Performance of optimum wavelet waveform for DS‐CDMA chip waveform over QS‐AWGN channel

In this paper, we search for a better chip waveform based on orthogonal wavelets for direct sequence‐code division multiple access (DS‐CDMA) signals to improve the probability of error (P_e) performance with minimal signal bandwidth variations. First, we derive the P_e expression over a quasi‐synchronous additive white Gaussian noise channel for DS‐CDMA signals, which use various pulse shaping waveforms including orthogonal wavelets as chip waveforms. It is observed that this expression depends on the chip waveform. Then, we design an optimum wavelet by using the relationship between wavelets and filter coefficients to reduce the probability of error. The DS‐CDMA system using the optimum wavelet waveform results in a lower probability of error than those using the conventional chip waveforms such as raised cosine, half‐sine and rectangular waveforms. Especially, the P_e of the optimum wavelet‐based scheme becomes significantly better than those of the conventional chip waveforms‐based schemes under the heavy loading that is the case for commercial wireless systems. When the systems work with full load (i.e. the number of users equals the processing gain), the optimum wavelet‐based system results in 0.5, 2.1 and 4 dB better SNR values than those of the raised cosine, half‐sine and rectangular‐based systems, respectively, for a P_e value of 10^?3. Copyright © 2005 John Wiley & Sons, Ltd.