In this paper, the authors study the performance of Filter Bank based Multi-Carrier (FBMC) transmission systems over doubly-dispersive channels. FBMC generalizes traditional Orthogonal Frequency-Division Multiplexing (OFDM) schemes, allowing a non-rectangular sub-channel pulse shape in the time domain. This approach leads to a better spectral containment that improves interference mitigation in several time-variant environments. A general analysis describes the trans-multiplexer structure and the time-variant multipath channel model. They specify rectangular filters and short Perfect Reconstruction (PR) filters that give rise to two families of FBMC transceivers.