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.
KEYWORDS: Signal to noise ratio, Fermium, Frequency modulation, Receivers, Radar, Transmitters, Oscillators, Modulation, Linear filtering, Interference (communication)
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.
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.
Full waveform Lidar systems have the ability of recording the complete signal reflected from the illuminated target. Therefore, more detail information can be obtained compared to conventional Lidar systems. The problem that is faced in using full waveform Lidar is the acquisition of high volume data, a solution proposed to solve this problem is compressive sensing. By using a compressive sensing approach we can reduce the sampling rate and still be able to recover the signal. The reduction is incorporated in the acquisition hardware, where we perform sensing of the signal with compression. In this paper we propose to use a deterministic compressive sensing approach by using a chaotic signal as the sensing matrix. The proposed approach gives the range profile information without the requirement of further processing techniques. For comparison we used two different types of transmitted signals: chaotic and Linear Frequency Modulated (LFM) signals. Simulations demonstrate that chaotic signals give better results than the LFM signals. By using a chaotic signal we can obtain the impulse response of the target by using less than 20 percent of the samples.
KEYWORDS: LIDAR, Compressed sensing, Semiconductor lasers, Signal to noise ratio, Interference (communication), Sensing systems, 3D image enhancement, Digital imaging, 3D acquisition, 3D image processing
Full waveform lidar systems are capable of recording the complete return signal from the laser illuminated target. By making use of the return full waveform, one can obtain more detailed information about the target of interest than the simple target range. The development of better methods to extract information from the return signal can lead to better target characterization. Several methods have been proposed in the literature to obtain the complete range profile or radar cross section of the target.1, 2 In a previous work, we proposed to use a compressive sensing scheme to acquire and compress the received signal, and at a post-processing stage reconstruct the signal to obtain the range profile of the target. We extend this previous work on full waveform lidar using chaotic signal by including additive white Gaussian noise into the acquisition stage of the lidar system. The objective is to test the robustness of the previously developed approach based on compressive sensing to different noise level intensities. The simulation software Digital Imaging and Remote Sensing Image Generation (DIRSIG) was used to simulate the range profile corresponding to a three-dimensional scene. The simulation results indicate that the full range profile can be reconstructed with a compressive sensing acquisition as low as 25 percent of the total number of samples and with low root-mean-square error (RMSE). The proposed lidar system with compressive sensing can be used to sense with compression and recover the range target profile.
KEYWORDS: Fermium, Frequency modulation, Signal generators, Complex systems, Time-frequency analysis, Control systems, Nonlinear optics, Information operations, Electroluminescence, Interference (communication)
In previous work, we constructed wideband FM signals for high range resolution applications using the non-linear
Lorenz system, which has a set of three state variables and three control parameters. The FM signals were generated
using any one of the three state variables as the instantaneous frequency which was then controlled by adjusting the
values of the parameters in the chaotic regime. We now determine the spectral characteristics of the Lorenz FM signal
and compare the spectral characteristics to those of a similar FM signal based on the Lang-Kobayashi system. We show
that for either chaotic system, the local linearity of the attractor yields an FM signal with a distinct chirp behavior.
Irrespective of the statistical independence of the chaotic flow samples, we show that the chaotic FM signal follows
Woodward's theorem in the sense that the spectrum of the FM signal follows the shape of the probability density
function of the state variable. The chirp rate of the FM signal can be controlled through a time-scale parameter that
compresses or expands the chaotic flow. As the chaotic flow evolves in time, so does the spectrum of the corresponding
FM signal, which experiences changes in center frequency and bandwidth. We show that segments of the signal with a
high chirp rate can be significantly compressed to achieve high range-Doppler resolution. The ability to change the
center frequency and the shape of the spectrum is interpreted as added frequency agility.
Compared to microwave radar systems, chaotic ladar has the potential for providing a range resolution well into the mm
range. The purpose of this project is to determine the signal processing schemes required to extract range and Doppler
information from a chaotic signal scattered by environmental targets. Specifically, a ladar would be driven into the
coherence collapse through an external optical resonator, thus generating a chaotic electromagnetic field with a wide rms
bandwidth of several GHz. The reflected field would be processed though optical correlation to extract range and
Doppler information. Simulations show that the power spectral density properties of the field are dependent on the
Lyapunov exponent of the chaotic field, which be exploited to obtain optimum range resolution. A complete statistical
analysis of the wideband ambiguity function of the field reveals that the signal has better performance than noise-like
signals generated via electro-optic amplitude modulation, thus allowing for high resolution imaging of terrains with
pseudo random reflectivity variations.
In previous work, we proposed to generate random samples using chaotic maps. More specifically, we demonstrated that Gaussian samples can be obtained via two random number generators that utilize first order or second order chaotic maps. In this paper we extend this work and propose to utilize the chaos-based random generators to develop a Gaussian FM signal that can be exploited for radar imaging. For this purpose, we fine-tune the chaotic map parameters of the Gaussian FM signal until we obtain a white wide-band spectrum, which is computed as an ensemble average, and analyze the corresponding ambiguity surface of the signal. We observe that the ensemble average of the ambiguity surface approaches an ideal two dimensional delta with uniformly distributed sidelobes on the range-Doppler plane. On average the sidelobes of the surface have intensity inversely proportional to the length of the processed echo. For completeness, we compare the variance of the Gaussian FM ambiguity function to that of a random binary phase code with comparable bandwidth. Furthermore, we show through simulations that Fourier processing of the Gaussian FM signal can yield a high-resolution range-Doppler image aircraft with prominent point scattering points over a substantial SNR dynamic range.
The purpose of this project is threefold: To determine the optimum range-Doppler characteristics of an FM broadcast, to
characterize a typical FM broadcast signal in terms of the properties of the ambiguity function, and to develop a model
for the FM broadcast signal as a band-limited multi-tone FM stochastic process. The way to achieve these objectives is
to analyze the response of a matched filter at the receiver by considering two modulating input signals. The inputs are a
band-limited white Gaussian noise and a segment of a typical broadcast. The analysis of these signals is performed in
the range-Doppler domain by observing the behavior of the ambiguity function. The results of the analysis show that the
band-limited white Gaussian noise yields an optimum ambiguity function with a narrow mainlobe and low sidelobes
evenly distributed over the range-Doppler plane. In contrast, the ambiguity function of a typical broadcast will exhibit a
wider mainlobe and higher sidelobes. By adjusting parameters of the multi-tone FM stochastic process, a good match to
the observed characteristics of an actual FM broadcast can be obtained. Thus, the signal model can be used to estimate
the limitations in the detection of moving targets by means of a radar system that exploits FM signals of opportunity.
We evaluated two random number generator algorithms using first-order and second-order chaotic maps. The first algorithm, which is based on the central limit theorem, allows us to approximate a Gaussian random variable as the sum of a given chaotic sequence. We considered two first-order maps (Bernoulli, Tent) and two second-order maps (Logistic, and Quadratic). In each instance, we verified that the sequence of random numbers had kurtosis of 3. In the case of the Bernoulli map, we determined that the statistical independence of samples is dependent on the map parameter B. The second algorithm, which is based on Von Neumann's Method, allowed us to reject samples from a chaotic sequence with uniform distribution to obtain a Gaussian distribution within a specific range (U, V). For the first-order maps, we estimated their probability density function in this range and computed deviations from the theoretical Gaussian density. In summary, we determined that samples generated via these two algorithms satisfied statistical tests for normal distributions, thus demonstrating that chaotic maps can be effectively to generate Gaussian samples.
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