Most of the advances in current radar systems are aimed at improving their resolution. As a result, their operating frequency has been increased from 10GHz up to 94GHz, and new millimeter-wave (100-300GHz) radar systems are currently being studied. One of the major concerns with these frequencies is the associated large bandwidth requirement. Compressive Sensing (CS), also known as Compressive Sampling, has been proposed as a solution to overcome the aforementioned problems by exploiting the sparsity of the radar signal. Using the CS method, a sparse signal can be reconstructed even if it is sampled below the Nyquist rate. This method provides a completely new way to reconstruct the signal using optimization techniques and a minimum number of observations. The objective of this research project is to investigate and develop a Chaotic Radar Imaging system that leverages Compressive Sensing (CS) technology to improve the image resolution without increasing the amount of processed data. In addition to demonstrating the validity of the proposed approach through simulations, this project seeks to develop and implement hardware prototypes for the proposed imaging radar system. Simulated chaotic radar data was generated and loaded to the FPGA board to test the algorithms and their performance. The results from implementing the Orthogonal Matching Pursuit (OMP), the Compressive Sensing Matching Pursuit (CSMP), and the Stagewise Orthogonal Matching Pursuit (StOMP) algorithms to a Xilinx ZedBoard will be presented.
Matched filters are used in radar systems to identify echo signals embedded in noise. They allow us to extract range and Doppler information about the target from the reflected signal. In high frequency radars, matched filters make the system expensive and complex. For that reason, the radar research community is looking at techniques like compressive sensing or compressive sampling to eliminate the use of matched filters and high frequency analog-to-digital converters. In this work, compressive sensing is proposed as a method to increase the resolution and eliminate the use of matched filters in chaotic radars. Two basic scenarios are considered, one for stationary targets and one for non-stationary targets. For the stationary targets, the radar scene was a one dimensional vector, in which each element from the vector represents a target position. For the non-stationary targets, the radar scene was a two dimensional matrix, in which one direction of the matrix represents the target’s range, and the other direction represents the target’s velocity. Using optimization techniques, it was possible to recover both radar scenes from an under sampled echo signal. The reconstructed scenes were compared against a traditional matched filter system. In both cases, the matched filter was capable of recovering the radar scene. However, there was a considerable amount of artifacts introduced by the matched filter that made target identification a daunting task. On the other hand, using compressive sensing it was possible to recover both radar scenes perfectly, even when the echo signal was under sampled.
Current generation radars employ a first order approximation to compensate the frequency shift due to target's velocity.
This approach is inadequate when high velocity targets are considered; however, real targets do not possess such high
velocities. For that reason, this research analyzes how the increment of the Time-Bandwidth (TBW) product and the
target velocity would impact the analysis of radar signals when a first order approximation is implemented to
compensate the Doppler shift. The common approach to improved resolution and performance of radar system is to
increase the time-bandwidth product of the transmitted signal. The problem of using the first order approximation to
compensate the Doppler is that it is limited only to the first two terms of a power series expansion of a full Doppler
compensation. As a consequence, an increment on the target's velocity or the time-bandwidth product of the transmitted
signal will result in a significant error at the output of the matched filter.
On this research a Linear FM (chirp) signal with a large TBW is considered as the transmitted signal. First, to observe
the effects of increasing the time-bandwidth product and target velocity the received signal is modeled using a full
Doppler compensation and a first order approximation. Second, each signal is applied to the input of one matched filter
in which the transmitted signal is used as a reference. Finally, the outputs from both matched filters are analyzed in order
to observe the effects of using the first order approximation to model the Doppler induced on the reflected signal. This
analysis was performed assuming that the target was moving at a constant velocity. By increasing the time-bandwidth
product of the transmitted signal the output of both matched filters are compared and analyzed to observe the differences
between modeling the reflected signal using the first order compensation and the full Doppler compensation. The
simulation results showed that, by increasing the time-bandwidth product of the transmitted signal the output of the
matched filter using the first order approximation deviates significantly with respect to the matched filter that contains
the signal modeled using the full Doppler compensation. From these results it is concluded that a dramatic increase in
time-bandwidth product of the received signal, results in a significant error at the output of the matched filter if the first
order approximation is used to model the reflected signal instead of the Full Doppler compensation.
Standard radar systems commonly use a first-order phase compensation to account for the Doppler effect. As target
speed increases, higher-order phase terms are needed to compensate a large time-bandwidth product signal. For
extremely high speeds, a relativistic scheme based on the Lorentz Transformation of the wave 4-vector is more desirable
since it provides correct results. Since the echo location problem involves transmission of the signal from a stationary
frame and signal reflection from a moving frame, the wave 4-vector must be transformed twice to simulate a round trip.
We show that for relative motion in one direction, the round-trip Lorentz transformation is equivalent to compressing the
instantaneous frequency of the signal. The frequency compression factor is a nonlinear function of speed v. The
nonlinearity is apparent only for relativistic speeds. In this paper, we analyze the ambiguity surface of the linear FM
(chirp) signal to compare first-order and relativistic (full) compensation, and demonstrate that at relativistic speeds the
ambiguity surface of the fully compensated linear FM compensated shows a linear delay-Doppler coupling.
Classical work in the field of high-resolution radar often assumes that an echo signal is made of a number of components that can be decomposed via Fourier analysis. Adjacent components are said to be resolved in the frequency domain if the intensity between them drops at least 3 decibels. This working definition is an extension of Lord Rayleigh's criterion for optical resolution. The problem with this approach is that whereas Rayleigh's criterion assumes signal incoherence, thus allowing for the addition of power components, a high-resolution radar signal is often the coherent sum of sinusoids, which implies voltage addition. The purpose of this paper is to discuss the consequences of using Rayleigh's criterion in the analysis of radar signals. Specifically, computer simulations using a complex signal are analyzed via the periodogram as the relative phase between the two components of the signal is allowed to change. The net effect introduced by this phase variation is to reduce or increase the spacing and intensity between two adjacent spectral peaks. These changes are due to constructive or destructive interference of spectral cross terms that cannot be ignored when attempting to resolve frequency components from one another. For instance, the simulations show that when using the averaged periodogram, the intensity in-between two adjacent components is above the -3 decibel threshold for a phase range of 1.2π radians, although the standard resolution criterion of c/2β is satisfied. Similar results are obtained when using a number of windows that are known to control sidelobe levels. Thus, the use of Rayleigh's criterion to define the resolution of a high-resolution radar system is technically inconsistent and undermines our ability to perform quantitative comparisons of target profiles, Doppler profiles and range-Doppler images. In this light, the authors promote the adoption of alternative criteria for judging resolution gains based on the norm of the signal in the (spatial) frequency domain.
Conference Committee Involvement (11)
Radar Sensor Technology XXV
12 April 2021 | Online Only, Florida, United States
Radar Sensor Technology XXIV
27 April 2020 | Online Only, California, United States
Radar Sensor Technology XXIII
15 April 2019 | Baltimore, MD, United States
Radar Sensor Technology XXII
16 April 2018 | Orlando, FL, United States
Radar Sensor Technology XXI
10 April 2017 | Anaheim, CA, United States
Radar Sensor Technology XX
18 April 2016 | Baltimore, MD, United States
Radar Sensor Technology XIX
20 April 2015 | Baltimore, MD, United States
Radar Sensor Technology XVIII
5 May 2014 | Baltimore, MD, United States
Radar Sensor Technology XVII
29 April 2013 | Baltimore, Maryland, United States
Radar Sensor Technology XVI
23 April 2012 | Baltimore, Maryland, United States
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