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

Orthogonal matching pursuit (OMP) and orthogonal least squares (OLS) are widely used for sparse signal reconstruction in under-determined linear regression problems. The performance of these compressed sensing (CS) algorithms depends crucially on the \textit{a priori} knowledge of either the sparsity of the signal ($k_0$) or noise variance ($\sigma^2$). Both $k_0$ and $\sigma^2$ are unknown in general and extremely difficult to estimate in under determined models. This limits the application of OMP and OLS in many practical situations. In this article, we develop two computationally efficient frameworks namely TF-IGP and RRT-IGP for using OMP and OLS even when $k_0$ and $\sigma^2$ are unavailable. Both TF-IGP and RRT-IGP are analytically shown to accomplish successful sparse recovery under the same set of restricted isometry conditions on the design matrix required for OMP/OLS with \textit{a priori} knowledge of $k_0$ and $\sigma^2$. Numerical simulations also indicate a highly competitive performance of TF-IGP and RRT-IGP in comparison to OMP/OLS with \textit{a priori} knowledge of $k_0$ and $\sigma^2$.

Signal and Noise Statistics Oblivious Sparse Reconstruction using OMP/OLS

Fractional frequency reuse (FFR) is an inter-cell interference coordination scheme that is being actively researched for emerging wireless cellular networks. In this work, we consider hexagonal tessellation based planned FFR deployments, and derive expressions for the coverage probability and normalized average rate for the downlink. In particular, given reuse $\frac{1}{3}$ (FR$3$ ) and reuse $1$ (FR$1$) regions, and a Signal-to-Interference-plus-noise-Ratio (SINR) threshold $S_{th}$ which decides the user assignment to either the FR$1$ or FR$3$ regions, we theoretically show that: $(i)$ The optimal choice of $S_{th}$ which maximizes the coverage probability is $S_{th} = T$, where $T$ is the required target SINR (for ensuring coverage), and $(ii)$ The optimal choice of $S_{th}$ which maximizes the normalized average rate is given by the expression $S_{th}=\max(T, T')$, where $T'$ is a function of the path loss exponent and the fade parameters. For the optimal choice of $S_{th}$, we show that FFR gives a higher rate than FR$1$ and a better coverage probability than FR$3$. The impact of frequency correlation over the sub-bands allocated to the FR$1$ and FR$3$ regions is analysed, and it is shown that correlation decreases the average rate of the FFR network. Numerical results are provided, and these match with the analytical results.

Optimal Thresholds for Coverage and Rate in FFR Schemes for Planned Cellular Networks.

We present a novel method for centralized collaborative spectrum sensing for IoT network leveraging cognitive radio network. Based on an online learning framework, we propose an algorithm to efficiently combine the individual sensing results based on the past performance of each detector. Additionally, we show how to utilize the learned normalized weights as a proxy metric of detection accuracy and selectively enable the sensing at detectors. Our results show improved performance in terms of inter-user collision and misdetection. Further, by selectively enabling some of the devices in the network, we propose a strategy to extend the field life of devices without compromising on detection accuracy.

Leveraging Online Learning for CSS in Frugal IoT Network

Given the increasing number of devices that is going to get connected to wireless networks with the advent of Internet of Things, spectrum scarcity will present a major challenge. Application of opportunistic spectrum access mechanisms to IoT networks will become increasingly important to solve this. In this paper, we present a cognitive radio network architecture which uses multi-stage online learning techniques for spectrum assignment to devices, with the aim of improving the throughput and energy efficiency of the IoT devices. In the first stage, we use an AI technique to learn the quality of a user-channel pairing. The next stage utilizes a non-parametric Bayesian learning algorithm to estimate the Primary User OFF time in each channel. The third stage augments the Bayesian learner with implicit exploration to accelerate the learning procedure. The proposed method leads to significant improvement in throughput and energy efficiency of the IoT devices while keeping the interference to the primary users minimal. We provide comprehensive empirical validation of the method with other learning based approaches.

A Non-parametric Multi-stage Learning Framework for Cognitive Spectrum Access in IoT Networks.

In this work, we analytically study the impact of spectrum allocation scheme in picocells on the coverage probability (CP) of the Pico User (PU), when the macro base stations (MBSs) employ either fractional frequency reuse (FFR) or soft frequency reuse (SFR). Assuming a fixed size for the picocell, the CP expression is derived for a PU present in either a FFR or SFR based deployment, and when the PU uses either the centre or the edge frequency resources. Based on these expressions, we propose two possible frequency allocation schemes for the picocell when FFR is employed by the macrocell. The CP and the average rate expressions for both these schemes are derived, and it is shown that these schemes outperform the conventional scheme where no inter-cell interference coordination (ICIC) is assumed. The impact of both schemes on the macro-user performance is also analysed. When SFR is used by the MBS, it is shown that the CP is maximized when the PU uses the same frequency resources as used by the centre region.

Sheetal Kalyani

Papers

Signal and Noise Statistics Oblivious Sparse Reconstruction using OMP/OLS

Optimal Thresholds for Coverage and Rate in FFR Schemes for Planned Cellular Networks.

Leveraging Online Learning for CSS in Frugal IoT Network

A Non-parametric Multi-stage Learning Framework for Cognitive Spectrum Access in IoT Networks.

Spectrum Allocation for ICIC Based Picocell