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Direct-sequence spread spectrum with differential phase shift-keying (DPSK) modulation and code-division multiple-access is a promising approach for wireless communications in an indoor environment, which is characterized in this paper by a Rayleigh-fading multipath channel. In this study, we consider two specific channel models having different path-delay distributions and average path power profiles. A star configuration, in which each user exercises average power control in transmitting to a central station, is the basic communication unit, which could be one cell in a cellular hierarchy. We obtain the performance of a single link between a user and its receiver in the central station, and consider two types of diversity, selection diversity and predetection combining to exploit the multipath. A similar system with coherent PSK (CPSK) modulation has been studied previously for one of the channel models considered here. For the same channel model, we show that the irreducible error probability with selection diversity is about half an order of magnitude higher when DPSK is used instead of CPSK. With predetection combining, the performance improves significantly in comparison with selection diversity as the diversity order increases. DPSK modulation with predetection combining is akin to coherent PSK with optimal maximal-ratio combining, but is simpler to implement. The performance with selection diversity for a second channel model, which is based on measurements in an office building, is not significantly different. This indicates that the spreadspectrum approach is rather robust to the path-delay distribution and average path-power profile.