Abstract
Many previously proposed communications systems based on chaos
disregard common channel distortions and fail to work under
realistic channel conditions. In this paper, optimal
estimation and sequential channel equalization
algorithms are proposed for chaotic communications systems where
information is encoded using symbolic dynamics
representations. For the optimal estimate of the transmitted signal,
the symbolic dynamics representation of
chaotic systems is first exploited to represent the chaotic dynamics of the signal
by an equivalent trellis diagram. Then,
the Viterbi algorithm is used to achieve an optimal
estimate of the noise corrupted chaotic sequence. For the
sequential channel equalization algorithm, the dynamics-based
trellis diagram is expanded to accommodate a finite impulse
response (FIR) model of the channel. Once the initial estimate of the
channel parameters is obtained through the training sequence,
then the Viterbi algorithm is used to estimate the chaotic
sequence. If necessary, channel parameters can then be updated through successive
estimates of the chaotic sequence. The proposed algorithms are simulated for
both time-invariant and time-varying channels.