Computing a k-sparse n-length Discrete Fourier Transform using at most 4k samples and O(k log k) complexity

Given an $n$-length input signal \mbf{x}, it is well known that its Discrete Fourier Transform (DFT), \mbf{X}, can be computed in $O(n \log n)$ complexity using a Fast Fourier Transform (FFT). If the spectrum \mbf{X} is exactly $k$-sparse (where $k<<n$), can we do better? We show that asymptotically in $k$ and $n$, when $k$ is sub-linear in $n$ (precisely, $k \propto n^{\delta}$ where $0 < \delta <1$), and the support of the non-zero DFT coefficients is uniformly random, we can exploit this sparsity in two fundamental ways (i) {\bf {sample complexity}}: we need only $M=rk$ deterministically chosen samples of the input signal \mbf{x} (where $r < 4$ when $0 < \delta < 0.99$); and (ii) {\bf {computational complexity}}: we can reliably compute the DFT \mbf{X} using $O(k \log k)$ operations, where the constants in the big Oh are small and are related to the constants involved in computing a small number of DFTs of length approximately equal to the sparsity parameter $k$. Our algorithm succeeds with high probability, with the probability of failure vanishing to zero asymptotically in the number of samples acquired, $M$.Comment: 36 pages, 15 figures. To be presented at ISIT-2013, Istanbul Turke

Array Signal Processing for Synthetic Aperture Radar (SAR)

Synthetic aperture radar (SAR) is a kind of imaging radar that can produce high resolution images of targets and terrain on the ground. At present, most of SAR processing algorithms are based on matched filtering. This method is easy to implement and can produce stable results. However, It also has some limitations. This approach must obey the Nyquist sampling theorem and the resolution depends on bandwidth of pulses. This means that the matched filter approach must be based on a large amount of raw data but the performance is limited. With the development of radar imaging, it is difficult for the matched filtering approach to meet the requirement of high resolution SAR images. In this thesis, a new processing method based on the least squares (LS) beamforming is utilized in the processing of SAR raw data. The model of SAR simulates a virtual linear array. The processing of SAR data can also be seen as a process of beamforming. The 1- D azimuth direction echo data is processed using the beamforming method. Simulation results based on the least squares design method are compared with the matched filtering method and the conventional beamforming method with different windows

Efficient FFT Algorithms for Mobile Devices

Increased traffic on wireless communication infrastructure has exacerbated the limited availability of radio frequency ({RF}) resources. Spectrum sharing is a possible solution to this problem that requires devices equipped with Cognitive Radio ({CR}) capabilities. A widely employed technique to enable {CR} is real-time {RF} spectrum analysis by applying the Fast Fourier Transform ({FFT}). Today’s mobile devices actually provide enough computing resources to perform not only the {FFT} but also wireless communication functions and protocols by software according to the software-defined radios paradigm. In addition to that, the pervasive availability of mobile devices make them powerful computing platform for new services. This thesis studies the feasibility of using mobile devices as a novel spectrum sensing platform with focus on {FFT}-based spectrum sensing algorithms. We benchmark several open-source {FFT} libraries on an Android smartphone. We relate the efficiency of calculating the {FFT} to both algorithmic and implementation-related aspects. The benchmark results also show the clear potential of special {FFT} algorithms that are tailored for sparse spectrum detection

Wide-Angle Multistatic Synthetic Aperture Radar: Focused Image Formation and Aliasing Artifact Mitigation

Traditional monostatic Synthetic Aperture Radar (SAR) platforms force the user to choose between two image types: larger, low resolution images or smaller, high resolution images. Switching to a Wide-Angle Multistatic Synthetic Aperture Radar (WAM-SAR) approach allows formation of large high-resolution images. Unfortunately, WAM-SAR suffers from two significant implementation problems. First, wavefront curvature effects, non-linear flight paths, and warped ground planes lead to image defocusing with traditional SAR processing methods. A new 3-D monostatic/bistatic image formation routine solves the defocusing problem, correcting for all relevant wide-angle effects. Inverse SAR (ISAR) imagery from a Radar Cross Section (RCS) chamber validates this approach. The second implementation problem stems from the large Doppler spread in the wide-angle scene, leading to severe aliasing problems. This research effort develops a new anti-aliasing technique using randomized Stepped-Frequency (SF) waveforms to form Doppler filter nulls coinciding with aliasing artifact locations. Both simulation and laboratory results demonstrate effective performance, eliminating more than 99% of the aliased energy

