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_4: Dense wireless networks are a promising solution to meet the huge capacity demand in 5G wireless systems. However, there are two implementation issues, namely, the interference and backhaul issues. To resolve these issues, we propose a novel network architecture called the backhaul-limited cached dense wireless network (C-DWN), where a physical layer (PHY) caching scheme is employed at the base stations (BSs), but only a fraction of the BSs have wired payload backhauls. The PHY caching can replace the role of wired backhauls to achieve both the cache-induced multiple-input–multiple-output (MIMO) cooperation gain and cache-assisted multihopping gain. Two fundamental questions are addressed. Can we exploit the PHY caching to achieve linear capacity scaling with limited payload backhauls? If so, how much cache is needed? We show that the capacity of the backhaul-limited C-DWN indeed scales linearly with the number of BSs if the BS cache size is larger than a threshold that depends on the content popularity. We also quantify the throughput gain due to cache-induced MIMO cooperation over conventional caching schemes (which exploit purely the cached-assisted multihopping). Interestingly, the minimum BS cache size needed to achieve a significant cache-induced MIMO cooperation gain is the same as that needed to achieve the linear capacity scaling.
  @cite_25: We consider the problem of caching in next generation mobile cellular networks where small base stations (SBSs) are able to store their users' content and serve them accordingly. The SBSs are stochastically distributed over the plane and serve their users either from the local cache or internet via limited backhaul, depending on the availability of requested content. We model and characterize the outage probability and average content delivery rate as a function of the signal-to-interference-ratio (SINR), base station intensity, target file bitrate, storage size and file popularity. Our results provide key insights into the problem of cache-enabled small cell networks.
  @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: Furthermore, a tradeoff between the small BS density and total storage size is firstly presented in @cite_25 , where each small BS caches the most popular contents. Using the optimal caching scheme, @cite_23 shows that the helper density can be traded by the cache size to achieve a target area spectral efficiency. Note that the tradeoff studies in @cite_25 @cite_23 are conducted numerically only without theoretical analysis. Deriving and analyzing the tradeoff theoretically has not been solved. In @cite_4 , the authors address the question that how much caching is needed to achieve the linear capacity scaling in the dense wireless network based on scaling law method.