Title :
Free Deconvolution for Signal Processing Applications
Author :
Ryan, O. ; Debbah, M.
Author_Institution :
Univ. of Oslo, Oslo
Abstract :
Situations in many fields of research, such as digital communications, nuclear physics and mathematical finance, can be modelled with random matrices. When the matrices get large, free probability theory is an invaluable tool for describing the asymptotic behaviour of many systems. It will be explained how free probability can be used to estimate covariance matrices. Multiplicative free deconvolution is shown to be a method which can aid in expressing limit eigenvalue distributions for sample covariance matrices, and to simplify estimators for eigenvalue distributions of covariance matrices.
Keywords :
covariance matrices; deconvolution; eigenvalues and eigenfunctions; estimation theory; statistical distributions; covariance matrix estimation; free probability theory; limit eigenvalue distributions; multiplicative free deconvolution; random matrices; signal processing applications; Convolution; Covariance matrix; Deconvolution; Digital communication; Eigenvalues and eigenfunctions; Finance; Informatics; Nuclear physics; Sensor phenomena and characterization; Signal processing; Free Probability Theory; G-analysis; Random Matrices; deconvolution; limiting eigenvalue distribution;
Conference_Titel :
Information Theory, 2007. ISIT 2007. IEEE International Symposium on
Conference_Location :
Nice
Print_ISBN :
978-1-4244-1397-3
DOI :
10.1109/ISIT.2007.4557490
