2013
DOI: 10.1080/02331888.2012.695376
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On the real representation of quaternion random variables

Abstract: For the first time, the matrix-variate quaternion normal and quaternion Wishart distributions are derived from first principles, i.e. from their real counterparts, exposing the relations between their respective densities and characteristic functions. Applications of this theory in hypothesis testing are presented, and the density function of Wilks' statistic is derived for quaternion Wishart matrices.

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Cited by 6 publications
(10 citation statements)
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“…In a similar fashion, using Theorem 9 of Loots et al [18], we have the following important result: α = 1, . . .…”
Section: The Matrix Variate Quaternion Elliptical Distributionmentioning
confidence: 82%
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“…In a similar fashion, using Theorem 9 of Loots et al [18], we have the following important result: α = 1, . . .…”
Section: The Matrix Variate Quaternion Elliptical Distributionmentioning
confidence: 82%
“…Although quaternion field of algebra has many applications in quantum physics, geostatics, the figure and pattern recognition, molecular modeling and the space telemetry (see Liu [17], Wang [21] and Karney [14]), its statistical applications are not considered well yet. It also should be noticed that the statistical theory of quaternions is well proposed (see Anderson [1], Kabe [15], Rautenbach and Roux [20], Dimitriu and Koev [8], Diaz-Garcia and Jaimez [7] and more recently Loots et al [18]). …”
Section: Introductionmentioning
confidence: 99%
“…where δ is STO and ϵ is CFO in the receiver and z n is additive proper white Gaussian noise. This model is extended to a more elaborated version in (12) for the simulations in Section 6 (also called memoryless channel throughout this work). Considering that the complex components of the quaternion are s 1 and s 2 C i , the exponential factor in the right side of ( 13) should be applied to the left of the quaternion delayed symbol s nÀδ so that the same CFO is introduced over both components.…”
Section: Dp-ofdm Synchronization Based On Cpmentioning
confidence: 99%
“…A formal demonstration of this result is beyond the scope of this work. A guideline for the derivation of the above equation is to express the received quaternion symbol by a complex-valued pair, as in (12), which allows for the independence of the simplex and perplex parts' expected values in a development similar to Appendix A. In this way, that derivation procedure may allow for the independent computation of the CRLB of the simplex and perplex parts, which are homomorphic to (25).…”
Section: Crlbs For Sto and Cfo Estimatesmentioning
confidence: 99%
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