Lyapunov Exponent Testing for AWGN Generator System


Additive White Gaussian Noise (AWGN) is common to every communication channel. It is statistically random radio noise characterized by a wide frequency range with regards to a signal in communication channels. In this paper, AWGN signal is generated through design an analogue circuit method, and then the multiple recursive method is also used to generate random data signal that is used for testing by Lyapunov exponent. Furthermore an algorithm for software generating of Additive White Gaussian Noise is presented. Lyapunov exponent test for chaos is used to distinguish between regular and chaotic dynamics of the generated data by the two methods. Simulation results are enhanced with the use of Microcontroller chip, since the hardware of the application is implemented by microcontroller-embedded system to obtain computerized noise generator. The results show that the generated AWGN signal by the analogue method and the multiple recursive method is chaotic which implies the random like-noise behavior.

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M. Hathal, H. , A. Abdulhussein, R. and Ibrahim, S. (2014) Lyapunov Exponent Testing for AWGN Generator System. Communications and Network, 6, 201-208. doi: 10.4236/cn.2014.64022.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Xiao, P. (2009) Effect of Additive White Gaussian Noise (AWGN) on the Transmitted Data. 1-15.
[2] Gentle, J.E. (2003) Random Number Generation and Monte Carlo Methods. 2nd Edition, Springer, Berlin.
[3] Deng, L.-Y., Shiau, J.-J.H. and Shing Lu, H.H. (2011) Large-Order Multiple Recursive Generators with Modulus 231-1. INFORMS Journal on Computing, 1-12.
[4] Deng, L.-Y., Shiau, J.-J.H. and Shing Lu, H.H. (2012) Efficient Computer Search of Large-Order Multiple Recursive Pseudo-Random Number Generators. Journal of Computational and Applied Mathematics, 236, 3228-3237.
[5] Giacobazzi, R. and Ranzato, F. (1998) Some Properties of Complete Multiple Recursive Lattices. Algebra Universe, 40, 189-200.
[6] Jovic, B. (2011) Synchronization Techniques for Chaotic Communication Systems. Springer, Berlin.
[7] Aziz, M.M. and Faraj, M.N. (2012) Numerical and Chaotic Analysis of CHUA’S CIRCUT. Journal of Emerging Trends in Computing and Information Sciences, 3.
[8] Alligood, K.T., Sauer, T.D. and Yorke, J.A. (1996) Chaos: An Introduction to Dynamical Systems. Springer, Berlin.
[9] Sun, Y. (2011) Fault Detection in Dynamic Systems Using the Largest Lyapunov Exponent. Thesis, Texas.

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