The downlink performance of two-tier (macro/pico) multi-antenna cellular heterogeneous networks (HetNets) employing space division multiple access (SDMA) technique is analyzed in this paper. The number of users simultaneously served with SDMA by each BS in a resource block depends on user distribution, unlike previous studies which assume the number to be any arbitrary value. By exploiting the feasibility of deploying larger number of antennas at macro BS, we propose to utilize the excess spatial degrees of freedom for interference nulling to pico users from their corresponding nearest (dominant) macro BSs. Biased-nearest-distance based user association scheme is proposed as those introduced in previous studies are unsuitable for analyzing the proposed multi-antenna scheme. Coverage probability and average data rate of a typical user are then evaluated. Our results demonstrate that the proposed interference nulling scheme has strong potential to improve performance. However, the system parameters such as association bias, and number of dedicated antennas at each macro BS for serving its own users must be carefully tuned.