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Energy Efficiency of Downlink Networks with Caching at Base Stations

Dong Liu, Chenyang Yang

arXiv:1505.06615v3cs.ITcs.NI

TL;DR

The paper asks whether caching popular contents at base stations improves energy efficiency despite cache-power costs and interacting network factors. It derives an approximated closed-form energy-efficiency model and analyzes cache capacity and key operating conditions. The results show that caching can improve energy efficiency with power-efficient cache hardware, but more cached content need not yield higher efficiency, with larger gains under stringent backhaul, low interference, skewed popularity, and pico-base-station caching.

  • Problem

    Whether local base-station caching improves energy efficiency, and which network and caching factors determine its gain, remains unclear.

  • Method

    The paper derives a closed-form approximation of energy efficiency and analyzes caching conditions, cache capacity, and gain under varying network factors.

  • Results

    Caching can improve energy efficiency with power-efficient cache hardware, but increasing cached content does not necessarily increase efficiency; gains are larger with stringent backhaul, low interference, skewed popularity, and pico-base-station caching.

  • Takeaways & Limitations

    Energy-efficiency gains from caching arise from increased throughput, reduced backhaul consumption, and exploiting content popularity when backhaul capacity is limited.

Abstract

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Caching popular contents at base stations (BSs) can reduce the backhaul cost and improve the network throughput. Yet whether locally caching at the BSs can improve the energy efficiency (EE), a major goal for 5th generation cellular networks, remains unclear. Due to the entangled impact of various factors on EE such as interference level, backhaul capacity, BS density, power consumption parameters, BS sleeping, content popularity and cache capacity, another important question is what are the key factors that contribute more to the EE gain from caching. In this paper, we attempt to explore the potential of EE of the cache-enabled wireless access networks and identify the key factors. By deriving closed-form expression of the approximated EE, we provide the condition when the EE can benefit from caching, find the optimal cache capacity that maximizes the network EE, and analyze the maximal EE gain brought by caching. We show that caching at the BSs can improve the network EE when power efficient cache hardware is used. When local caching has EE gain over not caching, caching more contents at the BSs may not provide higher EE. Numerical and simulation results show that the caching EE gain is large when the backhaul capacity is stringent, interference level is low, content popularity is skewed, and when caching at pico BSs instead of macro BSs.

I. INTRODUCTION

The paper examines whether caching popular contents at base stations improves energy efficiency in wireless access networks and identifies the factors governing any gain. It develops an analytical framework that accounts for caching, backhaul, interference, deployment, and demand characteristics.

  • Motivation: Caching at base stations may reduce backhaul cost and energy consumption, but its energy-efficiency benefit remains uncertain because caching also consumes power.The paper highlights the tension between edge caching and cache hardware consumption.
  • Research questions: The study asks whether base-station caching provides an energy-efficiency gain, under what conditions, and how cache size affects network energy efficiency.It also investigates whether cache capacity should be optimized rather than simply increased.
  • Approach: The analysis optimizes cache placement, cache capacity, and each base station’s maximal transmit power using user-demand statistics under different interference levels.Caching is assumed to be placed during off-peak broadcasting, so delivery energy is analyzed while cache-placement energy is ignored.
  • Approach: The paper derives a closed-form approximation of energy efficiency that includes base-station transmit, circuit, backhaul, and caching power consumption.The model uses a simple scenario with circular cells, equal-size contents, static popularity, homogeneous user distribution, and nearest-base-station association.
  • Contributions: The analysis identifies conditions for caching gains, an energy-efficiency-maximizing cache capacity, and the maximum gain achievable through caching.The cache policy stores the most popular contents at each base station under the stated static-demand assumptions.
  • Findings: Caching at base stations may not improve network energy efficiency, and increasing cached content does not necessarily increase energy efficiency when caching is beneficial.The paper also reports higher caching gains at pico base stations than at macro base stations.

III. EE OF THE CACHE-ENABLED NETWORK

The paper defines network energy efficiency as throughput divided by total base-station power, then derives average throughput by separating cache-hit and cache-miss traffic. Approximations are introduced to obtain a tractable closed-form expression.

  • Energy-efficiency formulation: Network energy efficiency is defined as the ratio of average network throughput to average total power consumed at the base stations.Expectations account for small-scale fading, user locations, and the number of users.
  • Energy-efficiency formulation: The derivation first obtains average throughput and average total power consumption, whose ratio gives network energy efficiency.The throughput calculation uses the common configuration and caching strategy across base stations.
  • Throughput derivation: Average cell throughput is conditioned on the number of served users and cache-hit users, combining cache-hit and cache-miss average sum rates.The joint probability is decomposed into the user-count probability and the conditional cache-hit probability.
  • Throughput derivation: The cache-hit probability is determined by the fraction of requested contents stored in the local base-station cache.Under the model, cache-hit users obtain requested contents locally while cache-miss users contribute to backhaul traffic.
  • Throughput approximation: Closed-form approximations are derived for cache-hit and cache-miss average rates to support further energy-efficiency analysis.The cache-hit approximation is stated to be accurate when both SINR and λ/N_b are high, while another approximation is accurate in a high-SINR regime when λ/N_b is high and N_t, N_b →∞.
  • Throughput approximation: The resulting network-throughput expression combines the two approximate rates with the user-count and cache-hit probabilities.The expression uses the approximations for cache-hit and cache-miss rates together with their corresponding conditional probabilities.

B. Average Total Power Consumption

The power model extends a conventional base-station consumption model with caching and backhaul terms. Total power includes transmit, circuit, caching, and backhaul consumption, with active and idle base stations treated separately.

