Error Analysis for Ultra-Wideband DS- and Hybrid DS/TH-CDMA with Arbitrary Chip-Duty

In this paper, ultra-wideband (UWB) multiple access systems are introduced by using direct-sequence (DS) and hybrid directsequence time-hopping (DS/TH) code division multiple access (CDMA) that use arbitrary chip-duty of the spreading sequences. The bit error probabilities are presented. First of all, the variances of the multiple access interference are developed by investigating the collision properties of the signals. Afterward, various approximations are applied. The standard Gaussian approximation (SGA) for the DS system is shown to become extremely optimistic as the chip-duty becomes low. Though the hybrid system performs better, the SGA still remains optimistic. To obtain accurate results, Holtzman’s simplified improved Gaussian approximation (SIGA) and Morrow and Lehnert’s improved Gaussian approximation (IGA) are used. A shortcoming of the SIGA is rediscovered that renders it unusable for low-duty DS systems, especially, at high signal-to-noise ratio. However, for the hybrid system, the SIGA works as an excellent tool. The IGA is used to get accurate results for the low-duty DS systems. It is shown that lowering of chip-duty by keeping chip rate and chip length unchanged improves performance for asynchronous DS and both asynchronous and synchronous hybrid systems. However, under the same processing gain, a high-duty system performs better than a low-duty system. Performance of synchronous DS system remains independent of chip-duty. key words: ultra-wideband, code division multiple access, error analysis, standard and improved Gaussian approximations