Optimal communications with infinite impulse response matched filters

Marko S. Milosavljevic, Ned J. Corron and Jonathan N. Blakely

Chaos, Solitons & Fractals, 2020, vol. 138, issue C

Abstract: Optimal communication waveforms matched to a large and practically important class of filters are investigated and shown to be chaotic. Filters of this class are defined by an infinite impulse response (IIR) and a transfer function comprising a finite number of distinct stable poles. This class contains many of the most popular and widely used filter families, including Butterworth, Chebyshev (type I), and Bessel. For such a filter, a matched basis function is derived and convolved with a random binary sequence to construct a communication waveform. It is shown that this waveform is chaotic in the sense that it is deterministic and characterized by a positive Lyapunov exponent. This result supports a recent conjecture that optimal communication waveforms matched to stable IIR filters are chaotic, and it further establishes that chaos is fundamental to modern communication theory.

Keywords: Communication theory; Infinite impulse response; Matched filter; Chaos; Chaotic waveform (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920302228

DOI: 10.1016/j.chaos.2020.109822

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