Fractal interpolation functions as PN waveform generators for broadband communications

This paper is concerned with the novel use of iterated function systems (IFS) as generators of pseudo-noise (PN) spreading waveforms for broadband communications applications. The motivation for this proposal indirectly arises from the interest in alternative methods of spread spectrum modulation, for example, via the use of synchronising chaotic carriers and localized wavelet filters. IFS related signals and systems have already shown themselves to be significantly important in modelling and analysis, from multiresolution wavelet methods to fractal image coding techniques. While these applications tend to emphasize the time-frequency localization, we show that IFS are capable of creating dispersive PN signatures. Concentrating on fractal interpolation functions (FIF), we show how their construction can be written in terms of a chaotic Markov shift system and use this to qualify a proposed whitening procedure. The role of waveform sampling is emphasised. Finally, we apply them as signatures in the provision of CDMA communications.