Berenice Verdin

Bistatic radar chaotic system synchronization

We propose a scheme for bistatic radar that uses a three-dimensional chaotic system to generate a wideband signal that is replicated at the receiver to extract high resolution information from targets. The setup for the bistatic radar includes a drive oscillator at the transmitter and a response oscillator at the receiver. The challenge for this setup is synchronizing the response oscillator of the radar receiver utilizing a scaled version of the transmitted signal that is a function of one drive oscillator state variable where the scaling factor accounts for antenna gain, system losses, and space propagation. Since the scaling factor is not known a priori, the response oscillator must be able to accept the scaled version of the state variable as an input. Thus, we improve upon a generalized projective synchronization technique that introduces a controller variable and a controller parameter into the Lorenz system and show that the synchronization is achievable. We verify through simulations that, once synchronization is achieved, the short-time correlation of the driver and response state variables is high and that this correlation is consistent over long periods of time.

Analysis of chaotic FM system synchronization for bistatic radar

We propose a scheme for bistatic radar that uses a chaotic system to generate a wideband FM signal that is reconstructed at the receiver via a conventional phase lock loop. The setup for the bistatic radar includes a 3 state variable drive oscillator at the transmitter and a response oscillator at the receiver. The challenge is in synchronizing the response oscillator of the radar receiver utilizing a scaled version of the transmitted signal sr(t, x) = αst(t, x) where x is one of three driver oscillator state variables and α is the scaling factor that accounts for antenna gain, system losses, and space propagation. For FM, we also assume that the instantaneous frequency of the received signal, xs, is a scaled version of the Lorenz variable x. Since this additional scaling factor may not be known a priori, the response oscillator must be able to accept the scaled version of x as an input. Thus, to achieve synchronization we utilize a generalized projective synchronization technique that introduces a controller term –μe where μ is a control factor and e is the difference between the response state variable xs and a scaled x. Since demodulation of sr(t) is required to reconstruct the chaotic state variable x, the phase lock loop imposes a limit on the minimum error e. We verify through simulations that, once synchronization is achieved, the short-time correlation of x and xs is high and that the self-noise in the correlation is negligible over long periods of time.

High resolution digital radar design using chaotic AM signals

A digital chaotic radar scheme that can be used in bistatic configuration is proposed. The generation of the transmitted AM signal and all post-processing are performed digitally. The proposed methodology is simulated and then validated with an anechoic chamber test. Results indicate that chaotic AM signals have autocorrelation sidelobe levels below -20 dB. The methodology was evaluated at two bandwidths, 0.5 GHz and 1 GHz. In presence of interference, sidelobe levels of the matched filter stay below -15 dB for a SNR of 0 dB. The proposed methodology makes the use of chaotic signals in bistatic radar possible without the requirement of chaotic system synchronization.

2D and 3D Far-Field Radiation Patterns Reconstruction Based on Compressive Sensing

The measurement of far-field radiation patterns is time consuming and expensive. Therefore, a novel technique that reduces the samples required to measure radiation patterns is proposed where random far-field samples are measured to reconstruct two-dimensional (2D) or three-dimensional (3D) far-field radiation patterns. The proposed technique uses a compressive sensing algorithm to reconstruct radiation patterns. The discrete Fourier transform (DFT) or the discrete cosine transform (DCT) are used as the sparsity transforms. The algorithm was evaluated by using 3 antennas modeled with the High-Frequency Structural Simulator (HFSS) — a half-wave dipole, a Vivaldi, and a pyramidal horn. The root mean square error (RMSE) and the number of measurements required to reconstruct the antenna pattern were used to evaluate the performance of the algorithm. An empirical test case was performed that validates the use of compressive sensing in 2D and 3D radiation pattern reconstruction. Numerical simulations and empirical tests verify that the compressive sensing algorithm can be used to reconstruct radiation patterns, reducing the time and number of measurements required for good antenna pattern measurements.

Reconstruction of missing sections of radiation patterns using compressive sensing

Far field radiation pattern measurement is a key factor in performing antenna characterization. In some cases, the complete radiation pattern is not available. We present a study of the reconstruction of a missing section of antenna patterns. The proposed method uses a compressive sensing algorithm to reconstruct the missing data. The algorithm is based on a sparsity domain of the radiation patterns, in this case the discrete Fourier transform. The analysis is demonstrated by evaluating the proposed algorithm using three different radiation patterns obtained from λ/2, 3λ/2, and 5λ/2 length dipole antennas. Results show that the compressive sensing algorithm can reconstruct a missing section up to 45% of the total number of samples.

