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Downlink Single-Snapshot Localization and Mapping with a Single-Antenna Receiver
TL;DR: In this article, a joint maximum likelihood estimation problem is formulated and its solution formally derived for single-snapshot localization and mapping in the more challenging case of a user equipped with a single-antenna receiver.
Abstract: 5G mmWave MIMO systems enable accurate estimation of the user position and mapping of the radio environment using a single snapshot when both the base station (BS) and user are equipped with large antenna arrays. However, massive arrays are initially expected only at the BS side, likely leaving users with one or very few antennas. In this paper, we propose a novel method for single-snapshot localization and mapping in the more challenging case of a user equipped with a single-antenna receiver. The joint maximum likelihood (ML) estimation problem is formulated and its solution formally derived. To avoid the burden of a full-dimensional search over the space of the unknown parameters, we present a novel practical approach that exploits the sparsity of mmWave channels to compute an approximate joint ML estimate. A thorough analysis, including the derivation of the Cramer-Rao lower bounds, reveals that accurate localization and mapping can be achieved also in a MISO setup even when the direct line-of-sight path between the BS and the user is severely attenuated.
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TL;DR: This study considers an intermediate approach, which consists of four phases—downlink data transmission, multi-dimensional channel estimation, channel parameter clustering, and simultaneous localization and mapping (SLAM) based on a novel likelihood function.
Abstract: 5G communication systems operating above 24 GHz have promising properties for user localization and environment mapping. Existing studies have either relied on simplified abstract models of the signal propagation and the measurements, or are based on direct positioning approaches, which directly map the received waveform to a position. In this study, we consider an intermediate approach, which consists of four phases-downlink data transmission, multi-dimensional channel estimation, channel parameter clustering, and simultaneous localization and mapping (SLAM) based on a novel likelihood function. This approach can decompose the problem into simpler steps, thus leading to lower complexity. At the same time, by considering an end-to-end processing chain, we are accounting for a wide variety of practical impairments. Simulation results demonstrate the efficacy of the proposed approach.
43 citations
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TL;DR: It is shown that thanks to the use of a reconfigurable intelligent surface (RIS), joint localization and synchronization is possible with only downlink MISO transmissions and attains the Cramér-Rao lower bound even for moderate values of the system parameters.
Abstract: MmWave multiple-input single-output (MISO) systems using a single-antenna receiver are regarded as promising solution for the near future, before the full-fledged 5G MIMO will be widespread. However, for MISO systems synchronization cannot be performed jointly with user localization unless two-way transmissions are used. In this paper we show that thanks to the use of a reconfigurable intelligent surface (RIS), joint localization and synchronization is possible with only downlink MISO transmissions. The direct maximum likelihood (ML) estimator for the position and clock offset is derived. To obtain a good initialization for the ML optimization, a decoupled, relaxed estimator of position and delays is also devised, which does not require knowledge of the clock offset. Results show that the proposed approach attains the Cram\'er-Rao lower bound even for moderate values of the system parameters.
29 citations
References
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TL;DR: This paper presents convergence properties of the Nelder--Mead algorithm applied to strictly convex functions in dimensions 1 and 2, and proves convergence to a minimizer for dimension 1, and various limited convergence results for dimension 2.
Abstract: The Nelder--Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder--Mead algorithm. This paper presents convergence properties of the Nelder--Mead algorithm applied to strictly convex functions in dimensions 1 and 2. We prove convergence to a minimizer for dimension 1, and various limited convergence results for dimension 2. A counterexample of McKinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the Nelder--Mead algorithm converges to a nonminimizer. It is not yet known whether the Nelder--Mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions.
7,141 citations
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TL;DR: The motivation for new mm-wave cellular systems, methodology, and hardware for measurements are presented and a variety of measurement results are offered that show 28 and 38 GHz frequencies can be used when employing steerable directional antennas at base stations and mobile devices.
