An orthogonal linear frequency modulation (OLFM) communications system has an OFDM transmitter and receiver communcating data on a series of multiplexed sub-carriers over a communications medium. A linear frequency modulator provided at the transmitter subjects the sub-carriers to linear frequency modulation to produce a series of sub-sweeps for transmission over the communications medium. A linear frequency demodulator at the receiver produces the sub-carriers from the received sub-sweeps for subsequent demodulation to recover the data.