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Cache-enabled Small Cell Networks: Modeling and Tradeoffs

Ejder Baştuğ, Mehdi Bennis, Marios Kountouris, Mérouane Debbah

arXiv:1405.3477v2cs.ITcs.NI

TL;DR

The paper addresses how caching at small base stations can alleviate finite-backhaul pressure while satisfying user demand. It develops a stochastic network model and performance analysis for cache-enabled SBSs, showing that a target outage or QoE level can be pursued through either denser deployment or greater storage.

  • Problem

    The paper studies how cache-enabled SBS deployments can serve demand while alleviating finite-backhaul constraints.

  • Method

    It models stochastically distributed SBSs with storage and derives outage-probability and average-delivery-rate expressions for the cache-enabled system.

  • Results

    A certain outage probability or QoE level can be achieved by deploying more SBSs or increasing the storage size of existing SBSs.

  • Takeaways & Limitations

    Network operators have two supported deployment choices for reaching a target performance level: more base stations or more storage per existing deployment.

Abstract

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We consider a network model where small base stations (SBSs) have caching capabilities as a means to alleviate the backhaul load and satisfy users' demand. The SBSs are stochastically distributed over the plane according to a Poisson point process (PPP), and serve their users either (i) by bringing the content from the Internet through a finite rate backhaul or (ii) by serving them from the local caches. We derive closed-form expressions for the outage probability and the average delivery rate as a function of the signal-to-interference-plus-noise ratio (SINR), SBS density, target file bitrate, storage size, file length and file popularity. We then analyze the impact of key operating parameters on the system performance. It is shown that a certain outage probability can be achieved either by increasing the number of base stations or the total storage size. Our results and analysis provide key insights into the deployment of cache-enabled small cell networks (SCNs), which are seen as a promising solution for future heterogeneous cellular networks.

I. INTRODUCTION

The paper studies cache-enabled small cell networks with stochastically distributed SBSs and finite backhaul, coupling caching decisions with physical-layer performance. It derives performance expressions and identifies a deployment tradeoff between SBS density and total storage size.

  • Mobile traffic growth motivates caching content at network-edge base stations to reduce backhaul use and improve user satisfaction.
  • Existing wireless caching proposals often rely on approximate or heuristic solutions because the wireless environment is difficult to analyze.
  • The paper models stochastically distributed SBSs equipped with storage units and limited backhaul capacity.
  • Outage probability and average delivery rate are expressed as functions of SINR, SBS number, target bitrate, storage size, file length, and popularity distribution.
  • A given outage probability can be achieved by increasing SBS count with fixed total storage or increasing total storage with fixed SBS count.
  • The work distinguishes its deployment analysis from prior stochastic-geometry studies through a different system model and performance metrics.

II. SYSTEM MODEL

The system models SBS locations with a PPP and users associated with their nearest SBSs. Requests are served through finite-rate backhaul or local caches, while QoE depends on downlink rate and backhaul constraints.

  • SBS locations follow a Poisson point process with density λ, and each user associates with its nearest SBS.
  • Each SBS has finite backhaul whose per-SBS capacity decreases with SBS density because total broadband capacity is shared among links.
  • Each SBS stores the most popular catalog files subject to storage capacity S.
  • The downlink uses constant transmit power, an unbounded power-law pathloss model with α > 2, and Rayleigh fading.
  • Users request files according to the popularity distribution and receive them through the Internet backhaul or local cache depending on file availability.
  • QoE requires downlink rate at least T, while cache misses can additionally be limited by the finite backhaul rate.

III. PERFORMANCE METRICS AND MAIN RESULTS

The paper defines outage probability and average delivery rate for a typical user in a cache-enabled small-cell network. It derives general expressions incorporating downlink SINR, local-cache availability, backhaul capacity, and file popularity.

