A data communications system for conveying a series of input data symbols includes a transmitter subsystem and a receiver subsystem. The transmitter subsystem generates a series of composite waveforms corresponding to a series of input data symbols by selecting from a set of mutually orthogonal component waveforms, then combines contemporaneous portions of at least two of the component waveforms so as to form a composite waveform which is unique to the data symbol. The transmit subsystem uses the composite waveform to modulate a carrier signal and transmits the carrier signal over a communications channel. The receiver subsystem receives the carrier signal and recovers the composite waveform from the carrier signal. The receiver subsystem identifies the data symbol by, at least in part, decompositioning the composite waveforms into their constituent component waveforms so as to identify which composite waveforms have been transmitted.