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Wireless Content Caching for Small Cell and D2D Networks

Maria Gregori, Jesús Gómez-Vilardebó, Javier Matamoros, Deniz Gündüz

arXiv:1603.04341v1cs.IT

TL;DR

The paper addresses how edge caching can manage growing wireless traffic and constrained, energy-intensive backhaul links. It jointly optimizes transmission and caching for SBS and D2D scenarios with known demands, showing that constant-rate caching enables convex optimization and substantial MBS energy reductions.

  • Problem

    Growing wireless traffic and constrained wireless backhaul motivate studying caching policies that account jointly for pre-downloading and local caching gains.

  • Method

    The paper formulates continuous-time joint transmission-and-caching optimization for centralized SBS and distributed user caches, using constant-rate caching to obtain convex programs.

  • Results

    MBS energy consumption is reduced by 53.59% in the SBS scenario and 61.78% in the D2D scenario versus traditional non-caching solutions at 25% cache capacity.

  • Takeaways & Limitations

    Joint transmission and caching exploits both pre-downloading and local caching gains across centralized SBS and distributed D2D deployments.

Abstract

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The fifth generation wireless networks must provide fast and reliable connectivity while coping with the ongoing traffic growth. It is of paramount importance that the required resources, such as energy and bandwidth, do not scale with traffic. While the aggregate network traffic is growing at an unprecedented rate, users tend to request the same popular contents at different time instants. Therefore, caching the most popular contents at the network edge is a promising solution to reduce the traffic and the energy consumption over the backhaul links. In this paper, two scenarios are considered, where caching is performed either at a small base station, or directly at the user terminals, which communicate using \ac{D2D} communications. In both scenarios, joint design of the transmission and caching policies is studied when the user demands are known in advance. This joint design offers two different caching gains, namely, the \textit{pre-downloading} and \textit{local caching gains}. It is shown that the finite cache capacity limits the attainable gains, and creates an inherent tradeoff between the two types of gains. In this context, a continuous time optimization problem is formulated to determine the optimal transmission and caching policies that minimize a generic cost function, such as energy, bandwidth, or throughput. The jointly optimal solution is obtained by demonstrating that caching files at a constant rate is optimal, which allows to reformulate the problem as a finite-dimensional convex program. The numerical results show that the proposed joint transmission and caching policy dramatically reduces the total cost, which is particularised to the total energy consumption at the \ac{MBS}, as well as to the total economical cost for the service provider, when users demand economical incentives for delivering content to other users over the D2D links.

I. INTRODUCTION

The paper studies joint transmission and caching for small-base-station and D2D networks to address traffic growth and backhaul constraints. It combines pre-downloading and local caching gains under dynamically managed caches and known demands.

  • Motivation: Wireless traffic growth, driven especially by on-demand video, is amplified by asynchronous reuse of a few popular files.More than 127 exabytes of worldwide mobile traffic was forecast for 2020.
  • Motivation: Small-cell densification improves spatial reuse but leaves wireless backhaul links constrained by limited capacity and significant energy consumption.Wireless backhaul is favored for rapid deployment, self-configuration, and cost despite these constraints.
  • Motivation: Conventional placement and delivery phases assume free content placement and no cache updates during delivery, limiting proactive-caching benefits.These assumptions motivate accounting for caching costs and dynamic cache filling.
  • Approach: The paper dynamically fills initially empty caches, accounting for download costs while exploiting pre-downloading during low-traffic periods.Pre-downloading can avoid unfavorable channels, equalize backhaul rates, reduce peak load, and improve energy efficiency.
  • Approach: Joint transmission and caching are optimized for a generic cost function in centralized SBS-cache and distributed user-cache scenarios.In the distributed scenario, users share proactively cached content through D2D communications.
  • Optimization: Constant-rate caching is optimal within each time slot, enabling convex reformulations for both the SBS and D2D scenarios.The SBS scenario additionally uses dual decomposition and a subgradient algorithm, while the D2D scenario also has constant-rate file transmission.
  • Evaluation: Numerical simulations compare centralized and distributed caches, quantify pre-downloading and local caching gains, and assess incentive-dependent D2D costs.The study also examines how the MBS cost changes with economic incentives for D2D transmission.

A. System model and problem formulation

The paper models joint MBS transmission and SBS caching over a finite-capacity cache, using known user demands to minimize a convex backhaul cost. The formulation captures both pre-downloading and local caching through demand, transmission, and caching policies.

