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Cooperative Caching and Transmission Design in Cluster-Centric Small Cell Networks

Zheng Chen, Jemin Lee, Tony Q. S. Quek, Marios Kountouris

arXiv:1601.00321v1cs.NI

TL;DR

The paper studies how cluster-centric cooperative caching and transmission can reduce backhaul burdens while balancing replicated popular content against diversified partition storage. It combines MPC/LCD caching with JT/PT delivery, derives cluster-center SCDP results, and optimizes cache allocation. The reported results show a tradeoff between transmission and content diversity, with design choices adapting to rate, energy, network, and popularity conditions.

  • Problem

    Dense SCNs face backhaul traffic and energy burdens, motivating cache placement and cooperative delivery designs that balance content diversity with transmission reliability.

  • Method

    The paper combines replicated MPC caching and partition-based LCD caching with JT or PT CoMP delivery, analyzing cluster-center SCDP under PPP and hexagonal-cluster models.

  • Results

    The analysis finds an inherent tradeoff between transmission diversity and content diversity, while simulations report performance gains from cache-level and signal-level cooperation.

  • Takeaways & Limitations

    Optimal MPC cache allocation can be selected for cache service probability or energy efficiency using network parameters, QoS requirements, and content popularity.

Abstract

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Wireless content caching in small cell networks (SCNs) has recently been considered as an efficient way to reduce the traffic and the energy consumption of the backhaul in emerging heterogeneous cellular networks (HetNets). In this paper, we consider a cluster-centric SCN with combined design of cooperative caching and transmission policy. Small base stations (SBSs) are grouped into disjoint clusters, in which in-cluster cache space is utilized as an entity. We propose a combined caching scheme where part of the available cache space is reserved for caching the most popular content in every SBS, while the remaining is used for cooperatively caching different partitions of the less popular content in different SBSs, as a means to increase local content diversity. Depending on the availability and placement of the requested content, coordinated multipoint (CoMP) technique with either joint transmission (JT) or parallel transmission (PT) is used to deliver content to the served user. Using Poisson point process (PPP) for the SBS location distribution and a hexagonal grid model for the clusters, we provide analytical results on the successful content delivery probability of both transmission schemes for a user located at the cluster center. Our analysis shows an inherent tradeoff between transmission diversity and content diversity in our combined caching-transmission design. We also study optimal cache space assignment for two objective functions: maximization of the cache service performance and the energy efficiency. Simulation results show that the proposed scheme achieves performance gain by leveraging cache-level and signal-level cooperation and adapting to the network environment and user QoS requirements.

I. INTRODUCTION

The paper addresses backhaul bottlenecks in dense small cell networks by combining cluster-level cooperative caching with cooperative transmission. It models clustered SBSs and develops a design that balances content diversity and transmission diversity.

  • Motivation: Dense SCNs face growing traffic demands, while limited backhaul availability and capacity can become performance and cost bottlenecks.
  • Related Work: Prior proactive caching commonly uses homogeneous placement, causing different SBSs to cache identical popular content or follow identical probabilistic policies.
  • Contributions: The proposed design assigns cluster cache space either to replicated popular content or to different partitions of less popular files across SBSs.
  • Contributions: The paper derives SCDP results for cooperative transmission and optimizes MPC cache allocation for cache service probability and energy efficiency.
  • Network Model: SBSs follow a homogeneous PPP, while disjoint clusters follow a hexagonal grid; analysis conditions on a cluster centered at the origin.

B. Cache Placement Strategies

The caching strategy divides each file into partitions and splits cluster cache space between replicated popular content and diversified partition placement. JT serves replicated files, while PT serves partitioned files and is evaluated through SCDP definitions.

  • Content Model: The finite library contains N files ranked by popularity, with requests following a specified distribution such as Zipf with skewness parameter γ.
  • Cache Placement: Each SBS stores up to M files, and every file is divided into K equal-size partitions across a cluster of K cooperative SBSs.
  • Cache Placement: A proportion ρ of each SBS cache stores the most popular files in every SBS, while the remaining 1−ρ stores disjoint partitions of less popular files.
  • Cache Placement: The cache hit probability decreases monotonically with ρ, so reserving more space for LCD caching increases content diversity.
  • Transmission Schemes: MPC files use JT, whereas LCD files use parallel streams; PT-SS shares spectrum with SIC, while PT-OS assigns each SBS 1/K of the spectrum.
  • Performance Metric: SCDP measures whether S bits are delivered within bandwidth W and time T, based on the received SINR.

B. SCDP of MPC-JT strategy

For MPC files replicated at all cooperating SBSs, the paper analyzes coherent JT delivery to a cluster-center user under a distance-dependent fading and interference model.

