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Large Class of Optimal Communication Waveforms Exhibit Chaos
Keywords: Chaos, Communication, Filters
Chaotic properties are shown to be embedded in a large class of waveforms matched to linear filters. Recently, a conjecture theorized that any stable infinite impulse response (IIR) filter yields optimal communication waveforms that are chaotic. Under the conjecture’s assumption of using infinite impulse response filters as matched filters, we establish proof for a large class of systems that the optimal com- munication waveform is chaotic. By introducing a general approach of analyzing these waveforms, we show that any bounded solution is deterministic and everywhere expanding. Our approach surprisingly uncovers low-order dynamics, regular timing, and embedded shift maps within this large class. These techniques are applied to the matched waveform of a seventh-order Chebyshev filter as an example of a relatively high-order filter’s underlying low- order dynamics and conjugacy to shift maps. This result confirms the conjecture for a large class of systems and asserts that chaos is fundamental in practical communication signals.
Marko Milosavljevic, Graduate Student
U. S. Army Aviation & Missile Res., Dev., & Eng. Center
Tempe, Arizona

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