an optimal design of a cylindrical polarimetric phased array radar for weather sensing

8/20/2019 An Optimal Design of a Cylindrical Polarimetric Phased Array Radar for Weather Sensing

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An optimal design of a cylindrical polarimetric phased array

radar for weather sensing

Shaya Karimkashi1 and Guifu Zhang2,3

Received 18 April 2011; revised 7 February 2012; accepted 8 March 2012; published 24 April 2012.

[1] An optimal design of a cylindrical polarimetric phased array radar (CPPAR) for weather sensing is presented. A recently introduced invasive weed optimization (IWO)technique is employed to obtain the desired radiation pattern of the CPPAR. Insteadof optimizing each element excitation in a large array (with expensive calculation costs),the modified Bernstein polynomial distribution, defined by seven parameters, is used tooptimize the current distribution for the CPPAR. The simulation results show that thedesired sidelobe levels (SLLs) and beam width are achieved in a computationally effectivemanner. Furthermore, the imaged feed arrangement is used to suppress the cross-

polarization level. Both co-polar and cross-polar radiation patterns for broadside andoff-broadside directions are presented to show the performance of the optimized CPPAR.

Citation: Karimkashi, S., and G. Zhang (2012), An optimal design of a cylindrical polarimetric phased array radar for weather sensing, Radio Sci., 47 , RS2017, doi:10.1029/2011RS004753.

1. Introduction

[2] Phased array radar (PAR) technology has recently been introduced to the weather community. The first phasedarray radar dedicated to weather observation, the NationalWeather Radar Testbed (NWRT) was developed in Norman,Oklahoma [ Zrnic et al., 2007]. Operating at a wavelength of 9.38 cm, the NWRT is able to make reliable weather mea-surements. Compared to conventional reflector antennas withmechanically steered beams, the NWRT takes advantage of electronic beam steering, resulting in shorter surveillance

times and faster data updates. In addition, the NWRT has thecapability to steer the beam mechanically in the azimuthdirection, allowing for multiple measurements of the samemeteorological volume [Yu et al., 2007; Heinselman et al.,2008; Zhang et al., 2011a; Le et al., 2009; Zhang and Doviak , 2007, 2008; Yeary et al., 2010].

[3] While PAR is starting to receive attention in theweather community, radar polarimetry has already maturedto the stage where Weather Surveillance Radar 1988 Doppler (WSR-88D) radars are being upgraded with dual-polarizationcapability [ Doviak et al., 2000]. It is desirable to combineelectronic beam steering and polarimetry capabilities. How-ever, a planar polarimetric phased array radar (PPPAR) hassome deficiencies when the beam is scanned off-broadside.The PPPAR, with multiple faces to scan the whole azimuth

space, suffers from the disadvantages of increase in beamwidth, loss of sensitivity and coupling in dual-polarizationswhen the beam is pointed away from the broadside angle[ Zhang et al., 2009].

[4] The cylindrical polarimetric phased array radar (CPPAR)has been recently proposed to overcome the deficienciesencountered with PPPAR. The CPPAR principle and poten-tial performance was studied by Zhang et al. [2011b] ascompared with the WSR-88D radar. It has the advantages of azimuth scan-invariant pattern and orthogonal polarizations.

Although the CPPAR has several advantages compared toPPPAR, there is a concern as how to achieve desired per-formance for a given antenna size, including low sidelobelevel (SLL) (


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2005; Ferreira and Ares, 1997]. Although optimizationtechniques are more efficient in obtaining the desired radia-tion pattern, they are very expensive for large array antennas,especially when an accurate analysis is considered. On theother hand, a huge number of evaluations is needed to obtainthe optimized values for all the variables. Therefore, applyingany optimization method to a CPPAR with a few thousandelements will be very expensive.

[6] In this paper, an optimal design of the cylindrical polarimetric phased array radar (CPPAR) for weather mea-surements is presented. A recently introduced optimizationtechnique, Invasive Weed Optimization (IWO) [ Karimkashiand Kishk , 2009, 2010] is employed to optimize the elementsexcitation current of the CPPAR to obtain the desired SLLs

and beam width. A two dimensional (2D) modified Bernstein polynomial [ Boeringer and Werner , 2005] is used to definethe amplitude distribution of the CPPAR to improve

computational efficiency. Optimizing the modified Bernstein polynomial distribution (defined by seven parameters) instead

of each element ’s amplitude substantially reduces the computational burden. By using such a smooth and unimodalamplitude distribution, the active element pattern technique is

Figure 1. The CPPAR configuration.

