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Analysis on Cache-enabled Wireless Heterogeneous Networks

Chenchen Yang, Yao Yao, Zhiyong Chen, Bin Xia

arXiv:1508.02797v1cs.IT

TL;DR

Rapid wireless traffic growth motivates a cache-enabled three-tier HetNet that combines BS, relay, and D2D delivery. The paper models node locations as independent PPPs, analyzes access and queueing performance, and reports a 57.3% global throughput gain over no caching.

  • Problem

    Rapid wireless traffic growth and concentrated multimedia demand motivate caching popular content closer to users to reduce cellular traffic.

  • Method

    The paper models BSs, relays, and users as independent PPPs, develops a content-access protocol, and analyzes rates, outage, queueing, throughput, and delay.

  • Results

    57.3% global throughput gain is reported for the cache-enabled system compared with the system without caching ability.

  • Takeaways & Limitations

    Caching popular content at relays and cache-enabled users during off-peak periods enables reuse for frequent access and local D2D sharing.

Abstract

from arXiv · show

Caching the popular multimedia content is a promising way to unleash the ultimate potential of wireless networks. In this paper, we contribute to proposing and analyzing the cache-based content delivery in a three-tier heterogeneous network (HetNet), where base stations (BSs), relays and device-to-device (D2D) pairs are included. We advocate to proactively cache the popular contents in the relays and parts of the users with caching ability when the network is off-peak. The cached contents can be reused for frequent access to offload the cellular network traffic. The node locations are first modeled as mutually independent Poisson Point Processes (PPPs) and the corresponding content access protocol is developed. The average ergodic rate and outage probability in the downlink are then analyzed theoretically. We further derive the throughput and the delay based on the \emph{multiclass processor-sharing queue} model and the continuous-time Markov process. According to the critical condition of the steady state in the HetNet, the maximum traffic load and the global throughput gain are investigated. Moreover, impacts of some key network characteristics, e.g., the heterogeneity of multimedia contents, node densities and the limited caching capacities, on the system performance are elaborated to provide a valuable insight.

I. INTRODUCTION

Rapidly growing wireless traffic and concentrated multimedia demand motivate caching in heterogeneous networks, but prior models often rely on idealized topology or omit coexistence between RAN and D2D caching.

  • Motivation: Wireless traffic growth threatens the throughput gains that LTE-Advanced networks can afford.The paper cites a 1000-fold increase in 2020 mobile data traffic relative to 2010.
  • Motivation: HetNets increase capacity by deploying heterogeneous nodes closer to users, but their traffic growth requires high-speed backhaul connections.The cited infrastructure includes macro, micro, pico, femto BSs and relays.
  • Caching motivation: Multimedia traffic is highly concentrated: a small fraction of popular contents is consumed by most users.Caching these contents at BSs, relays, and devices can bring content closer and reduce duplicate transmissions.
  • Research gap: Prior caching research often assumes global topology knowledge or regular grids, which may not capture random HetNet node locations.The paper contrasts these assumptions with PPP-based models for realistic heterogeneous networks.
  • Research gap: Existing approaches also leave the coexistence of RAN caching and D2D caching insufficiently investigated in cooperative wireless HetNets.The paper identifies the theoretical performance improvement from caching as an open question.

B. Contributions

The paper proposes a three-tier cache-enabled HetNet with proactive caching at relays and some users, then develops analytical models for access, rate, outage, queueing performance, and steady-state traffic limits.