Abstract: The global bandwidth shortage facing wireless carriers has motivated the exploration of the underutilized millimeter wave (mm-wave) frequency spectrum for future broadband cellular communication networks. There is, however, little knowledge about cellular mm-wave propagation in densely populated indoor and outdoor environments. Obtaining this information is vital for the design and operation of future fifth generation cellular networks that use the mm-wave spectrum. In this paper, we present the motivation for new mm-wave cellular systems, methodology, and hardware for measurements and offer a variety of measurement results that show 28 and 38 GHz frequencies can be used when employing steerable directional antennas at base stations and mobile devices.
6,708 citations
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TL;DR: While massive MIMO renders many traditional research problems irrelevant, it uncovers entirely new problems that urgently need attention: the challenge of making many low-cost low-precision components that work effectively together, acquisition and synchronization for newly joined terminals, the exploitation of extra degrees of freedom provided by the excess of service antennas, reducing internal power consumption to achieve total energy efficiency reductions, and finding new deployment scenarios.
Abstract: Multi-user MIMO offers big advantages over conventional point-to-point MIMO: it works with cheap single-antenna terminals, a rich scattering environment is not required, and resource allocation is simplified because every active terminal utilizes all of the time-frequency bins. However, multi-user MIMO, as originally envisioned, with roughly equal numbers of service antennas and terminals and frequency-division duplex operation, is not a scalable technology. Massive MIMO (also known as large-scale antenna systems, very large MIMO, hyper MIMO, full-dimension MIMO, and ARGOS) makes a clean break with current practice through the use of a large excess of service antennas over active terminals and time-division duplex operation. Extra antennas help by focusing energy into ever smaller regions of space to bring huge improvements in throughput and radiated energy efficiency. Other benefits of massive MIMO include extensive use of inexpensive low-power components, reduced latency, simplification of the MAC layer, and robustness against intentional jamming. The anticipated throughput depends on the propagation environment providing asymptotically orthogonal channels to the terminals, but so far experiments have not disclosed any limitations in this regard. While massive MIMO renders many traditional research problems irrelevant, it uncovers entirely new problems that urgently need attention: the challenge of making many low-cost low-precision components that work effectively together, acquisition and synchronization for newly joined terminals, the exploitation of extra degrees of freedom provided by the excess of service antennas, reducing internal power consumption to achieve total energy efficiency reductions, and finding new deployment scenarios. This article presents an overview of the massive MIMO concept and contemporary research on the topic.
6,184 citations
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10 Sep 2007
TL;DR: This new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded, and adopts an object-oriented style particularly suited to scientific applications.
Abstract: Co-authored by four leading scientists from academia and industry, Numerical Recipes Third Edition starts with basic mathematics and computer science and proceeds to complete, working routines. Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Please visit www.nr.com or www.cambridge.org/us/numericalrecipes for more details. New key features: 2 new chapters, 25 new sections, 25% longer than Second Edition Thorough upgrades throughout the text Over 100 completely new routines and upgrades of many more. New Classification and Inference chapter, including Gaussian mixture models, HMMs, hierarchical clustering, Support Vector MachinesNew Computational Geometry chapter covers KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres New sections include interior point methods for linear programming, Monte Carlo Markov Chains, spectral and pseudospectral methods for PDEs, and many new statistical distributions An expanded treatment of ODEs with completely new routines Plus comprehensive coverage of linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory And much, much more! Visit the authors' web site for information about electronic subscriptions www.nr.com/aboutNR3book.html
4,130 citations
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TL;DR: This paper describes the simultaneous localization and mapping (SLAM) problem and the essential methods for solving the SLAM problem and summarizes key implementations and demonstrations of the method.
Abstract: This paper describes the simultaneous localization and mapping (SLAM) problem and the essential methods for solving the SLAM problem and summarizes key implementations and demonstrations of the method. While there are still many practical issues to overcome, especially in more complex outdoor environments, the general SLAM method is now a well understood and established part of robotics. Another part of the tutorial summarized more recent works in addressing some of the remaining issues in SLAM, including computation, feature representation, and data association
3,760 citations