A new cross-layer design taking advantage of OFDMA in ad hoc networks is presented. OFDMA technology is exploited at the physical layer to improve data rate through multiuser diversity and to enhance channel throughput by enabling multiple concurrent transmissions over orthogonal subchannels, each consisting of a group of tones or subcarriers. The proposed Subchannel Selection Algorithm (SSA) addresses the distribution of subchannels and the new Tone Assignment Algorithm (TAS) takes advantage of fading and is adapted to the limitations of ad hoc networks. TAS operates alongside the signaling of the resulting medium access control (MAC) protocol called Concurrent Communication medium Access or CoCo-MAC. The new MAC addresses the synchronization requirements of OFDMA and the needs of the tone assignment algorithm, and also enables concurrent initiation of data transmissions from multiple nodes to the same receiver or from a single transmitter to multiple receivers. We present analysis and simulation results on the throughput advantages of our technique compared to previous spectrum allocation and MAC protocols based on the avoidance of multiple access interference.