Probabilistic Caching in Multi-tier Heterogeneous Networks: Optimization and Tradeoff

In this paper, we study the probabilistic caching for an N-tier wireless heterogeneous network (HetNet) using stochastic geometry. A general and tractable expression of the successful delivery probability (SDP) is first derived. We then optimize the caching probabilities for maximizing the SDP in the high signal-to-noise ratio (SNR) region. The problem is proved to be convex and solved efficiently. We next establish an interesting connection between N-tier HetNets and single-tier networks. It is found that the performance upper bound of the N-tier HetNet is determined by an equivalent single-tier network. We further show that with uniform caching probabilities regardless of content popularities, to maintain a target SDP, there exists a tradeoff between the BS density and caching capability, namely, the BS density is inverse to the BS cache size. Specifically, the BS density of a tier can be reduced by increasing the cache size of the tier when the cache size is larger than a threshold.