In this paper, we derive the Chernoff bound of the pairwise error probability (PEP) and the exact PEP of convolutional codes in a time-varying Rician fading channel. With the assumptions that the channel estimator is a finite impulse response filter and the interleaving depth is finite, we are able to investigate the estimation-diversity tradeoff resulting from the effects of the Doppler spread on the system performance, via the channel estimation accuracy and the channel diversity. In addition, we verify that, in the special case when the pilot signal-to-noise ratio is infinitely large and the channel estimator is well-designed, our analysis leads to the same result as the existing perfect channel-state information analysis. Finally, the analytical results are compared with results from Monte Carlo simulation, and the comparison shows that the analytical results match well with the simulation results.