A Note on Functional Averages over Gaussian Ensembles. (11th July 2013)

• Record Type: Journal Article
• Authors: Tucci, Gabriel H.; Vega, Maria V.
• Other Names: Thavaneswaran Aera Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2013(2013)
• Publication Date: 2013-07-11
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2013/941058
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : We find a new formula for matrix averages over the Gaussian ensemble. Let H be an n × n Gaussian random matrix with complex, independent, and identically distributed entries of zero mean and unit variance. Given an n × n positive definite matrix A and a continuous function f : ℝ + → ℝ such that ∫ 0 ∞ ‍ e - α t | f ( t ) | 2 d t < ∞ for every α > 0, we find a new formula for the expectation 𝔼 [ Tr ( f ( H A H * ) ) ] . Taking f ( x ) = l o g ( 1 + x ) gives another formula for the capacity of the MIMO communication channel, and taking f ( x ) = ( 1 + x ) - 1 gives the MMSE achieved by a linear receiver.