Design and simulation of a high frequency exact solvable chaotic oscillator

Beal, Aubrey N.; Bailey, John; Hale, Sidni; Dean, Robert N.; Hamilton, Michael C.; Tugnait, J.K.; Hahs, Daniel W.; Corron, Ned J.

doi:10.1109/milcom.2012.6415803

Cited by 12 publications

(6 citation statements)

References 10 publications

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“…As noted earlier, the benefits of this system can degrade with unwanted delays between the stretching and folding mechanisms. This type of latency has been shown to cause distortion in the chaotic waveform, thus, compromising its solvability [17,18] in COTS implementations. As mentioned earlier, compensation methods have been theoretically examined to correct for these imperfections while retaining solvability [17].…”

Section: Generating Solvable Chaos At Radio Frequenciesmentioning

confidence: 99%

“…In this manuscript, these compensation techniques are realized for the first time in hardware, where the compensation circuitry is shown in Figure 6. The circuit was fabricated as described in [16][17][18] with op-amps of type LT1361, 0805 passive components and R = 1.77 kΩ (variable through a 5 kΩ potentiometer), L = 48 mH and C = 330 pF.…”

Section: Generating Solvable Chaos At Radio Frequenciesmentioning

confidence: 99%

“…The hybrid nature of solvable chaos paired with the aim for higher operational frequencies makes electronic implementation difficult [17]. As a result, physical implementations have historically contained deviations from the ideal analytic solution at frequencies above ranges of 200 kHz [18]. In this manuscript, we will examine a circuit representation of a technique for mitigating these design issues.…”

Section: Introductionmentioning

confidence: 99%

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

Beal

Cohen

Syed

2020

Sensors

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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.

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Section: Generating Solvable Chaos At Radio Frequenciesmentioning

confidence: 99%

Section: Generating Solvable Chaos At Radio Frequenciesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Beal

Cohen

Syed

2020

Sensors

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“…is an exact analytic solution to a physically realizable chaotic oscillator [17][18][19][20][21][22][23]. Remarkably, the autonomous oscillation of this system generates a waveform constructed of acausal basis functions.…”

Section: (B) Integrate-and-dump Resistor-inductor-capacitor Matched Filtermentioning

confidence: 99%

Chaos in optimal communication waveforms

Corron¹,

Blakely²

2015

Proc. R. Soc. A.

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The properties of nonlinear dynamics and chaos are shown to be fundamental to optimal communication signals subject to two practical and realistic design requirements: (i) operation in a noisy environment and (ii) simple hardware implementation. Starting with a simple electronic circuit, a linear filter receiver is presumed, and the matched optimal communication waveform that maximizes the receiver signal-to-noise performance is derived. A return map using samples from this optimal waveform is conjugate to a shift, thereby implying the waveform is chaotic. The optimal communication waveform for a second simple receiver is similarly derived, and it is found to be an exact solution to a physically realizable chaotic oscillator. Thus, a practical consequence of chaos in these waveforms is the potential for simple and efficient signal generation using chaotic oscillators. A conjecture is made that the optimal communication waveform for any stable infinite impulse response filter is similarly chaotic.

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“…Although surprisingly simple systems constructed from both familiar [6] and exotic [7] components have been shown to behave chaotically, such systems do not readily lend themselves to control. Simulations have shown that hardware can be developed for a potentially controllable chaotic system with an exact solution [8], but this hardware relies on many analogue components that are not expected to scale well with high-speed operation.…”

mentioning

confidence: 99%

High‐frequency reverse‐time chaos generation using digital chaotic maps

et al. 2014

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Reverse-time chaos can be used to realise hardware chaotic systems that can operate at speeds equivalent to existing state-of-the-art while requiring significantly less complex circuitry. Unlike traditional chaotic systems, which require significant analogue hardware that is difficult to realise at high speed, the reverse-time system can be realised with a field programmable gate array calculating a digital iterated map. The resulting output forgoes the need for digital-to-analogue conversion by directly driving a series RLC filter. Since the dynamics of this system are determined by an iterated map, precise control of this system is possible by adjusting the map's initial condition. Hardware results for the controllable reverse-time system demonstrate chaotic behaviour at an operating frequency of 1.8 MHz and show promise for extension to higher frequencies.Introduction: Chaotic electronic systems have been previously investigated for their potential utility in many applications including communication [1] and radar [2]. Previous work has shown that such systems can be constructed and tuned, such that they possess dynamics advantageous for their specific application [3]. Control schemes have also been devised that can maintain these systems on desired trajectories while in operation [4]. By combining these characteristics with matched filter decoding [5], many of the necessary components for a modern high-performance communication system or radar may be realised with chaotic dynamics.Actually realising physical systems that exhibit the chaotic dynamics necessary for these applications has long proven to be a difficult task. Although surprisingly simple systems constructed from both familiar [6] and exotic [7] components have been shown to behave chaotically, such systems do not readily lend themselves to control. Simulations have shown that hardware can be developed for a potentially controllable chaotic system with an exact solution [8], but this hardware relies on many analogue components that are not expected to scale well with high-speed operation.Reverse-time chaos provides a potential solution for realising chaos in hardware with both solvable and controllable properties without sacrificing the ability to scale in frequency. First proposed by Corron et al. in [9], reverse-time chaos describes behaviour that differs from traditional chaos by using the current state of the system to represent all of its past states instead of all of its future states. Despite this difference, reversetime chaos retains a positive Lyapunov exponent and a corresponding sensitivity to initial conditions that defines traditional chaotic systems.

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Design and simulation of a high frequency exact solvable chaotic oscillator

Cited by 12 publications

References 10 publications

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

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

Chaos in optimal communication waveforms

High‐frequency reverse‐time chaos generation using digital chaotic maps

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