Ultra-wideband millimeter-wave (mmWave) propagation measurements were conducted in the 28- and 73-GHz frequency bands in a typical indoor office environment in downtown Brooklyn, New York, on the campus of New York University. The measurements provide large-scale path loss and temporal statistics that will be useful for ultra-dense indoor wireless networks for future mmWave bands. This paper presents the details of measurements that employed a 400 Megachips-per-second broadband sliding correlator channel sounder, using rotatable highly directional horn antennas for both co-polarized and crosspolarized antenna configurations. The measurement environment was a closed-plan in-building scenario that included a line-of-sight and non-line-of-sight corridor, a hallway, a cubicle farm, and adjacent-room communication links. Well-known and new single-frequency and multi-frequency directional and omnidirectional large-scale path loss models are presented and evaluated based on more than 14 000 directional power delay profiles acquired from unique transmitter and receiver antenna pointing angle combinations. Omnidirectional path loss models, synthesized from the directional measurements, are provided for the case of arbitrary polarization coupling, aswell as for the specific cases of co-polarized and cross-polarized antenna orientations. The results show that novel large-scale path loss models provided here are simpler and more physically based compared to previous 3GPP and ITU indoor propagation models that require more model parameters and offer very little additional accuracy and lack a physical basis. Multipath time dispersion statistics formmWave systems using directional antennas are presented for co-polarization, crosspolarization, and combined-polarization scenarios, and show that the multipath root mean square delay spread can be reduced when using transmitter and receiver antenna pointing angles that result in the strongest received power. Raw omnidirectional path loss data and closed-form optimization formulas for all path loss models are given in the Appendices.

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Indoor Office Wideband Millimeter-Wave Propagation Measurements and Channel Models at 28 and 73 GHz for Ultra-Dense 5G Wireless Networks

A system and method for estimating the position of wireless devices within a wireless communication network combines measured RF channel characteristics for the wireless device with one or more predicted performance lookup tables, each of which correlates an RF channel characteristic to some higher order network performance metric and/or a position within an environmental model. Measured RF channel characteristics for wireless devices are compared against the performance lookup tables to determine the sent of lookup tables that most closely match the measured RF channel characteristics. The positions within the environmental model corresponding to the selected set of matching lookup tables are identified as possible locations for the wireless device. The performance lookup tables are uniquely constructed by site-specific location, technology, wireless standard, and equipment types, and/or the current operating state of the communications network.

System, method, and apparatus for determining and using the position of wireless devices or infrastructure for wireless network enhancements

In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/84479E2B03A9BFFE0F9CD46CF9FCD289/S0962492919000060a.pdf/div-class-title-derivative-free-optimization-methods-div.pdf

Derivative-free optimization methods

A system and method for providing security to a wireless communication system having wireless communication components positioned at different locations within a physical environment are provided. The wireless communication components include an access point and a network device. A site-specific computerized representation of the physical environment displays the location of the wireless communication components including the access point and network device. The access point and network device identify the presence or a physical location of a possible intruder or intruder devices. An indicator is presented in the site-specific representation on the display when an erroneous authentication request or other undesired transmission is received by the network device or the access point.

System and method for indicating the presence or physical location of persons or devices in a site specific representation of a physical environment

In the paper, the global optimization problem of a multidimensional "black-box" function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. A new efficient algorithm for solving this problem is presented. At each iteration of the method a number of possible Lipschitz constants are chosen from a set of values varying from zero to infinity. This idea is unified with an efficient diagonal partition strategy. A novel technique balancing usage of local and global information during partitioning is proposed. A new procedure for finding lower bounds of the objective function over hyperintervals is also considered. It is demonstrated by extensive numerical experiments performed on more than 1600 multidimensional test functions that the new algorithm shows a very promising performance.

Global Search Based on Efficient Diagonal Partitions and a Set of Lipschitz Constants

The DIRECT (DIviding RECTangles) algorithm of Jones, Perttunen, and Stuckman (Journal of Optimization Theory and Applications, vol. 79, no. 1, pp. 157–181, 1993), a variant of Lipschitzian methods for bound constrained global optimization, has proved effective even in higher dimensions. However, the performance of a DIRECT implementation in real applications depends on the characteristics of the objective function, the problem dimension, and the desired solution accuracy. Implementations with static data structures often fail in practice, since it is difficult to predict memory resource requirements in advance. This is especially critical in multidisciplinary engineering design applications, where the DIRECT optimization is just one small component of a much larger computation, and any component failure aborts the entire design process. To make the DIRECT global optimization algorithm efficient and robust on large-scale, multidisciplinary engineering problems, a set of dynamic data structures is proposed here to balance the memory requirements with execution time, while simultaneously adapting to arbitrary problem size. The focus of this paper is on design issues of the dynamic data structures, and related memory management strategies. Numerical computing techniques and modifications of Jones' original DIRECT algorithm in terms of stopping rules and box selection rules are also explored. Performance studies are done for synthetic test problems with multiple local optima. Results for application to a site-specific system simulator for wireless communications systems (S4W) are also presented to demonstrate the effectiveness of the proposed dynamic data structures for an implementation of DIRECT.

