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Some Bounds on the Distribution of Certain Quadratic Forms in Normal Random Variables

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The paper derives bounds on the distribution of the quadratic forms Z = yH(XΓXH)−1y and W = yH(2I + XΓXH)−1y, where the elements of the M× 1 vector y and the M×N matrix X are independent identically distributed (i.i.d.) complex zero mean Normal variables, Γ is some N×N diagonal matrix with positive diagonal elements, I, is the identity, 2 is a constant and H denotes the Hermitian transpose. The bounds are convenient for numerical work and appear to be tight for small values of M. This work has applications in digital mobile radio for a specific channel where M antennas are used to receive a signal with N interferers. Some of these applications in radio communication systems are discussed.
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Keywords: Autocorrelation; direction of maximum curvature; observed information matrix

Document Type: Research Article

Affiliations: Victoria University of Wellington

Publication date: March 1, 1998

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