Recent advancements in the design of CubeSats, a type of nanosatellite, have allowed missions to include lunar, asteroid, and planetary destinations. Communication for deep space CubeSats poses new challenges for researchers in terms of transmitting and receiving range capabilities, reliability, and power and size limitations. An X-band downlink communication system is designed to address link budget and CubeSat system requirements for a lunar orbit. An Archimedean spiral antenna array backed by a novel sloped wall cavity and fed with a Klopfenstein impedance taper and power splitter is designed and characterized. An X-band transmitter is designed to fulfill the link budget and is analyzed for RF performance.