Cache-Enabled Heterogeneous Cellular Networks: Optimal Tier-Level Content Placement

Caching popular contents at <italic>base stations</italic> (BSs) of a <italic>heterogeneous cellular network</italic> (HCN) avoids frequent information passage from content providers to the network edge, thereby reducing latency and alleviating traffic congestion in backhaul links. The potential of caching at the network edge for tackling 5G challenges has motivated recent studies on optimal content placement in large-scale HCNs. However, due to the complexity of the network performance analysis, the existing strategies were mostly based on approximation, heuristics, and intuition. In general, optimal strategies for content placement in HCNs remain largely unknown and deriving them forms the theme of this paper. To this end, we adopt the popular random HCN model, where <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> tiers of BSs are modeled as independent <italic>Poisson point processes</italic> distributed in the plane with different densities. Furthermore, the <italic>random caching</italic> scheme is considered, where each of a given set of <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> files with corresponding popularity measures is placed at each BS of a particular tier with a corresponding probability, called <italic>placement probability</italic>. The probabilities are identical for all BSs in the same tier but vary over tiers, giving the name <italic>tier-level content placement</italic>. We consider the network performance metric, <italic>hit probability</italic>, defined as the probability that a file requested by the typical user is delivered successfully to the user. Leveraging existing results on HCN performance, we maximize the hit probability over content placement probabilities, which yields the optimal tier-level placement policies. For the case of uniform received signal-to-interference (SIR) thresholds for successful transmissions for BSs in different tiers, the policy is in closed-form, where the placement probability for a particular file is proportional to the <italic>square-root of the corresponding popularity measure</italic> with an offset depending on BS caching capacities. For the general case of non-uniform SIR thresholds, the optimization problem is non-convex and a sub-optimal placement policy is designed by approximation, which has a similar structure as in the case of uniform SIR thresholds and shown by simulation to be close-to-optimal.