  • JT Model: MPC requests are served by coordinated JT, combining coherently the signals from K cooperating SBSs.
  • Channel Model: Each SBS uses transmit power Pt and pathloss r−α with α > 2, while small-scale fading is Rayleigh and thermal noise is modeled explicitly.
  • SIR Analysis: The analysis then considers an interference-limited network and neglects background thermal noise when forming the received SIR.
  • SCDP Result: Using the SIR formulation and interference Laplace transform, the paper derives an analytical SCDP expression for JT with K cooperating SBSs.

C. SCDP of LCD-PT strategy

For LCD files, cooperating SBSs transmit different partitions in parallel. The paper analyzes spectrum-sharing PT with SIC and orthogonal-spectrum PT using cluster-center SCDP expressions.

  • Parallel Transmission: LCD requests are delivered through simultaneous parallel streams carrying different file partitions from cooperating SBSs.
  • PT-SS: PT-SS uses the same spectrum for K streams and decodes them with SIC, ordered here by increasing SBS distance for tractability.
  • PT-SS: During SIC, previously decoded in-cluster signals are canceled, while remaining in-cluster and out-of-cluster signals contribute interference; the final step has only out-of-cluster interference.
  • PT-SS: The paper derives an analytical SCDP expression for PT-SS with K cooperating SBSs using the ordered-distance approximation.
  • PT-OS: PT-OS assigns orthogonal frequency bandwidth to different partition streams, yielding separate received SIRs and an analytical SCDP expression.

IV. OPTIMIZATION DESIGN OF CACHE UTILIZATION STRATEGY

The proposed cache-utilization design balances transmission diversity against content diversity by assigning cache space between repeated popular content and partitioned less-popular content. The paper formulates cache-service optimization and derives an optimal MPC allocation based on transmission reliability and cluster conditions.

  • Transmission Diversity vs. Content Diversity: Lower ρ increases cache hit probability through greater content diversity, while higher ρ increases joint-transmission opportunities and transmission reliability.Thus, cache placement exposes an inherent tradeoff between content diversity and transmission diversity.
  • Cache service optimization: The cache service probability requires both the requested file to be cached inside the cluster and successful delivery from cooperative SBSs.The optimization selects ρ to maximize the percentage of requests successfully served by local caches.
  • Optimal cache assignment: The optimal MPC cache percentage depends on the relative transmission reliability of JT and PT schemes.The derived solution approaches ρ∗ ≃ 1 when JT is much more reliable than PT, whereas ρ∗ ≃ 0 favors content diversity when their reliabilities are similar.
  • Adaptive implementation: Central controllers can compute the optimal MPC allocation using the number of in-cluster SBSs and out-of-cluster interfering SBS density.The resulting assignment can then guide cache placement in cooperative SBSs.

C. Optimal Design for Energy Efficiency (EE)

The EE design accounts for cache-hit delivery, cache misses requiring backhaul retrieval, and the associated transmission and backhaul power consumption. Because the resulting optimization is involved, the paper uses numerical optimization of an approximated EE expression.

  • Energy-efficiency model: Cache misses add backhaul delay and energy consumption because the requested file must be downloaded from the core network before delivery.Cache-hit delivery uses locally cached content, whereas cache-miss delivery includes backhaul retrieval and joint transmission.
  • Energy-efficiency model: The average power consumption combines SBS transmit power for cache hits with transmit and wireline backhaul power for cache misses.For K cooperative SBSs, the model includes Pt and Pb weighted by cache-hit and cache-miss probabilities.
  • Optimal EE allocation: The EE objective selects ρ∗ to maximize energy efficiency for a cluster containing K cooperative SBSs.The formulation uses cache-hit probabilities for MPC and LCD content together with the cache-miss probability.
  • Optimal EE allocation: Under γ < 1 and M ≪ N, the paper approximates popularity-dependent cache probabilities with continuous functions of ρ for numerical optimization.This approximation produces a continuous EE expression used to obtain numerical optimal values.
  • Optimization limitation: No closed-form solution for the EE-maximizing ρ∗ is available because of the involved expression.Standard optimization methods are used instead, and the approximation's accuracy is verified through simulations.
  • Modeling assumption: The EE model excludes static baseband-processing and site-cooling power because it is treated as identical across MPC, LCD, and cache-miss cases.The paper states that adding static power is equivalent to using a higher SBS transmit power Pt in the model.

V. SIMULATION RESULTS

The simulations validate the cooperative caching and transmission analysis in a PPP-based, hexagonal-cluster SCN and compare the combined design with MPC-only and LCD-only caching. Empty reference clusters occur in only 3% of realizations under the stated settings.

  • Simulation setup: The simulations compare the proposed cooperative caching and transmission design with MPC-only and LCD-only caching schemes.This comparison evaluates the combined strategy against designs using only one caching type.
  • Simulation setup: 3% of realizations have an empty reference cluster under the stated network settings.The paper excludes these cases and reports that this has little impact on overall network performance.

A. Successful Content Delivery Probability

The section evaluates SCDP for JT and PT under conditioned cluster sizes, comparing theoretical analysis with simulation. It also identifies how cluster size affects the two schemes and notes an approximation boundary in the analysis.