  • System and caching design: Popular multimedia contents are broadcast during off-peak periods to relays and cache-enabled users for later reuse.Cache-enabled users also provide local sharing links to requesting users.
  • System and caching design: The three-tier HetNet models BSs, relays, and users as mutually independent PPPs with different densities.Only part of the users has caching ability, and relay and user cache capacities are limited.
  • Analytical performance: The analysis derives average ergodic rates and outage probabilities for users in different access cases.The cases distinguish user caching ability and whether requested contents are locally cached or available through other tiers.
  • Traffic and queueing analysis: Multiclass processor-sharing queues and a continuous-time Markov process are used to analyze class-specific throughput and delay.The paper also defines a steady-state critical point to evaluate maximum traffic load and network throughput.
  • Performance factors: The study evaluates how cache-enabled users, content popularity, and limited storage capacity affect network performance.It includes both cellular and local D2D content delivery.
  • Content access protocol: Requests are served from local storage or the closest responding BS, relay, or cache-enabled user according to the access protocol.Relay service is classified as backhaul-free when the requested content is cached and backhaul-needed otherwise.

C. The Probability of the Tier Association Priority

The paper derives tier-association priorities from independent PPP node locations and received-power rankings, distinguishing users with and without caching ability.

  • Model: Node locations are modeled as mutually independent PPPs, and a reference user is placed at the origin for the association analysis.The analysis considers typical users with or without caching ability.
  • Users without caching: For users without caching ability, association priorities depend on the ordering of maximum received powers across tiers.The paper derives probabilities for each received-power ranking and first-associated tier.
  • Cache-enabled users: For cache-enabled users, the association probabilities change when the requested content is absent from local storage.Such users then select among the relay and BS tiers according to received-power ordering.
  • Association implication: Users prefer tiers with higher transmit power and node density, while caching ability changes the resulting tier-association priorities.The paper summarizes these probabilities for the three-tier network.

D. The Density of the Active D2D Transmitters

The active D2D transmitter density depends on which users can be served through local sharing, and a critical caching-user fraction separates regimes where D2D activity is limited by transmitters or requesting users.

  • Scope and state model: The model treats backhaul between BSs and relays as the relevant wired backhaul and excludes the multimedia-server-to-BS backhaul from scope.User states include the access case and whether backhaul is needed.
  • D2D density: The density of D2D-served users is determined by the probability of successful D2D access and the density of users without caching ability.The resulting active D2D transmitter density is λ0G3,1(1−α)F(1, M1).
  • Low caching-user fraction: When few users have caching ability, all cache-enabled users may need to operate as D2D transmitters to meet demand.In this regime, D2D link counts are limited by cache-enabled users.
  • High caching-user fraction: When many users have caching ability, some cache-enabled users serve no requester, so D2D activity is instead limited by non-caching users.Consequently, not all cache-enabled users are active transmitters.
  • Critical caching fraction: The critical point α* is jointly determined by user cache size, content popularity, transmit powers, node densities, and path-loss exponent.The paper reports that α* increases with M1, γ, and β.
  • Density maximum: Active D2D transmitter density increases with α up to bα and decreases thereafter, implying at most bα D2D links per unit area.This turning point follows from the derivative of the D2D transmitter-density expression.

III. THE AVERAGE ERGODIC RATE

The paper models downlink ergodic rate in a three-tier HetNet under Rayleigh fading, PPP-distributed nodes, tier association, and interference from BSs, relays, and D2D transmitters. Under interference-dominant conditions, caching and D2D activity create distinct rate regimes governed by the cache-enabled-user fraction.

  • Rate formulation: The average ergodic rate averages channel fading and PPP spatial randomness, first conditioning on serving distance and then averaging over that distance.The analyzed rate is measured in nats/s/Hz, with 1 nat equal to 1.443 bits.
  • Interference-dominant regime: When interference is dominant, Case 1's average ergodic rate is independent of the tier selected by the user.This follows from the simplified rate expressions under negligible noise.
  • Case 1 behavior: When α < α∗, Case 1's average ergodic rate remains constant as the cache-enabled-user fraction varies.All cache-enabled users are active as D2D transmitters in this region.
  • Case 1 behavior: Higher D2D-transmitter density brings cached content closer to users while adding interference, leaving the rate unchanged in the small-α regime.Increasing transmit power or service-node density likewise raises desired signal and interference by the same amount, so they offset.
  • Caching effects: For larger α, more users can obtain content through D2D links or local caches, changing the cache-enabled network's sum rate.The supplied passages describe this effect without providing a numerical sum-rate value.

