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On Minimal Eigenvalues of a Class of Tridiagonal Matrices

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2 Author(s)
Cheng, J. ; Dept. of Electr. Eng., Nat. Tsing Hua Univ., Hsinchu, Taiwan ; Berger, T.

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,pi]. We also obtain lower bounds and upper bounds on the minimal eigenvalues which improve on previously known results in the literature.

Published in:

Information Theory, IEEE Transactions on  (Volume:55 ,  Issue: 11 )