  Optimal link adaption to the scattering function of wide sense stationary
uncorrelated mobile communication channels is still an unsolved problem despite
its importance for next-generation system design. In multicarrier transmission
such link adaption is performed by pulse shaping, i.e. by properly adjusting
the transmit and receive filters. For example pulse shaped Offset--QAM systems
have been recently shown to have superior performance over standard cyclic
prefix OFDM (while operating at higher spectral efficiency).In this paper we
establish a general mathematical framework for joint transmitter and receiver
pulse shape optimization for so-called Weyl--Heisenberg or Gabor signaling with
respect to the scattering function of the WSSUS channel. In our framework the
pulse shape optimization problem is translated to an optimization problem over
trace class operators which in turn is related to fidelity optimization in
quantum information processing. By convexity relaxation the problem is shown to
be equivalent to a \emph{convex constraint quasi-convex maximization problem}
thereby revealing the non-convex nature of the overall WSSUS pulse design
problem. We present several iterative algorithms for optimization providing
applicable results even for large--scale problem constellations. We show that
with transmitter-side knowledge of the channel statistics a gain of $3 - 6$dB
in $\SINR$ can be expected.
