A chaotic communication system with a receiver estimation engine

A chaotic communications system utilizing a receiver estimation engine has been designed and simulated. This estimation engine both synchronizes and recovers data by mapping probability calculation results onto the chaotic dynamics via a strange attractor geometrical approximation. The restrictive standard chaotic synchronization requirements of either a stable/unstable subspace separation or a chaotic system inversion are thereby avoided. These techniques can be implemented with any chaotic system for which a suitable geometric model of the attractor can be found.;Two versions of the same attractor are employed for the transmission of the logical states of zero and one such that the continuous range of transmitted values is identical for both states. Any received value is therefore valid for either logical state, confusing the issue of message recovery for the unintended listener.;The design of the estimation engine involves the determination and modeling of both the logical zero and logical one versions of the strange attractor, as well as the transmitted chaotic sequence probability density function (PDF). A lossless non-fading additive white Gaussian noise (AWGN) channel is assumed, which enables the estimation of channel noise power via a probabilistic calculation utilizing a numerical nonlinear root determination technique that iteratively modifies the root. Two estimates of the transmitted value are created from the received iterate by different calculations, based on probability and the transmitted PDF. A third estimate is generated from the chaotic processing of the previous receiver final decision. The three estimates are combined using a probability-based weighted average into the initial current decision. The final current decision incorporates chaotic dynamics by mapping the initial decision onto the geometrical model of the attractors via a minimum Euclidean distance metric.;In the case detailed here, the estimation engine is built upon the approximation of the Henon attractor by four parabolic sections and the modeling of the transmit PDF by a DC value plus a summation of Gaussian functions. It recovers data with as little as two chaotic iterates per bit for a large enough signal-to-noise ratio (SNR) and exhibits better bit error rate (BER) values as the number of iterates per bit increases.