As we prepare for space explorations, particularly for Mars planet missions, reliable communication systems are increasingly essential. This paper evaluates the potential of using the Ka-band (32-34.2 GHz) for Earth-Mars communication, covering both direct communication and a relay satellite system positioned at the L4/L5 Lagrange points. It presents the design of a1.5-meter diameter parabolic reflector antenna, optimized at 33 GHz with a peak gain of 47 dBi. A thorough link budget analysis for two scenarios – direct Earth-Mars communication and communication via a relay satellite – shows that both approaches are feasible. The relay satellite provides continuous coverage during solar conjunctions. The antenna achieves high radiation efficiency of 98.7% at 32 GHz and 97.5% at 34.2 GHz and strong directivity, making it suitable for long-range data transmission. These results highlight the promise of Ka-band communication systems for future deep-space missions, offering enhanced performance and efficiency.