On the d-dimensional Quasi-Equally Spaced Sampling

Abstract: 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.