Publication

Proof of the Outage Probability Conjecture for MISO Channels

Emre Telatar, Emmanuel Abbé
2013
Journal Articles

Abstract

It is conjectured that the covariance matrices minimizing the outage probability under a power constraint for multiple-input multiple-output channels with Gaussian fading are diagonal with either zeros or constant values on the diagonal. In the multiple-input single-output (MISO) setting, this is equivalent to conjecture that the Gaussian quadratic forms having largest tail probability correspond to such diagonal matrices. This paper provides a proof of the conjecture in this MISO setting.

Official source

https://infoscience.epfl.ch/entities/publication/6dbbe9bc-b474-44f8-91cb-043d3654dec2

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Emre Telatar, Emmanuel Abbé
2013
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6dbbe9bc-b474-44f8-91cb-043d3654dec2

About this result

Related concepts (24)

Diagonal matrix

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).

Diagonalizable matrix

In linear algebra, a square matrix is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix and a diagonal matrix such that , or equivalently . (Such , are not unique.) For a finite-dimensional vector space , a linear map is called diagonalizable if there exists an ordered basis of consisting of eigenvectors of .

Block matrix

In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines, which break it up, or partition it, into a collection of smaller matrices. Any matrix may be interpreted as a block matrix in one or more ways, with each interpretation defined by how its rows and columns are partitioned.

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