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Dynamic Data Structures for a Direct Search Algorithm

VTDIRECT95 is a Fortran 95 implementation of D. R. Jones' deterministic global optimization algorithm called DIRECT, which is widely used in multidisciplinary engineering design, biological science, and physical science applications. The package includes both a serial code and a data-distributed massively parallel code for different problem scales and optimization (exploration vs. exploitation) goals. Dynamic data structures are used to organize local data, handle unpredictable memory requirements, reduce the memory usage, and share the data across multiple processors. The parallel code employs a multilevel functional and data parallelism to boost concurrency and mitigate the data dependency, thus improving the load balancing and scalability. In addition, checkpointing features are integrated into both versions to provide fault tolerance and hot restarts. Important algorithm modifications and design considerations are discussed regarding data structures, parallel schemes, error handling, and portability. Using several benchmark functions and real-world applications, the software is evaluated on different systems in terms of optimization effectiveness, data structure efficiency, parallel performance, and checkpointing overhead. The package organization and usage are also described in detail.

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Remark on Algorithm 897: VTDIRECT95: Serial and Parallel Codes for the Global Optimization Algorithm DIRECT

A global optimization technique is applied to solve the optimal transmitter placement problem for indoor wireless systems. An efficient pattern search algorithm - DIviding RECTangles (DIRECT) of Jones et al.- has been connected to a parallel three-dimensional radio propagation ray tracing modeler running on a 200-node Beowulf cluster of Linux workstations. Surrogate functions for a parallel wideband code-division multiple-access (WCDMA) simulator were used to estimate the system performance for the global optimization algorithm. Power coverage and bit-error rate are considered as two different criteria for optimizing locations of a specified number of transmitters across the feasible region of the design space. This paper briefly describes the underlying radio propagation and WCDMA simulations and focuses on the design issues of the optimization loop.

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Globally optimal transmitter placement for indoor wireless communication systems

Modeling and analysis techniques are used to investigate the performance of a massively parallel version of DIRECT, a global search algorithm widely used in multidisciplinary design optimization applications. Several high-dimensional benchmark functions and real world problems are used to test the design effectiveness under various problem structures. In this second part of a two-part work, theoretical and experimental results are compared for two parallel clusters with different system scales and network connectivities. The first part studied performance sensitivity to important parameters for problem configurations and parallel schemes, using performance metrics such as memory usage, load balancing, and parallel efficiency. Here linear regression models are used to characterize two major overhead sources, interprocessor communication and processor idleness, and also applied to the isoefficiency functions in scalability analysis. For a variety of high-dimensional problems and large-scale systems, the massively parallel design has achieved reasonable performance. The results of the performance study provide guidance for efficient problem and scheme configuration. More importantly, the design considerations and analysis techniques generalize to the transformation of other global search algorithms into effective large-scale parallel optimization tools.

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Performance Modeling and Analysis of a Massively Parallel Direct - Part 2

This paper describes several massively parallel implementations for a global search algorithm DIRECT. Two parallel schemes take different approaches to address DIRECT's design challenges imposed by memory requirements and data dependency. Three design aspects in topology, data structures, and task allocation are compared in detail. The goal is to analytically investigate the strengths and weaknesses of these parallel schemes, identify several key sources of inefficiency, and experimentally evaluate a number of improvements in the latest parallel DIRECT implementation. The performance studies demonstrate improved data structure efficiency and load balancing on a 2200 processor cluster.

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Jian He

Papers

Dynamic Data Structures for a Direct Search Algorithm

Remark on Algorithm 897: VTDIRECT95: Serial and Parallel Codes for the Global Optimization Algorithm DIRECT

Globally optimal transmitter placement for indoor wireless communication systems

Performance Modeling and Analysis of a Massively Parallel Direct - Part 2

Design and implementation of a massively parallel version of DIRECT