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

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

Radar Waveform Generation and Optimization based on Rossler Chaotic System

The concept of Multiple-Input Multiple-Output (MIMO) radars has drawn considerable attention recently. Unlike the traditional Single-Input Multiple-Output (SIMO) radar which emits coherent waveforms to form a focused beam, the MIMO radar can transmit orthogonal (incoherent) waveforms. These waveforms can be used to increase the system spatial resolution. The challenge is on how to generate the large set of incoherent waveforms. Contemporary research has focused on using chaotic systems to generate these waveforms. With Chaotic waveforms obtained from a dynamical system, different radar waveforms can be generated from a single dynamical system; one only needs to change the control parameters and the initial conditions of the system. This scheme for radar waveform generation reduces the need for a comprehensive library of waveforms in a radar system and generates waveforms with good properties for both secure communications and high spatial resolution. This paper proposes the use of Rossler system– a type of a dynamical system to generate radar waveforms. Through Matlab/Simulink Simulations, it is shown that the Rossler waveforms, which are characterized by control variables and initial conditions are comparable to the Linear Frequency Modulated (LFM) waveforms, the most commonly used class of radar waveforms in terms of the ambiguity diagram and the frequency components and yet versatile enough to generate a large number of independent waveforms. An ambiguity diagram is a plot of an ambiguity function of a transmitted waveform and is a metric that characterizes the compromise between range and Doppler resolutions. It is a major tool for analyzing and studying radar waveforms. Impulsive synchronization theory is used to develop the ambiguity diagram. Keywords: Chaos, Rossler system, ambiguity function, impulsive synchronization theor

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

Chaotic Phase-Coded Waveforms with Space-Time Complementary Coding for MIMO Radar Applications

A framework for designing orthogonal chaotic phase-coded waveforms with space-time complementary coding (STCC) is proposed for multiple-input multiple-output (MIMO) radar applications. The phase-coded waveform set to be transmitted is generated with an arbitrary family size and an arbitrary code length by using chaotic sequences. Due to the properties of chaos, this chaotic waveform set has many advantages in performance, such as anti-interference and low probability of intercept. However, it cannot be directly exploited due to the high range sidelobes, mutual interferences, and Doppler intolerance. In order to widely implement it in practice, we optimize the chaotic phase-coded waveform set from two aspects. Firstly, the autocorrelation property of the waveform is improved by transmitting complementary chaotic phase-coded waveforms, and an adaptive clonal selection algorithm is utilized to optimize a pair of complementary chaotic phase-coded pulses. Secondly, the crosscorrelation among different waveforms is eliminated by implementing space-time coding into the complementary pulses. Moreover, to enhance the detection ability for moving targets in MIMO radars, a method of weighting different pulses by a null space vector is utilized at the receiver to compensate the interpulse Doppler phase shift and accumulate different pulses coherently. Simulation results demonstrate the efficiency of our proposed method

Passive UWB Beamforming: a N to M Compression Study

International audience—Recent works have demonstrated the feasibility of microwave imaging using compressive techniques, exempting the use the of active delay lines, phase shifters, or moving parts to achieve beamforming. With this method, waves are coded in a passive way by a compressive device to reduce the complexity of the transmitter and/or receiver chains of the telecommunication and radar systems requiring beamsteering. Since this technique is based on frequency diversity, the reduction of the compressive device's volume imposes a diminution of the amount of driven antennas. In this article, the improvement brought by simultaneous excitations of the compressive device is presented. Adapting a new mathematical formulation, it is shown that M inputs can send independent waveforms allowing the beamsteering of an N-elements antenna array, while maintaining N > M

Generation of pseudo-random sequences for noise radar applications

Noise Radar Technology (NRT) is nowadays a promising tool in radar systems. It is based on the transmission of waveforms composed of many noisy samples, which behave as LPI (Low Probability of Intercept) and antispoofing signals. Each noisy sequence is theoretically uncorrelated with the others. In the paper we propose a scheme to generate a “tailored” pseudo-random sequences (limited in amplitude). It will be followed by an analysis of the main performances in terms of the Peak Side Lobe Ratio (PSLR) of the autocorrelation function, cross-correlation analysis to evaluate the orthogonality, bandwidth and energy efficiency