Spectral convergence for a general class of random matrices

Let be an M×N complex random matrix with i.i.d. entries having mean zero and variance 1/N and consider the class of matrices of the type , where , and are Hermitian nonnegative definite matrices, such that and have bounded spectral norm with being diagonal, and is the nonnegative definite square root of . Under some assumptions on the moments of the entries of , it is proved in this paper that, for any matrix with bounded trace norm and for each complex z outside the positive real line, almost surely as M,N-->[infinity] at the same rate, where [delta]M(z) is deterministic and solely depends on and . The previous result can be particularized to the study of the limiting behavior of the Stieltjes transform as well as the eigenvectors of the random matrix model . The study is motivated by applications in the field of statistical signal processing.