B. The Average Ergodic Rate in Case 2

Case 2 analyzes ergodic rate when D2D transmission introduces additional interference. Its rate first decreases with the cache-enabled-user fraction, reaches a minimum at the critical point for active D2D transmitters, and then increases.

  • Case 2 comparison: Case 2's average ergodic rate is lower than Case 1's because D2D transmitters create additional unnecessary interference.The comparison is made between the corresponding average-rate expressions.
  • Rate versus α: The number of active D2D transmitters increases with α below bα and decreases monotonically when α ≥ bα.More active D2D transmitters produce unnecessary interference for Case 2 users.
  • Rate versus α: The rate decreases over [α∗, bα] because additional D2D activity increases interference, then rises after bα as fewer transmitters remain active.After bα, the balance between desired signal power and interference changes.
  • Parameter effects: Node density, content popularity, transmit power, path-loss parameter, and caching ability can all affect Case 2's rate trend.The passages do not specify the direction of each parameter's effect.
  • Local caching: Users reading directly from local caches do so immediately, and higher content popularity or caching ability raises their probability of being active in Case 4.The local-cache reading speed is described as extremely fast.

IV. THE OUTAGE PROBABILITY

The paper analyzes outage probability as the chance that a randomly located user's instantaneous SINR falls below a threshold. In interference-dominant conditions, outage is tier-independent, while unnecessary D2D interference worsens some cases.

  • Metric definition: Average outage probability is the SINR CDF over the network and equivalently the fraction of cell area below a specified SINR threshold.The threshold is denoted τ.
  • Theoretical analysis: Theorems 4, 5, and 6 establish average outage-probability expressions for users associated with the tiers and cases studied.The theorem statements cover Cases 1, 2, and 3, including interference-dominant specializations.
  • Interference-dominant regime: When interference is dominant, average outage probability is unaffected by which tier serves the user.This parallels the tier-independence result for average ergodic rate.
  • Case comparisons: For Case 1 with few cache-enabled users, transmit-power or node-density changes scale desired signal and interference together.The supplied text states this balance without giving a numerical outage value.
  • Case comparisons: Unnecessary D2D-transmitter interference worsens outage probability in Cases 2 and 3.Users served from local caching have outage probability P_l described as approximately zero because content is read immediately.

V. THE THROUGHPUT AND THE DELAY

The paper models requests in a typical HetNet cell using multiclass processor-sharing queues and a continuous-time Markov process to derive throughput, delay, and stability conditions. Stability requires each class's traffic demand to remain below its critical value, while local caching can provide extremely high throughput and near-zero delay.

  • Queueing model: Requests are organized into eight user classes according to caching, transmission, and association states, with class densities derived from matrix D.The class-state mapping is represented by g:(C,T,W)→(i,j).
  • Rate and backhaul: The service-rate matrix A uses the ergodic rates from Section III, bandwidth w, and a nat-to-bit conversion factor η = 1.443.Backhaul-served users instead use a rate f(Um,j) smaller than Um,j under the stated assumption.
  • Queueing model: Each service node is modeled as a multiclass processor-sharing queue with round-robin service and equal time portions.The queue includes BSs, relays, and cache-enabled users acting as service nodes.
  • Queueing model: The class-count process Xj(t) is represented as a continuous-time Markov process over the queue's discrete state space.The state records the number of requests in different classes at a service node.
  • Stability and capacity: The network is steady only when σj < σc,j for every queue class, and these critical conditions determine maximum load and throughput.Lower infrastructure densities increase users per service node and can cause queue congestion.
  • Caching benefit: Local caching yields extremely high throughput per request and zero delay because cached content is read immediately.This is represented by the extremely high service rate A7,4 = Ul.