  • System model: The system contains U users served by an SBS with cache capacity C and a wireless backhaul connection to an MBS.The MBS accesses the core network, while the MBS and SBS use different frequency bands.
  • Demand model: User demand rates are defined over N time slots, with each user requesting one file per slot from the file set F.Files have lengths l_j and duration T_s; f_0 represents slots without requests.
  • Assumptions: The model assumes an offline setting in which user demand variables are known throughout the optimization horizon.Cached data is represented using request-indexed transmission, caching, and demand-rate variables.
  • Demand model: The SBS demand removes duplicate requests for the same file within a slot, so simultaneous users need only one download from the MBS.The request with the smallest user index is counted without loss of generality.
  • Optimization problem: The MBS transmission rate r(t) and SBS caching rate c(t) are jointly designed to minimize a time-integrated convex, increasing backhaul cost g(r(t)).Examples include energy, bandwidth, throughput, and traffic minimization.
  • Caching gains: The cache provides pre-downloading and local caching gains, but both are constrained by cache capacity and the SBS demand rate.Pre-downloaded data comes from the MBS, whereas locally cached data is controlled by the SBS caching policy.
  • Scope: The analysis treats each SBS independently by assigning orthogonal MBS resources and assuming non-overlapping SBS coverage areas.Multicasting and cooperation among overlapping SBSs are identified as out of scope.

B. Optimal transmission strategy for a fixed caching policy

For a fixed SBS caching policy, the paper characterizes the minimum-cost MBS transmission through a data-departure-curve construction. The resulting comparison shows that fewer transmitted bits need not imply lower cost, because rate equalization can be beneficial.

  • Caching effects: Caching f2 before its next request eliminates MBS transmission in the third slot in the illustrated policy.This policy anticipates user 2's later request using data cached during user 1's second-slot request.
  • Optimal transmission: For a fixed caching policy, the optimal MBS data-departure curve is the tightest string connecting the origin to the required endpoint.This characterization applies to the cumulative data transmitted over the horizon.
  • Optimal transmission: Strictly convex instantaneous costs yield a unique optimal departure curve, whereas linear costs allow multiple optimal curves.The uniqueness distinction follows directly from the cost function's curvature.
  • Caching effects: Caching changes both the upper cache-capacity bound and the lower bound imposed by residual SBS demand.Caching f2 in the second slot tightens the upper bound and relaxes the third-slot demand bound.
  • Policy comparison: The policy requiring fewer transmitted bits does not necessarily minimize MBS cost, because another policy may lower cost by equalizing rates across slots.Thus, transmission and caching must be optimized jointly rather than selecting solely for reduced data volume.

C. Jointly optimal caching and transmission policies

The paper derives jointly optimal caching and transmission policies by exploiting structural properties that reduce a continuous-time problem to a finite-dimensional convex program.

  • Problem reformulation: The infinite-dimensional problem is reformulated using per-slot cached data q_nu and MBS transmission rates r_n.These variables represent the amount cached for each request in each slot and the MBS rate in each slot.
  • Caching structure: Constant-rate caching within each slot is optimal, so the caching policy can be represented as a step-wise function.The optimal local caching rate may be non-unique but changes only across slot intervals.
  • Transmission structure: The optimal data departure curve is piece-wise linear, with transmission-rate changes only at slot transitions.The rate may change at times n · T_s for n = 1, . . . , N − 1.
  • Convexity: The resulting formulation is a convex program because its objective is convex and its constraints are affine.Relaxing integer data-unit constraints is justified because data units are small relative to file sizes and cache capacities.
  • Solution method: Dual decomposition separates the optimization over transmission and caching variables, enabling projected subgradient optimization.The method converges to optimal dual variables when the step size is correctly chosen, and the duality gap is zero under the stated conditions.
  • Caching decisions: The sign of W_nu determines whether the associated file is uncached, fully cached, or partially cached.Positive W_nu yields no caching, negative W_nu yields complete caching, and zero W_nu permits a partial amount.

A. System model and problem formulation

The paper formulates two caching scenarios: an SBS serves multiple users, or user devices cache content and serve one another over D2D links. Both are optimized using generic transmission costs and explicit cache-flow constraints.

  • User-device caching: In the user-device scenario, closely located users act as SBSs for one another through dedicated D2D links.D2D links use frequency resources different from those used by the MBS.
  • Terminal architecture: Each user terminal combines a user module with an SBS module containing a cache for pre-downloaded and previously cached content.The SBS module downloads only content corresponding to its own demand from the MBS.
  • Cost model: The joint objective minimizes a general cost over MBS and D2D rates, including transmission costs and user incentives.The cost functions can model energy, energy cost, bandwidth, or traffic minimization.
  • Model assumption: To maintain tractability, overlapping caching by different users is forbidden.The paper states that allowing overlapping user caches has a combinatorial structure whose optimal solution remains open.
  • Flow constraints: The formulation constrains each user’s MBS departure curve between demand and cache-capacity bounds.The lower bound reflects net MBS demand after local caching and D2D service, while the upper bound prevents cache overflow.

B. Jointly optimal strategy

For the D2D scenario, the paper shows that optimal caching and D2D transmission are piece-wise constant within slots, enabling a finite-dimensional convex formulation that can be solved efficiently.

