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

We treat decision-directed channel tracking (DDCT) in mobile orthogonal frequency-division multiplexing (OFDM) systems as an outlier contaminated Gaussian regression problem, where the source of outliers are the incorrect symbol decisions. Existing decision-directed estimators such as the expectation-max- imization (EM)-based estimators and the 2-D-MMSE estimator do not appropriately downweight incorrect/poor decisions while defining the channel estimator, and hence suffer from error propagation at high fade rates. We propose to use generalized M estimators for decision-directed channel estimation and apply ex- treme value theory in conjunction with the Huber's cost function for outlier detection and downweighting. Significant reduction in error propagation is obtained by identifying and downweighting those symbol decisions that act as outliers before using them for channel estimation. The proposed estimators clearly outperform the 2-D-MMSE and the EM-based estimators in terms of simu- lated error rate performance at high fade rates. These estimators also have performance comparable to (or better than) pilot-as- sisted Kalman-filter-based channel tracking schemes with only modest increase in complexity. Thus, a 6% to 12% increase in data throughput is obtained without loss in performance when compared with the pilot-assisted schemes, even when DDCT is applied over frame durations experiencing two to three fade cycles.

Mitigation of Error Propagation in Decision Directed OFDM Channel Tracking Using

We look at the performance of turbo coded OFDM systems in the presence of narrowband interference (NBI) and co-channel interference (CCI). In systems employing standards such as the IEEE 802.16d/e, CCI behaves like NBI with the number of affected subcarriers ranging from 10% to 30%. Hence we treat symbol detection in such systems as detection in contaminated Gaussian (CG) noise and propose a robust log- likelihood ratio (LLR) computation for it. The proposed LLR computation method exploits the fact that NBI/CCI has a CG probability density function (pdf) but does not assume knowledge of the NBI power, NBI pdf and the fraction of subcarriers affected by NBI. Simulation results indicate that the proposed method performs very close to the optimal method which would have complete knowledge of the CG pdf parameters.

Interference Mitigation in Turbo-Coded OFDM Systems Using Robust LLRs

In this work, we study the outage probability (OP) at the destination of an intelligent reflecting surface (IRS) assisted communication system in the presence of phase error due to quantization at the IRS when a) source-destination (SD) link is present and b) SD link is absent. First,an exact expression is derived and then we derive three simple approximations for the OP using the following approaches: (i) uni-variate dimension reduction, (ii) moment matching and,(iii) Kullback-Leibler divergence minimization. The resulting expressions for OP are simple to evaluate and quite tight even in the tail region. The validity of these approximations is demonstrated using extensive Monte Carlo simulations.

Outage Probability Expressions for an IRS-Assisted System with and without Source-Destination Link for the Case of Quantized Phase Shifts

Expressions are derived for the coverage probability and average rate of both multi-user multiple input multiple output (MU-MIMO) and single input multiple output (SIMO) systems in the context of a fractional frequency reuse (FFR) scheme. In particular, given a reuse region of $\frac{1}{3}$ (FR3) and a reuse region of 1 (FR1) as well as a signal-to-interference-plus-noise-ratio (SINR) threshold $S_{th}$ , which decides the user assignment to either the FR1 or FR3 regions, we theoretically show that: $1)$ the optimal choice of $S_{th}$ which maximizes the coverage probability is $S_{th} = T$ , where $T$ is the target SINR required for ensuring adequate coverage, and $2)$ the optimal choice of $S_{th}$ which maximizes the average rate is given by $S_{th}= T^{\prime}$ , where $T^{\prime}$ is a function of the path loss exponent, the number of antennas and of the fading parameters. The impact of frequency domain correlation amongst the OFDM sub-bands allocated to the FR1 and FR3 cell-regions is analysed and it is shown that the presence of correlation reduces both the coverage probability and the average throughput of the FFR network. Furthermore, the performance of our FFR-aided MU-MIMO and SIMO systems is compared. Our analysis shows that the (2 $\times$ 2) MU-MIMO system achieves 22.5% higher rate than the (1 $\times$ 3) SIMO system and for lower target SINRs, the coverage probability of a (2 $\times$ 2) MU-MIMO system is comparable to a (1 $\times$ 3) SIMO system. Hence the former one may be preferred over the latter. Our simulation results closely match the analytical results.

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Coverage Probability and Achievable Rate Analysis of FFR-Aided Multi-User OFDM-Based MIMO and SIMO Systems

In this letter, we propose a peak-to-average power ratio (PAPR) efficient non-coherent orthogonal frequency division multiplexing with index modulation (OFDM-IM). It is shown that the non-coherent OFDM-IM design, which minimizes PAPR, is a non-linear optimization problem. This can be visualized as the optimization of the phase factor in selected mapping (SLM) technique. Further, a special case is considered, where the inputs take only real values. We then show how to approximately solve it using simple linear integer programming and explicitly quantify the gap between the approximate and the optimal solutions. A computationally efficient heuristic scheme is developed to obtain a suboptimal solution of the integer optimization problem. Finally, our simulation results indicate the merits of the proposed schemes.

Sheetal Kalyani

Papers

Mitigation of Error Propagation in Decision Directed OFDM Channel Tracking Using

Interference Mitigation in Turbo-Coded OFDM Systems Using Robust LLRs

Outage Probability Expressions for an IRS-Assisted System with and without Source-Destination Link for the Case of Quantized Phase Shifts

Coverage Probability and Achievable Rate Analysis of FFR-Aided Multi-User OFDM-Based MIMO and SIMO Systems

An Optimized SLM for PAPR Reduction in Non-coherent OFDM-IM