A small hemispherical helical antenna array with multibeam output for GPS beam-forming is designed and characterized. A Butler matrix beam-forming network is designed to provide four spatial beams in a two-dimensional directional space. The original design of the hemispherical helical antenna elements is modified in order to match it to the system impedance. Our study shows that even after an ∼30° scan from the normal direction, the maximum change in beam width is only 6°, the maximum change in axial ratio is 1.4 dB, and the maximum change in power gain is 1.1 dB. These characteristics indicate that the array can be potentially used for GPS beam-forming.
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 The advantages of using adaptive beam-forming for GPS signal reception have been frequently addressed in previous studies [Miller and Miller, 1994; Pohner and Steensen, 1994; Ramos et al., 1996; Alonso et al., 1996; Zooghby et al., 1998; Blazquez et al., 1999; Kim and Iltis, 2000; Lin, 2000; Hatke et al., 2000]. These include the rejections of multipath signals and interferences which are among the main causes for the inability of current GPS receivers to further increase their accuracies. While many adaptive beam-forming algorithms have been proposed in the past years, studies of the antenna arrays suitable for beam-forming are still very rare in the literature. This was mainly due to the difficulties in designing antenna arrays with good and stable scanning characteristics, especially the axial ratio. In this paper, we study a small hemispherical helical antenna array driven by a Butler matrix beam-forming network. The array consists of four circular polarization antenna elements deployed in a 2 × 2 square form. Four beams spanning in a two-dimensional (2-D) directional space are produced by the Butler matrix. The use of hemispherical helical antennas as array elements provides circular polarization over a wide scanning angular range [Hui et al., 2003]. The original design of the hemispherical helical antenna is not matched. In this study, we introduce a modification to match to the system impedance. It was shown that, for the designed array, even after an ∼30° scan from the normal direction, the maximum change in beam width is only 6°, the maximum change in axial ratio is 1.4 dB, and the maximum change in power gain is 1.1 dB. These characteristics show that the array can be potentially used for GPS beam-forming.
2. Design Procedure
 The proposed multibeam antenna array consists of two main parts: the beam-forming network and the antenna array. The former part is a phase-control feeding network, forming four spatial beams in two orthogonal directions and the latter part is a four-element antenna array forming the respective beam patterns. Their design is described below. Both software and hardware designs are implemented.
2.1. Butler Matrix Beaming Network
 The beam-forming network is a Butler matrix consisted of four microstrip quadrature hybrid circuits as shown in Figure 1. The design of the hybrid circuits was aided by using the Advanced Design System (ADS) (http://eesof.tm.agilent.com/). The dimensions of the quadrature hybrids are shown in Figure 2. The Butler matrix is to form four beams in a 2-D directional space [Detrick and Rosenberg, 1990]. The azimuth angles of the four beams are ϕ = 45°, 135°, 225°, and 315°, respectively. The elevation angle θ is calculated by considering two linear sublinear arrays placed perpendicularly to each. The formula is:
where N is the number of elements in a sublinear array, d is the desired element spacing, and λ is the wavelength. The factor cos 45° is to account for the effective interelement spacing seen by a wave coming from the direction of ϕ = 45° (instead of ϕ = 0° as in the 1-D beam-forming case). The formula in (1) is derived for the first time and is a 2-D extension of the 1-D formula for the calculation of beam direction of a single linear array in the work of Hensen . Putting N = 2 and d = 0.7λ into (1) (see the next section for the determination of the element spacing), the elevation angle of the four beams is calculated to be 30.3°.
