Direction of arrival estimation using robust complex Lasso

The Lasso (Least Absolute Shrinkage and Selection Operator) has been a popular technique for simultaneous linear regression estimation and variable selection. In this paper, we propose a new novel approach for robust Lasso that follows the spirit of M-estimation. We define $M$-Lasso estimates of regression and scale as solutions to generalized zero subgradient equations. Another unique feature of this paper is that we consider complex-valued measurements and regression parameters, which requires careful mathematical characterization of the problem. An explicit and efficient algorithm for computing the $M$-Lasso solution is proposed that has comparable computational complexity as state-of-the-art algorithm for computing the Lasso solution. Usefulness of the $M$-Lasso method is illustrated for direction-of-arrival (DoA) estimation with sensor arrays in a single snapshot case.Comment: Paper has appeared in the Proceedings of the 10th European Conference on Antennas and Propagation (EuCAP'2016), Davos, Switzerland, April 10-15, 201

Multichannel sparse recovery of complex-valued signals using Huber's criterion

In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vectors. This requires careful characterization of robust complex-valued loss functions as well as Huber's criterion function for the multivariate sparse regression problem. We devise a greedy algorithm based on simultaneous normalized iterative hard thresholding (SNIHT) algorithm. Unlike the conventional SNIHT method, our algorithm, referred to as HUB-SNIHT, is robust under heavy-tailed non-Gaussian noise conditions, yet has a negligible performance loss compared to SNIHT under Gaussian noise. Usefulness of the method is illustrated in source localization application with sensor arrays.Comment: To appear in CoSeRa'15 (Pisa, Italy, June 16-19, 2015). arXiv admin note: text overlap with arXiv:1502.0244

Экспериментальное исследование системы передачи на основе FBMC/OQAM

Introduction. This paper investigates a transmission system based on FBMC/OQAM multiplexing. This system is characterized by a high spectral efficiency, thereby attracting interest as an alternative transmission method in future wireless mobile communication standards. However, a disadvantage of the system is the high complexity of signal processing. There are numerous publications that study the FBMC/OQAM system from a theoretical perspective. This paper presents an experimental study of a transmission system based on FBMC/OQAM.Aim. Verification of a transmission system based on FBMC/OQAM multiplexing in a wireless channel.Materials and methods. Computer simulation modeling in Matlab and experimental research using Keysight and Rohde & Schwarz certified measuring instruments.Results. A model of synthesis and signal processing was developed, and a frame structure was proposed. The processing included synchronization, since the study was carried out in a wireless double-dispersive channel. Time synchronization was provided by the method of time-domain correlation. A preamble consisting of two symbols was used for CFO compensation. Channel estimation in FBMC/OQAM was conducted by pilot symbols spread over the time-frequency domain, a method with an auxiliary pilot to compensate for intrinsic interference, as well as Zero Forcing and a linear interpolator. As a result, dependences of the bit error rate on the Eb/N0 in various channels were obtained. An error rate of 10−4 was achieved under the Eb/N0 equal to 13.4 dB, 15.3 dB and 20.9 dB in the first, second and third channel, respectively.Conclusion. A FBMC/OQAM-based transmission system with a linear equalizer can operate without a cyclic prefix in a multipath wireless channel, providing comparable noise immunity to OFDM-CP. Long frames should be used to obtain greater spectral efficiency, due to the presence of a transition zone at the beginning and end of the FBMC/OQAM frame.Введение. Данная работа посвящена исследованию системы передачи на основе мультиплексирования FBMC/OQAM. Актуальность исследования связана с высокой спектральной эффективностью данной системы, благодаря которой она рассматривается как альтернативный метод передачи в будущих стандартах беспроводной мобильной связи. Однако недостатком системы является высокая сложность обработки сигналов. Среди отечественных и зарубежных публикаций встречается множество работ с теоретическим исследованием системы FBMC/OQAM. В данной статье представлены результаты экспериментального исследования системы передачи на ее основе.Цель работы. Верификация модели системы передачи данных на основе FBMC/OQAM в беспроводном канале связи.Материалы и методы. В работе используется метод имитационного компьютерного моделирования в среде Matlab и экспериментальное исследование с использованием сертифицированного измерительного оборудования Keysight и Rohde & Schwarz.Результаты. Была разработана модель формирования и обработки сигнала, а также предложена структура  кадра.  Покадровая  обработка  выполнялась  с  учетом  временной  и  частотной  синхронизации,  поскольку  исследование  проводилось  в  беспроводном  канале  с  частотно-временным  рассеянием.  Временная синхронизация обеспечивалась корреляционным методом во временной области. Для компенсации  рассогласования  опорных  генераторов  применялась  оценка  с  помощью  преамбулы,  состоящей из двух символов. В работе использовалась оценка канала методом Zero Forcing, а также эквалайзер с линейным  интерполятором.  Для  корректной  оценки  канала  в  FBMC/OQAM  использовались  пилотные символы, распределенные по всей частотно-временной сетке, а также метод с дополнительным пилотом для компенсации межканальной интерференции. В результате работы получены зависимости коэффициента битовых ошибок от отношения энергии, приходящейся на бит информации, к энергии шума в различных  каналах.  Достигнут  коэффициент  ошибок  10−4  при  отношениях  энергии,  приходящейся  на  бит информации, к мощности шума, равных 13.4 дБ в первом канале, 15.3 дБ во втором и 20.9 дБ в третьем. Заключение. Система передачи на основе FBMC/OQAM с линейным эквалайзером может работать без циклического  префикса  в  беспроводном  канале  связи  с  многолучевостью,  обеспечивая  сравнимую  с OFDM-CP  помехоустойчивость.  Для  получения  большей  спектральной  эффективности  необходимо  использовать длинные кадры, поскольку в начале и конце кадра FBMC/OQAM имеется переходная зона

The Graph Curvature Calculator and the curvatures of cubic graphs

We classify all cubic graphs with either non-negative Ollivier-Ricci curvature or non-negative Bakry-\'Emery curvature everywhere. We show in both curvature notions that the non-negatively curved graphs are the prism graphs and the M\"obius ladders. We also highlight an online tool for calculating the curvature of graphs under several variants of these curvature notions that we use in the classification. As a consequence of the classification result we show, that non-negatively curved cubic expanders do not exist

System Properties of Implicit Passive Electrical Networks Descriptions

Redesigning systems by changing elements, topology, organization, augmenting the system by the addition of subsystems, or removing parts, is a major challenge for systems and control theory. A special case is the redesign of passive electric networks which aims to change the natural dynamics of the network (natural frequencies) by the above operations leading to a modification of the network. This requires changing the system to achieve the desirable natural frequencies and involves the selection of alternative values for dynamic elements and non-dynamic elements within a fixed interconnection topology and/or alteration of the interconnection topology and possible evolution of the network (increase of elements, branches). The use of state-space or transfer function models does not provide a suitable framework for the study of this problem, since every time such changes are introduced, a new state space or transfer function model has to be recalculated. The use of impedance and admittance modeling, provides a suitable framework for the study of network properties under the process of re-engineering transformations. This paper deals with the fundamental system properties of the impedance-admittance network description which provide the appropriate framework for network re-engineering. We identify the natural topologies expressing the structured transformations linked to the impedance-graph, admittance graph-topology of the network and examine issues such as network regularity, number of finite frequencies and provide characterization of them in terms of the basic network matrices. The implicit network representation introduced provides a natural framework for expressing the different types of re-engineering transformations which can be used for the study of the natural frequencies assignment