There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

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Tensor Decompositions and Applications

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Statistics for Spatial Data.

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Table Of Integrals Series And Products

The implementation of OFDM-based systems suffers from impairments such as in-phase and quadrature-phase (IQ) imbalances in the front-end analog processing. Such imbalances are caused by the analog processing of the radio frequency (RF) signal and can be present at both the transmitter and receiver. The resulting IQ distortion limits the achievable operating SNR at the receiver and the achievable data rates. In this paper, the effect of both the transmitter and receiver IQ imbalances in an OFDM system is studied and algorithms are developed to compensate for such distortions in the digital domain. The algorithms include post-FFT least-squares and adaptive equalization, as well as a pre-distortion scheme at the transmitter and a pre-FFT correction at the receiver

Joint compensation of transmitter and receiver impairments in OFDM systems

This paper provides a time-domain feedback analysis of gradient-based adaptive schemes. A key emphasis is on the robustness performance of the adaptive filters in the presence of disturbances and modeling uncertainties (along the lines of H/sup /spl infin//-theory and robust filtering). The analysis is carried out in a purely deterministic framework and assumes no prior statistical information or independence conditions. It is shown that an intrinsic feedback structure can be associated with the varied adaptive schemes. The feedback structure is motivated via energy arguments and is shown to consist of two major blocks: a time-variant lossless (i.e., energy preserving) feedforward path and a time-variant feedback path. The configuration is further shown to lend itself to analysis via a so-called small gain theorem, thus leading to stability and robustness conditions that require the contractivity of certain operators. Choices for the step-size parameter in order to guarantee faster rates of convergence are also derived, and simulation results are included to demonstrate the theoretical findings. In addition, the time-domain analysis provided in this paper is shown to extend the so-called transfer function approach to a general time-variant scenario without any approximations.

A time-domain feedback analysis of filtered-error adaptive gradient algorithms

The paper develops a unified approach to the transient analysis of adaptive filters with error nonlinearities. In addition to deriving earlier results in a unified manner, the approach also leads to new performance results without restricting the regression data to being Gaussian or white. The framework is based on energy-conservation arguments and avoids the need for explicit recursions for the covariance matrix of the weight-error vector.

Transient analysis of adaptive filters with error nonlinearities

Consider a set of nodes distributed spatially over some region forming a network, where every node takes measurements of an underlying process. The objective is for every node in the network to estimate some parameter of interest from these measurements by cooperating with other nodes. In this work we compare the performance of four adaptive implementations. Two of the implementations are distributed and network-based; they are spatial LMS and incremental LMS. In both algorithms, the nodes share information in a cyclic manner and both algorithms differ by the amount of information shared (less information is shared in the incremental case). The two other adaptive algorithms that we study deal with centralized implementations of spatial and incremental LMS. In these latter cases, all nodes exchange data with a fusion center where the computations are performed. In the centralized approach, all nodes receive the same estimates back from the fusion center, while these estimates differ among the nodes in the distributed implementation. We analyze and compare the performance of fusion-based and network-based versions of spatial LMS and incremental LMS processing and reveal some interesting conclusions. The results indicate that incremental LMS can outperform spatial LMS, and that network-based implementations can outperform the aforementioned fusion-based solutions in some revealing ways.

Analysis of Spatial and Incremental LMS Processing for Distributed Estimation

The article describes recent adaptive estimation algorithms over distributed networks. The algorithms rely on local collaborations and exploit the space-time structure of the data. Each node is allowed to communicate with its neighbors in order to exploit the spatial dimension, while it also evolves locally to account for the time dimension. Algorithms of the least-mean-squares and least-squares types are described. Both incremental and diffusion strategies are considered.

Ali H. Sayed

Papers

Joint compensation of transmitter and receiver impairments in OFDM systems

A time-domain feedback analysis of filtered-error adaptive gradient algorithms

Transient analysis of adaptive filters with error nonlinearities

Analysis of Spatial and Incremental LMS Processing for Distributed Estimation

Adaptive Processing over Distributed Networks