Optimal Estimation and Sequential Channel Equalization Algorithms for Chaotic Communications Systems

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