文档介绍：1
Free Deconvolution: from Theory to Practice
Florent Benaych-es, Merouane´ Debbah, Senior Member, IEEE
Abstract— In this paper, we provide an algorithmic method to called a mutative probability space, which we do not
compute the singular values of sum of rectangular matrices based introduce as our aim is to provide a more practical approach to
on the free cumulants approach and illustrate its application to these methods. Based on the moment/cumulant approach, the
munications. We first recall the algorithms working
for sum/products of square random matrices, which have already free probability framework has been quite essfully applied
been presented in some previous papers and we then introduce recently in the works [2], [3] to infer on the eigenvalues of
the main contribution of this paper which provides a general very simple models the case where one of the considered
method working for rectangular random matrices, based on matrices is unitarily invariant. This invariance has a special
the recent theoretical work of Benaych-es. In its full meaning in works and supposes that there is some
generality, putation of the eigenvalues requires some
sophisticated tools related to free probability and the explicit kind of symmetry in the problem to be analyzed. In the present
spectrum (eigenvalue distribution) of the matrices can hardly be contribution, although focused on munications,
obtained (except for some trivial cases). From an implementation we show that the cumulant/moment approach can be extended
perspective, this has led munity to the misconception that to more general models and provide explicit algorithms to
free probability has no practical application. This pute spectrums of matrices. In particular, we give an
takes the opposite view and shows how the free cumulants
approach in free probability provides the right shift from theory explicit relation between the spectrums of random matrices
∗∗∗
to practice. (M + N)(M + N) , MM and N