Abstract: This paper considers multi-carrier heterogeneous cellular networks where only limited information can be shared among Base Stations (BSs) via backhaul links. Considering that there is frequency offset between macro and micro BSs, an optimal precoder and a suboptimal precoder are proposed, aimed at maximizing the date rate of micro systems while ensuring the resulting interference to macro users to be less than an interference threshold, where either instantaneous or statistical interference channel information is known at micro BS. Analysis and simulation results show that the performance of the suboptimal algorithm with only one iteration is close to the performance of the optimal one, and hence it has a lower computational complexity. The proposed method requires only little amount of information to be exchanged between BSs via backhaul links, and thus has a low overhead for sharing information. The proposed method is applicable when there are multiple marco users around the micro BS.