On minimal eigenvalues of a class of tridiagonal matrices

Authors:
Jay Cheng;Toby Berger
Affiliations:
Department of Electrical Engineering and the Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan, R.O.C.;Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA
Venue:
IEEE Transactions on Information Theory
Year:
2009

Citing 2
Cited 0

Minimum probability of error for asynchronous Gaussian multiple-access channels

IEEE Transactions on Information Theory
The minimal eigenvalues of a class of block-tridiagonal matrices

IEEE Transactions on Information Theory

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Abstract

It is known that the worst case near-far resistance of optimum multiuser detectors for asynchronous Gaussian multiple-access channels can be expressed in terms of a class of block-tridiagonal matrices, and the minimal eigenvalues of such a class of block-tridiagonal matrices serve as a good measure of the worst case near-far resistance. In this paper, we focus on the two-user scenario where each block-tridiagonal matrix under consideration is a tridiagonal matrix. We derive closed-form expressions for the minimal eigenvalues of such a class of tridiagonal matrices in terms of the largest real solution of a trigonometric equation in [0, π]. We also obtain lower bounds and upper bounds on the minimal eigenvalues which improve on previously known results in the literature.