  We study a class of random matrices that appear in several communication and
signal processing applications, and whose asymptotic eigenvalue distribution is
closely related to the reconstruction error of an irregularly sampled
bandlimited signal. We focus on the case where the random variables
characterizing these matrices are d-dimensional vectors, independent, and
quasi-equally spaced, i.e., they have an arbitrary distribution and their
averages are vertices of a d-dimensional grid. Although a closed form
expression of the eigenvalue distribution is still unknown, under these
conditions we are able (i) to derive the distribution moments as the matrix
size grows to infinity, while its aspect ratio is kept constant, and (ii) to
show that the eigenvalue distribution tends to the Marcenko-Pastur law as
d->infinity. These results can find application in several fields, as an
example we show how they can be used for the estimation of the mean square
error provided by linear reconstruction techniques.
