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.

/pdf/smart-radio-environments-empowered-by-reconfigurable-2uovma9m3w.pdf

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

Sparse channel estimation (SCE) in orthogonal frequency division multiplexing (OFDM) systems with large number of virtual sub-carriers and regularly spaced pilots is studied in this paper. Such OFDM systems are present in wireless standards like long term evolution (LTE). We numerically evaluate the performance of popular compressive sensing (CS) algorithms and shows that low complexity CS algorithms like OMP, subspace pursuit etc performs badly in these OFDM systems. We also provide analytical reasoning for this suboptimal performance. This paper points to the need of developing new low complexity CS algorithms for SCE in OFDM systems with large number of virtual sub-carriers and equispaced pilots.

Sparse Channel Estimation in OFDM Systems with Virtual Sub-Carriers

This paper derives the limiting distribution of the maximum end-to-end signal to noise ratio (SNR) in a cooperative relaying (CR) scenario with multiple relays capable of both time splitting (TS) and power splitting (PS) based energy harvesting (EH). Considering an opportunistic relay selection scenario, we derive the limiting distribution of end-to-end SNR over independent and non-identical relay links between the source and the destination. Contrary to the majority of literature in communication which uses extreme value theory (EVT) to derive the statistics of extremes of sequences of independent and identically distributed (i.i.d.) random variables (RVs), we demonstrate how tools from EVT can be used to derive the limiting statistics of sequences of independent and non-identically distributed (i.n.i.d.) SNR RVs and hence derive the corresponding expressions for asymptotic ergodic and outage capacities. Finally, we present the utility of the asymptotic results for deciding the optimum TS and PS factors of the hybrid EH relays to minimize outage probability at the destination. Furthermore, we demonstrate how results from stochastic ordering can be utilized for simplifying the corresponding optimization problem.

Cooperative relaying with energy harvesting relays : Asymptotic analysis using extreme value theory for non-identically distributed RVs.

This paper introduces an incremental training framework for compressing popular Deep Neural Network (DNN) based unfolded multiple-input-multiple-output (MIMO) detection algorithms like DetNet. The idea of incremental training is explored to select the optimal depth while training. To reduce the computation requirements or the number of FLoating point OPerations (FLOPs) and enforce sparsity in weights, the concept of structured regularization is explored using group LASSO and sparse group LASSO. Our methods lead to an astounding $98.9\%$ reduction in memory requirement and $81.63\%$ reduction in FLOPs when compared with DetNet without compromising on BER performance.

Green DetNet: Computation and Memory efficient DetNet using Smart Compression and Training

The framework of differential privacy protects an individual's privacy while publishing query responses on congregated data. In this work, a new noise addition mechanism for differential privacy is introduced where the noise added is sampled from a hybrid density that resembles Laplace in the centre and Gaussian in the tail. With a sharper centre and light, sub-Gaussian tail, this density has the best characteristics of both distributions. We theoretically analyze the proposed mechanism, and we derive the necessary and sufficient condition in one dimension and a sufficient condition in high dimensions for the mechanism to guarantee (${\epsilon}$,${\delta}$)-differential privacy. Numerical simulations corroborate the efficacy of the proposed mechanism compared to other existing mechanisms in achieving a better trade-off between privacy and accuracy.

Grafting Laplace and Gaussian distributions: A new noise mechanism for differential privacy

The embodiments described herein provide a method and system for improve link adaption performance in wireless networks. The method for modifying the MCS index for transmission using a computed offset is provided. The offset is calculated based on HARQ feedback of transmissions. A transition probability matrix with plurality of MCS indices is used for selecting the MCS index for transmission based on the highest probability of transition. A pattern sequence of MCS indices is formed and the presence of the pattern is determined in the history of the HARQ transmissions. The frequency of the pattern presence is also determined and the MCS index is selected for the HARQ transmissions. A frequency database of MCS indices is built using source encoding techniques. The transition probabilities that are estimated from the frequency database along with a cost function associated with each MCS index will be used to compute next MCS index.

Sheetal Kalyani

Papers

Sparse Channel Estimation in OFDM Systems with Virtual Sub-Carriers

Cooperative relaying with energy harvesting relays : Asymptotic analysis using extreme value theory for non-identically distributed RVs.

Green DetNet: Computation and Memory efficient DetNet using Smart Compression and Training

Grafting Laplace and Gaussian distributions: A new noise mechanism for differential privacy

Adaptive link adaptation system and method