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We consider the effect of mobility on a wideband direct sequence spread spectrum (DSSS) communication system, and study a scale-lag Rake receiver capable of leveraging the diversity that results from mobility. A wideband signal has a large bandwidth-to-center frequency ratio, such that the typical narrowband Doppler spread assumptions do not apply to mobile channels. Instead, we assume a more general temporal scaling phenomenon, i.e., a dilation of the transmitted signal's time support. Based on a uniform ring of scatterers model, we determine that the wideband scattering function, which quantifies the average scale spreading, has a "bathtub-shaped" scale profile. We compare the performances of a scale-lag Rake and a frequency-lag Rake, each capable of leveraging the diversity that results from mobility. Such analysis applies, for example, to ultra-wideband (UWB) radio frequency channels and underwater wideband acoustic channels.