Outage Performance Analysis of Improper Gaussian Signaling for Two-User Downlink NOMA Systems with Imperfect Successive Interference Cancellation.

The improper Gaussian signaling (IGS) technique can improve the achievable rate of an interference-limited network by fully exploiting the second-order statistics of complex signaling. This paper addresses the outage performance analysis of a two-user downlink non-orthogonal multiple access (NOMA) system using the IGS technique in the presence of imperfect successive interference cancellation (SIC). The strong channel user (SU) adopts the IGS, while the weak channel user (WU) adopts the traditional proper Gaussian signaling (PGS).

Optimization in Quaternion Dynamic Systems: Gradient, Hessian, and Learning Algorithms.

The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions typically require the calculation of the gradient and Hessian. However, real functions of quaternion variables are essentially nonanalytic, which are prohibitive to the development of quaternion-valued learning systems.

Quaternion-valued echo state networks.

Quaternion-valued echo state networks (QESNs) are introduced to cater for 3-D and 4-D processes, such as those observed in the context of renewable energy (3-D wind modeling) and human centered computing (3-D inertial body sensors). The introduction of QESNs is made possible by the recent emergence of quaternion nonlinear activation functions with local analytic properties, required by nonlinear gradient descent training algorithms. To make QENSs second-order optimal for the generality of quaternion signals (both circular and noncircular), we employ augmented quaternion statistics to introduce widely linear QESNs.

Performance Bounds of Quaternion Estimators.

The quaternion widely linear (WL) estimator has been recently introduced for optimal second-order modeling of the generality of quaternion data, both second-order circular (proper) and second-order noncircular (improper). Experimental evidence exists of its performance advantage over the conventional strictly linear (SL) as well as the semi-WL (SWL) estimators for improper data. However, rigorous theoretical and practical performance bounds are still missing in the literature, yet this is crucial for the development of quaternion valued learning systems for 3-D and 4-D data.

Application of multivariate empirical mode decomposition for seizure detection in EEG signals.

We present a method for the analysis of electroencephalogram (EEG) signals which has the potential to distinguish between ictal and seizure-free intracranial EEG recordings. This is achieved by analyzing common frequency components in multichannel EEG recordings, using the multivariate empirical mode decomposition (MEMD) algorithm. The mean frequency of the signal is calculated by applying the Hilbert-Huang transform on the resulting intrinsic mode functions (IMFs).

An augmented echo state network for nonlinear adaptive filtering of complex noncircular signals.

A novel complex echo state network (ESN), utilizing full second-order statistical information in the complex domain, is introduced. This is achieved through the use of the so-called augmented complex statistics, thus making complex ESNs suitable for processing the generality of complex-valued signals, both second-order circular (proper) and noncircular (improper). Next, in order to deal with nonstationary processes with large nonlinear dynamics, a nonlinear readout layer is introduced and is further equipped with an adaptive amplitude of the nonlinearity.