Quasi-orthogonal wideband radar waveforms based on chaotic systems

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 137-138).With the development of A/D converters possessing sufficiently high sampling rates, it is now feasible to use arbitrary, wideband waveforms in radar applications. Large sets of quasi-orthogonal, wideband waveforms can be generated so that multiple radars can simultaneously operate in the same frequency band. Each individual radar receiver can process its own return as well as the orthogonal returns from the other radars, which opens the possibility for developing algorithms that combine data from multiple radar channels. Due to the random nature of chaotic signals, it is possible to develop a procedure for generating large sets (> 50) of quasi-orthogonal radar waveforms using deterministic chaos. Deterministic chaos is defined as a bounded, aperiodic flow with a sensitive dependence on initial conditions. There are many different types of chaotic systems. In this thesis, waveforms will be generated from the well-studied Lorenz system. Each waveform from the Lorenz system can be fully characterized by three parameters (o, b, and r) and a set of initial conditions, (xo, yo, zo). The particular parameter values greatly affect quality of the Lorenz waveform as quasi-orthogonal radar waveform. Therefore, this thesis conducts a parameter study to quantify how the parameters affect various radar waveform metrics. Additionally, this thesis proposes a procedure for modifying the Lorenz waveform in order to improve its performance on these metrics.by Matt Willsey.M.Eng

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.United States. Air Force (Contract FA8721-05-C-0002)Massachusetts Institute of Technology. Research Laboratory of ElectronicsBAE SystemsTexas Instruments Incorporated. Leadership University Consortium Progra

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.United States. Air Force Office of Scientific Research (Contract number FA8721-05-C-0002