A discrete model for the efficient analysis of time-varying narrowband communication channels

Abstract

We derive an efficient numerical algorithm for the analysis of certain classes of Hilbert-Schmidt operators that naturally occur in models of wireless radio and sonar communications channels.We show that many narrowband finite lifelength systems such as wireless radio communications can be well modelled by smooth and compactly supported spreading functions. Further, we exploit this fact to derive a fast algorithm for computing the matrix representation of such operators with respect to well time-frequency localized Gabor bases (such as pulseshaped OFDM bases). Hereby we use a minimum of approximations, simplifications, and assumptions on the channel. Moreover, ve use a multivariate setting to allow for applications to, for example, antenna arrays.The derived algorithm and software can be used, for example, for comparing how different system settings and pulse shapes affect the diagonalization properties of an OFDM system acting on a given channel.

Sparsity in Time-Frequency Representations

“…[34]. Indeed, (1.4) is a common finite dimensional model of wireless channels [3,10,17,25] and sonar [24,31] where physical considerations often suggest that x is rather sparse. First results were obtained in [26], on which we will improve here.…”

Reconstruction of the scattering function of overspread radar targets

“…Ordinarily, the stochastic target is assumed to be 'underspread', that is, the support of C(t, γ) is required to be contained in a rectangle of area <1. Building on recent results in operator identification [7][8][9][10][11] and following ideas from [12], we give a novel method to compute C(t, γ) from the stochastic response of the stochastic operator to a deterministic sounding signal. Our method does not require the bounding region of C(t, γ) to be rectangular; it benefits from prior knowledge of the support of the scattering function and zooms in on the region of relevance.…”

Identification of Matrices Having a Sparse Representation

“…In wireless communications ( [13,28,41] and references within) and sonar [39,50], for example, the narrowband regime of a transmission channel can generally be well approximated by a linear combination * School of Engineering and Science, Jacobs University Bremen, 28759 Bremen, Germany, g.pfander@jacobs-university. like to emphasize that the common framework of the identification problem for matrices with a sparse representation and the sparse signal recovery problem implies that the results achieved on the recovery of matrices with a sparse representation in the dictionary of time-frequency shift matrices are at the same time results for the recovery of signals with a sparse representation in Gabor frames.…”