Design and Optimization of Physical Waveform-Diverse and Spatially-Diverse Radar Emissions

With the advancement of arbitrary waveform generation techniques, new radar transmission modes can be designed via precise control of the waveform's time-domain signal structure. The finer degree of emission control for a waveform (or multiple waveforms via a digital array) presents an opportunity to reduce ambiguities in the estimation of parameters within the radar backscatter. While this freedom opens the door to new emission capabilities, one must still consider the practical attributes for radar waveform design. Constraints such as constant amplitude (to maintain sufficient power efficiency) and continuous phase (for spectral containment) are still considered prerequisites for high-powered radar waveforms. These criteria are also applicable to the design of multiple waveforms emitted from an antenna array in a multiple-input multiple-output (MIMO) mode. In this work, three spatially-diverse radar emission design methods are introduced that provide constant amplitude, spectrally-contained waveforms implemented via a digital array radar (DAR). The first design method, denoted as spatial modulation, designs the radar waveforms via a polyphase-coded frequency-modulated (PCFM) framework to steer the coherent mainbeam of the emission within a pulse. The second design method is an iterative scheme to generate waveforms that achieve a desired wideband and/or widebeam radar emission. However, a wideband and widebeam emission can place a portion of the emitted energy into what is known as the `invisible' space of the array, which is related to the storage of reactive power that can damage a radar transmitter. The proposed design method purposefully avoids this space and a quantity denoted as the Fractional Reactive Power (FRP) is defined to assess the quality of the result. The third design method produces simultaneous radar and communications beams in separate spatial directions while maintaining constant modulus by leveraging the orthogonal complement of the emitted directions. This orthogonal energy defines a trade-space between power efficiency gained from constraining waveforms to be constant amplitude and power efficiency lost by emitting energy in undesired directions. The design of FM waveforms via traditional gradient-based optimization methods is also considered. A waveform model is proposed that is a generalization of the PCFM implementation, denoted as coded-FM (CFM), which defines the phase of the waveform via a summation of weighted, predefined basis functions. Therefore, gradient-based methods can be used to minimize a given cost function with respect to a finite set of optimizable parameters. A generalized integrated sidelobe level (GISL) metric is used as the optimization cost function to minimize the correlation range sidelobes of the radar waveform. System specific waveform optimization is explored by incorporating the linear models of three different loopback configurations into the GISL metric to match the optimized waveforms to the particular systems

Target localization in passive and active systems : performance bonds

The main goal of this dissertation is to improve the understanding and to develop ways to predict the performance of localization techniques as a function of signal-to-noise ratio (SNR) and of system parameters. To this end, lower bounds on the maximum likelihood estimator (MLE) performance are studied. The Cramer-Rao lower bound (CRLB) for coherent passive localization of a near-field source is derived. It is shown through the Cramer-Rao bound that, the coherent localization systems can provide high accuracies in localization, to the order of carrier frequency of the observed signal. High accuracies come to a price of having a highly multimodal estimation metric which can lead to sidelobes competing with the mainlobe and engendering ambiguity in the selection of the correct peak. The effect of the sidelobes over the estimator performance at different SNR levels is analyzed and predicted with the use of Ziv-Zakai lower bound (ZZB). Through simulations it is shown that ZZB is tight to the MLEs performance over the whole SNR range. Moreover, the ZZB is a convenient tool to assess the coherent localization performance as a function of various system parameters. The ZZB was also used to derive a lower bound on the MSE of estimating the range and the range rate of a target in active systems. From the expression of the derived lower bound it was noted that, the ZZB is determined by SNR and by the ambiguity function (AF). Thus, the ZZB can serve as an alternative to the ambiguity function (AF) as a tool for radar design. Furthermore, the derivation is extended to the problem of estimating target’s location and velocity in a distributed multiple input multiple output (MIMO) radar system. The derived bound is determined by SNR, by the product between the number of transmitting antennas and the number of receiving antennas from the radar system, and by all the ambiguity functions and the cross-ambiguity functions corresponding to all pairs transmitter-target-receiver. Similar to the coherent localization, the ZZB can be applied to study the performance of the estimator as a function of different system parameters. Comparison between the ZZB and the MSE of the MLE obtained through simulations demonstrate that the bound is tight in all SNR regions

