On the asymptotic eigenvalue distribution of concatenated vector-valued fading channels

Journal article
(Original article)


Publication Details

Author(s): Müller R
Journal: IEEE Transactions on Information Theory
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Publication year: 2002
Volume: 48
Journal issue: 7
Pages range: 2086-2091
ISSN: 0018-9448
Language: English


Abstract


The linear vector-valued channel x → ∏ M x + z with z and M denoting additive white Gaussian noise and independent random matrices, respectively, is analyzed in the asymptotic regime as the dimensions of the matrices and vectors involved become large. The asymptotic eigenvalue distribution of the channel's covarianee matrix is given in terms of an implicit equation for its Stieltjes transform as well as an explicit expression for its moments. Additionally, almost all eigenvalues are shown to converge toward zero as the number of factors grows over all bounds. This effect cumulates the total energy in a vanishing number of dimensions. The channel model addressed generalizes the model introduced in [1] for communication via large antenna arrays to N-fold scattering per propagation path. As a byproduct, the multiplicative free convolution is shown to extend to a certain class of asymptotically large non-Gaussian random covariance matrices.


FAU Authors / FAU Editors

Müller, Ralf Prof. Dr.-Ing.
Professur für Informationsübertragung


How to cite

APA:
Müller, R. (2002). On the asymptotic eigenvalue distribution of concatenated vector-valued fading channels. IEEE Transactions on Information Theory, 48(7), 2086-2091. https://dx.doi.org/10.1109/TIT.2002.1013149

MLA:
Müller, Ralf. "On the asymptotic eigenvalue distribution of concatenated vector-valued fading channels." IEEE Transactions on Information Theory 48.7 (2002): 2086-2091.

BibTeX: 

Last updated on 2019-20-07 at 14:53