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Pulse-position modulation (PPM) is widely used in impulse radio (IR) due to the simplicity of its transceiver structure and signal detection. It is usually used along with time hopping (TH) to support multiple users in IR and to take the advantage of a small collision probability among simultaneous users. This advantage, however, is achieved at the cost of a wider frame length and the concentration of each user's frame signal energy on a single pulse. Thus, it is likely that the TH-PPM information can totally be damaged whenever a collision occurs. In this paper, we take a different philosophy to evenly distribute the signal energy over the entire frame, ending up with a novel ultrawideband (UWB) IR multiple-access scheme, which is called code division multiple access (CDMA)-PPM, for low-rate wireless-personal- area-network application. The new scheme is superior to the conventional one in terms of error performance, as evidenced by theoretical analysis and simulations. We also examine the power spectrum of CDMA-PPM signals, which is found to be comparable to its TH-PPM counterpart.