  Caching at base stations (BSs) is a promising way to offload traffic and
eliminate backhaul bottleneck in heterogeneous networks (HetNets). In this
paper, we investigate the optimal content placement maximizing the successful
offloading probability in a cache-enabled HetNet where a tier of multi-antenna
macro BSs (MBSs) is overlaid with a tier of helpers with caches. Based on
probabilistic caching framework, we resort to stochastic geometry theory to
derive the closed-form successful offloading probability and formulate the
caching probability optimization problem, which is not concave in general. In
two extreme cases with high and low user-to-helper density ratios, we obtain
the optimal caching probability and analyze the impacts of BS density and
transmit power of the two tiers and the signal-to-interference-plus-noise ratio
(SINR) threshold. In general case, we obtain the optimal caching probability
that maximizes the lower bound of successful offloading probability and analyze
the impact of user density. Simulation and numerical results show that when the
ratios of MBS-to-helper density, MBS-to-helper transmit power and
user-to-helper density, and the SINR threshold are large, the optimal caching
policy tends to cache the most popular files everywhere.
