K. Max Wong, Jiangfeng Wu, Timothy N. Davidson and Qu Jin.
Wavelet packet division multiplexing and wavelet packet design under
timing error effects.
IEEE Transactions on Signal Processing,
45(12):2877-2890, December 1997.
Wavelet Packet Division Multiplexing (WPDM) is a multiple signal transmission technique in which the message signals are waveform coded onto wavelet packet basis functions for transmission. The overlapping nature of such waveforms in time and frequency provides a capacity improvement over the commonly used frequency division multiplexing (FDM) and time division multiplexing (TDM) schemes, whilst their orthogonality properties ensure that the overlapping message signals can be separated by a simple correlator receiver. The interference caused by timing offset in transmission is examined. A design procedure which exploits the inherent degrees of freedom in the WPDM structure to mitigate the effects of timing error is introduced and a waveform which minimizes the energy of the timing error interference is designed. An expression for the probability of error due to the presence of Gaussian noise and timing error for the transmission of binary data is derived. The performance advantages of the designed waveform over standard wavelet packet basis functions are demonstrated by both analytical and simulation methods. The capacity improvement of WPDM, its simple implementation, and the possibility of having optimum waveform designs indicate that WPDM holds considerable promise as a multiple signal transmission technique.
We have also analysed the performance of this system in impulsive noise environments.
We have also proposed various `hopping' schemes reminiscent of frequency hopping schemes.
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