Abstract
This paper presents a general expression for the marginal distributions of the ordered eigenvalues of certain important random matrices. The expression, given in terms of matrix determinants, is compacter in representation and more efficient in computational complexity than existing results in the literature. As an illustrative application of the new result, we then analyze the performance of the multiple-input multiple-output singular value decomposition system. Analytical expressions for the average symbol error rate and the outage probability are derived, assuming the general double-scattering fading condition.
Highlights
Random matrix theory, since its inception, has been known as a powerful tool for solving practical problems arising in physics, statistics, and engineering [1,2,3]
In single-user multiple-input multiple-output (MIMO) systems, the eigenvalue distributions of Wishart matrices
For channels that are not Rayleigh/Rician faded, the eigenvalue distributions of Wishart matrices played an essential role in the performance analysis of MIMO systems [23,24,25,26,27,28,29,30]
Summary
Since its inception, has been known as a powerful tool for solving practical problems arising in physics, statistics, and engineering [1,2,3]. It is worth noting that, different from the Rayleigh/Rician fading channels, where the performance of MIMO SVD were well-studied in [18], the behaviors of MIMO SVD in double-scattering channels is still not clear (expect for some primary results in [47] by the authors) In this context, we derive first the joint eigenvalue distribution of the MIMO channel matrix, using the law of total probability. A ∼ CNm×n(M, Ω, Σ) denotes that A is an m × n complex Gaussian matrix with a mean value M ∈ Cm×n, a row correlation Ω ∈ Cm×m, and a column correlation Σ ∈ Cn×n
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