<title>Chaotic signals for wideband radar imaging</title>

Abstract

We explore the characteristics of chaos for wideband radar imaging. Chaos can be generated via nonlinear functions that produce statistically independent samples with invariant probability density functions. By feeding this type of chaos to the input of a voltage-controlled oscillator, a stochastic frequency modulated signal with fractal features is generated. The FM signal is an ergodic and stationary process with initial random phase. The power spectral density of such signal is typically broadband. We show that the time autocorrelation associated with the FM signal provides high range resolution for zero Doppler and dies out rapidly for increasing Doppler shifts. Furthermore, we show that a set of realizations of the signal can be processed into a set of ambiguity surfaces that when averaged yield a low self-noise pedestal.

Assessment and improvement of autocorrelation performance of chaotic sequences using a phase space method

“…Its main peak is sharp and prominent, while its side lobe is low and hardly distinguishable, so the performance is very good. Although the performance of the Tent sequence's autocorrelation is good, after Random Frequency Modulation (RFM) [3][4][5][6], the performance deteriorates. As shown in Figure 2, there are many obvious side lobes.…”

“…We treat the state variable of a dynamic system as a random variable [3][4][5][6][19][20][21][22][23][24].…”

“…However, the problem of how to judge whether a sequence's autocorrelation performance is good has, hitherto, not been completely solved, and we have no simple method to assess and improve the autocorrelation performance of a chaotic sequence. Therefore, applications of chaotic sequences are limited [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

“…In some cases, the autocorrelation performance of chaotic sequences is poor, while in others, although some chaotic sequences achieve good autocorrelation performance, the performance degrades after a number of modulations [3][4][5][6], which impedes the detection and identification of signals. As a result, the autocorrelation of chaotic sequences has attracted the attention of many researchers [2][3][4][5][6][7].…”

“…Recently, chaotic sequences have been used in noise radar as a noise source [1][2][3][4][5][6][7][8][9][10][11]18], thereby exposing the autocorrelation problem. In some cases, the autocorrelation performance of chaotic sequences is poor, while in others, although some chaotic sequences achieve good autocorrelation performance, the performance degrades after a number of modulations [3][4][5][6], which impedes the detection and identification of signals.…”