Details of Grant 

EPSRC Reference:	GR/J07754/01
Title:	CHAOTIC DYNAMICS APPLIED TO SIGNAL COMMUNICATIONS
Principal Investigator:	Durrani, Professor T
Other Investigators:
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Department:	Electronic and Electrical Engineering
Organisation:	University of Strathclyde
Scheme:	Standard Research (Pre-FEC)
Starts:	01 May 1993	Ends:	30 April 1995	Value (£):	66,105
EPSRC Research Topic Classifications:	Digital Signal Processing
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Summary on Grant Application Form
The key objectives of the research are to investigate the use of chaotic signals and systems for the provision of secure and reliable signal transmission, or more generally, to develop techniques which embed data in and extract data from chaotic signals. The initial objective involves the analysis and improvement of performance of chaos based masking and signalling schemes particularly in relation to the synchronisation and decoding stages. The second main aim is the extension to alternative nonlinear methods of data transmission. Progress:The first motivation for the use of chaotic nonlinear oscillators as carrier generators was the discovery of self-synchronising systems which allow for the recovery of the carrier signal and dependent state variables at a receiver. These transmission schemes have focused on exploiting specific stability properties associated with a class of nonlinear systems known as synchronised chaotic systems. To improve on the performance of the above, this research has developed new algorithms which employ system independent state estimators based on a nonlinear generalisation of the Luenberger observer for application to data transmission. These estimators are able to operate with systems where no self synchronisation exists. We have shown the connection between the estimators and general embedding techniques through their relation to differential embedding coordinates, which provides an analysis of the robustness of the estimators with respect to the system attractor. This motivates the use of variants of the estimators for cases where the associated gain is close to singular at certain points in state space, through the construction of reduced and increased order observers. The latter, in conjunction with singular value decomposition, is analogous to the use of local principal components in state reconstruction embeddings. We have investigated the use of discriminant and likelihood based decoders to improve receiver error rates by employing the above estimators in a dynamic matched filter' arrangement. These have relied on minimum error classification, and $k$-means and ML estimation using the EM algorithm, respectively. The techniques have been employed in a number of transmission schemes including those based on modulation, masking and signalling. Investigation into increasing security in the latter scheme has led to the proposal of novel communications methods using fractal functions as chaos generating discrete time dynamics whose signals are more difficult to detect. Furthermore, on going research has suggested great promise in the general use of fractal curves as carrier 'signals'. The work has been reported at IEE Colloquium on Exploiting Chaos in Signal Processing, June 1994, the European Signal Processing Conference, September 1994, and an invited presentation will be made at IEEE Workshop on Nonlinear Signal and Image Processing in June 1995.
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Organisation Website:	http://www.strath.ac.uk