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

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Müller R
Zeitschrift: IEEE Transactions on Information Theory
Verlag: Institute of Electrical and Electronics Engineers (IEEE)
Jahr der Veröffentlichung: 2002
Band: 48
Heftnummer: 7
Seitenbereich: 2086-2091
ISSN: 0018-9448
Sprache: Englisch


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-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

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


Zitierweisen

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.

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