Performance of wavelet based Multi‐Chip Rate DS‐CDMA signals over multi‐path Nakagami‐m fading channels

Multi‐Chip Rate/Direct Sequence‐Code Division Multiple Access (MCR/DS‐CDMA) technique using scaled chip waveforms has been designed as an alternative to multi‐data rate DS‐CDMA techniques having constant chip rates. In this work, the probability of error (P_e) expression for MCR/DS‐CDMA signals is derived over multi‐path Nakagami‐m fading channels to investigate the effects of chip waveforms on it. This paper also proposes the use of orthogonal wavelets as chip waveforms of MCR/DS‐CDMA signals over the considered channel. For numerical calculations, Daubechies‐22 (D₂₂) wavelet is used because its side lobes are 40 dB below its main lobe in frequency domain. D₂₂ is compared with a Square Root Raised Cosine (SRRC) chip waveform. In the numerical calculations, only first four scales of the chip waveforms relating to four different chip/data rates are considered. The results for the P_e performance and the capacity (the number of user per Hertz for a same P_e level) show that D₂₂ significantly outperforms the SRRC chip waveform at all data rates, due to low cross correlations among different scales of orthogonal wavelets. Besides, by increasing the number of scales, the advantage of the use of orthogonal wavelets will increase furthermore. Copyright © 2007 John Wiley & Sons, Ltd.