  • Caching and D2D policy: Within each slot, users optimally cache and transmit over D2D links at constant rates.This structural result reduces the continuous-time policies to slot-level variables.
  • Policy representation: The optimal caching and D2D rates are represented by piece-wise constant functions over the slot intervals.The variables encode cached data for each request and data transmitted from one user to another.
  • MBS transmission: The optimal data departure curve for each user is piece-wise linear, so MBS transmission rates can also be represented per slot.The resulting rate is the optimal MBS transmission rate to each user in each slot.
  • Finite-dimensional formulation: The reformulated problem uses cached data, D2D-transmitted data, and per-slot MBS rates as optimization variables.These variables provide a finite-dimensional representation of the original continuous-time problem.
  • Optimization: The discrete problem is a convex program because its objective is convex and its constraints are linear.It can therefore be solved efficiently using methods such as interior-point algorithms.

IV. NUMERICAL RESULTS

The numerical evaluation compares caching strategies in SBS and D2D scenarios under varying cache capacities, file popularity, and D2D incentives. The jointly optimal policy reduces MBS energy consumption and adapts to the best available caching gain.

  • Simulation setup: The evaluation uses 20 ten-second slots, 2,000 video files, Zipf-distributed requests, and Shannon power-rate models for SBS and D2D scenarios.The SBS uses the full 10 MHz bandwidth, while the D2D scenario splits it evenly across users.
  • Energy versus cache capacity: The jointly optimal policy reduces MBS energy consumption by 53.59% in the SBS scenario and 61.78% in the D2D scenario at cache capacity 25% of average user traffic.The reported cache capacity is Ĉ = 25, and further energy savings are possible with larger total cache capacity.
  • Energy versus cache capacity: MBS energy consumption decreases with cache capacity in both scenarios, while the optimal policy outperforms traditional non-caching solutions.The figure compares caching at the SBS with caching directly at users for γ = 1 and U = 3.
  • SBS and D2D comparison: The SBS scenario consumes energy no greater than the D2D scenario, while distributed storage across users increases D2D energy consumption.The comparison is attributed to Jensen’s inequality and the distribution of total storage capacity across users.
  • Popularity distribution: When file popularity becomes more skewed, MBS energy consumption is dramatically reduced because repeated file requests become more likely.For γ = 0, PDCA outperforms LRU and LCA, while the policies’ performance crossing shifts with the scenario and number of users.
  • Economic incentives: As the incentive per D2D-transmitted data increases, D2D usage eventually falls until the MBS serves all traffic at very large incentive values.The economic cost includes both the MBS electricity bill and incentives paid to users.

V. CONCLUSIONS

The paper jointly optimizes transmission and caching for SBS and D2D scenarios, identifying pre-downloading and local caching gains. It obtains substantial energy savings and shows that the dominant gain depends on file-popularity skew.

  • Jointly designing transmission and caching reduces a generic transmission cost in both SBS-cache and user-terminal D2D scenarios.The formulation covers energy, bandwidth, or traffic costs, while the numerical evaluation focuses on MBS energy consumption.
  • 53%+ energy savings are achieved when cache capacity is only 25% of one user’s average traffic.This result is reported for minimizing energy consumption at the MBS.
  • Pre-downloading gain exceeds local caching gain under uniform file popularity, whereas local caching gain is greater for skewed popularity.The comparison concerns the two caching gains enabled by joint policy design.
  • The optimal offline policies provide a lower bound for evaluating online policies, and LRU performs far from optimal because it omits pre-downloading gain.The paper motivates online methods using partial future-request knowledge or learned daily behaviors.

APPENDIX

The appendix relaxes the original problem to slot-transition constraints and proves that a constant-rate caching policy is optimal. The resulting transmission and caching pair is feasible and optimal for the original problem as well.

  • Relaxed problem: The relaxed problem enforces data-departure constraints only at slot transitions while retaining nonnegative transmission and bounded caching constraints.The transition times are t = nT_s, and the relaxed constraints specify bounds a_n and b_n for data departure.
  • Relaxed problem: The transition values a_n and b_n are known, and any caching policy satisfying the relaxed caching constraints is optimal to the relaxed problem.The appendix states that these values are known and that policies satisfying (9d)-(9e) share optimality for the relaxed formulation.
  • Relaxed problem: The relaxed problem’s optimal departure curve is piece-wise linear and is obtained as the tightest string between the prescribed endpoints.The construction follows from the convexity of the cost function and an integral form of Jensen’s inequality.
  • Optimal caching policy: Figure 10 represents the relaxed problem’s formulation and graphical solution.The figure is identified as a representation of the relaxed problem in (9).
  • Optimal caching policy: Constant-rate caching c⋆ satisfies the relaxed constraints, and its associated maximum and minimum departure curves are piece-wise linear.The curves satisfy A(t,c⋆) = ¯A(t) ≤ D(t,¯r⋆) ≤ ¯B(t) = B(t,c⋆) over the considered interval.
  • Optimal caching policy: The pair {¯r⋆, c⋆} is optimal for the relaxed problem and also feasible and optimal for the original problem.Its feasibility for the original problem follows because it satisfies the constraints relaxed in the first formulation, with the same objective value.
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