Fractal PN signals for broadband communications: Interpolation functions and PN wavelets

There has been much interest recently in alternative methods of providing spread spectrum communications through the use of novel modulating carriers such as nonlinear chaotic signals, and localized wavelet and multirate filters. This paper presents research extending recent studies undertaken by the authors into the provision of CDMA spread spectrum through the use of iterated function system (IFS) or alternatively, multiscale difference equation (MSDE) defined pseudo-noise (PN) functions. While such equations are already important in the construction of wavelets and other models for signal coding and representation, here we are concerned with their ability to construct pseudo-random functions for use as broadband CDMA modulation signatures. Concentrating on fractal interpolation functions (FIF), we show how their construction can be written in terms of a Markov shift system and use this to qualify a proposed whitening procedure, and apply them as CDMA signatures. We subsequently use these functions in the construction of PN scaling functions and orthogonal wavelets.