Figure 2. The configuration of patch antenna fed by probes with (top) top view and (bottom) side view.

Figure 3. The co-polar and cross-polar radiation patterns of the single element and one active element within a 3 3array in (a) vertical and (b) horizontal planes.

KARIMKASHI AND ZHANG: CYLINDRICAL PHASED ARRAY RADAR RS2017RS2017

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used where the element pattern of each element is calculatedin the presence of its neighboring elements.

[7] This paper is organized as follows. Section 2 presentsthe modeling and design principles of the CPPAR. Appli-cation of the IWO to the CPPAR is presented in section 3.The antenna optimization results are shown in section 4.Finally the conclusion is drawn in section 5.

2. CPPAR Modeling and Design

[8] The configuration of the CPPAR consisting of M Ndual polarized microstrip patch radiating elements is shownin Figure 1. Although, in principle, any number of beamscan be formed, it has been found that a four-beam system isappropriate in either the planar or cylindrical configuration[ Zhang et al., 2011b]. Each active sector of the antenna, a quarter of the cylinder, generates a beam with the broadsidedirection along the bisector of that sector. The azimuth beamsteering is achieved by commutation, and the elevation beamsteering is electronic and ranges from 0 degree to 30 degrees.

[9] Each microstrip patch antenna working at the fre-quency of 2.8 GHz is designed on an RT/Duriod 5880 sub-strate of thickness of 3.175 mm. The square patch antenna isexcited by using 50 W probe feeds (Figure 2).

[10] In order to account for the mutual coupling betweenelements, a 3 3 array is modeled when the central element is excited and the other elements are terminated to matched

loads. The simulated results are shown in Figure 3. Theseresults indicate that the coupling between elements mostlyaffects the cross-polar radiation pattern. Including the neighboring elements in calculating the element ’s active pattern isadequate. It should be mentioned that the cross polarizationlevel is below 40 dB at the vertical plane (E-plane).

[11] After obtaining the element pattern, the total radiatedfield of the CPPAR can be obtained by:

E q;8 ð Þ ¼X M

m¼1

X N n¼1

EP m;n q;8 ð Þ A m; nð Þ

exp jk R sinq cos 8 8 mð Þ þ z n cosqð Þð Þ ð1Þ

where EP m,n(q, 8 ) are the active element pattern, A(m, n) arethe element excitation complex current, k is the free spacewave number, R is the radius of the cylinder and d is thedistance between elements. 8 m and z n are the location of eachelement on the cylinder coordinate system. It is desirable for CPPAR to have a comparable performance to WSR-88D,which has a reflector antenna with a diameter of 8.54 m. Tohave the same effective size of the WSR-88D reflector for each active sector, the CPPAR should have a height of 8.54 m and a radius of R = 6.05 m.

3. CPPAR Optimization

[12] In this section, the optimization algorithm is appliedto the CPPAR antenna to obtain the desired SLLs and beamwidths for both the broadside and off-broadside radiation patterns. The IWO algorithm is briefly described and thenthe optimization procedure, inter-element spacing betweenelements and cross-polarization minimization are discussed.

3.1. IWO Algorithm

[13] The IWO algorithm has been introduced recently.This algorithm has attracted much attention and been applied

to different problems. It has been shown that the IWO canoutperform both the GA and the PSO in the convergence rate

Table 1. Some of the Key Terms Used in the IWO

Term Explanation

Agent/seed Each individual in the colony containinga value of each optimization variable

Fitness A value representing the goodnessof the solution for each seed

Plant One agent/seed after evaluating its fitnessColony The entire agents or seeds

Population size The num ber of plants in the colonyMaximum number of plants The maximum number of plants allowedto produce new seeds in the colony

Figure 4. Flowchart showing the IWO algorithm.


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as well as the final error level. Considering the algorithm process, the key terms used to describe this algorithm should be introduced. Some of these terms are presented in Table 1.Each individual or agent, a set containing a value of eachoptimization variable, is called a seed. Each seed grows to a

flowering plant in the colony. The meaning of a plant isone individual or agent after evaluating its fitness. Therefore,growing a seed to a plant corresponds to evaluating anagent ’s fitness [ Karimkashi and Kishk , 2010].

