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

When the user channel experiences Nakagami-m fading, the coverage probability expressions are theoretically compared for the following cases: (i). The N interferers are independent $\eta$-$\mu$ random variables (RVs). (ii). The N interferers are correlated $\eta$-$\mu$ RVs. It is analytically shown that the coverage probability in the presence of correlated interferers is greater than or equal to the coverage probability in the presence of independent interferers when the shape parameter of the channel between the user and its base station (BS) is not greater than one. Further, rate is compared for the following cases: (i). The user channel experiences $\eta$-$\mu$ RV and the $N$ interferers are independent $\eta$-$\mu$ RVs. (ii). The N interferers are correlated $\eta$-$\mu$ RVs. It is analytically shown that the rate in the presence of correlated interferers is greater than or equal to the rate in the presence of independent interferers. Simulation results are provided and these match with the obtained theoretical results. The utility of our results are also discussed.

Impact of Correlation between Interferers on Coverage Probability and rate in Cellular Systems

We design the phase shifts of an intelligent reﬂecting surface (IRS)-assisted single-input-multiple-output communication system to minimize the outage probability (OP) and to maximize the ergodic rate. Our phase shifts design uses only statistical channel state information since these depend only on the large-scale fading coefﬁcients; the obtained phase shift design remains valid for a longer time frame. We further assume that one has access to only quantized phase values. The closed-form expressions for OP and ergodic rate are derived for the considered system. Next, two optimization problems are formulated to choose the phase shifts of IRS such that (i) OP is minimized and (ii) the ergodic rate is maximized. We used the multi-valued particle swarm optimization (MPSO) and particle swarm optimization (PSO) algorithms to solve the optimization problems. Numerical simulations are performed to study the impact of various parameters on the OP and ergodic rate. We also discuss signaling overhead between BS and IRS controller. It is shown that the overhead can be reduced up to 99 . 69% by using statistical CSI for phase shift design and 5 bits to represent the phase shifts without signiﬁcantly compromising on the performance. the performance loss is negligible. We also discussed the impact of statistical CSI-based phase shift design and quantized phase shift on the reduction of overhead between BS and IRS controller. It was shown that the overhead could be reduced up to

Instantaneous Channel Oblivious Phase Shift Design for an IRS-Assisted SIMO System with Quantized Phase Shift

Recent research in the design of end to end communication system using deep learning has produced models which can outperform traditional communication schemes. Most of these architectures leveraged autoencoders to design the encoder at the transmitter and decoder at the receiver and train them jointly by modeling transmit symbols as latent codes from the encoder. However, in communication systems, the receiver has to work with noise corrupted versions of transmit symbols. Traditional autoencoders are not designed to work with latent codes corrupted with noise. In this work, we provide a framework to design end to end communication systems which accounts for the existence of noise corrupted transmit symbols. The proposed method uses deep neural architecture. An objective function for optimizing these models is derived based on the concepts of variational inference. Further, domain knowledge such as channel type can be systematically integrated into the objective. Through numerical simulation, the proposed method is shown to consistently produce models with better packing density and achieving it faster in multiple popular channel models as compared to the previous works leveraging deep learning models.

Design of Communication Systems using Deep Learning: A Variational Inference Perspective

In this paper, approximate outage probability (OP) expressions are derived for uplink cell-free massive multiple-input-multiple-output (CF-mMIMO) system. The access points (APs) of the system considered have imperfect channel state information (CSI). The approximate expressions are derived first using conditional expectations and then using a novel dimension reduction method that approximates higher-order integration by several single order integrations. Using the same approach, closed-form approximations are also derived for conventional massive MIMO (mMIMO) systems. The OP approximations are then used to characterize the performance of cell-edge users of CF-mMIMO systems and compare the designs of CF-mMIMO and mMIMO systems. The derived expressions have a close match with the simulated expression for OP.

Outage Probability of Uplink Cell-Free Massive MIMO Network with Imperfect CSI Using Dimension-Reduction Method.

Approximate Symbol error rate (SER) expressions are derived for receive diversity system employing optimum combining, when both the desired and the interfering signals are subjected to Rician fading, for the case of a) equal power uncorrelated interferers b) unequal power interferers c) interferer correlation. The derived expressions are applicable for an arbitrary number of receive antennas and interferers and for any QAM constellation. Furthermore, we derive a simple closed form expression for SER in the interference-limited regime, for the special case of Rayleigh faded interferers. A close match is observed between the SER result obtained through the derived analytical expression and the one obtained from Monte-Carlo simulations, for a variety of QAM constellations.

Sheetal Kalyani

Papers

Impact of Correlation between Interferers on Coverage Probability and rate in Cellular Systems

Instantaneous Channel Oblivious Phase Shift Design for an IRS-Assisted SIMO System with Quantized Phase Shift

Design of Communication Systems using Deep Learning: A Variational Inference Perspective

Outage Probability of Uplink Cell-Free Massive MIMO Network with Imperfect CSI Using Dimension-Reduction Method.

SER for Optimal Combining in Rician Fading with Co-channel Interference.