Eigen-inference moments method for cognitive wireless communications

In many situations, telecommunication engineers are faced with the problem of extracting information from the network. This corresponds in many cases to infer on functionals of spectrum of random matrices with only a limited knowledge on the statistics of the matrix entries. Here, the inference on the spectrum of random matrices is realized by moments method. In its full generality, the problem requires some sophisticated tools related to free probability theory and the explicit spectrum (complete information) can hardly be obtained (except for some trivial cases). Results in the asymptotic case and in the finite case are presented and simulations show how the moments method approach can be applied in practice. Several still open problems in this field are also presented.