On the eigenstructure of underspread WSSUS channels

We consider the problem of finding pulses that suffer from minimum distortion when transmitted over an underspread time-varying multipath propagation channel. Mathematically, this corresponds to the design of properly time/frequency localized functions that are approximate eigenfunctions of the channel. We consider the problem of determining this localization in terms of the channel's spreading function (deterministic case) and scattering function (stochastic WSSUS case).