Robust MIMO Channel Estimation from Incomplete and Corrupted Measurements

Location-aware communication is one of the enabling techniques for future 5G networks. It requires accurate temporal and spatial channel estimation from multidimensional data. Most of the existing channel estimation techniques assume that the measurements are complete and noise is Gaussian. While these approaches are brittle to corrupted or outlying measurements, which are ubiquitous in real applications. To address these issues, we develop a lp-norm minimization based iteratively reweighted higher-order singular value decomposition algorithm. It is robust to Gaussian as well as the impulsive noise even when the measurement data is incomplete. Compared with the state-of-the-art techniques, accurate estimation results are achieved for the proposed approach

R-dimensional ESPRIT-type algorithms for strictly second-order non-circular sources and their performance analysis

High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) non-circular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the R-D NC Standard ESPRIT and the R-D NC Unitary ESPRIT algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals. They are applicable to shift-invariant R-D antenna arrays and do not require a centrosymmetric array structure. Moreover, we present a first-order asymptotic performance analysis of the proposed algorithms, which is based on the error in the signal subspace estimate arising from the noise perturbation. The derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. We also provide mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required, but no assumptions about its statistics are necessary. As a main result, we analytically prove that the asymptotic performance of both R-D NC ESPRIT-type algorithms is identical in the high effective SNR regime. Finally, a case study shows that no improvement from strictly non-circular sources can be achieved in the special case of a single source.Comment: accepted at IEEE Transactions on Signal Processing, 15 pages, 6 figure

Nanoscale diffractive probing of strain dynamics in ultrafast transmission electron microscopy

The control of optically driven high-frequency strain waves in nanostructured systems is an essential ingredient for the further development of nanophononics. However, broadly applicable experimental means to quantitatively map such structural distortion on their intrinsic ultrafast time and nanometer length scales are still lacking. Here, we introduce ultrafast convergent beam electron diffraction (U-CBED) with a nanoscale probe beam for the quantitative retrieval of the time-dependent local distortion tensor. We demonstrate its capabilities by investigating the ultrafast acoustic deformations close to the edge of a single-crystalline graphite membrane. Tracking the structural distortion with a 28-nm/700-fs spatio-temporal resolution, we observe an acoustic membrane breathing mode with spatially modulated amplitude, governed by the optical near field structure at the membrane edge. Furthermore, an in-plane polarized acoustic shock wave is launched at the membrane edge, which triggers secondary acoustic shear waves with a pronounced spatio-temporal dependency. The experimental findings are compared to numerical acoustic wave simulations in the continuous medium limit, highlighting the importance of microscopic dissipation mechanisms and ballistic transport channels

Matrix and Tensor-based ESPRIT Algorithm for Joint Angle and Delay Estimation in 2D Active Broadband Massive MIMO Systems and Analysis of Direction of Arrival Estimation Algorithms for Basal Ice Sheet Tomography

