Open Access

Niklas Grip, Götz E. Pfander

• We derive and describe a Matlab implementation of 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. A common short-time model of these channels writes the channel output as a weighted superposition of time- and frequency shifted copies of the transmitted signal, where the weight function is often called the spreading function of the channel operator. It is often believed that a good channel model must allow for spreading functions containing Dirac delta distributions. However, we show that many narrow-band finite lifelength channels such as wireless radio communications can be well modelled by smooth and compactly supported spreading functions. We derive a fast algorithm for computing the matrix representation of such operators with respect to well time-frequency localized Gabor bases, such as pulse shaped OFDM bases. Hereby we use a minimum of approximations, simplifications, and assumptions on the channel. The primary intended target application is comparisons of how different parameter settings and pulse shapes affect the diagonalization properties of an OFDM system acting on a given channel. Finally, we provide and demonstrate the use of a Matlab implementation that is fast enough for the number of carrier frequencies typically in use today. A shortened and improved version of the main results in this report is published in the journal paper [GP07], which excludes some discussions, proofs and the software documentation contained here.