The Generalized Frequency Hopping (GFH) OFDMA system developed in this paper permeates FH benefits to multi-carrier CDMA transmissions through unknown frequency-selective multipath channels. No single user suffers from consistent fading effects and multiuser interference is eliminated by design. Constellation-irrespective channel identifiability is guaranteed, and a host of blind channel estimation algorithms are developed trading off complexity with performance. An important variant corresponding to fast-hopping is also addressed. Performance analysis and simulation results illustrate the merits of GFH-OFDMA relative to conventional OFDMA and long code CDMA with RAKE reception.