  Heterogeneous networks (HetNets) with offloading is considered as an
effective way to meet the high data rate demand of future wireless service.
However, the offloaded users suffer from strong inter-tier interference, which
reduces the benefits of offloading and is one of the main limiting factors of
the system performance. In this paper, we investigate the use of an
interference nulling (IN) beamforming scheme to improve the system performance
by carefully managing the inter-tier interference to the offloaded users in
downlink two-tier HetNets with multi-antenna base stations. Utilizing tools
from stochastic geometry, we derive a tractable expression for the rate
coverage probability of the IN scheme. Then, we optimize the design parameter,
i.e., the degrees of freedom that can be used for IN, to maximize the rate
coverage probability. Specifically, in the asymptotic scenario where the rate
threshold is small, by studying the order behavior of the rate coverage
probability, we characterize the optimal design parameter. For the general
scenario, we show some properties of the optimal design parameter. Finally, by
numerical simulations, we show the IN scheme can outperform both the simple
offloading scheme without interference management and the almost blank
subframes scheme in 3GPP LTE, especially in large antenna regime.
