Atomic Norm decomposition for sparse model reconstruction applied to positioning and wireless communications

This thesis explores the recovery of sparse signals, arising in the wireless communication and radar system fields, via atomic norm decomposition. Particularly, we focus on compressed sensing gridless methodologies, which avoid the always existing error due to the discretization of a continuous space in on-grid methods. We define the sparse signal by means of a linear combination of so called atoms defined in a continuous parametrical atom set with infinite cardinality. Those atoms are fully characterized by a multi-dimensional parameter containing very relevant information about the application scenario itself. Also, the number of composite atoms is much lower than the dimension of the problem, which yields sparsity. We address a gridless optimization solution enforcing sparsity via atomic norm minimization to extract the parameters that characterize the atom from an observed measurement of the model, which enables model recovery. We also study a machine learning approach to estimate the number of composite atoms that construct the model, given that in certain scenarios this number is unknown. The applications studied in the thesis lay on the field of wireless communications, particularly on MIMO mmWave channels, which due to their natural properties can be modeled as sparse. We apply the proposed methods to positioning in automotive pulse radar working in the mmWave range, where we extract relevant information such as angle of arrival (AoA), distance and velocity from the received echoes of objects or targets. Next we study the design of a hybrid precoder for mmWave channels which allows the reduction of hardware cost in the system by minimizing as much as possible the number of required RF chains. Last, we explore full channel estimation by finding the angular parameters that model the channel. For all the applications we provide a numerical analysis where we compare our proposed method with state-of-the-art techniques, showing that our proposal outperforms the alternative methods.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Juan José Murillo Fuentes.- Secretario: Pablo Martínez Olmos.- Vocal: David Luengo Garcí