Kevin M. Cuomo

Synchronization of Lorenz-based chaotic circuits with applications to communications

A circuit implementation of the chaotic Lorenz system is described. The chaotic behavior of the circuit closely matches the results predicted by numerical experiments. Using the concept of synchronized chaotic systems (SCSs), two possible approaches to secure communications are demonstrated with the Lorenz circuit implemented in both the transmitter and receiver. In the first approach, a chaotic masking signal is added at the transmitter to the message, and at the receiver, the masking is regenerated and subtracted from the received signal. The second approach utilizes modulation of the coefficients of the chaotic system in the transmitter and corresponding detection of synchronization error in the receiver to transmit binary-valued bit streams. The use of SCSs for communications relies on the robustness of the synchronization to perturbations in the drive signal. As a step toward further understanding the inherent robustness, we establish an analogy between synchronization in chaotic systems, nonlinear observers for deterministic systems, and state estimation in probabilistic systems. This analogy exists because SCSs can be viewed as performing the role of a nonlinear state space observer. To calibrate the robustness of the Lorenz SCS as a nonlinear state estimator, we compare the performance of the Lorenz SCS to an extended Kalman filter for providing state estimates when the measurement consists of a single noisy transmitter component. >

MIMO radar theory and experimental results

The continuing progress of Moores law has enabled the development of radar systems that simultaneously transmit and receive multiple coded waveforms from multiple phase centers and to process them in ways that have been unavailable in the past. The signals available for processing from these multiple-input multiple-output (MIMO) radar systems appear as spatial samples corresponding to the convolution of the transmit and receive aperture phase centers. The samples provide the ability to excite and measure the channel that consists of the transmit/receive propagation paths, the target and incidental scattering or clutter. These signals may be processed and combined to form an adaptive coherent transmit beam, or to search an extended area with high resolution in a single dwell. Adaptively combining the received data provides the effect of adaptively controlling the transmit beamshape and the spatial extent provides improved track-while-scan accuracy. This paper describes the theory behind the improved surveillance radar performance and illustrates this with measurements from experimental MIMO radars.

Signal processing in the context of chaotic signals

Signals generated by chaotic systems represent a potentially rich class of signals both for detecting and characterizing physical phenomena and in synthesizing new classes of signals for communications, remote sensing, and a variety of other signal processing applications. Since classical techniques for signal analysis do not exploit the particular structure of chaotic signals there is both a significant challenge and an opportunity in exploring new classes of algorithms matched to chaotic signals. The authors outline a variety of signal processing issues associated with the analysis and synthesis of chaotic signals. In addition two examples are described in detail, illustrating some possible ways in which the characteristics of chaotic signals and systems can be exploited. One example is a binary signaling scheme using chaotic signals. The second example is the use of synchronized chaotic systems for signal masking and recovery.<<ETX>>

Chaotic signals and systems for communications

The authors propose and demonstrate two approaches to communications based on synchronized chaotic signals and systems. In the first approach, a chaotic masking signal is added at the transmitter and regenerated and subtracted at the receiver. The second approach utilizes modulation of the coefficients of the chaotic system in the transmitter and corresponding detection of synchronization error in the receiver to transmit binary-valued bit streams. Both approaches are demonstrated using a transmitter circuit with dynamics that are governed by the chaotic Lorenz system. A synchronizing receiver circuit which exploits the ideas of synchronized chaotic systems is used for signal recovery.<<ETX>>

ROBUSTNESS AND SIGNAL RECOVERY IN A SYNCHRONIZED CHAOTIC SYSTEM

Recent papers have demonstrated that synchronization in the Lorenz system is highly robust to additive perturbation of the drive signal. This property has led to a concept known as chaotic signal masking and recovery. This paper presents experiments and an approximate analytical model that quantify and explain the observed robustness of synchronization in the Lorenz system. In particular, we explain why speech and other narrowband perturbations can be recovered faithfully, even though the synchronization error is comparable in power to the message itself.

Quasi-Orthogonal Wideband Radar Waveforms Based on Chaotic Systems

Many radar applications, such as those involving multiple-input, multiple-output (MIMO) radar, require sets of waveforms that are orthogonal, or nearly orthogonal. As shown in the work presented here, a set of nearly orthogonal waveforms with a high cardinality can be generated using chaotic systems, and this set performs comparably to other waveform sets used in pulse compression radar systems. Specifically, the nearly orthogonal waveforms from chaotic systems are shown to possess many desirable radar properties including a compact spectrum, low range sidelobes, and an average transmit power within a few dB of peak power. Moreover, these waveforms can be generated at essentially any practical time length and bandwidth. Since these waveforms are generated from a deterministic process, each waveform can be represented with a small number of system parameters. Additionally, assuming these waveforms possess a large time-bandwidth product, a high number of nearly orthogonal chaotic waveforms exist for a given time and bandwidth. Thus the proposed generation procedure can potentially be used to generate a new transmit waveform on each pulse.

Distributed Coherent Aperture Measurements for Next Generation BMD Radar

This paper describes the distributed coherent aperture work being carried out at MIT Lincoln Laboratory in support of the next generation radar (NGR) program under the direction of the Radar Systems Technology (RST) group within the Missile Defense Agency/Advanced Systems (MDA/AS) Directorate. The NGR concept achieves transportability and high-radar sensitivity by coherently combining multiple distributed radar apertures in a building block manner. The operational concept uses orthogonal noise-like waveforms and multiple-input multiple-output (MIMO) techniques for cohere-on-receive operation and for adaptively estimating the transmit coherence parameters. In cohere-on-transmit mode, like waveforms are used and the relative phase and transmit time of each transmit pulse is adaptively adjusted so that the transmitted pulses arrive at the target in-phase and at the same time. In cohere-on-receive mode, an N2 signal-to-noise ratio (SNR) gain is achieved over a single aperture when the orthogonal waveforms are combined coherently. In cohere-on-transmit mode, full coherence is achieved on both transmit and receive for an N2 SNR gain over a single radar. The NGR concept and recent highly-successful distributed aperture measurement campaigns are described. These measurements were carried out at the white sands missile range (WSMR) using the Lincoln Laboratory Wideband MIMO Distributed Aperture Test System in July 2005 and at the Air Force Research Laboratory (AFRL) Ipswich Antenna Range Facility in August 2004. Wideband coherence on transmit and receive was demonstrated at X-band in real time against live targets. A performance analysis, including comparison to the Cramer-Rao bounds, is given for the coherence parameter estimators during the presentation. Future plans are briefly discussed, including experiments with more radar channels and plans to demonstrate additional benefits of using MIMO techniques with distributed apertures and through spatial diversity

Channel equalization for self-synchronizing chaotic systems

Most strategies proposed for utilizing chaotic signals for communications exploit the self-synchronization property of a class of chaotic systems. Any realistic communication channel will introduce distortion including time-dependent fading, dispersion, and modification of the frequency content due to channel filtering and multipath effects. All of these distortions will affect the ability of the chaotic receiver to properly synchronize. This paper develops and illustrates some specific approaches to channel equalization to compensate for these distortions for self-synchronizing chaotic systems. The approaches specifically exploit the properties of chaotic drive signals and the self-synchronization properties of the receiver.

SYNTHESIZING SELF-SYNCHRONIZING CHAOTIC SYSTEMS

A systematic approach is developed for synthesizing N-dimensional dissipative chaotic systems which possess the self-synchronization property. The ability to synthesize new chaotic systems further enhances the usefulness of synchronized chaotic systems for communications.

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.