The issue of multicarrier transmission with high spectral efficiency and low interference over time-frequency (TF) dispersive channels is addressed in this paper. Specifically, we propose a digital signal transmission scheme employing overcomplete Weyl-Heisenberg (W-H) frames as modulation pulses. The proposed W-H frame transmission scheme, which relaxes the conventional orthogonality/biorthogonality constraints for perfect transmultiplexing, can be viewed as a generalization of the orthogonal frequency division multiplexing (OFDM) and nonorthogonal (biorthogonal) frequency division multiplexing (NOFDM). With this new transmission scheme, one can not only achieve higher spectral efficiency effectively but also design the pulse shape more flexibly to combat the impact of the propagation channel. In order to optimally mitigate the intersymbol interference (ISI) and interchannel interference (ICI) caused by the wireless channel, the selections of the Gaussian pulse shape and T-F grid parameters are addressed jointly from the viewpoint of minimum energy perturbation for several typical channel scattering functions. Simulation results are presented to study the performance of the proposed system. It is shown that the proposed overcomplete W-H frame transmission system with a lower-order constellation is more robust against the TF dispersive channels than the incomplete Riesz basis system employing a higher-order constellation with the same spectral efficiency.