INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS Int. J. Commun. Syst. 2007; 20:1081–1095 Published online 20 November 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/dac.863 Performance of optimum wavelet for DS-CDMA chip waveform over multi-path Rayleigh fading channels Ertan O ¨ ztu¨rk* ,y and Barıs ¸ S ¸ ahin Department of Electrical and Electronics Engineering, Zonguldak Karaelmas University, Zonguldak 67100, Turkey SUMMARY In this paper, the probability of error ðP e Þ expression of asynchronous direct sequence-code division multiple access (DS-CDMA) signals using band-limited chip waveforms is derived over multi-path Rayleigh fading channels. In receiver, a matched filter-based rake receiver in conjunction with maximum ratio combiner (MRC) is considered. Numerical values for the P e are calculated for various chip waveforms including an optimum wavelet waveform. Analytical results are verified by conducting simulations. Results show that the optimum wavelet-based scheme outperforms time-limited raised cosine, half sine, rectangular and band-limited square-root raised cosine chip waveform-based schemes in terms of the P e and the capacity defined as the number of users per Hertz for a same P e level. Copyright # 2006 John Wiley & Sons, Ltd. Received 5 June 2006; Accepted 13 September 2006 KEY WORDS: DS-CDMA; chip waveform; optimum wavelet; multi-path Rayleigh fading channel; asynchronous channel 1. INTRODUCTION In recent years, direct sequence-code division multiple access (DS-CDMA) is the dominating method of multiple access (MA) in third-generation (3G) mobile communication systems and one of the most promising MA techniques for future [1]. In DS-CDMA using direct sequence spread spectrum (DSSS), spreading codes are used to differentiate the users on the channel and to spread out the information frequency band to a much larger bandwidth than the bandwidth *Correspondence to: Ertan O ¨ ztu¨rk, Department of Electrical and Electronics Engineering, Zonguldak Karaelmas University, Zonguldak 67100, Turkey. y E-mail: oztuert@iit.edu Contract/grant sponsor: The Scientific and Technical Research Council of Turkey; contract/grant number: PN: EEEAG 103E009 Contract/grant sponsor: Zonguldak Karaelmas University Research Fund; contract/grant number: PN: 2003-45-08-09 Copyright # 2006 John Wiley & Sons, Ltd.