Title :
On the spectrum of large random hermitian finite-band matrices
Author :
Somekh, Oren ; Simeone, Osvaldo ; Zaidel, Benjamin M. ; Poor, H. Vincent ; Shamai, Shlomo
Author_Institution :
Dept. of Electr. Eng., Princeton Univ., Princeton, NJ
fDate :
Jan. 27 2008-Feb. 1 2008
Abstract :
The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their main diagonal regardless of their size. Two different communication setups which may be modeled using such matrices are presented: a simple cellular uplink channel, and a time varying inter-symbol interference channel. Selected recent information-theoretic works dealing directly with such channels are reviewed. Finally, several characteristics of the still unknown limiting spectrum of such matrices are listed, and some reflections are touched upon.
Keywords :
Hermitian matrices; cellular radio; information theory; intersymbol interference; random processes; telecommunication channels; Shannon transform; cellular uplink channel; communication setup; information theory; intersymbol interference channel; large random Hermitian finite-band matrices; limiting spectrum; Additive noise; Convergence; Eigenvalues and eigenfunctions; Information theory; Interference channels; Mutual information; Random variables; Reflection; Signal to noise ratio; Vectors;
Conference_Titel :
Information Theory and Applications Workshop, 2008
Conference_Location :
San Diego, CA
Print_ISBN :
978-1-4244-2670-6
DOI :
10.1109/ITA.2008.4601092