Generating and Detecting Solvable Chaos at Radio Frequencies with Consideration to Multi-User Ranging

Abstract

High entropy waveforms exhibit desirable correlation properties in radar and sonar applications when multiple systems are used in close proximity. Unfortunately, the information content of these signals can impose high sampling requirements for digital detection techniques. Solvable chaotic oscillators have been proposed to address such issues due to their simple, matched filters, where hardware has been demonstrated with a bandwidth of 10–20 kHz. To extend applications of these systems, we present theory, design, and experimental verification of solvable chaos at 1 MHz using simple off-the-shelf components. The waveforms produced by this system were propagated over a 2.45 GHz RF link and detected with an RLC-based, purely analog matched filter. Further, we show that properties of this special class of chaotic systems can be exploited to yield RF noise sources that are generally advantageous for multi-user ranging applications when compared to conventional techniques. The result is a simple, low-cost, and potentially low-power RF ranging system that requires very little digital signal processing.

Extracting Communication, Ranging and Test Waveforms with Regularized Timing from the Chaotic Lorenz System

“…Chaotic waveforms play a significant role in the development of spread spectrum communication [1][2][3][4], radar [5][6][7], sonar [8,9] and emerging dual-purpose [10,11] systems. Additionally, these waveforms are often used to test time series prediction algorithms [12,13] due to their essentially unpredictable nature [14,15].…”

Synthesis of Analog Matched Filters for Signals of Different Durations

“…A group of scientists [10] studied the process of radio signal transmission in a transmission channel used by other users to transmit and receive information. To improve the characteristics of information transmitted over a shared channel, it was proposed to use chaos generators.…”

“…The publications cited, encompassing references [1][2][3][4][5][6][7][8][9][10][11][12][13][14], lack the necessary information for making a reasoned selection of filter parameters tailored to a specific implementation case. Consequently, it becomes imperative to explore the correlation between signal parameters and filter parameters to ensure the minimal usage of filter elements and maintain the stability of their characteristics-an aspect thoroughly addressed in this article.…”

“…Relations (10) and ( 11) have a deep physical meaning. The first of them can be called the condition of compensation of the initial phases in the signal spectrum, since the phase shift in the filter −𝜃 𝑝 (𝜔) is equal in magnitude and inverse in sign to the initial phase of the corresponding component of the spectrum 𝑃(𝜔) of the input signal.…”

Drastically reduced sensor hardware for solvable chaos‐based sonar

“…Introduction: Chaotic waveforms provide advantages in communication [1], ranging [2][3][4] and joint communication/ranging [5] systems. Recently, solvable chaotic systems have produced optimal waveforms with elegant matched filter receivers [6][7][8]. Milestone demonstrations established noise ranging schemes with sub-Nyquist sampling [9] and were recognized for potential multipath resilience [10], though this feature has never been shown experimentally in a ranging system.…”