Time-frequency synthesis of statistically matched Weyl-Heisenberg prototype signals

The use of a family of time-frequency shifted versions of a prototype signal, namely Weyl-Heisenberg (WH) sets, is a common feature of various concepts in signal analysis, processing and digital communication. The authors discuss the matching of WH prototype signals to important nonstationary environments. The statistical window optimization for the STFT/Gabor expansion of nonstationary processes is shown to be formally equivalent to optimal signal design for narrowband WSSUS channels. For the case of underspread channels/processes the authors derive approximate solutions to the optimization problem