  • Theoretical and simulation SCDP results are compared for JT and PT with K = {2, 3, 4} SBSs in the cluster.
  • The results validate the analysis in (12) and (17), especially when K is close to the average number of SBSs per cluster.
  • The circular approximation of the cluster area has negligible impact on the SCDP analysis.
  • The PT approximation error arises when conditioned in-cluster SBS density differs from the density of out-of-cluster PPP SBSs.
  • Higher K increases JT SCDP but decreases PT SCDP because JT gains received signal strength while PT multiplies the success probabilities of more streams.

1) Cache Service Probability Maximization:

The proposed combined caching scheme allocates cache space between MPC and partition-based LCD caching, with the optimal MPC percentage depending on target rate, popularity concentration, cluster size, and objective. Theoretical optima track exhaustive-search or simulation results, while combined caching outperforms single-policy baselines.

  • Cache service probability maximization: Theoretical ρ∗ accurately estimates the exhaustive-search optimum for cache service probability when K = 3.The optimal MPC percentage increases with target data rate and is higher for γ = 0.9 because concentrated popularity limits the benefit of caching more distinct files.
  • Cache service probability maximization: For K = {2, 3, 4}, larger cooperative clusters yield a smaller optimal MPC cache percentage.More SBSs increase the potential cooperation gain from reserving cache space for partition-based LCD caching.
  • Cache service probability maximization: The proposed scheme always outperforms caching with only MPC or only LCD, converging to those policies at the extreme cache allocations.Average cache service probability is evaluated over K ∈[1, 10].
  • Energy efficiency maximization: Under energy-efficiency maximization, the theoretical ρ∗matches exhaustive-search simulation results and decreases as backhaul delay increases.For β = 0.3, more cache space is assigned to LCD caching to avoid fetching requested content through the backhaul.
  • Energy efficiency maximization: The combined scheme outperforms only-MPC and only-LCD caching in average energy efficiency and improves energy efficiency relative to no cache capacity.The comparison uses the energy-efficiency-optimal ρ and includes a no-cache baseline.
  • Limitations: At high data-rate requirements, PT-based cooperative caching has limited benefit because transmission reliability is insufficient.More advanced SIC techniques could improve performance but are outside the paper’s scope.
  • Limitations: The evaluation assumes a cluster-center user, while optimizing randomly located users requires general-user SCDP expressions that are difficult to obtain neatly.The authors use the cluster-center analysis to provide insights into cooperative caching and transmission design.

APPENDIX

The appendix models cooperating SBSs inside a circular cluster and derives distance and interference distributions needed for joint-transmission SCDP analysis.

  • Cluster and distance model: The cluster of interest is approximated by the circular area B(0, R), whose in-cluster SBSs form the cooperation set.The derivation conditions on K cooperative SBSs jointly transmitting to a cluster-center user.
  • Cluster and distance model: Independent uniform SBS locations produce individual and joint probability density functions for the link distances.The distances are integrated through the joint density of r = [r1, . . . , rK].
  • Interference model: Out-of-cluster interference is modeled with PPP-distributed SBSs beyond minimum distance R, using its Laplace transform in the SCDP derivation.The transform uses the PPP probability generating functional and a change of variables.

B. Proof of Lemma 2

The proof derives PT-SS successful content delivery probability by requiring every SIC-decoded stream to exceed its target SIR and integrating over ordered SBS distances.

  • PT-SS success event: PT-SS delivery succeeds when all K streams after SIC satisfy SIRk > θ2.The event is expressed jointly as P[SIRi > θ2, . . . , SIRK > θ2].
  • SIC and interference: At each SIC step, interference is approximated using a homogeneous PPP, with a separate expression for the last decoded stream.The resulting SCDP incorporates the interference Laplace transform conditioned on the distance vector.
  • Distance integration: The derivation integrates the joint density of ordered in-cluster SBS distances to obtain the PT-SS SCDP.The ordered distances use the furthest-SBS density and conditional nearest-neighbor distance distributions.

C. Proof of Lemma 3

The PT-OS analysis uses orthogonal in-cluster transmissions and establishes strict concavity of the cache service probability, yielding a case-dependent optimal MPC allocation.

  • PT-OS SCDP: PT-OS success requires every independently received stream to satisfy SIRi > θ1, with interference coming only from out-of-cluster SBSs.The SCDP is obtained by integrating over the approximated joint distance density.
  • Optimization structure: The cache service probability f(ρ) is strictly concave because its second derivative is always negative.This reduces optimization to examining the first-order derivative and boundary cases.
  • Optimal allocation: When the relevant condition satisfies pJT d,K(θ2) ≥ K, f(ρ) increases monotonically and the optimum is ρ∗ = 1.The alternative condition pJT d,K(θ2) < K yields an interior solution satisfying f′(ρ) = 0.
  • Optimal allocation: The final closed-form rule combines the boundary and stationary-point cases from the derivative analysis.Lemma 4 follows by combining both optimization cases.
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