Federal Research and Development Needs and Priorities for Phased Ar-
ray Radar, C ommittee for Cooperative Research Joint Action Group for
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Shaya Karimkashi (S’08–M’11) received the B.S.
degree in electrical engineering from K. N. Toosi
University of Technology, Tehran, Iran, in 2003,
the M.S. degree in electrical engineering from the
University of Tehran, Tehran, in 2006, and the Ph.D.
degree in electrical engineering from the University
of Mississippi, University, MS, USA, in 2011.
He joined the Advanced Radar Research Center,
University of Oklahoma, Norman, OK, USA, in
2011, where he is currently a Research Scientist and
an Adjunct Assistant Professor. He has published
over 30 referred journal and conference papers. His research interests include
the area of antenna arrays, polarimetric phased-array radars, focused antennas,
based station antennas, computer-aided design for antennas, and optimization
techniques in electromagnetics.
Dr. Karimkashi is a member of IEEE Antennas and Propagation, Phi Kappa
Phi, and Sigma Xi societies.
Guifu Zhang (S’97–M’98–SM’02) received the
B.S. degree in physics from Anhui University, Hefei,
China, in 1982, the M.S. degree in radio physics from
Wuhan University, Wuhan, China, in 1985, and the
Ph.D. degree in electrical engineering from the Uni-
versity of Washington, Seattle, WA, USA, in 1998.
From 1985 to 1993, he was an Assistant and
Associate Professor with the Space Physics Depart-
ment, Wuhan University. In 1989, he was a Visiting
Scholar with the Communication Research Labo-
ratory, Japan. From 1993 to 1998, he studied and
worked in the Department of Electrical Engineering, University of Washington,
where he ﬁrst was a Visiting Scientist and later a Ph.D. student. He was a
Scientist with the National Center for Atmospheric Research during the period
of 1998–2005. After that, he joined the School of Meteorology, University
of Oklahoma, Norman, OK, where he is now a Professor. He modeled and
calculated wave scattering from fractal trees and that from a target buried under
a rough surface. He explored the detection of targets in the presence of clutter
using angular correlation functions. He developed algorithms for retrieving
raindrop size distributions. He led to develop advanced signal processing to
improve weather radar data quality. He formulated theory of weather radar
interferometry and that of phased-array radar (PAR) polarimetry. His research
interests include wave propagation and scattering in random and complex
media, remote sensing theory and technology for geophysical applications,
algorithms for retrieving physical states and processes, cloud and precipitation
microphysics and model parameterization, target detection and classiﬁcation,
clutter identiﬁcation and ﬁltering, radar signal processing, and optimal estima-
tion. He is currently interested in the design and development of polarimetric
PARs for weather measurements and multimission capability.