text: In this paper, we study the probabilistic caching for an @math -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) regime. The problem is proved to be convex and solved efficiently. We next establish an interesting connection between @math -tier HetNets and single-tier networks. Unlike the single-tier network where the optimal performance only depends on the cache size, the optimal performance of @math -tier HetNets depends also on the BS densities. The performance upper bound is, however, determined by an equivalent single-tier network. We further show that with uniform caching probabilities regardless of content popularities, to achieve a target SDP, 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; otherwise the BS density and BS cache size can be increased simultaneously. It is also found analytically that the BS density of a tier is inverse to the BS cache size of the same tier and is linear to BS cache sizes of other tiers.
  @cite_9: Heterogeneous wireless networks (HetNets) provide a powerful approach to meeting the dramatic mobile traffic growth, but also impose a significant challenge on backhaul. Caching and multicasting at macro and pico base stations (BSs) are two promising methods to support massive content delivery and reduce backhaul load in HetNets. In this paper, we jointly consider caching and multicasting in a large-scale cache-enabled HetNet with backhaul constraints. We propose a hybrid caching design consisting of identical caching in the macro-tier and random caching in the pico-tier, and a corresponding multicasting design. By carefully handling different types of interferers and adopting appropriate approximations, we derive tractable expressions for the successful transmission probability in the general signal-to-noise ratio (SNR) and user density region as well as the high SNR and user density region, utilizing tools from stochastic geometry. Then, we consider the successful transmission probability maximization by optimizing design parameters, which is a very challenging mixed discrete-continuous optimization problem. By exploring structural properties, we obtain a near optimal solution with superior performance and manageable complexity. This solution achieves better performance in the general region than any asymptotically optimal solution, under a mild condition. The analysis and optimization results provide valuable design insights for practical cache-enabled HetNets.
  @cite_13: In this work we consider the problem of an optimal geographic placement of content in wireless cellular networks modelled by Poisson point processes. Specifically, for the typical user requesting some particular content and whose popularity follows a given law (e.g. Zipf), we calculate the probability of finding the content cached in one of the base stations. Wireless coverage follows the usual signal-to-interference-and noise ratio (SINR) model, or some variants of it. We formulate and solve the problem of an optimal randomized content placement policy, to maximize the user's hit probability. The result dictates that it is not always optimal to follow the standard policy “cache the most popular content, everywhere”. In fact, our numerical results regarding three different coverage scenarios, show that the optimal policy significantly increases the chances of hit under high-coverage regime, i.e., when the probabilities of coverage by more than just one station are high enough.
  @cite_6: In this work we investigate optimal geographical caching in heterogeneous cellular networks where different types of base stations (BSs) have different cache capacities. Users request files from a content library according to a known probability distribution. The performance metric is the total hit probability, which is the probability that a user at an arbitrary location in the plane will find the content that it requires in one of the BSs that it is covered by. We consider the problem of optimally placing content in all BSs jointly. As this problem is not convex, we provide a heuristic scheme by finding the optimal placement policy for one type of base station conditioned on the placement in all other types. We demonstrate that these individual optimization problems are convex and we provide an analytical solution. As an illustration, we find the optimal placement policy of the small base stations (SBSs) depending on the placement policy of the macro base stations (MBSs). We show how the hit probability evolves as the deployment density of the SBSs varies. We show that the heuristic of placing the most popular content in the MBSs is almost optimal after deploying the SBSs with optimal placement policies. Also, for the SBSs no such heuristic can be used; the optimal placement is significantly better than storing the most popular content. Finally, we show that solving the individual problems to find the optimal placement policies for different types of BSs iteratively, namely repeatedly updating the placement policies, does not improve the performance.
  @cite_23: In this paper, we investigate the optimal caching policy, respectively, maximizing the success probability and area spectral efficiency (ASE) in a cache-enabled heterogeneous network (HetNet), where a tier of multi-antenna macro base stations (MBSs) is overlaid with a tier of helpers with caches. Under the probabilistic caching framework, we resort to stochastic geometry theory to derive the success probability and ASE. After finding the optimal caching policies, we analyze the impact of critical system parameters and compare the ASE with traditional HetNet where the MBS tier is overlaid by a tier of pico BSs (PBSs) with limited-capacity backhaul. Analytical and numerical results show that the optimal caching probability is less skewed among helpers to maximize the success probability when the ratios of MBS-to-helper density, MBS-to-helper transmit power, user-to-helper density, or the rate requirement are small, but is more skewed to maximize the ASE in general. Compared with traditional HetNet, the helper density is much lower than the PBS density to achieve the same target ASE. The helper density can be reduced by increasing cache size. With given total cache size within an area, there exists an optimal helper node density that maximizes the ASE.
summary: Recently, caching strategy optimization is extended to wireless heterogeneous networks. The combination of the optimal caching and the network heterogeneity brings more gains in network capacity. Utilizing the tool of stochastic geometry, the works @cite_9 @cite_23 investigate the optimal probabilistic caching at helper stations while assuming deterministic caching at macro stations to maximize the successful transmission probability in a two-tier HetNet. Based on @cite_13 , the work @cite_6 considers different types of BSs with different cache capacities. The cache optimization problem for the first type of BSs is solved by assuming that the placement strategy for other types of BSs is given. The joint probabilistic caching optimization problem for all types of BSs is yet not considered, and little analytical insight on the cache design and system performance is available. In general, the joint optimization for probabilistic cache placements in different tiers of a HetNet is very challenging due to the different tier association probabilities brought by the content diversity as well as the complicated interference distribution by the nature of network heterogeneity.