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PHY 43-1 - Pulse shaping, localization and the approximate eigenstructure of LTV channels

: Jung, P.


Institute of Electrical and Electronics Engineers -IEEE-:
IEEE Wireless Communications and Networking Conference, WCNC 2008. Conference proceedings : 31 March - 3. April 2007, Las Vegas, Nevada, USA
Piscataway, NJ: IEEE, 2008
ISBN: 978-1-4244-1997-5
ISBN: 978-1-4244-1996-8
Wireless Communications and Networking Conference (WCNC) <2008, Las Vegas/Nev.>
Conference Paper
Fraunhofer HHI ()
ofdm modulation; pulse shaping; time-varying channels

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(sub 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.