2.2. Hemispherical Helical Antenna Array
 The antenna array was designed using four hemispherical helical antennas [Hui et al., 2003]. The reason to choose the hemispherical helical antenna is that it can produce circular polarization over a wide scanning angle. This characteristic is especially important for constructing arrays for satellite communications. The four antenna elements are placed in a square lattice as shown in Figure 3 to form a planar array with dimensions dx = dy = 0.7λ (λ is the wavelength at 1.575 GHz) and δ1 = δ2 = δ3 = δ4 = 0° [Hui et al., 2004]. Although hemispherical helical antennas have good circular polarization characteristic, their original design is not matched [Hui et al., 2003]. Here we introduce a slight modification to the original design. As show in Figure 4, a matching section consists of 3 straight wires are used to match the antenna to a 50 Ω system impedance. By adjusting L1 = 2 mm, L2 = 37.5 mm, and L3 = 5 mm, significant improvement in return loss can be obtained. The matching section is to neutralize the large capacitive reactance of the hemispherical part [Hui et al., 2003] by introducing an inductive reactance. The dimensions of this section were found by trial and error using computer simulations. The other dimensions of the antenna elements are: radius of the hemispherical helix = 37.5 mm, number of turns = 5, and wire radius = 0.5 mm. One of the difficulties of matching the input impedances of antenna elements to the system impedance is the existence of mutual coupling. With the above dimension, the return losses at 1.575 GHz for element 1, element 2, element 3, and element 4 are measured to be −23.6 dB, −10.7 dB, −27.7 dB, and −13.2 dB, respectively. The design of the single antenna element and the array was carried out by computer simulation using the moment method [Harrington, 1993]. The final array design is shown in Figure 5.
3. Array Characteristics
 The antenna array in Figure 3 is fed by the Butler matrix feeding network in Figure 1 by connecting port A to element A and port B to element B, etc, using four coaxial cables all of one guided wavelength. This is to guarantee that the impedances looking from the hybrids are same as the input impedances of the antenna elements. By exciting the four input ports (port 1 to port 4), four spatial beams can be obtained in two orthogonal directions. The measured return losses of the individual ports are shown in Figure 6. At 1.575 GHz, the return losses for port 1, port 2, port 3, and port 4 are −21.0 dB, −21.0 dB, −22.0 dB, and −18.0 dB, respectively. The measured and simulated beam patterns (the Eϕ component) at 1.575 GHz are shown in Figure 7. The respective beam directions, half-power beam widths, axial ratios, and power gains are tabulated in Table 1. It can be seen that the measured beam directions are somewhat different from those calculated by using formula (1). The reason is that the input impedances of the antenna elements are not all identical but with some differences being introduced during the construction process. These differences in the input impedance lead to some extra phases added to the phases provided by the Butler matrix beam-forming network. Another reason is that the beam direction of each antenna element may not be exactly in the normal direction (i.e., θ = 0° and ϕ = 0°). This has actually reflected in the measured normal beam direction in Table 1, which shows that the normal beam has a direction of θ = 2°. It should be noted that the error due to the Butler matrix feeding network is very small as it can be fabricated very accurately. Notwithstanding these errors, the beam patterns simulated by the moment method are very close to the measured ones. The axial ratios of the four beams are all smaller than 3 dB, indicating good circular polarization. The power gains are relatively constant as the four beams are actually positioned around a circle with the array as the center. In Table 1, we have also obtained the axial ratios and power gains of the beam patterns from simulation. It can be seen that the degradation of axial ratio and power gain from those of the normal beam is still small even after an ∼30° scan. The maximum change in beam width is only 6°, the maximum change in axial ratio is 1.4 dB, and the maximum change in power gain is 1.1 dB. The normal beam is obtained by exciting the array through a 1-to-4 power divider. From Figure 7, it can be further observed that the beam crossover levels are about 3 dB on the ϕ = 45° and 225° plane and about 4 dB on the ϕ = 135° and 315° plane. From the above study, we see that this array is suitable for further developing into adaptive antenna arrays for GPS or satellite beaming, in which a good circular polarization characteristic maintained over a wide scanning angle is desirable.
Table 1. Calculated Axial Ratios and Power Gains of the Four Beams
Measured Beam Direction, Eϕ
Measured Half-Power Beam Width Eϕ, deg
Simulated Axial Ratio, dB
Simulated Power Gain, dB
ϕ = 45°, θ = 24°
ϕ = 135°, θ = 25°
ϕ = 225°, θ = 22°
ϕ = 315°, θ = 28°
ϕ = 0°, θ = 2°
 A small hemispherical helical antenna array with multibeam output for GPS beam-forming has been designed and characterized. A Butler matrix feeding network was designed to provide four spatial beams in a 2-D directional space. The original design of the hemispherical helical antenna elements was modified to match it to the system impedance. Our study shows that even after an ∼30° scan from the normal direction, the maximum change in beam width is only 6°, the maximum change in axial ratio is 1.4 dB, and the maximum change in power gain is 1.1 dB. These characteristics show that the array can be used for GPS beam-forming.