The channel estimate and carrier frequency offset (CFO) acquisition are two essential bases for multiple-inputmultiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) techniques. In high-mobility scenario, the fast time varying channel and the serious Doppler frequency shift will make the channel tracking and CFO estimation much more challenging. In this paper, the achievable limits of joint basis expansion-model (BEM)-based channel tracking and CFO estimation are derived in terms of the Bayesian Cramer-Rao lower bound (BCRLB) to reveal the impact of dependent factors, like the pilot and BEM modeling error. The BCRLB analysis shows that, the measurement reliability, BEM modeling error, channel correlation and the statistical channel dynamics will dominate the achievable limits. And smaller pilot space seems to be an imperative choice to improve the joint estimate performance.