Optimal communications with infinite impulse response matched filters

Abstract

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.