Optimal Content Placement for Offloading in Cache-enabled Heterogeneous   Wireless Networks
  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. 
Dong Liu and Chenyang Yang
cs.IT math.IT