  • Network model: The downlink SINR depends on the user's random distance from its serving SBS and interference from all other SBSs.The typical user is located at the origin, while SBSs are randomly distributed according to a PPP.
  • Performance metrics: Outage probability is defined as the complement of the probability that the downlink rate exceeds the requested file bitrate and the file is locally cached.A cached file with sufficient downlink rate avoids limited-backhaul use and playback interruption.
  • Main results: Theorem 1 gives the typical user's outage probability from its tagged base station as a function of the system parameters and β(T, α).β(T, α) is specified separately, with the Gamma function appearing in the associated expression.
  • Performance metrics: Average delivery rate assigns rate T when the cached file is available and the downlink rate exceeds T, but limits delivery to C(λ) otherwise.The model assumes C(λ) < T, reflecting a backhaul bottleneck when the requested file is not cached.
  • Main results: Theorem 2 provides the typical user's average delivery rate from its tagged base station using the same β(T, α) definition as Theorem 1.The general expressions can be evaluated after specifying interference, backhaul capacity, and file-popularity distributions.

A. Special Cases

The special-case results impose explicit assumptions on noise, pathloss, fading, backhaul capacity, and file popularity. Under these assumptions, outage probability and average delivery rate have simpler computable expressions.

  • Assumptions: The special cases assume positive noise power, pathloss exponent α = 4, and Rayleigh interference fading with exponential channel gains.These assumptions support the specialized outage and delivery-rate expressions.
  • Assumptions: The backhaul capacity follows a specified form with C(λ) < T, reflecting the assumed limitation of costly high-speed links in dense SBS deployments.C1 > 0 and C2 ≥ 0 parameterize the capacity model.
  • Assumptions: File popularity is modeled by a power law with shape parameter γ > 1.The paper motivates this choice by noting that several real-world distributions exhibit power-law behavior.
  • Specialized results: Proposition 1 gives a specialized outage-probability expression for α = 4, involving ρ(T, 4) and the standard Gaussian tail probability Q(x).The resulting expression is derived under the stated special-case assumptions.
  • Specialized results: Proposition 2 gives the corresponding specialized average delivery-rate expression, using the same ρ(T, 4) and Q(x) definitions.The special-case expressions require no integration and can be evaluated with lookup tables or standard numerical packages.

IV. VALIDATION OF THE PROPOSED MODEL

The paper validates its analytical outage and average-delivery-rate results with Monte Carlo simulations over PPP-distributed SBS deployments and sampled traffic and channel variables. The simulation curves match the theoretical results closely, with a slight mismatch attributed to discretization choices.

  • Simulation method: The validation averages results over 1000 realizations in which SBSs are distributed according to a PPP.File requests, signal powers, and interfering powers are sampled from their corresponding distributions.
  • Simulation method: Outage probability and average delivery rate are computed from SINR and cache-hit statistics.These quantities are compared with the analytical expressions.
  • Validation results: All simulation curves match the theoretical curves, although a slight mismatch is observed.The discrepancy is attributed to avoiding more precise discretization of continuous variables to keep simulation times affordable.

A. Impact of storage size

Storage size lowers outage probability and raises average delivery rate, while target bitrate, popularity shape, and SBS density also affect outage. The paper frames SBS density and total storage as interchangeable resources for achieving a target outage probability.

  • Impact of storage size: Increasing storage size reduces outage probability and increases average delivery rate.This behavior is observed in both theoretical and simulation curves.
  • Impact of SBS density: Increasing SBS density decreases outage probability, and increasing SBS storage can improve this decrement further.
  • Impact of target file bitrate: Increasing the target file bitrate raises outage probability, but increasing SBS storage can compensate for this reduction in performance.The impact of storage size becomes smaller as the target bitrate increases.
  • Impact of file popularity shape: Increasing the popularity shape parameter γ reduces outage probability because storage requirements decrease, although its effect is limited at very low and high γ.Higher γ concentrates popularity on a smaller portion of files, whereas lower γ produces more uniform popularity.
  • SBS density versus total storage: For a fixed target outage probability p† = 0.3, increasing total storage permits fewer SBSs, while increasing SBS count permits less total storage.The tradeoff is characterized by achievable pairs (λ⋆, Stotal), with Stotal = λS.
  • SBS density versus total storage: The density–storage tradeoff scales and shifts when T ∈{0.1, 0.2} or L ∈{1, 2}, and adding more SBSs may incur deployment and operation costs.The paper leaves detailed tightening of the optimal region for future work.

