A journey from improper Gaussian signaling to asymmetric signaling
The deviation of continuous and discrete complex random variables from the traditional
proper and symmetric assumption to a generalized improper and asymmetric …
proper and symmetric assumption to a generalized improper and asymmetric …
The quaternion LMS algorithm for adaptive filtering of hypercomplex processes
The quaternion least mean square (QLMS) algorithm is introduced for adaptive filtering of
three-and four-dimensional processes, such as those observed in atmospheric modeling …
three-and four-dimensional processes, such as those observed in atmospheric modeling …
The theory of quaternion matrix derivatives
A systematic framework for the calculation of the derivatives of quaternion matrix functions
with respect to quaternion matrix variables is introduced. The proposed approach is …
with respect to quaternion matrix variables is introduced. The proposed approach is …
Properness and widely linear processing of quaternion random vectors
In this paper, the second-order circularity of quaternion random vectors is analyzed. Unlike
the case of complex vectors, there exist three different kinds of quaternion properness, which …
the case of complex vectors, there exist three different kinds of quaternion properness, which …
Quaternion ICA from second-order statistics
This paper addresses the independent component analysis (ICA) of quaternion random
vectors. In particular, we focus on the Gaussian case and therefore only consider the …
vectors. In particular, we focus on the Gaussian case and therefore only consider the …
The HR-calculus: Enabling information processing with quaternion algebra
From their inception, quaternions and their division algebra have proven to be
advantageous in modelling rotation/orientation in three-dimensional spaces and have seen …
advantageous in modelling rotation/orientation in three-dimensional spaces and have seen …
Adaptive beamforming based on complex quaternion processes
J Tao, W Chang - Mathematical Problems in Engineering, 2014 - Wiley Online Library
Motivated by the benefits of array signal processing in quaternion domain, we investigate
the problem of adaptive beamforming based on complex quaternion processes in this paper …
the problem of adaptive beamforming based on complex quaternion processes in this paper …
A novel combined beamformer based on hypercomplex processes
JW Tao, WX Chang - IEEE Transactions on Aerospace and …, 2013 - ieeexplore.ieee.org
The problem of beamforming based on hypercomplex processes is considered for an
airborne electromagnetic (EM) vector-sensor array. The quaternion domain facilitates …
airborne electromagnetic (EM) vector-sensor array. The quaternion domain facilitates …
Generalized likelihood ratios for testing the properness of quaternion Gaussian vectors
In a recent paper, the second-order statistical analysis of quaternion random vectors has
shown that there exist two different kinds of quaternion widely linear processing, which are …
shown that there exist two different kinds of quaternion widely linear processing, which are …
Quaternion multiplier inspired by the lifting implementation of plane rotations
M Parfieniuk, A Petrovsky - … on Circuits and Systems I: Regular …, 2010 - ieeexplore.ieee.org
A lifting-based structure for quaternion multipliers with unit-magnitude constant coefficients
is proposed, whose development was inspired by the well-known implementation of a plane …
is proposed, whose development was inspired by the well-known implementation of a plane …