In this article we show the relation between the theory of pulse shaping for
WSSUS channels and the notion of approximate eigenstructure for time-varying
channels. We consider pulse shaping for a general signaling scheme, called
Weyl-Heisenberg signaling, which includes OFDM with cyclic prefix and
OFDM/OQAM. The pulse design problem in the view of optimal WSSUS--averaged SINR
is an interplay between localization and "orthogonality". The localization
problem itself can be expressed in terms of eigenvalues of localization
operators and is intimately connected to the concept of approximate
eigenstructure of LTV channel operators. In fact, on the L_2-level both are
equivalent as we will show. The concept of "orthogonality" in turn can be
related to notion of tight frames. The right balance between these two sides is
still an open problem. However, several statements on achievable values of
certain localization measures and fundamental limits on SINR can already be
made as will be shown in the paper.Comment: 6 pages, 2 figures, invited pape