[14] To simulate the colonizing behavior of weeds, thefollowing steps, pictorially shown in Figure 4, are consid-ered [ Karimkashi and Kishk , 2009, 2010]:

[15] 1-First of all, the N optimization parameters (variables)should be chosen. For each of these variables in the N -dimensional solution space, a maximum and minimumvalue should be assigned (Define the solution space).

[16] 2-Each seed takes a random position over the d dimensional problem (Initialize a population).

[17] 3-Each initialized seed grows to a flowering plant. In

other words, the fitness function returns a fitness value to beassigned to each plant, and then these plants are ranked basedon their assigned fitness values (Evaluate fitness and ranking).

[18] 4-Every plant produces seeds based on its assignedfitness or ranking. The number of seeds each plant producesdepends on the ranking of that plant and increases from itsminimum possible seed production (S min) to its maximum(S max) (Reproduction).

[19] 5-The produced seeds in this step are being dispreadover the search space by normally distributed randomnumbers with mean equal to the location of producing plantsand varying standard deviations. The standard deviation at

the present time step can be expressed by:

s iter ¼ iter max iter ð Þ

n

iter maxð Þn s inital s final

þ s final ð2Þ

where iter max is the maximum number of iterations. s initial and s final are defined initial and final standard deviations,respectively and n is the nonlinear modulation index (Spatial

dispersion).[20] 6-After that all seeds have found their positions over the

search area, the new seeds grow to the flowering plants and then,they are ranked together with their parents. Plants with lower ranking in the colony are eliminated to reach the maximumnumber of plants in the colony, P max (Competitive exclusion).

[21] 7-After this process carried out for all of the plants,the process is repeated at step 3 until either the maximum

Figure 5. The simulated radiation patterns of the CPPAR with different element spacing in (a) vertical and (b) hori-zontal planes.

Figure 6. 2 2 sub-array for (a) baseline and (b) imagedfeed arrangements.


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number of iteration is reached or the fitness criterion is met (Repeat).

3.2. Optimization Procedure

[22] The IWO with restricted boundary condition isapplied to the problem of synthesizing the far field radiation pattern of the CPPAR antenna. The phase shifts are chosento make a phase front in the direction of the chosen scanangle. Therefore, only the amplitude weights of elements areoptimized to achieve the desired sidelobe levels. The objec-tive is to obtain sidelobe levels less than a tapered sidelobemask decreasing linearly from 30 dB to 40 dB in therange of 1 ≤ |q| ≤ 10, 1 ≤ |8 | ≤ 10 and less than 40 dBfor |q| > 1 0, |8 | > 1 0. A “do not exceed criterion” isutilized in the objective function. That is, an error will bereported if the obtained radiation pattern exceeds the desired

sidelobe level. The optimization process for a few thousandradiating elements is computationally very expensive. Inorder to avoid expensive computations in finding optimalweights for each element, a modified Bernstein polynomial[ Boeringer and Werner , 2005] is utilized to define the cur-rent distribution of the array antenna. In other words, insteadof optimizing the excitation coefficients of array elements, a two dimensional function defined by seven variables specifiesa smooth and uni-modal current distribution on the array

elements. A one dimensional modified Bernstein polynomialis defined as [ Boeringer and Werner , 2005]:

f uð Þ ¼

C 0 þ 1 C 0

A N 0 A 1 Að Þ N 0 1 Að Þ ⋅ u N 0 A 1 uð Þ N 0 1 Að Þ; 0 ≤ u ≤ A

C 1 þ 1 C 0

A N 1 A 1 Að Þ N 1 1 Að Þ ⋅ u N 1 A 1 uð Þ N 1 1 Að Þ; A ≤ u ≤ 1

8>><>>:

ð3Þ

where A, C 0, C 1, N 0, and N 1 specify the shift of the excitationmaximum, the left and right endpoint values, and the left andright sharpness of the peak of f(u). For the cylindrical arrayantenna, a two dimensional modified Bernstein polynomialis generated by multiplication of two 1D functions in the 8 and z directions.

[23] Since the desired envelope is symmetrical in theazimuth plane, we exploit the symmetry of current distribution in this plane. Therefore, f( 8 m ) is defined with two parameters since N 0 = N 1, C 0 = C 1, and A = 0.5. After some simple manipulation f( 8 m ) can be expressed as:

f 8 mð Þ ¼ C 0 1 C 0ð Þ2 N 08 m

N 0=2 1 8 mð Þ

N 0=2 : ð4Þ

[24] Using the new expression, only seven parameters,instead of ten, are optimized to obtain the desired current distributions. Having fewer variables makes the optimization process simpler and faster.

