An Experimental Investigation of Performance Improvement of Digital Signal Processing Systems Using Band-Limited Nonlinearities

摘要

In this thesis we demonstrate experimentally a number of practical results of the applicationof nonlinearities in different digital signal processing scenarios, including chaosgeneration and synchronisation, noise-induced signal-to-noise ratio improvements andpossible stochastic resonant behaviour exhibited by digitally implemented nonlinearities.Somewhat non-intuitively, all these phenomena that appear only in nonlinear systems,already affect many aspects of signal processing and communications, and have the potentialfor even greater impact.We implement a hybrid secure communication system with chaotic masking via a freespace, point-to-point optical channel. The chaos generation is based on nonlinear digitalsignal processing techniques, and the encrypted signal is created electronically. Previously,successful synchronisation and recovery have been achieved for such systemsconnected directly with a coaxial cable. Here, the communication through an optical linkis successfully realised by imprinting this signal into the output of a semiconductor laser,and by converting this signal back into electronic form using a photodetector. The performanceof the system with an optical channel is evaluated for different nonlinearities,and also compared to the implementation with the cable link. Successful communicationthrough a free-space channel exposed to interference and noise and including multiplesignal conversions presents an experimental validation of the practical usability of thiscommunication technique.We investigate performance improvements obtained by the use of band-pass nonlinearities,which can be implemented in analog or digital form. The focus is on thedifferences in behaviour resulting from different implementations of functionally thesame nonlinearity. We show that the behaviour of a static nonlinearity with the samefunctional description depends on its physical implementation (discrete or analog),and agrees with the predictions of the theory developed using the approach that correspondsto the way the nonlinearity was implemented. In other words, a band-limited nonlinearitythat is implemented digitally displays different behaviour from its analog counterpart.We demonstrate a clear dependence of the observed noise-induced improvementson the discretisation frequency. Our results bring closer two conflicting theoretical modelsdescribing the behaviour of static nonlinearities. We also formulate a hypothesis thataliasing of spectrally correlated components is the cause of the observed differences inbehaviour.We further investigate the behaviour of digitally implemented nonlinearities in lightof our ‘aliasing’ hypothesis. We implement randomised sampling schemes, in order toeliminate aliasing, and techniques for spectral analysis of non-uniformly sampled signals.Our investigation demonstrates difficulties in spectral analysis by means of thesetechniques, and shows the limited applicability of random sampling in this context, dueto the excessive requirements on computational power, time and storage.The results from the experiment in which controlled aliasing is introduced, furtherstrengthen our hypothesis about the role of aliasing in creating the previously observedbehaviour, and differences between analog and digitally implemented nonlinearities.