Chaos In Circuits And Systems
With a combination of overview, tutorial and technical articles, this book describes state-of-the-art research on significant problems in the field of chaos in circuits and systems.
TABLE OF CONTENTS Chaos In Circuits And Systems
22.6: CSK with Two Basis Functions
22.6 CSK with Two Basis Functions
22.6.1 Modulation
In CSK with two basis functions, the elements of the signal set are given by
where the basis functions g 1( t) and g 2( t) are derived from chaotic sources.
In a special case of binary CSK, also called "chaotic switching" [12], the two elements of the signal set are simply weighted basis functions; the transmitted sample functions are 
and 
, representing symbols "1" and "0," respectively. The corresponding signal vectors are
where E b denotes the average energy per bit.
The signal-space diagram for chaotic switching and orthonormal basis functions g 1( t) and g 2( t) is shown in Fig. 22.13. Note that the Euclidean distance between the two message points is 
, which is the same as for COOK but is less than that of antipodal CSK with one basis function. This implies that the noise performance of chaotic switching is at best 3 dB worse than that of the antipodal modulation scheme described in Sec. 22.5.
Figure 22.13: Signal-space diagram of chaotic switching.
22.6.2 Demodulation
22.6.2.1 Coherent correlation receiver
A coherent correlation receiver, as shown in Fig. 22.14, may be used to estimate the elements s mj of the signal vector. In the noise-free case, with perfect regeneration of the basis functions, y 1( t) = g 1( t) and y 2( t) = g 2( t).
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