Journal of Probability and Statistics
Volume 2013 (2013), Article ID 941058, 6 pages
http://dx.doi.org/10.1155/2013/941058
Research Article

A Note on Functional Averages over Gaussian Ensembles

Gabriel H. Tucci1 and Maria V. Vega2

1Bell Laboratories, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill, NJ 07974, USA
2William Paterson University, Mathematics Department, 300 Pompton Road, Wayne, NJ 07470, USA

Received 30 April 2013; Accepted 18 June 2013

Academic Editor: Aera Thavaneswaran

Copyright © 2013 Gabriel H. Tucci and Maria V. Vega. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We find a new formula for matrix averages over the Gaussian ensemble. Let be an Gaussian random matrix with complex, independent, and identically distributed entries of zero mean and unit variance. Given an positive definite matrix and a continuous function such that for every , we find a new formula for the expectation . Taking gives another formula for the capacity of the MIMO communication channel, and taking gives the MMSE achieved by a linear receiver.