Private communication over fading channels with chaotic DS/SS

We consider chaotic spread spectrum (DS/SS) systems for secure communication over fading channels, whereby a symbol stream is linearly modulated on a spreading sequence generated by iterating an initial condition through a suitably chosen chaotic map. For a class of these systems, we develop methods for quantifying the uncoded probability of error, Pr(ε), of unintended receivers that do not know the initial condition. We show that the Pr(ε) of unintended receivers exploiting K degrees of diversity decays as 1/√(SNR), in contrast to the intended receiver Pr(ε) that decays as 1/(SNR)^K, demonstrating that these systems can provide reliable and private communication over fading channels.