Software-hardware systems for the Internet-of-Things

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages [187]-201).Although interest in connected devices has surged in recent years, barriers still remain in realizing the dream of the Internet of Things (IoT). The main challenge in delivering IoT systems stems from a huge diversity in their demands and constraints. Some applications work with small sensors and operate using minimal energy and bandwidth. Others use high-data-rate multimedia and virtual reality systems, which require multiple-gigabits-per-second throughput and substantial computing power. While both extremes stress the computation, communications, and energy resources available to the underlying devices, each intrinsically requires different solutions to satisfy its needs. This thesis addresses both bandwidth and energy constraints by developing custom software-hardware systems. To tackle the bandwidth constraint, this thesis introduces three systems. First, it presents AirShare, a synchronized abstraction to the physical layer, which enables the direct implementation of diverse kinds of distributed protocols for loT sensors. This capability results in a much higher throughput in today's IoT networks. Then, it presents Agile-Link and MoVR, new millimeter wave devices and protocols which address two main problems that prevent the adoption of millimeter wave frequencies in today's networks: signal blockage and beam alignment. Lastly, this thesis shows how these systems enable new IoT applications, such as untethered high-quality virtual reality. To tackle the energy constraint, this thesis introduces a VLSI chip, which is capable of performing a million-point Fourier transform in real-time, while consuming 40 times less power than prior fast Fourier transforms. Then, it presents Caraoke, a small, low-cost and low-power sensor, which harvests its energy from solar and enables new smart city applications, such as traffic management and smart parking.by Omid Salehi-Abari.Ph. D

Elevation and Deformation Extraction from TomoSAR

3D SAR tomography (TomoSAR) and 4D SAR differential tomography (Diff-TomoSAR) exploit multi-baseline SAR data stacks to provide an essential innovation of SAR Interferometry for many applications, sensing complex scenes with multiple scatterers mapped into the same SAR pixel cell. However, these are still influenced by DEM uncertainty, temporal decorrelation, orbital, tropospheric and ionospheric phase distortion and height blurring. In this thesis, these techniques are explored. As part of this exploration, the systematic procedures for DEM generation, DEM quality assessment, DEM quality improvement and DEM applications are first studied. Besides, this thesis focuses on the whole cycle of systematic methods for 3D & 4D TomoSAR imaging for height and deformation retrieval, from the problem formation phase, through the development of methods to testing on real SAR data. After DEM generation introduction from spaceborne bistatic InSAR (TanDEM-X) and airborne photogrammetry (Bluesky), a new DEM co-registration method with line feature validation (river network line, ridgeline, valley line, crater boundary feature and so on) is developed and demonstrated to assist the study of a wide area DEM data quality. This DEM co-registration method aligns two DEMs irrespective of the linear distortion model, which improves the quality of DEM vertical comparison accuracy significantly and is suitable and helpful for DEM quality assessment. A systematic TomoSAR algorithm and method have been established, tested, analysed and demonstrated for various applications (urban buildings, bridges, dams) to achieve better 3D & 4D tomographic SAR imaging results. These include applying Cosmo-Skymed X band single-polarisation data over the Zipingpu dam, Dujiangyan, Sichuan, China, to map topography; and using ALOS L band data in the San Francisco Bay region to map urban building and bridge. A new ionospheric correction method based on the tile method employing IGS TEC data, a split-spectrum and an ionospheric model via least squares are developed to correct ionospheric distortion to improve the accuracy of 3D & 4D tomographic SAR imaging. Meanwhile, a pixel by pixel orbit baseline estimation method is developed to address the research gaps of baseline estimation for 3D & 4D spaceborne SAR tomography imaging. Moreover, a SAR tomography imaging algorithm and a differential tomography four-dimensional SAR imaging algorithm based on compressive sensing, SAR interferometry phase (InSAR) calibration reference to DEM with DEM error correction, a new phase error calibration and compensation algorithm, based on PS, SVD, PGA, weighted least squares and minimum entropy, are developed to obtain accurate 3D & 4D tomographic SAR imaging results. The new baseline estimation method and consequent TomoSAR processing results showed that an accurate baseline estimation is essential to build up the TomoSAR model. After baseline estimation, phase calibration experiments (via FFT and Capon method) indicate that a phase calibration step is indispensable for TomoSAR imaging, which eventually influences the inversion results. A super-resolution reconstruction CS based study demonstrates X band data with the CS method does not fit for forest reconstruction but works for reconstruction of large civil engineering structures such as dams and urban buildings. Meanwhile, the L band data with FFT, Capon and the CS method are shown to work for the reconstruction of large manmade structures (such as bridges) and urban buildings