SIGNAL PROCESSING APPLICATIONS OF FREE PROBABILITY THEORY

Øyvind Ryan (1) , Merouane Debbah (2)

1 UiO - University of Oslo
2 SUPELEC-Campus Gif

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 shown how free probability can be used to aid in source detection for certain systems. Sample covariance matrices for systems with noise are the starting point in our source detection problem. 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.

Mots clés: Free probability

Domaines: Traitement du signal et de l'image [eess.SP]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Traitement du signal et de l'image [eess.SP]

Øyvind Ryan, Merouane Debbah. SIGNAL PROCESSING APPLICATIONS OF FREE PROBABILITY THEORY. 15th European Signal Processing Conference EUSIPCO 2007, Sep 2007, Poznan, Poland. pp.Annals. ⟨hal-00280590⟩