In our quest for enhanced antenna performance, we turn to the Dolph-Chebyshev distribution to minimize side lobes and increase directivity. This technique effectively curtails unwanted radiation in non-primary directions, thus elevating antenna efficiency. Our simulations and performance evaluations rely on scattering parameter analysis to ensure accuracy and efficiency. This analysis covers a bandwidth centered around 500 MHz, a critical range for Ku band applications and millimeter wave operations. Our study demonstrates the practicality of employing a cross-polarized antenna configuration in Ku band frequencies and millimeter wave applications. We present a clear and concise outline of the antenna's design process, simplifying the antenna array while preserving its essential properties. In conclusion, our research underscores the importance of designing a dual-polarized antenna array that meets the rigorous demands of Ku band applications."