The trial network deployment and initial commercial spread for the 5th generation mobile network (5G) is programmed for 2020. 5G network, among other promises, targets 100 times user data rate, 1/10 times the energy consumption 10 times higher reliability and 1000 times number of devices with respect to 4G mobile network. Satellites can play a key role in several areas of the 5G network, including coverage extension, content distribution and spectrum utilization. Even though the targets established for 5G are predominantly for terrestrial communication, they can still serve to set some targets by satellite community. Given the fact that there is little room for larger channel bandwidths and new frequency bands suitable for wireless mobile communications, new technological improvements and novel signal processing and digital communication techniques play a central role to achieve the 5G goals. In particular, new interference mitigation and enhanced signal space design will be required to assure the stringent energy consumption, high data rate and reliability. In this project, titled “Enhanced Signal Space opTImization for satellite comMunication Systems”, we address both the interference mitigation and signal design problem in satellite communication. The term “enhanced” is defined by the qualifiers optimized, reduced complexity and robust. Both singleuser and multiuser multiple-input and multiple-output (MIMO) channels are considered. In order to achieve the desired performance, we need to understand the short comings of existing methods in the satellite communication (SATCOM) systems and to optimize the existing methods to perform close to the predicted theoretical limits.To this end, we consider three main problems: 1) designing low complexity and robust symbol level precoder. 2) constellation design for optical wireless channels and channels with fading. 3) joint precoder and constellation design for multiuser MIMO channels with interference. We also provide ene-to-end in-lab validation for the most promising cases.