Abstract: Systems and methods for orthogonal frequency division multiplexing are provided. In one embodiment, a multi-carrier modem comprises: a receiver configured to de-modulate symbols from at least one of a plurality of spectrally overlapping carrier signals to produce a receiver output; a transmitter configured to modulate symbols onto at least one of a plurality of the spectrally overlapping carrier signals; a processor coupled to the transmitter, wherein the processor outputs data for transmission by the transmitter, wherein the processor applies an inverse Fourier transform to the data transmitted by the transmitter; the processor coupled to the receiver, wherein the processor applies a Fourier transform to the receiver output; and a controller programmed to instruct the transmitter to transmit at least one symbol representing a request for bandwidth allocation on a first carrier; wherein the controller is further programmed to determine when a collision has occurred on the first carrier.