A generalization of tent map and its use in EKF based chaotic parameter modulation/demodulation

First, the one-dimensional tent map is generalized to extend the range of parameters for chaotic behavior. Then, a chaotic spread spectrum communication scheme is proposed by employing a generalized symmetric tent map to implement high efficiency binary message modulation. Binary bit streams are represented by noise-like and broadband chaotic sequences generated from a symmetric tent map with different parameter sets. Generalizing the tent map by finding the largest parameter set that drives this map to chaos allows modulation of multiple bits by one chaotic sequence at a time, thus the message carrying capacity is greatly improved in the proposed system. The original binary message is recovered by employing an extended Kalman filter to estimate the state of the chaotic system and identify the parameters of the received noise contaminated chaotic sequence, therefore extracting the binary message by matching the parameter sets with the corresponding binary bit stream. Bit error rate performance is presented in simulation studies.