Described are several embodiments of parabolic reflective antenna systems where rigid parabolic dishes based on shape memory materials are deployed to full size and shape from compact pre-folded preforms by application of heat. Several shape memory feeds working with the dishes are presented. Feed preforms include corrugated, telescopic and flattened ribbon types which extend or unfurl into final shapes upon application of heat. Several dish and feed embodiments also contain supports for secondary reflectors and patch antennas.