This paper addresses the problem of channel estimation in time-division duplex (TDD) multi-cell cellular systems, where the performance of such systems are usually bounded by a bottleneck resulted from pilot contamination. We propose two channel estimation schemes that completely remove pilot contamination. The exact closed-form expression for average Mean Square Error (MSE) of the proposed estimators are derived. More importantly, our proposed estimators do not need to know the second-order statistics of neither desired user channels nor interfering user channels. Finally, simulated results confirms gains over existing channel estimation schemes.