In this thesis, we apply and analyze three direction of arrival algorithms (DoA) to tackle two distinct problems: one belongs to wireless communication, the other to radar signal processing. Though the essence of these two problems is DoA estimation, their formulation, underlying assumptions, application scenario, etc. are totally different. Hence, we write them separately, with ESPRIT algorithm the focus of Part I and MUSIC and MLE detailed in Part II. For wireless communication scenario, mobile data traffic is expected to have an exponential growth in the future. In order to meet the challenge as well as the form factor limitation on the base station, 2D "massive MIMO" has been proposed as one of the enabling technologies to significantly increase the spectral efficiency of a wireless system. In "massive MIMO" systems, a base station will rely on the uplink sounding signals from mobile stations to figure out the spatial information to perform MIMO beamforming. Accordingly, multi-dimensional parameter estimation of a ray-based multi-path wireless channel becomes crucial for such systems to realize the predicted capacity gains. In the first Part, we study joint angle and delay estimation for 2D "massive MIMO" systems in mobile wireless communications. To be specific, we first introduce a low complexity time delay and 2D DoA estimation algorithm based on unitary transformation. Some closed-form results and capacity analysis are involved. Furthermore, the matrix and tensor-based 3D ESPRIT-like algorithms are applied to jointly estimate angles and delay. Significant improvements of the performance can be observed in our communication scheme. Finally, we found that azimuth estimation is more vulnerable compared to elevation estimation. Results suggest that the dimension of the antenna array at the base station plays an important role in determining the estimation performance. These insights will be useful for designing practical "massive MIMO" systems in future mobile wireless communications. For the problem of radar remote sensing of ice sheet topography, one of the key requirements for deriving more realistic ice sheet models is to obtain a good set of basal measurements that enables accurate estimation of bed roughness and conditions. For this purpose, 3D tomography of the ice bed has been successfully implemented with the help of DoA algorithms such as MUSIC and MLE techniques. These methods have enabled fine resolution in the cross-track dimension using synthetic aperture radar (SAR) images obtained from single pass multichannel data. In Part II, we analyze and compare the results obtained from the spectral MUSIC algorithm and an alternating projection (AP) based MLE technique. While the MUSIC algorithm is more attractive computationally compared to MLE, the performance of the latter is known to be superior in most situations. The SAR focused datasets provide a good case study to explore the performance of these two techniques to the application of ice sheet bed elevation estimation. For the antenna array geometry and sample support used in our tomographic application, MUSIC performs better originally using a cross-over analysis where the estimated topography from crossing flightlines are compared for consistency. However, after several improvements applied to MLE, i.e., replacing ideal steering vector generation with measured steering vectors, automatic determination of the number of scatter sources, smoothing the 3D tomography in order to get a more accurate height estimation and introducing a quality metric for the estimated signals, etc., MLE outperforms MUSIC. It confirms that MLE is indeed the optimal estimator for our particular ice bed tomographic application. We observe that, the spatial bottom smoothing, aiming to remove the artifacts made by MLE algorithm, is the most essential step in the post-processing procedure. The 3D tomography we obtained lays a good foundation for further analysis and modeling of ice sheets

