Generation of high resolution radar signals using three dimensional chaotic flows

Chandra Sekhar Pappu, University of Texas at El Paso


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 (-fs/2, fs/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.