THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

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Table Of Integrals Series And Products

We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

Reconfigurable intelligent surfaces (RISs) are an emerging transmission technology for application to wireless communications. RISs can be realized in different ways, which include (i) large arrays of inexpensive antennas that are usually spaced half of the wavelength apart; and (ii) metamaterial-based planar or conformal large surfaces whose scattering elements have sizes and inter-distances much smaller than the wavelength. Compared with other transmission technologies, e.g., phased arrays, multi-antenna transmitters, and relays, RISs require the largest number of scattering elements, but each of them needs to be backed by the fewest and least costly components. Also, no power amplifiers are usually needed. For these reasons, RISs constitute a promising software-defined architecture that can be realized at reduced cost, size, weight, and power (C-SWaP design), and are regarded as an enabling technology for realizing the emerging concept of smart radio environments (SREs). In this paper, we (i) introduce the emerging research field of RIS-empowered SREs; (ii) overview the most suitable applications of RISs in wireless networks; (iii) present an electromagnetic-based communication-theoretic framework for analyzing and optimizing metamaterial-based RISs; (iv) provide a comprehensive overview of the current state of research; and (v) discuss the most important research issues to tackle. Owing to the interdisciplinary essence of RIS-empowered SREs, finally, we put forth the need of reconciling and reuniting C. E. Shannon’s mathematical theory of communication with G. Green’s and J. C. Maxwell’s mathematical theories of electromagnetism for appropriately modeling, analyzing, optimizing, and deploying future wireless networks empowered by RISs.

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Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces: How It Works, State of Research, and The Road Ahead

New expressions for symbol error probability (SEP) in the presence of peak-to-average-power-ratio/clipping are derived from the orthogonal frequency division multiplexing systems. These expressions are significantly tighter than the expression in the existing literature, since we model the peak behavior using a peak over threshold approach. An adaptive back-off scheme is also proposed and its SEP is derived. It is shown that with negligible SEP degradation, the adaptive back-off scheme saves power.

Modeling the Behavior of Peaks of OFDM Signal Using ‘Peaks Over Threshold’ Approach

In this work, we characterize the outage probability (OP) of an intelligent reﬂecting surface (IRS) assisted multi-user multiple-input-single-output (MU-MISO) communication system. Using a two-step approximation method, we approximate the signal-to-interference-plus-noise ratio (SINR) for any downlink user by a Log-Normal random variable. The impact of various system parameters is studied using the closed-form expression of OP. It is concluded that the position of IRS has a critical role, but an appropriate increase in the number of IRS elements would help to compensate for the loss in performance if the position of IRS is suboptimal.

SINR Analysis of an IRS Assisted MU-MISO System

The traffic patterns of users in a base station coupled with the sub-frame blanking due to HetNets leads to partially loaded base stations and dynamic interference patterns. Hence, the channel quality indicator information obtained through pilots at a particular time instant would not be reflective of the interference that a user might experience in the immediate future. In this letter, we consider interference prediction in a slot using previous interference values. We observe that conventional Wiener filter based linear prediction that minimizes mean square error performs very badly and hence propose a variant where the weights used for prediction are biased. We also use an asymmetric cost function called Linex and observe through simulations that these two methods perform significantly better than conventional linear prediction. In some cases, the ergodic rate obtained due to the predicted interference is nearly 90% of the actual rate achievable.

Interference Prediction in Partially Loaded Cellular Networks Using Asymmetric Cost Functions

This paper considers the joint power control and resource allocation for a device-to-device (D2D) underlay cellular system with a multi-antenna base station (BS) employing ADCs with different resolutions. We propose a four-step algorithm that optimizes the ADC resolution profile at the BS to reduce the energy consumption and perform joint power control and resource allocation for D2D users (DUEs) and cellular users (CUEs) and thereby improve the D2D reliability and maximize CUE rate.

Joint power and resource allocation for D2D communication with low-resolution ADC

A closed form expression for the Cramer Rao lower bound (CRB) for parameter estimation in the presence of a two component Gaussian mixture noise model is derived. It is further shown that this closed form expression can be lower bounded by a simple two term expression. Closed form expressions are also derived for the variance of the maximum likelihood estimator (MLE) when the parameters of the Gaussian mixture model are misspecified. It is then shown that the MLE can handle a significant amount of misspecification of the parameters of the Gaussian mixture model and yet maintain a variance close to the CRB.

Sheetal Kalyani

Papers

Modeling the Behavior of Peaks of OFDM Signal Using ‘Peaks Over Threshold’ Approach

SINR Analysis of an IRS Assisted MU-MISO System

Interference Prediction in Partially Loaded Cellular Networks Using Asymmetric Cost Functions

Joint power and resource allocation for D2D communication with low-resolution ADC

On CRB for Parameter Estimation in Two Component Gaussian Mixtures and the Impact of Misspecification