## 2 Proposed Array Antenna
Furthermore, to derive the experimental Formulas (2) and (3) of \(C_{c}\) and \(k\), the resulting curves are fitted by the summation of the exponential and polynomial equations using the nonlinear least square solutions. The detailed coefficients of the fitted curves are \(a_{0}=2.5\), \(a_{1}=0.05\), \(a_{2}=0.2\), \(a_{3}=-0.02\), \(b_{0}=1.6\), \(b_{1}=0.01\), \(b_{2}=0.2\), \(b_{3}=-0.002\), \(b_{4}=0.4\), \(b_{5}=-0.05\), and \(b_{6}=-0.02\). \[C_{c}(w,t)\ =\ a_{0}+a_{1}\exp(a_{2}w)+a_{3}wt, \tag{2}\]  
\[k(w,t)\ =\ b_{0}+b_{1}\exp(b_{2}w)+b_{3}\exp(b_{4}t)+b_{5}w+b_{6}t. \tag{3}\]  
The results demonstrate that such adjustments of the proposed antenna geometry enable simultaneous achievement of the low mutual coupling and good impedance matching. Besides, each element with perpendicular current directions can provide near orthogonal radiation patterns with a low pattern correlation due to the apparent modal difference between them. These low pattern correlations can also be maintained since the active element patterns for individual elements are similar to the single element patterns of the monopole and patch antennas. To further enhance the array  
Figure 4: Mutual couplings in accordance with the variations of \(C_{c}\) and \(k\). Figure 3: Comparison of mutual coupling performance effects of the proposed arrays according to the electric and magnetic coupling strengths. performance, we optimize the detailed array antenna parameters using the full-wave electromagnetic (EM) simulation software of WIPL-D [42] at the target frequency of 1.6 GHz, where the optimized antenna can be applied to signal reception applications such as GPS, global navigation satellite system (GNSS), and satellite digital audio radio service (SDARS). The detailed optimized parameters are \(l\) = 41.2 mm, \(w\) = 14.2 mm, \(l_{s}\) = 60 mm, \(t\) = 10.5 mm, \(l_{g}\) = 200 mm, \(h\) = 43.7 mm, and \(d\) = 14.4 mm. Figure 6 shows the photographs of the fabricated array antenna. To confirm the feasibility of the proposed structure, the antenna characteristics, such as the reflection coefficients, radiation patterns, and gains, are measured in a full anechoic chamber. Figure 7 represents the measured and simulated reflection coefficients, where the blue and red lines indicate the array elements of the monopole and patch, respectively. Both array elements show low reflection coefficients of \(-\)10 dB and \(-\)10.7 dB for the monopole and patch elements at 1.6 GHz, respectively, where the measured results are in good agreement with the simulations. Figure 8 provides magnitude and phase response of the mutual coupling between the two feeding ports as a function of frequency. At 1.6 GHz, the measured magnitude and phase of the mutual coupling are \(-\)20.7 dB and 37\({}^{\circ}\), respectively, and those by simulation are \(-\)21.1 dB and 31.4\({}^{\circ}\), which maintains low mutual coupling values even with an extremely close interport spacing. Figure 9 represents the maximum gains obtained in the upper hemisphere, and the measured peak gains of the monopole and patch elements are 3.8 dBi and 6.1 dBi. Figure 10a,d present measured and simulated 2D active element patterns of the monopole and patch elements. They illustrate co- and cross-polarization in \(zx\)- and \(zy\)-planes (H- and E-planes) at 1.6 GHz. Note that the shapes of the active element patterns are noticeably similar to the radiation patterns of the standalone monopole and patch antennas, even though the two antennas are very close to each other. The patch element shows half power beam widths of 76.1\({}^{\circ}\) and 85.2\({}^{\circ}\) in \(zx\)- and  
Figure 5: Coupling capacitance \(C_{c}\) and coefficient \(k\) according to the adjustment of \(w\) and \(t\): (**a**) coupling capacitance \(C_{c}\); (**b**) coupling coefficient \(k\). Figure 4:0 Photographs of the fabricated array antenna: (**a**) isometric view; (**b**) bottom view. _zy_-planes, respectively.