Quantitative comparisons of digital chaotic circuits for use in communications

Chaotic spread spectrum communication systems are sought after for their high levels of security, derived from the apparent randomness of the underlying chaotic spreading signal. Traditionally this "randomness" is quantified by the use of Lyupanov exponent(s) that give rates of chaotic state divergence, for continuous-time chaotic circuits. The downside of such continuous-time analog chaotic systems is that they are difficult to synchronize, leading to reduced channel capacity via re-synchronization overhead or compromises in security. These chaotic signals also possess colored spectra, leading to detection and channel utilization disadvantages. Discrete-time and -amplitude systems are simpler to implement, yet more difficult to quantify their "chaotic-ness;" the rate of state divergence is dependent on both computational precision and sampling intervals in sequence generation. Moreover, the existence of a well-defined chaotic attractor is evidence of a failure to meet the desired maximal entropy signal characteristic required for maximum channel capacity throughput. This paper presents comparative simulation measures quantifying the underlying randomness and computational sensitivities for a collection of digital chaotic mappings, qualifying their suitability for use in secure communication systems. Under most measures, the tent map and the logistic map fail to meet the needed performance. The skew tent mapping is found to be better, yet techniques for closed field calculations are found to be superior, without a significant increase in computational resources.