Optimal Geographical Caching in Heterogeneous Cellular Networks with Nonhomogeneous Helpers

We investigate optimal geographical caching in heterogeneous cellular networks, where different types of base stations (BSs) have different cache capacities. The content library contains files with different popularities. The performance metric is the total hit probability. The problem of optimally placing content in all BSs jointly is not convex in general. However, we show that when BSs are deployed according to homogeneous Poisson point processes (PPP), independently for each type, we can formulate the problem as a convex problem. We give the optimal solution to the joint problem for the PPP deployment. For the general case, we provide a distributed local optimization algorithm (LOA) that finds the optimal placement policies for different types of BSs. We find the optimal placement policy of the small BSs (SBSs) depending on the placement policy of the macro BSs (MBSs). We show that storing the most popular content in the MBSs is almost optimal if the SBSs are using optimal placement policy. Also, for the SBSs no such heuristic can be used; the optimal placement is significantly better than storing the most popular content. Finally, we numerically verify that LOA gives the same hit probability as the joint optimal solution for the PPP model.