This　paper　investigates　fast　time-varying　channel　estimation　in　LTE-R　communication　systems.　The　Basis　Expansion　Model　(BEM)　is　adopted　to　fit　the　fast　time-varying　channel　in　a　high-speed　railway　communication　scenario.　The　channel　impulse　response　is　modeled　as　the　sum　of　basis　functions　multiplied　by　different　coefficients.　The　optimal　coefficients　are　obtained　by　theoretical　analysis.　Simulation　results　show　that　a　Generalized　Complex-Exponential　BEM　(GCE-BEM)　outperforms　a　Complex-Exponential　BEM　(CE-BEM)　and　a　polynomial　BEM　in　terms　of　Mean　Squared　Error　(MSE).　Besides,　the　MSE　of　the　CE-BEM　decreases　gradually　as　the　number　of　basis　functions　increases.　The　GCE-BEM　has　a　satisfactory　performance　with　the　serious　fading　channel.　©　2016　Chongqing　University　of　Posts　and　Telecommuniocations