Selecting the Lorenz parameters for Wideband Radar waveform Generation

Radar waveforms based on chaotic systems have occasionally been suggested for a variety of radar applications. In this paper, radar waveforms are constructed with solutions from a particular chaotic system, the Lorenz system, and are called Lorenz waveforms. Waveform properties, which include the peak autocorrelation function side-lobe and the transmit power level, are related to the system parameters of the Lorenz system. Additionally, scaling the system parameters is shown to correspond to an approximate time and amplitude scaling of Lorenz waveforms and also corresponds to scaling the waveform bandwidth. The Lorenz waveforms can be generated with arbitrary time lengths and bandwidths and each waveform can be represented with only a few system parameters. Furthermore, these waveforms can then be systematically improved to yield constant-envelope output waveforms with low autocorrelation function sidelobes and limited spectral leakage. Index Terms Radar, Waveforms, Wideband, Chaos, Lorenz, Time-Scaling.