[25] It should be noticed that the current distribution can be defined as the summation of some orthogonal functionslike Bessel and Cosine; however, it might not be realizablein practice due to the coupling effects that tend to smooth out

Table 2. IWO Parameter Values for the Array Optimization

it max pmax smax smin n s initial s final

30 10 5 0 3 0.1 0.01

Figure 7. The simulated co-polar and cross-polar radiation pattern of the optimized CPPAR for broad-side pattern in the (a and b) vertical and (c and d) horizontal planes.


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the effective amplitude distribution. Furthermore, using themodified Bernstein polynomial causes a gradual decrease of sidelobe levels by moving the observation angle away fromthe main beam. In addition, the simulation results show that the maximum sidelobe levels occur in the principle planes.Thus, defining the sampling points at the principle planes

and around the main beam guarantees obtaining the desiredsidelobe levels in all the directions.

3.3. Inter-element Spacing

[26] In order to achieve a cost-efficient design for theCPPAR, the number of elements should be minimized. Theadvantage of minimizing the element number is clear fromthe point of view of T/R modules. Minimizing the number of elements for periodic array antennas means increasingelement spacing, causing the appearance of grating lobes. Inorder to compromise between the number of elements andappearance of grating lobes, a case study is done. Simulated

radiation patterns of the CPPAR for different element spac-ing in both the vertical and horizontal planes are shown inFigure 5. It should be noted that the radiation patterns in thevertical plane are computed for the case where the main beamis pointed to its maximum scan angle (q = 30 degrees).Therefore, element spacing in the vertical and horizontal planes is chosen to be 0.65l and 0.6l, respectively. Suchelement spacing yields 122 elements in each vertical column

and 592 elements in each ring around the cylinder.

3.4. Cross-Polarization Minimization

[27] In order to suppress the level of cross-polarization,the mirrored feed arrangement is considered [Woelders and Granholm, 1997; Granholm and Woelders, 2001; Rahmat-

Figure 8. The simulated images of the optimized CPPAR (a) co-polar radiation pattern, (b) cross-polar radiation pat-tern, and (c) current distribution.

Figure 9. A comparison between the optimized and WSR-88D tapering current distribution of the CPPAR for (a) thesimulated radiation pattern in the vertical plane, (b) the sim-ulated radiation pattern in the horizontal plane, and (c) thesimulated current distribution in the horizontal plane.


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Figure 10. The simulated co-polar and cross polar radiation patterns of the optimized CPPAR for scandirection 10 in the (a and b) vertical and (c and d) horizontal planes.

Figure 11. The simulated co-polar and cross-polar radiation patterns of the optimized CPPAR for scandirection 20 in the (a and b) vertical and (c and d) horizontal planes.


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Samii et al., 2006]. For the sake of illustration, an arrayconsisting of identical 2 2 subarrays is considered. The feedarrangements for the conventional (baseline) and mirroredfeed arrangements are shown in Figures 6a and 6b, respec-tively. The ports with a negative sign ‘-’ mark are fed 180

out of phase compared to the port marked with a positive

sign ‘+’. It will be seen that using the image feed arrange-ments substantially suppresses the cross-polarization level.

4. Optimization Results

[28] In this section, the simulated radiation patterns of theoptimized CPPAR for different scan directions are presented.The optimization is applied to the co-polar pattern in eachscan direction and the cross-polar pattern is computed for the two arrangements shown in section 3.3. It should bementioned that only the vertically polarized radiation patternare shown for brevity. In this case, E q is copular and E 8 iscross-polar component, respectively. The parameters usedfor the IWO are summarized in Table 2.

4.1. Broadside Pattern

[29] Figure 7 shows the simulated radiation patterns of theCPPAR in both the vertical and horizontal planes. It can beseen that the desired sidelobe levels and beam widths areachieved. Moreover, the effect of mirrored feed arrangement on the suppression of the cross-polar pattern is observed.The simulated co-polar and cross-polar radiation patternimages of the CPPAR are shown in Figure 8. The higher sidelobe levels in the principle planes confirm the affectivityof the observation points defined on the principle planes.Figure 8b shows that higher cross-polarization levels occur

at the locations far beyond the main beam. The optimizedcurrent distribution of the array is shown in Figure 8c. It isseen that a very smooth tapering is achieved.

