The GlobalFi approach will be to put all of the antenna gain required on the space side, so it can close high-throughput links to ordinary smartphones without requiring the user to buy a hotspot antenna, satphone sleeve, or other dongle/device. This does require very large antennas on the satellite, but will enable the system to address a market of billions of smartphone users.
The GlobalFi satellites will be in high LEO, not GEO (the DARPA Constructable Platform contract is focused on GEO platforms, but GlobalFi platforms would be in LEO).
Each antenna will have multiple steered beams. The primary reflector is fed by an array of our SWIFT radios acting (sort of) as a phased array. The SWIFT radios are software defined radios, and they have the ability to vary their frequencies to account for doppler effects.