The distribution of the eigenvalues of Wishart matrices and Gaussian quadratic forms is of great interest in communication theory, especially in relation to multiple-input multiple-output (MIMO) systems. In this paper we present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of Wishart matrices, using the tensor operator T (.), which was first introduced in [1]. We obtain both the joint probability distribution function (p.d.f.) of the eigenvalues and the expectation of arbitrary functions of the eigenvalues, including the moments, for the case of both ordered and unordered eigenvalues. These expressions are extremely compact and easy to handle. Application to MIMO systems are discussed.
Joint distribution of an arbitrary subset of the ordered eigenvalues of Wishart matrices / M. Chiani; A. Zanella. - STAMPA. - 1:(2008), pp. 1-6. (Intervento presentato al convegno Proc. IEEE Int. Symp. on Personal, Indoor and Mobile Radio Commun. (PIMRC) tenutosi a Cannes, France nel Sep. 2008).
Joint distribution of an arbitrary subset of the ordered eigenvalues of Wishart matrices
CHIANI, MARCO;
2008
Abstract
The distribution of the eigenvalues of Wishart matrices and Gaussian quadratic forms is of great interest in communication theory, especially in relation to multiple-input multiple-output (MIMO) systems. In this paper we present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of Wishart matrices, using the tensor operator T (.), which was first introduced in [1]. We obtain both the joint probability distribution function (p.d.f.) of the eigenvalues and the expectation of arbitrary functions of the eigenvalues, including the moments, for the case of both ordered and unordered eigenvalues. These expressions are extremely compact and easy to handle. Application to MIMO systems are discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