VI. NUMERICAL RESULTS

Numerical results compare cache-enabled delivery with baseline behavior across association, rate, outage, queue, and throughput metrics. Caching and D2D access can offload BS and relay traffic, but interference and limited D2D coverage create operating trade-offs.

  • User association: Increasing content concentration raises D2D or local-cache access and increases cache-hit probability.More concentrated contents reduce requests reaching relays or BSs.
  • Average ergodic rate: Case 2 and Case 3 have lower rates than Case 1 because they receive no caching benefit but experience unnecessary D2D interference.With limited D2D transmit power and coverage, α∗=0 and bα=31.62% in the alternative setting.
  • Outage probability: Outage decreases with a lower SINR target, while Case 1 remains constant before α∗ and then decreases; Cases 2 and 3 have higher outage.For SINR = −10 dB, Case 2’s CDF is below Case 3’s at α=0.05 and approximately equal at α=0.1.
  • Queue and throughput: D2D TX throughput per request exceeds the baseline BS value by 46.8%-58.1%, while caching offloads BS and relay traffic.Some classes perform worse because D2D interference or wired-backhaul fetching affects service.
  • Network throughput: The BS queue determines the maximum network load, and throughput gain reaches 13.3% for γ=0.8 and 57.3% for γ=1.8 versus baseline.Relay and D2D steady rulers are smaller than the BS’s, while deployment in high-density areas and D2D access can improve cellular offloading.

VII. CONCLUSION

The paper models and evaluates cache-enabled content delivery in a three-tier HetNet with BSs, relays, and D2D links. It derives rate, outage, throughput, delay, and steady-state traffic-load measures, reporting a 57.3% global-throughput gain over a system without caching.

  • VII. CONCLUSION: Caching is available at relays and some users, with popular multimedia contents proactively broadcast during off-peak periods for later reuse.The network combines relay caching and D2D caching.
  • VII. CONCLUSION: Node locations are modeled as mutually independent PPPs, and users are classified into four cases according to caching ability and service-node type.Users can connect flexibly to cellular or D2D links under maximum received-power association.
  • VII. CONCLUSION: Average ergodic rates and downlink outage probabilities are theoretically analyzed for the different user cases.
  • VII. CONCLUSION: Throughput and delay are derived using a multiclass processor-sharing queue and a continuous-time Markov process.The resulting steady-state rule determines the maximum traffic load and throughput of the HetNet.
  • VII. CONCLUSION: 57.3% is the reported increase in global throughput for the cache-enabled system compared with the system without caching ability.

APPENDIX

The appendix develops probability and interference calculations supporting the paper's rate analysis. It derives joint distance distributions, association-related probabilities, Laplace transforms, and average ergodic-rate expressions.

  • APPENDIX: The appendix derives joint probability-density functions for distances from a reference user to multiple tiers or node classes.The derivations integrate over Euclidean regions defined by ordered association metrics.
  • APPENDIX: For a selected tier, the association probability requires its metric to exceed the corresponding metrics of all other tiers.The ordering among the other tiers need not be specified in this case.
  • APPENDIX: Laplace-transform and tail-probability steps are combined with SINR expressions to obtain the reference user's average ergodic rate.The derivation explicitly uses ln(1 + SINR_i(x)) and integrates the positive random-variable tail probability.
  • APPENDIX: The interference analysis uses mutually independent PPPs and the density of actually active nodes in each tier.The nearest interfering-node distance and Laplace transforms are introduced in the derivation.

F. Proof of Theorem 3

This proof section transforms the interference expressions for the relevant cases and uses them to derive the average outage probability. It concludes by establishing the stated theorem.

  • F. Proof of Theorem 3: The proof rewrites the relevant expression and derives Laplace transforms for interference from tiers 2 and 3.
  • F. Proof of Theorem 3: The resulting expressions are substituted into the outage formulation to obtain the average outage probability.
  • F. Proof of Theorem 3: The proof then invokes the theorem and completes the derivation.
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