# Generation of high resolution radar signals using three dimensional chaotic flows

#### Abstract

The purpose of this project is to investigate the system parameter and certain signal processing techniques to achieve wide bandwidth and frequency agility in order to build a high resolution radar. The technique relies on the output of an n-dimensional (n>2) non-linear system that exhibits chaotic behavior.^ Firstly, the compressed Lorenz attractor is considered which has a set of three state variables x, y and z and three control parameters ρ, β, and σ. By varying ρ and β as function of time highly chaotic parameter space region is simulated such that chaotic signal behaves optimally. ^ For comparison purpose we introduced the Lang-Kobayashi attractor which also has a set of three state variables the electric field e, its phase component ϕ and the excess carrier number z and two main control parameters L and η for. The FM signals are generated from both the attractors using anyone of the state variables as an instantaneous frequency.^ In both cases, we demonstrated that the obtained FM signal is ergodic and stationary and that the time samples exhibit an invariant probability density function. The corresponding pseudo-phase space trajectories reveal themselves as a strange attractor that may take on the shape of a Mobius strip depending on the time evolution of the signal. ^ A time-frequency analysis of the FM signal shows that the spectrum is centered on a time-dependent carrier frequency. Thus, the FM signal has a high time-bandwidth product and fractional bandwidth similar to that of a chirp. However, the carrier frequency continuously shifts in a linear or quadratic pattern that folds over range of (-f_{s}/2, f_{s}/2).^ The time averaged autocorrelation has main width inversely proportional to bandwidth of the FM signal. The ambiguity surface reveals that the optimized chaotic based FM signal has shape as a set of mountain ridges with low sidelobes both in range and Doppler which is desirable for obtaining high resolution radar and range-Doppler imaging. ^

#### Subject Area

Engineering, Electronics and Electrical|Engineering, System Science

#### Recommended Citation

Pappu, Chandra Sekhar, "Generation of high resolution radar signals using three dimensional chaotic flows" (2010). *ETD Collection for University of Texas, El Paso*. AAI1479724.

http://digitalcommons.utep.edu/dissertations/AAI1479724