Multibeam radar system based on waveform diversity for RF seeker applications

Existing radiofrequency (RF) seekers use mechanically steerable antennas. In order to improve the robustness and performance of the missile seeker, current research is investigating the replacement of mechanical 2D antennas with active electronically controlled 3D antenna arrays capable of steering much faster and more accurately than existing solutions. 3D antenna arrays provide increased radar coverage, as a result of the conformal shape and flexible beam steering in all directions. Therefore, additional degrees of freedom can be exploited to develop a multifunctional seeker, a very sophisticated sensor that can perform multiple simultaneous tasks and meet spectral allocation requirements. This thesis presents a novel radar configuration, named multibeam radar (MBR), to generate multiple beams in transmission by means of waveform diversity. MBR systems based on waveform diversity require a set of orthogonal waveforms in order to generate multiple channels in transmission and extract them efficiently at the receiver with digital signal processing. The advantage is that MBR transmit differently designed waveforms in arbitrary directions so that waveforms can be selected to provide multiple radar functions and better manage the available resources. An analytical model of an MBR is derived to analyse the relationship between individual channels and their performance in terms of isolation and phase steering effects. Combinations of linear frequency modulated (LFM) waveforms are investigated and the analytical expressions of the isolation between adjacent channels are presented for rectangular and Gaussian amplitude modulated LFM signals with different bandwidths, slopes and frequency offsets. The theoretical results have been tested experimentally to corroborate the isolation properties of the proposed waveforms. In addition, the practical feasibility of the MBR concept has been proved with a radar test bed with two orthogonal channels simultaneously detecting a moving target

The design and implementation of an acoustic phased array transmitter for the demonstration of MIMO techniques

MIMO radar algorithms are the latest generation of techniques that can be applied to array radars. They offer the potential to improve the radar resolution, increase the number of targets that can be identified and give added flexibility in beampattern design. However, little experimental data demonstrating MIMO radar is available because radar arrays are already expensive systems and MIMO extends the com- plexity and cost further. An acoustic array, which works on the same principles as a radio frequency radar array, can be built at a fraction of the cost of a real radar system. The novel contribution of this project was the demonstration ofMIMO radar techniques on an acoustic array, which was designed and built for this purpose. To achieve the project objectives, the theory of traditional phased array radar techniques and MIMO techniques was researched. The phased array and MIMO techniques were also simulated under narrowband and wideband conditions, and the strengths and weaknesses of each were highlighted. This was followed by the design and implementation of a low cost audible acoustic transmitter array to be used with an existing receiver array to demonstrate the investigated array radar techniques. Finally, the techniques were tested on the hardware platform. The simulation and hardware test results were used to evaluate and compare the performance of phased array and MIMO radar techniques. The beampattern design flexibility that is offered by MIMO radar was demonstrated with the transmission and measurement of omnidirectional, single-lobed and multi-lobed MIMO beampat- terns. Also, parameter estimation experiments were performed where phased array and MIMO radar signals were transmitted. Phased array techniques were shown to be simple, effective and robust. The MIMO Capon, APES and GLRT parameter estimation techniques were shown to be sensitive to the type of signals transmitted, and in most cases, the added complexity of these techniques did not lead to improved target parameter estimation results. However, the MIMO technique of transmitter beamforming on reception gave high resolution target range and angle estimates, living up to the expectations placed on MIMO radar

OFDM passive radar employing compressive processing in MIMO configurations

A key advantage of passive radar is that it provides a means of performing position detection and tracking without the need for transmission of energy pulses. In this respect, passive radar systems utilising (receiving) orthogonal frequency division multiplexing (OFDM) communications signals from transmitters using OFDM standards such as long term evolution (LTE), WiMax or WiFi, are considered. Receiving a stronger reference signal for the matched filtering, detecting a lower target signature is one of the challenges in the passive radar. Impinging at the receiver, the OFDM waveforms supply two-dimensional virtual uniform rectangul ararray with the first and second dimensions refer to time delays and Doppler frequencies respectively. A subspace method, multiple signals classification (MUSIC) algorithm, demonstrated the signal extraction using multiple time samples. Apply normal measurements, this problem requires high computational resources regarding the number of OFDM subcarriers. For sub-Nyquist sampling, compressive sensing (CS) becomes attractive. A single snap shot measurement can be applied with Basis Pursuit (BP), whereas l1-singular value decomposition (l1-SVD) is applied for the multiple snapshots. Employing multiple transmitters, the diversity in the detection process can be achieved. While a passive means of attaining three-dimensional large-set measurements is provided by co-located receivers, there is a significant computational burden in terms of the on-line analysis of such data sets. In this thesis, the passive radar problem is presented as a mathematically sparse problem and interesting solutions, BP and l1-SVD as well as Bayesian compressive sensing, fast-Besselk, are considered. To increase the possibility of target signal detection, beamforming in the compressive domain is also introduced with the application of conve xoptimization and subspace orthogonality. An interference study is also another problem when reconstructing the target signal. The networks of passive radars are employed using stochastic geometry in order to understand the characteristics of interference, and the effect of signal to interference plus noise ratio (SINR). The results demonstrate the outstanding performance of l1-SVD over MUSIC when employing multiple snapshots. The single snapshot problem along with fast-BesselK multiple-input multiple-output configuration can be solved using fast-BesselK and this allows the compressive beamforming for detection capability

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement