Gain division multiple access (GDMA) is a non-orthogonal multiple access (NOMA) technique for uplink communications. In GDMA, the receiver employs both the magnitudes and phases of channel gains associated to the users to separate users. In the power-domain NOMA, the receiver employs the power levels associated to users to separate users. We apply the GDMA concept together with orthogonal frequency division multiple access (OFDM) to combat the collision problem in the ALOHA system. Our goal is to minimize the complexity of the devices (users) required for coordination and to obtain high throughput simultaneously in the random access protocol. For the proposed unslotted OFDM-GDMA-ALOHA, each user randomly chooses a Zadoff-Chu (ZC) sequence as its preamble for the transmitted packet so that the receiver can simultaneously obtain the information for timing and the information for coarse channel estimation. Moreover, fine channel estimation is obtained by using a cluster-based method. Simulation for a coded unslotted OFDM-GDMA-ALOHA system with BPSK modulation demonstrates that the obtained throughput performance can be better than that obtained by the slotted ALOHA system without using GDMA. We also provide simulation for slotted OFDM-GDMA-ALOHA, which shows that very high throughput can be achieved if the synchronization of slots can be obtained.INDEX TERMS gain devision multiple access (GDMA), non-orthogonal multiple access (NOMA), ALOHA, cluster-based channel estimation.