VI. CONCLUSIONS

The paper studies caching in stochastically distributed SBSs with finite-rate backhaul, deriving outage-probability and average-delivery-rate expressions and validating them numerically. Results indicate that target QoE can be pursued through either greater SBS density or larger storage.

  • The model considers cache-enabled SBSs stochastically distributed over the plane and connected through finite-rate backhaul links.
  • Closed-form expressions are derived for outage probability and average delivery rate, and the results are validated through numerical simulations.
  • Significant gains in outage probability and average delivery rate are possible with cache-enabled SBSs.
  • More base stations or increased storage size in an existing deployment can each achieve a certain QoE level.
  • Figure 7 examines the trade-off between SBS density and total storage size for different file targets.

APPENDIX A

The appendix derives outage probability by conditioning on the nearest SBS distance, decomposing independent events, and evaluating interference through the PPP's probability generating functional. Equal caching of popular files makes cache-hit probability independent of distance.

  • The outage derivation conditions on the nearest base station's distance from a typical user and decomposes the expression using independence and expectation linearity.
  • The derived components are substituted into the outage expression to complete the proof.
  • The conditional success probability is averaged over the nearest-SBS distance using its PPP probability density function.
  • The SINR inequality is rearranged to express the fading threshold in terms of distance, noise, and interference.
  • The interference term is evaluated with a Laplace transform, using independent fading, identically distributed channel variables, and the PPP probability generating functional.
  • Because every SBS caches the same popular files and has the same storage size, cache-hit probability is independent of distance.

APPENDIX B

The appendix formulates average achievable delivery rate by averaging over the PPP and fading distribution. Its component expectations follow from the delivery-rate definition, event independence, and the outage derivation.

  • Average achievable delivery rate is defined as the expectation of delivery rate over the PPP and fading distribution.
  • The rate decomposition follows from the delivery-rate definition together with independence of events and linearity of expectation.
  • The first rate component is derived by following the outage-proof steps from (14) through (19).
  • The second component uses the cache-hit probability's independence from distance.
  • The remaining component is written using similar arguments, and substituting the component expressions completes the proof.

APPENDIX C

The appendix derives a special-case result by following the earlier theorem's steps, then simplifies the interference transform under an exponential channel-gain assumption. The cache-hit term remains distance-independent.

  • The special-case proposition is derived by following the same steps as Theorem 1.
  • The Laplace transform is reformulated under the assumption that channel gain g follows an exponential distribution.
  • A change of variables and Gaussian-tail representation further simplify the resulting integral.
  • The first term's final expression is obtained before deriving the second term with arguments analogous to the earlier cache-hit calculation.
  • The cache-hit probability is independent of distance r, and the proof concludes after substituting the derived expressions.

APPENDIX D

Appendix D derives the outage-probability expression by decomposing the calculation into expectation terms and substituting previously established results. The derivation uses E[τ1] from Proposition 1 and evaluates E[τ2] by extracting T and applying equation (28).

  • The proposition is derived as a special case of Theorem 2 using similar steps.
  • E[τ1] is obtained from Proposition 1 and identified with part (i) of equation (22).The derivation then follows the steps from equations (23) to (27).
  • E[τ2] is obtained by taking T outside the expectation and substituting equation (28) into the formula.
  • The final expression follows after substituting equations (30), (31), and (32) into equation (29), with C(λ) defined by Assumption 1.
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