COMPRESSIVE SENSING RECONSTRUCTION OF WIDEBAND ANTENNA RADIATION CHARACTERISTICS

Characterization measurements of wideband antennas can be a time intensive and an expensive process as many data points are required in both the angular and frequency dimensions. Parallel compressive sensing is proposed to reconstruct the radiation-frequency patterns (RFP) of antennas from a sparse and random set of measurements. The modeled RFP of the dual-ridge horn, bicone, and Vivaldi antennas are used to analyze the minimum number of measurements needed for reconstruction, the difference in uniform versus non-uniform reconstruction, and the sparsity transform function used in the compressive sensing algorithm. The effect of additive white Gaussian noise (AWGN) on the minimum number of data points required for reconstruction is also studied. In a noise-free environment, the RFP of the antennas were adequately reconstructed using as little as 33% of the original data points. It was found that the RFPs were adequately reconstructed with less data points when the discrete cosine transforms (DCT), rather than the discrete Fourier transforms (DFT) was used in the compressive sensing algorithm. The presence of noise increases the number of data points required to reconstruct an RFP to a specified error tolerance, but the antenna RFPs can be reconstructed to within 1% root-mean-square-error of the original with a signal to noise ratio as low as −15 dB. The use of compressive sensing can thus lead to a new measurement methodology whereby a small subset of the total angular and frequency measurements is taken at random, and a full reconstruction of radiation and frequency behavior of the antenna is achieved during post-processing.

Generalization of susceptibility of RF systems through far-field pattern superposition

The purpose of this paper is to perform an analysis of RF (Radio Frequency) communication systems in a large electromagnetic environment to identify its susceptibility to jamming systems. We propose a new method that incorporates the use of reciprocity and superposition of the far-field radiation pattern of the RF system and the far-field radiation pattern of the jammer system. By using this method we can find the susceptibility pattern of RF systems with respect to the elevation and azimuth angles. A scenario was modeled with HFSS (High Frequency Structural Simulator) where the radiation pattern of the jammer was simulated as a cylindrical horn antenna. The RF jamming entry point used was a half-wave dipole inside a cavity with apertures that approximates a land-mobile vehicle, the dipole approximates a leaky coax cable. Because of the limitation of the simulation method, electrically large electromagnetic environments cannot be quickly simulated using HFSS’s finite element method (FEM). Therefore, the combination of the transmit antenna radiation pattern (horn) superimposed onto the receive antenna pattern (dipole) was performed in MATLAB. A 2D or 3D susceptibility pattern is obtained with respect to the azimuth and elevation angles. In addition, by incorporating the jamming equation into this algorithm, the received jamming power as a function of distance at the RF receiver Pr(Φr, θr) can be calculated. The received power depends on antenna properties, propagation factor and system losses. Test cases include: a cavity with four apertures, a cavity above an infinite ground plane, and a land-mobile vehicle approximation. By using the proposed algorithm a susceptibility analysis of RF systems in electromagnetic environments can be performed.

Calculation of the phase-center offset from 2D antenna radiation patterns

Centering the phase-center of an antenna onto the rotational axis used to measure its radiation pattern is an iterative and time consuming process. To facilitate this process, an algorithm has been developed to calculate the phase-center offset from the axis of rotation of a 2D antenna pattern. The hybrid algorithm is comprised of a combination of the two-point method to calculate the offset along the antenna mainbeam, and an antisymmetry method is used to calculate offset perpendicular to the mainbeam direction. The algorithm is tested on the E-plane radiation pattern of a cylindrical horn antenna calculated using the HFSS electromagnetic simulation engine, radiating at 5GHz. The algorithm calculates the phase-center offset to within 15%. Because the algorithm analyzes the unwrapped phase of the radiation pattern, which it converts to offset distance, no ambiguity due to offsets greater than a wavelength exist. Using this algorithm, the phase-center of the antenna can be placed coincident to the axis of rotation after the first antenna pattern is measured and analyzed.