Dual-hop amplify-and-forward cooperative relaying in the presence of Tx and Rx in-phase and quadrature-phase imbalance

In this study, dual-hop channel state information-assisted amplify-and-forward (AF) cooperative systems in the presence of in-phase and quadrature-phase (I/Q) imbalance, which refers to the mismatch between components in the I and Q branches, are investigated. First, the authors analyse the performance of the considered AF cooperative protocol without compensation for the I/Q imbalance as the benchmark. Then, a compensation algorithm for the I/Q imbalance is proposed, which makes use of the received signals at the destination, from the source and the relay nodes, together with their conjugations to detect the transmitted signal. Moreover, the authors study the considered AF cooperative system implemented with the opportunistic relay selection and the proposed compensation mechanism for the I/Q imbalance. The performance of the AF cooperative system under study is evaluated in terms of average symbol error probability, which is derived by considering transmission in a Rayleigh fading environment. Numerical results are provided and show that the proposed compensation algorithm can efficiently mitigate the effect of the I/Q imbalance. On the other hand, it is observed that the AF cooperative system with opportunistic relay selection acquires a performance gain beyond that without relay selection.

Application of complex extreme learning machine to multiclass classification problems with high dimensionality: a THz spectra classification problem

We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

Is it significant? Guidelines for reporting BCI performance

Recent growth in brain-computer interface (BCI) research has increased pressure to report improved performance. However, different research groups report performance in different ways. Hence, it is essential that evaluation procedures are valid and reported in sufficient detail. In this chapter we give an overview of available performance measures such as classification accuracy, cohen’s kappa, information transfer rate (ITR), and written symbol rate. We show how to distinguish results from chance level using confidence intervals for accuracy or kappa. Furthermore, we point out common pitfalls when moving from offline to online analysis and provide a guide on how to conduct statistical tests on (BCI) results.

Two-way CSI-assisted AF relaying with HPA nonlinearity

In this paper, we investigate half-duplex two-way dual-hop channel state information (CSI)-assisted amplify-and-forward (AF) relaying in the presence of high-power amplifier (HPA) nonlinearity at relays. The expression for the end-to-end signal-to-noise ratio (SNR) is derived as per the modified system model by taking into account the interference caused by relaying scheme and HPA nonlinearity. The system performance of the considered relaying network is evaluated in terms of average symbol error probability (SEP) in Nakagami-$m$ fading channels, by making use of the moment-generating function (MGF) approach. Numerical results are provided and show the effects of several parameters, such as quadrature amplitude modulation (QAM) order, number of relays, HPA parameters, and Nakagami parameter, on performance.

Rethinking the Conversion of Scotland in the fifth and sixth centuries

Reconsidering the initial Christian Conversion of Scotland in the fifth and sixth centuries AD, using archaeological and historical evidence, it is argued that this was carried out by missionaries from what had been Roman Britain. It is shown that this missionary activity - and similar British missions in Ireland - represents the first instance of Western missionary work beyond the former Roman imperial frontiers. The location of the northern frontier of Roman Britain in the fourth century, and the meaning of Pictish Class 1 symbol stones, are discussed as part of the broader argument.

Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation

The weak-constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The well-known result that for Gaussian error statistics the minimum of the weak-constraint inverse is equal to the maximum-likelihood estimate is rederived. Then several methods based on ensemble statistics that can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. they also avoid iterative searches in a Hilbert space, and error estimates can be obtained without much additional computational effort. the feasibility of the new methods is illustrated in a two-layer quasigeostrophic model.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.