Transactions on Antennas and Propagation

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Fig. 5 The tangent ogival radome.
For the permittivity profile expression in (8), it is shown in
[23] that the proper differs for different
rm
and radome thickness, while in [20] is chosen as 0.99 for the IPL ra- dome of half-wavelength thickness with
4
rm
. In this work, the
rm
is also 4 and the tangent ogival radome has also the half-wave wall. Fig. a) shows the maximum boresight error
(BSE) and transmission loss (TL) of the inhomogeneous tangent ogival radome. It can be found that TL decreases monotonously with the increase of curvature coefficient
, which is a demonstration of ameliorative impedance matching effect, whereas the variation of BSE is not monotonous. Although a small can yield very good BSE, its TL is considerably large. The that can yield smaller BSE than that of
=0.99 has TL larger than 1.7 dB, which is hardly acceptable in practice. Therefore, 0.99 is selected as the curvature coefficient. The continuous permittivity profile is realized by cascading thin layers. A layer number of 81 is determined through several trials as it can provide enough accuracy. In the following, if there is no additional declaration, inhomogeneous radome represents the inhomogeneous tangent ogival radome with
=0.99. ab) Fig. 6 Characteristics of inhomogeneous radome, CTR and VTR. (a) Maximum
BSE and TL of the inhomogeneous radome with different curvature coefficients. b) Thickness profiles of optimum CTR and single frequency VTR. The variable thickness radome (VTR) is obtained under the center frequency 9.4 GHz using the method proposed in [8], with the objectives BSE and TL weighted and summed to yield a single objective. The weights for BSE and TL are 0.7 and 0.3, respectively, and the normalized coefficients for BSE and TL are 0.52 mrad and 0.51 dB, respectively. The weights are chosen based on the conclusion in [8], that is, the weight on
BSE should be larger than on TL, and our trials. The normalized coefficients are selected from the previous results [8] and trials, and are approximately the best value that can be obtained. Moreover, 9 thickness variables are selected which are located almost uniformly along the z axis, that is, z = 1, 0.9, 0.8, … , 0.4,
0.3, 0.19 (unit m. The dynamic range of each variable is set as
[8 mm, 9.12 mm to be consistent with the casein. Under this condition, the optimum constant thickness radome (CTR) can be readily obtained, and the optimum thickness is 8.98 mm. The inhomogeneous radome also has constant thickness of 8.98 mm. The particle swarm optimization (PSO) algorithm with a mutation operator is employed to solve all the optimization problems in this two-part sequence of papers [29]. Based on the previous work in [8], we have chosen the parameters of the
PSO-based algorithms as follows the population size is 50; the maximum iteration number is 200; the inertia weight decreases linearly from 0.9 to 0.4 in the iteration process and the acceleration constants c
1
=c
2
=2; the maximum velocity is equal to the dynamic range in each dimension of the particle and the mutation rate is set as 0.5. In addition, the reflecting wall is adopted as it is more compatible with the mutation operator than other boundary conditions. The optimized variable thickness profile and the constant thickness line are shown in Fig. b. Although this paper focuses on the phase distortion and BSE, TL is also necessary in order to well understand the EM performance of the designs. Fig. 7 plots both BSE and TL of in- homogeneous radome, optimum CTR and VTR. VTR shows greatly improved BSE and TL compared with CTR. The in- homogeneous radome has smaller TL than VTR, especially under large antenna scan angles, which is due to the impedance match design. Another noteworthy characteristic of the inho- mogeneous radome is the BSE, which, in accord with there- sults in [27], has a maximum of about 3 mrad, and is obviously larger than that of VTR (even larger than that of the optimum

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Transactions on Antennas and Propagation
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CTR). One can naturally suppose from Fig. 4 that the inho- mogeneous radome has much smaller IPD than homogeneous radome (this will be detailedly shown later), as many con- stituent thin layers have a permittivity value close to 1 and permittivity is one of the crucial cause of radome IPD. Fur- thermore, as IPD is the cause of radome BSE, it is somewhat confusing that a substantial decrease of IPD, instead of leading to a conspicuous improvement of BSE, even increases the BSE to a certain degree.
(a)
(b)
Fig. 7 The EM performance comparison of inhomogeneous radome, optimum
VTR and CTR. (a) BSE comparison. (b) TL comparison.

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