Small cell densification is one of the effective ideas addressing the demand for higher capacity in cellular networks. The major problem faced in such networks is the wireless backhaul link and its limited capacity. Caching most popular files in the memories of small cells base station (SBSs) is an effective solution to this problem. One of the main challenges in caching is choosing the files that are going to be stored in the memory of SBS. In this paper, we model the described caching problem as a graph. This graph is divided into four sub-graphs including placement, access, SBSs and delivery graphs. By making some modifications to the SBS graph, we convert it to a graph that can be colored. Coloring of the generated graph is NP-hard and we use an algorithm proposed in graph-coloring area to color it. To overcome the complexity of above coloring technique, we then propose a simple graph-coloring method based on two point processes, Matern Core-type I and II. We model our network with a new weighted graph which simply can be colored and after that the files are cached accordingly. We evaluate the performance of our proposed methods through simulations. Our results show that by employing out proposed method in a typical considered SBSs network, the load on the macro base station can be reduced by around @math , at the distribution parameter of popularity of files equals to @math , compared to conventional policy which caches the most popular content every where.
Caching has been a subject of interest to many researchers. Extensive research has been conducted on studying the content-placement to obtain gains over the conventional policy which caches the most popular content everywhere @cite_24 . Different performance metrics have been considered to design the content-placement strategies in the literature such as average downloading delay @cite_25 @cite_34 @cite_0 , average BER @cite_6 , average caching failure probability @cite_36 , offloading probability @cite_23 , density of successful receptions @cite_47 , hit probability @cite_36 , average success probability of content delivery @cite_18 , and the expected backhaul rate and the energy consumption @cite_42 .
@cite_18 @cite_36 @cite_42 @cite_6 @cite_24 @cite_0 @cite_23 @cite_47 @cite_34 @cite_25
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To alleviate the backhaul burden and reduce user-perceived latency, content caching at base stations has been identified as a key technology. However, the caching strategy design at the wireless edge is challenging, especially when both wired backhaul condition and wireless channel quality are considered in the optimization. In this paper, taking into account the conditions of the backhaul in terms of delay and wireless channel quality, joint design and optimization of the caching and user association policy to minimize the average download delay is studied in a cache-enabled heterogeneous network. We first prove the joint caching and association optimization problem is NP-hard based on a reduction to the facility location problem. Furthermore, in order to reduce the complexity, a distributed algorithm is developed by decomposing the NP-hard problem into an assignment problem solvable by the Hungarian method and two simple linear integer subproblems, with the aid of McCormick envelopes and the Lagrange partial relaxation method. Simulation results reveal a near-optimal performance that performs up to 22 better in term of delay compared with those in the literatures at a low complexity of @math . We investigate the problem of coded caching for nonuniform demands when the structured clique cover algorithm proposed by Maddah-Ali and Niesen for decentralized caching is used for delivery. We apply this algorithm to all user demands regardless of their request probabilities. This allows for coding among the files that have different request probabilities but makes the allocation of memory to different files challenging during the content placement phase. As our main contribution, we analytically characterize the optimal placement strategy that minimizes the expected delivery rate under a storage capacity constraint. It is shown that the optimal placement follows either a two or a three group strategy, where a set of less popular files are not cached at all and the files within each of the other sets are allocated identical amounts of storage as if they had the same request probabilities. We show that for a finite set of storage capacities, that we call the base-cases of the problem, the two group strategy is always optimal. For other storage capacities, optimal placement is achieved by memory sharing between certain base-cases and the resulting placement either follows a two or a three group strategy depending on the corresponding base-cases used. We derive a polynomial time algorithm that determines the base-cases of the problem given the number of caches and popularity distribution of files. Given the base-cases of the problem, the optimal memory allocation parameters for any storage capacity are derived analytically. 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. Content delivery success in wireless caching helper networks depends mainly on cache-based channel selection diversity and network interference. For given channel fading and network geometry, both channel selection diversity and network interference dynamically vary according to what and how the caching helpers cache at their finite storage space. We study probabilistic content placement (or caching placement) to desirably control cache-based channel selection diversity and network interference in a stochastic wireless caching helper network, with sophisticated considerations of wireless fading channels, interactions among multiple users, such as interference and loads at caching helpers, and arbitrary memory size. Using stochastic geometry, we derive optimal caching probabilities in the closed form to maximize the average success probability of content delivery and propose an efficient algorithm to find the solution in a noise-limited network. In an interference-limited network, based on a lower bound of the average success probability of content delivery, we find near-optimal caching probabilities in the closed form to control the channel selection diversity and the network interference. We numerically verify that the proposed content placement is superior to other comparable content placement strategies.