Iterative Joint Equalization and Decoding Based on Soft Cholesky Equalization for General Complex Valued Modulation Symbols

2005 ◽  
pp. 267-282 ◽  
Author(s):  
Jochem Egle ◽  
Jürgen Lindner
Keyword(s):  
General Complex ◽  
Complex Valued

scholarly journals A Numerical Method for Computing the Roots of Non-Singular Complex-Valued Matrices

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 966
Author(s):  
Diego Caratelli ◽  
Paolo Emilio Ricci
Keyword(s):  
Numerical Method ◽  
Worked Examples ◽  
Higher Order ◽  
Singular Matrix ◽  
The Matrix ◽  
General Complex ◽  
Complex Valued

A method for the computation of the n th roots of a general complex-valued r × r non-singular matrix ? is presented. The proposed procedure is based on the Dunford–Taylor integral (also ascribed to Riesz–Fantappiè) and relies, only, on the knowledge of the invariants of the matrix, so circumventing the computation of the relevant eigenvalues. Several worked examples are illustrated to validate the developed algorithm in the case of higher order matrices.

scholarly journals General Complex-Valued Overlap Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ying Chen ◽  
Lvqing Bi ◽  
Bo Hu ◽  
Songsong Dai
Keyword(s):  
Fuzzy Sets ◽  
Aggregation Function ◽  
Construction Methods ◽  
General Complex ◽  
Complex Valued

Overlap function is a special type of aggregation function which measures the degree of overlapping between different classes. Recently, complex fuzzy sets have been successfully applied in many applications. In this paper, we extend the concept of overlap functions to the complex-valued setting. We introduce the notions of complex-valued overlap, complex-valued 0-overlap, complex-valued 1-overlap, and general complex-valued overlap functions, which can be regarded as the generalizations of the concepts of overlap, 0-overlap, 1-overlap, and general overlap functions, respectively. We study some properties of these complex-valued overlap functions and their construction methods.

scholarly journals ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR(p) PROCESSES

1999 ◽  
Vol 15 (2) ◽  
pp. 184-217 ◽  
Author(s):  
Tjacco van der Meer ◽  
Gyula Pap ◽  
Martien C.A. van Zuijlen
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Limit Distribution ◽  
Continuous Time ◽  
Convergence Result ◽  
Likelihood Estimator ◽  
Characteristic Roots ◽  
Least Squares Estimators ◽  
General Complex ◽  
Complex Valued

In this paper nearly unstable AR(p) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behavior of the least-squares estimators of the coefficients. A convergence result is presented for the general complex-valued case. The limit distribution is given by the help of some continuous time AR processes. We apply the results for real-valued nearly unstable AR(p) models. In this case the limit distribution can be identified with the maximum likelihood estimator of the coefficients of the corresponding continuous time AR processes.

scholarly journals Stability Analysis of Complex-Valued Nonlinear Differential System

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Tao Fang ◽  
Jitao Sun
Keyword(s):  
Stability Analysis ◽  
Differential System ◽  
Comparison Principle ◽  
Autonomous System ◽  
New Method ◽  
Stability Criteria ◽  
General Complex ◽  
The Stability ◽  
Nonlinear Autonomous System ◽  
Complex Valued

This paper studies the stability of complex-valued nonlinear differential system. The stability criteria of complex-valued nonlinear autonomous system are established. For the general complex-valued nonlinear non-autonomous system, the comparison principle in the context of complex fields is given. Those derived stability criteria not only provide a new method to analyze complex-valued differential system, but also greatly reduce the complexity of analysis and computation.

Charges solve the truncated complex moment problem

2018 ◽  
Vol 21 (04) ◽  
pp. 1850027
Author(s):  
K. Idrissi ◽  
E. H. Zerouali
Keyword(s):  
Moment Problem ◽  
Borel Measure ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Positive Borel Measure ◽  
General Complex ◽  
A Charge ◽  
Necessary And Sufficient ◽  
Complex Valued ◽  
Charge Formula

Let [Formula: see text], with [Formula: see text] and [Formula: see text], be a given complex-valued sequence. The complex moment problem (respectively, the general complex moment problem) associated with [Formula: see text] consists in determining necessary and sufficient conditions for the existence of a positive Borel measure (respectively, a charge) [Formula: see text] on [Formula: see text] such that [Formula: see text] In this paper, we investigate the notion of recursiveness in the two variable case. We obtain several useful results that we use to deduce new necessary and sufficient conditions for the truncated complex moment problem to admit a solution. In particular, we show that the general complex moment problem always has a solution. A concrete construction of the solution and an illustrating example are also given.

A Complex-Valued RTRL Algorithm for Recurrent Neural Networks

2004 ◽  
Vol 16 (12) ◽  
pp. 2699-2713 ◽  
Author(s):  
Su Lee Goh ◽  
Danilo. P. Mandic
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Adaptive Filters ◽  
Natural Extension ◽  
Activation Function ◽  
Complex Signals ◽  
General Complex ◽  
Nonlinear Adaptive Filtering ◽  
Fully Connected ◽  
Complex Valued

A complex-valued real-time recurrent learning (CRTRL) algorithm for the class of nonlinear adaptive filters realized as fully connected recurrent neural networks is introduced. The proposed CRTRL is derived for a general complex activation function of a neuron, which makes it suitable for nonlinear adaptive filtering of complex-valued nonlinear and nonstationary signals and complex signals with strong component correlations. In addition, this algorithm is generic and represents a natural extension of the real-valued RTRL. Simulations on benchmark and real-world complex-valued signals support the approach.

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