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This paper is concerned with the performance of biphase direct-sequence spread-spectrum multiple-access communication for a general class of fading channels. The channels considered are those for which the channel output consists of a strong stable specular signal plus a faded version of this signal. Such channels, which are referred to as Rician fading (or Rice fading) or specular-plus-Rayleigh fading, are the result of a transmission medium which gives rise to a major stable communication path and a number of additional weaker communication paths. The fading channel is modeled as a general wide-sense-stationary uncorrelatedscattering (WSSUS) channel-a model which is general enough to exhibit both time and frequency selectivity and to impose no restrictions on the fading rate. For the general WSSUS model, results are obtained on the average signal-to-noise ratio at the receiver output in terms of the spread-spectrum signature sequences and the covariance function for the fading process. These results are then specialized to each of two important classes of WSSUS channels: time-selective fading channels and frequency-selective fading channels. Numerical evaluations are presented for specific examples of each of these two types of channels. Analytical expressions are derived for a spread-spectrum multiple-access system with random signature sequences, and the use of these expressions in preliminary system design is discussed.