# Free deconvolution for signal processing applications

Conference Paper

### Authors:

Øyvind Ryan; Mérouane Debbah

### Source:

International Symposium on Information Theory, Nice, France (2007)

### 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.