You are right UMTS is 3G technology but it have nothing to do with EDGE. UMTS is WCDMA technology that operates on different frequency band (even new antennas should be introduced).
EDGE is an extension to GPRS, it is based on GSM technology. There are nine coding schemes from 1-4 the modulation is GMSK and from 5-9 is 8PSK. So you change only the carrier units to support 8PSK, use the same antenna feeders etc. But few phone manufacturers supports EDGE.