An apparatus and method for communicating data between at least two data devices, suitable for use as a wireless local-area network, that provides robust data communication via a radio communications channel corrupted by multipath interference, particularly at high data rates. A preferred embodiment of the invention represents data as a sequence of Walsh-function waveforms encoded by pseudo-noise direct-sequence spread-spectrum modulation. Walsh-function-encoding of the data provides a long symbol duration, thereby allowing the spread-spectrum modulation to provide processing gain sufficient to substantially overcome multipath interference, while providing a high data rate. In another preferred embodiment, Walsh-function modulation is supplemented with various forms of phase modulation, such as coherent PSK for bi-orthogonal signalling, and DPSK between orthogonal symbols for noncoherent bi-orthogonal signalling, thereby further increasing data rate without reducing processing gain. In another preferred embodiment, Walsh-function modulation is supplemented with spectral shaping to allow increased bandwidth occupancy, thereby further increasing the processing gain without sacrificing data rate.