Abstract: In this paper, the performance of low complexity zero-forcing (ZF) precoder in coordinated multipoint (CoMP) transmission for heterogeneous networks is investigated. We consider the low complexity precoder structure often applied in homogeneous networks, which is decoupled into a ZF beamformer followed by power allocation. The performance of cooperative transmission with sum power constraint and per base-station (BS) power constraint is analyzed, where the power allocation is to maximize the sum rate. The performance is compared to that of equal power allocation, which is usually used in practical systems. It is shown that the downlink cooperative transmission in multi-carrier heterogeneous networks is quite different from that in homogeneous networks. The performance of CoMP with per BS power constraint is much better than those with other power constraints. However, when the maximal power of the cooperative macro BS and that of micro BS are quite different, the performance of macro users with CoMP is even inferior to that without coordination, while the performance of micro users is improved as espected. This implies that when designing the cooperative precoder in heterogeneous networks we must consider the per BS power constraint, and we should not only optimize the power allocation with a given ZF beamformer.