Statistical analysis of Bernoulli, logistic, and tent maps with applications to radar signal design

Héctor Garcés; Benjamin C. Flores

doi:10.1117/12.666364

8 May 2006 Statistical analysis of Bernoulli, logistic, and tent maps with applications to radar signal design

Héctor Garcés, Benjamin C. Flores

Proceedings Volume 6210, Radar Sensor Technology X; 62100G (2006) https://doi.org/10.1117/12.666364
Event: Defense and Security Symposium, 2006, Orlando (Kissimmee), Florida, United States

Abstract

The uniqueness of the Bernoulli frequency modulated signal, and other chaos-based FM signals, can be exploited to improve the performance of the Synthetic Aperture Radar systems. Recent work suggests that the Bernoulli map has an unusual behavior compared to other one dimensional discrete maps, such as Logistic or Tent maps. Additional work indicates that the sum of consecutive Bernoulli samples is generally non-Gaussian, except when the map parameters A= 0.5 and B = 1.8. This motivates us to analyze the behavioral differences of the maps for various parameters using the Lyapunov exponent, pseudo-phase spatial trajectory and neighbor samples correlation. Specifically, the correlation of Bernoulli samples is analyzed in terms of the probability density function which is derived from experimental data. Some of statistical tools used include the Forbenius-Perron Operator, and the correlation properties of chaotic sequences. In addition, other measurements of chaos derived from nonlinear dynamical modeling will be used such as: the Lyapunov exponent and the bifurcation diagram. Results show differences between the calculated features; for example, the Lyapunov exponent is bigger for Bernoulli FM than Logistic or Tent FM. In summary, we determined that Bernoulli FM is more chaotic than Logistic or Tent FM. We have also found another singularity in the correlation of sequence samples for the Bernoulli map.

Citation Download Citation

Héctor Garcés and Benjamin C. Flores "Statistical analysis of Bernoulli, logistic, and tent maps with applications to radar signal design", Proc. SPIE 6210, Radar Sensor Technology X, 62100G (8 May 2006); https://doi.org/10.1117/12.666364

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available