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In this paper, we present the performance of a hybrid modulation technique derived from binary frequency shift keying. In the hybrid scheme, each frequency is allowed to be phase modulated with any of p discrete, equally spaced phase shifts. The spectral separation between frequencies, A f , is chosen to make the carriers orthogonal, thus generating a multidimensional modulation scheme. The performance of complete and expurgated phase codes is examined for the Gaussian and Rayleigh fading channels, and their spectral characteristics are determined.

SUMMARYIn 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 ðP e Þ 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 À3 :

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