New systems for quantum nonlinear optics

Photons travelling through free space do not interact with each other. This characteristic makes them perfect candidates to carry quantum information over long distances. On the other hand, processing the information they encode requires interaction mechanisms. In recent years, there have been growing efforts to realize strong, controlled interactions between photons by making them interact with individual atoms, which are intrinsically nonlinear objects. This, and the efforts to understand the phenomena that can emerge, have spawned the new field of`"quantum nonlinear optics." A number of approaches have been pursued to attain near-deterministic atom-photon interactions, including the use of cavities (CQED), of atomic ensembles, and more recently of dielectric nanostructures able to confine light without defocusing, thus enabling the interaction with atoms trapped in the proximity of the structures. While for the CQED case powerful theoretical tools have been developed to treat the interactions of photons, in the case of atomic ensembles, either in free space or coupled to nanophotonic structures, there is a general lack of theoretical methods beyond the linear regime. This relative lack of understanding also implies that there could be rich new physical phenomena that have thus far not been identified. The overall goal of this thesis is to explore these themes in greater detail. In Chapter 2 of this thesis we develop a new formalism to calculate the properties of quantum light when interfaced with atomic ensembles. The method consists of using a "spin model" that maps a quasi one-dimensional (1D) light propagation problem to the dynamics of an open 1D interacting spin system, where all of the photon correlations are obtained from those of the spins. The spin dynamics can be numerically solved using the toolbox of matrix product states (MPS), thus providing a technique to study strongly interacting photons in the true many-body limit. In Chapter 3 we investigate the possibility of creating exotic phases of matter using the recently realized photonic crystal waveguide (PCW)-atoms interface. In particular, we examine the consequences that arise from the strong interatomic forces mediated by the exchange of band gap photons, whose strengths also depend strongly on the internal atomic states (¿spins¿). Taking one realistic model, we show that "quantum crystallization" can occur, in which the emergent spatial orders of atoms depend intricately on the spin correlations. In Chapter 4 we investigate the possibility of implementing second-order nonlinear quantum optical processes with graphene nanostructures, as a more robust alternative to the use of atomic systems. We quantify the second-order nonlinear properties, showing that the tight confinement of surface plasmons (SP) in graphene gives rise to extraordinary interaction strengths at the single-photon level. Finally, we predict that opportunely engineered arrays of graphene nanostructures can provide a second harmonic generation efficiency comparable with that of state-of-the-art nonlinear crystals, with the high Ohmic losses of graphene serving as the fundamental limitation for deterministic processes. In Chapter 5 we investigate a new paradigm for quantum memories of light based upon ordered atomic arrays. In particular, we show that the strong constructive interference in optical emission can give rise to a significantly enhanced atom-light interface, as compared to a standard, disordered atomic ensemble. In the case of a single, 2D atomic layer, we find the impressive result that a memory realized with 16 atoms can have the same storage efficiency as an atomic ensemble with optical depth larger than 100.Los fotones que viajan por el espacio libre no interactúan entre sí. Esta característica los hace perfectos candidatos para transportar la información cuántica a largas distancias. Por otro lado, el procesamiento de la información que codifican requiere mecanismos de interacción. En los últimos años se han realizado esfuerzos crecientes para realizar interacciones fuertes y controladas entre los fotones y para comprender las leyes subyacentes que describen los fenómenos que pueden surgir, generando así el nuevo campo de la "óptica cuántica no lineal". Mientras que los materiales tridimensionales tienen coeficientes no lineales extremadamente débiles, se pueden obtener interacciones entre los fotones haciéndolos interactuar con átomos individuales, que son objetos intrínsecamente no lineales, teniendo la capacidad de absorber únicamente un solo fotón a la vez. La realización de interacciones determinísticas entre fotones y átomos es uno de los principales retos de la óptica cuántica no lineal. Para eludir las limitaciones debidas a la pequeña sección eficaz óptica de los átomos y el límite de difracción en el espacio libre, se han aplicado diferentes estrategias, entre ellas el uso de cavidades (CQED), de colectividades atómicas y, más recientemente, de nanoestructuras dieléctricas capaces de confinar la luz sin desenfocarse, permitiendo así la interacción con átomos atrapados en la proximidad de esas estructuras. Mientras que para el caso de la CQED se han desarrollado potentes herramientas teóricas para tratar las interacciones de los fotones, en el caso de colectividades atómicas hay una falta general de métodos teóricos más allá del régimen lineal. Esta relativa falta de comprensión también implica que podría haber nuevos fenómenos físicos interesantes que hasta ahora no se han identificado. El objetivo general de esta tesis es explorar estos temas con mayor detalle. En el capítulo 2 de esta tesis desarrollamos un nuevo formalismo para calcular las propiedades de la luz cuántica cuando interactúa con sistemas atómicos. El método consiste en utilizar un"`modelo de espines" que mapea un problema de propagación de luz cuasi unidimensional (1D) a la dinámica de un sistema abierto unidimensional de espines que interactúan entre sí, donde todas las correlaciones de fotones se obtienen a partir de las de los espines. La dinámica de los espines se puede resolver numéricamente utilizando la caja de herramientas de los estados producto de matrices (MPS), proporcionando así una técnica para estudiar los fotones que interactúan fuertemente en el regimen de la física de muchos cuerpos. En el capítulo 3 se investiga la posibilidad de crear fases exóticas de la materia utilizando la interfaz entre guía de ondas de cristales fotónicos (PCW) y átomos recientemente realizada experimentalmente, donde los modos de la banda de frecuencias prohibidas de la PCW se utilizan para mediar las interacciones de largo alcance entre los átomos. Encontramos un rico diagrama de fases de órdenes emergentes. En el capítulo 4 se investiga la posibilidad de implementar procesos ópticos cuánticos no lineales de segundo orden con nano-estructuras de grafeno, como una alternativa más robusta al uso de sistemas atómicos. Cuantificamos las propiedades no lineales de segundo orden, mostrando que el estrecho confinamiento da lugar a extraordinarias fuerzas de interacción a nivel de un solo fotón y predecimos que un diseño apropiado de las nano-estructuras del grafeno permitiría generar el segundo armónico con una eficiencia comparable a la de los cristales no lineales de última generación. En el capítulo 5, investigamos cómo la emisión cooperativa en memorias cuánticas realizadas con reticulos atómicos afecta su eficiencia, encontrando el impresionante resultado de que una memoria realizada con 16 átomos puede tener la misma eficiencia que un gas cuántico atómico de profundidad óptica mayor que 100.Postprint (published version