  The invariance of the Lyapunov exponent of a chaotic signal as it propagates
along a wireless transmission channel provides a theoretical base for the
application of chaos in wireless communication. In additive Gaussian channel,
the chaotic signal is proved to be the optimal coherent communication waveform
in the sense of using the very simple matched filter to obtain the maximum
signal-to-noise ratio. The properties of chaos can be used to reduce simply and
effectively the Inter-Symbol Interference (ISI) and to achieve low bit error
rate in the wireless communication system. However, chaotic signals need very
wide bandwidth to be transmitted in the practical channel, which is difficult
for the practical transducer or antenna to convert such a broad band signal. To
solve this problem, in this work, the chaotic signal is applied to a radio-wave
communication system, and the corresponding coding and decoding algorithms are
proposed. A hybrid chaotic system is used as the pulse-shaping filter to obtain
the baseband signal, and the corresponding matched filter is used at the
receiver, instead of the conventional low-pass filter, to maximize the
signal-to-noise ratio. At the same time, the symbol judgment threshold
determined by the chaos property is used to reduce the Inter-Symbol
Interference (ISI) effect. Simulations and virtual channel experiments show
that the radio-wave communication system using chaos obtains lower bit error
rate in the multi-path transmission channel compared with the traditional
radio-wave communication system using Binary Phase Shift Keying (BPSK)
modulation technology and channel equalization.