[30] In another effort, the optimized radiation pattern of the CPPAR is compared to the case where WSR-88Dtapering is applied to the CPPAR. The comparison between

the simulated radiation pattern of these two are shown inFigures 9a and 9b. The mainlobe of the optimized CPPAR pattern is very close to that of WSR-88D pattern, but thesidelobe level is much lower. A comparison between thecurrent distribution of these arrays in the azimuth planeare shown in Figure 9c. Although the modification in thecurrent distribution is minor, it causes great improvement in the radiation pattern of the array. In other words, thesidelobes levels are very sensitive to the small deviationsof the current distribution, indicating the importance of theoptimization.

4.2. Off Broadside Patterns

[31] The simulated radiation pattern of the array for scan

directions of 10 degrees, 20 degrees and 30 degrees areshown in Figures 10 – 12. It is seen that desired SLLs and beam widths are obtained for all the scan directions. It isalso seen that the mirrored feed arrangement suppressed thelevel of cross-polarization in all scan directions. Table 3shows the maximum cross-polarization Level for all thescan directions. It can be observed that by increasing thescan direction away from the broadside angle, the cross- polarization level is increased. It should be noticed that themaximum cross-polarization occurs at angles far from themain beam.

Figure 12. The simulated co-polar and cross-polar radiation pattern of the optimized CPPAR for scandirection 30 in the (a and b) vertical and (c and d) horizontal planes.


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4.3. CPPAR Sensitivity

[32] In Figure 13, the minimum detectable reflectivityfactor of CPPAR versus the distance from the antenna for different scan directions and different maximum power iscompared to that of the WSR-88D [ Doviak and Zrnic, 1993].

The reflectivity factor is Z ¼R

D6 N Dð ÞdD with D as thedrop diameter and N ( D) as the drop size distribution, which isthe normalized radar reflectivity of the backscattering cross

section per unit volume for Rayleigh scattering. The minimaldetectable reflectivity is defined such that the signal-to-noise(SNR) is zero dB. The calculations were made using Doviak and Zrnic [1993, equation (4.35)] by assuming 1 ms pulseand ignoring the transmission losses. It is shown that increasing the maximum allowed power from each single patch from 10 W to 100 W makes the CPPAR compatiblewith the WSR-88D having a 475 kW peak power. It is alsoseen that by increasing scan direction (q) the minimaldetectable reflectivity is increased, meaning a reduced sen-sitivity. Fortunately, such sensitivity reduction is within 3 dBand the reduced sensitivity is acceptable because the radar does not need to make measurements at long range at highelevation. It is noted that the sensitivity calculation appliesto a passive CPPAR without taking processing gain intoaccount. Had an active CPPAR been used with N T/R modules, there would be a sensitivity gain of 10log(N) dB.

5. Conclusion

[33] The IWO algorithm was applied to optimally designthe cylindrical polarimetric phased array radar for weather sensing applications. A Modified Bernstein polynomialdefined by seven variables was optimized to assign thecurrent amplitude to the microstrip patch elements of theCPPAR. Using the modified Bernstein polynomial, not onlyis the computational domain reduced, but a very smoothcurrent distribution is assigned to the CPPAR antenna,

increasing the antenna efficiency and minimizing the effect of coupling between elements. After minimizing the number of elements of the CPPAR, the amplitude weights of ele-ments are optimized while the phase weights are chosen tomake a phase front in the direction of the chosen scan angle.In addition, the imaged feed arrangement was used to

suppress the cross-polarization level. The simulation resultsshow that the desired sidelobe levels and beam widths areachieved for the broadside and off broadside angles. However, by increasing the scan angle in elevation, the beam width wasslightly increased. Moreover, the cross-polarization level has been suppressed by using the imaged feed technique. For the broadside beam pattern a very low cross-polarization level isobtained around the main beam. However, when the beam isscanned off broadside, the cross-polarization level increased.Considering the fact that an alternative transmission CPPAR system has much less stringent requirements, even theincreased cross-polarization level is acceptable. Using theCPPAR for simultaneous transmission requires heavier suppression of cross-polarization and should be subject to morestudies.

[34] Acknowledgments. The work is supported by NOAA grant NA08OAR4320904 and NSF grant AGS-1046171.

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an optimal design of a cylindrical polarimetric phased array radar for weather sensing

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