Abstract: In this paper, the Cramer-Rao Bound (CRB) to frequency offsets and channel impulse response estimation of Coordinate on Multiple Point downlink transmission system (CoMP) was derived for optimal training sequence design at first. However, the optimal sequence design criterion based on CRB was too complicated as the factor of channel impulse response and frequency offsets can't be eliminated in this criterion. So a sub-optimal design criterion based on minimum Mean Square Error (MSE) was proposed, then it was found out that the gauss sequence was the optimal sequence under this criterion.The numerical simulation verifies the theory analysis under the maximum likelihood (ML) estimation.The results show that the estimation performance approach CRB quiet well and gauss sequence outperform other sequences.