## 2 Design Methodology  
The design began with developing a single-element microstrip patch antenna, optimized to resonate at 28 GHz within the Ka-band spectrum. The base antenna element is a rectangular microstrip patch designed to resonate at 28 GHz within the Ka-band (26.5-40 GHz). The effective wavelength (\(\lambda\)) in the substrate was calculated using Equation (1). The width of the radiating patch was determined using Equation (2). The radiating patch length was calculated with Equation (3). Similarly, an extension in the length, \(\Delta\)L, was computed using Equation (5). The effective length of the antenna was calculated with Equation (6). The length and width of the substrate were computed using Equations (7) and (8). \[\lambda=\frac{c}{f\sqrt{ff}}=\frac{3\times 10^{8}}{28\times 10\sqrt{2.65}}=6.5\, \mathrm{mm} \tag{1}\]  
\[Wp=\frac{C}{2 fo}\sqrt{\frac{2}{\varepsilon r+1}} \tag{2}\]  
\[Lp=Leff+\Delta L \tag{3}\]  
\[\varepsilon eff=\frac{\varepsilon r+1}{2}+\frac{\varepsilon r-1}{2}\frac{1}{ \sqrt{1+12\frac{h}{Wp}}} \tag{4}\]  
\[\Delta\mathrm{L}=0.415\mathrm{h}[\frac{(\varepsilon eff+0.3)\left(\frac{Wp}{ h}+0.264\right)}{(\varepsilon eff-0.258)\left(\frac{Wp}{h}+0.8\right)}] \tag{5}\]  
\[Leff=\frac{c}{2 fo\sqrt{\varepsilon eff}} \tag{6}\]  
\[Ls=6h+Lp \tag{7}\]  
\[Ws=6h+Wp \tag{8}\]  
The microstrip edge feed is used to ensure impedance matching with the 50 \(\Omega\) input line. The antenna uses Rogers RO3003 (Roger Corporation, Chandler, AZ, USA)with a dielectric constant \(\varepsilon_{\mathrm{r}}=3\) chosen for its low dielectric loss and thermal stability at high frequencies. Material properties for the Rogers RO3003 dielectric constant (\(\varepsilon\)r): 3.0; loss tangent (tan \(\delta\)): 0.0013; thermal conductivity: 0.5 W/m\(\cdot\)K; and thickness: 1.574 mm. Figure 1 shows the evolution steps of the proposed 1 \(\times\) 6 linear series-fed array. The patch is designed for high gain and directionality. Figure 2 illustrates the evolutionary development of the antenna array, beginning with a single patch element and culminating in a six-element series-fed microstrip patch array. The goal of this design progression is to optimize impedance matching, enhance gain, and support effective beam steering at the target frequency of 28 GHz. The initial single-patch radiator has minimal return loss and poor impedance matching in the mm-wave band (25-31 GHz). The \(-10\) dB S11 bandwidth is narrow, reflecting high reflection losses and low radiation efficiency. (Two and Three Patches): Adding more elements gradually improves the return loss due to enhanced coupling and more effective energy radiation. These intermediate arrays begin showing better return loss but still do not reach optimal levels around the 28 GHz mark. (Four and Five Patches): These stages demonstrate improved impedance matching and directivity. As the number of elements increases, inter-element spacing and array length help tailor the resonant frequency and suppress side lobes. (Six Patches): The optimized array features six uniformly spaced rectangular patches, each tailored for resonance around 28 GHz. The progressive increase in elements fine-tunes the bandwidth and radiation efficiency. Notably, the final design achieves excellent impedance matching, as evidenced in the S11 results of the figure, providing low reflection loss and high gain. A two-element linear antenna array is constructed to enable beam steering and enhanced gain. Approximately 0.5\(\lambda\) (\(\sim\)3.25 mm) was used to avoid grating lobes while allowing for constructive interference in the desired directions. The interconnected layout  
Figure 1: Design evolution steps of the proposed 1 \(\times\) 6 linear series-fed array. Figure 2: Layout of the proposed antenna array with integrated power divider and 2.4 mm connector. (**a**) The 1 \(\times\) 6 antenna array; (**b**) 1 \(\times\) 6 arrays with integrated power divider. is optimized for phase control and symmetrical power distribution.