Three Corner Satellite is a constellation of three nanosatellites designed and built by students. New Mexico State University has taken on the design of the communications system for this constellation. The system includes the forward link, return link, and the crosslink. Due to size, mass, power, and financial constraints, we must design a small, light, power efficient, and inexpensive communications system. This thesis presents the design of a radio system to accomplish the data transmission requirements in light of the system constraints. In addition to the hardware design, the operational commands needed by the satellite's on-board computer to control and communicate with the communications hardware will be presented. In order for the hardware to communicate with the ground stations, we will examine the link budgets derived from the radiated power of the transmitters, link distance, data modulation, and data rate for each link. The antenna design for the constellation is analyzed using software and testing the physical antennas on a model satellite. After the analysis and testing, a combination of different systems will meet and exceed the requirements and constraints of the Three Corner Satellite constellation.