  • Power model: The total power consumed at each base station includes transmit, circuit, caching, and backhaul power.The model extends a standard base-station power model to account for caching.
  • Transmit and circuit power: Active base stations transmit with power P and use active circuit power, whereas idle base stations transmit no power and use idle circuit power.The number of active base stations follows a Binomial distribution under independent activity assumptions.
  • Caching power: Caching power is modeled as proportional to cache capacity through an energy-proportional hardware coefficient.For fixed cached content size, increasing the number of cached contents increases caching power.
  • Backhaul power: Backhaul power depends on the supported backhaul rate and the cache-miss traffic carried by the backhaul.Cache misses contribute to backhaul traffic and therefore to average backhaul power consumption.
  • Average power: Average total power consumption is obtained by averaging the modeled power terms over user counts and cache-hit counts.The resulting expression uses the same probability structure applied in the throughput derivation.

C. EE of the Network

The paper derives and analyzes an approximated closed-form network EE to determine when BS caching helps and how cache capacity affects EE. Caching can have an optimal finite capacity because cache power and backhaul savings trade off, with outcomes depending on system parameters.

  • EE model: The approximated network EE is obtained in closed form from average throughput and power-consumption expressions.The power terms include transmission and circuit, caching, and backhauling consumption.
  • Caching condition: Caching improves EE only when the condition in (27) holds; otherwise, caching cannot improve EE.The condition follows from comparing the energy-efficiency effect of caching one content and extends to larger cache sizes.
  • Backhaul capacity: When backhaul capacity is zero, BS caching always improves network EE, whereas unlimited backhaul reduces the benefit to a condition involving system parameters.The limiting cases expose how backhaul capacity affects whether caching is energy efficient.
  • Cache capacity: For normalized cache capacity η, EE increases and then decreases when η0 < 1, but is maximized by caching the entire catalog when η0 ≥ 1.The EE-maximal capacity is η∗ = η0 for η0 < 1 and η∗ = 1 otherwise.
  • Cache capacity: The EE-memory tradeoff reflects caching power increasing with η while backhauling power decreases first rapidly and then slowly.Thus, the optimal cache size depends on the tradeoff between backhauling and caching powers.
  • Parameter effects: The optimal normalized cache capacity increases with transmit and circuit power and backhaul power coefficient, but decreases with content size and cache power coefficient.It also increases as the catalog size decreases.

1) An Extreme Case of Cbh

In the unlimited-backhaul case, the paper examines how density, hardware, interference, and catalog characteristics shape caching’s EE benefits. Denser networks should cache less per BS but more in aggregate, while low interference and favorable hardware enlarge the benefit or tradeoff region.

  • Catalog size: The EE-memory tradeoff exists when the catalog size is no greater than the threshold Nth in the unlimited-backhaul case.This statement applies under the condition η0 ≥ 1.
  • Interference: When average cell-edge SNR is high, interference level β dominates the cache-delivery rate; reducing interference increases the catalog-size threshold for an EE-memory tradeoff.The tradeoff can therefore persist even for a large content catalog.
  • Network density: As network density increases over a fixed coverage area, the EE-optimal cache fraction decreases per BS while total network cache capacity increases.The result is stated for Cbh → ∞ and λ Nb → 0.
  • Network density: A pico BS should cache fewer contents than a macro BS to achieve maximal EE.The paper attributes this implication to the dependence of η0 on antenna number and transmit power.
  • EE gain: The maximal EE gain from caching increases with cache-hit rate and cache-delivery rate, and is higher when backhaul power is a larger share of power without caching.This explains why pico-BS caching may yield higher EE gain than macro-BS caching.

B. Relation Between Network EE and Transmit Power

Network EE depends on transmit power, backhaul capacity, and cache-related power consumption. In interference-limited networks EE decreases with transmit power, while in noise-limited networks it is unimodal and has an optimal transmit power.

  • EE decreases with transmit power when backhaul capacity is unlimited and the network is interference limited.
  • In noise-limited networks with unlimited backhaul capacity, EE first increases and then decreases with transmit power.
  • The transmit power maximizing EE should increase with cache capacity.
  • The approximation is not jointly concave in cache capacity and transmit power, so separate unimodality does not guarantee joint optimality.Numerical results show the candidate point is jointly optimal in the considered setup.
  • When backhaul capacity is limited, throughput and memory face a tradeoff, while caching EE gains depend on backhaul capacity and cache and backhaul power parameters.With unlimited backhaul, caching trades backhaul power against cache power; with limited backhaul, gains also include throughput increases.
  • For small content catalogs, EE and memory trade off; otherwise, each BS cache size should be optimized for network EE.

V. NUMERICAL AND SIMULATION RESULTS

The numerical and simulation results validate the approximations and examine how backhaul capacity, cache capacity, interference, and content updates affect throughput and EE. Throughput rises with both backhaul and cache capacity, with caching more effective when interference is low.

  • The simulations use a hexagonal region with radius 250 m and three pico-cell tiers to evaluate interference effects.
  • When Nc = 10^3, content-update energy is below 3% of total energy for u = 10% and T = 12 hours.
  • A. Validation of the Analysis: Simulation and numerical results almost overlap for the approximation involving β, especially when λ/Nb is high.The approximation is reported as accurate across β ∈ [0, 1].
  • A. Validation of the Analysis: Simulation and numerical results for average throughput versus backhaul capacity almost overlap, validating the throughput approximation even with Nt = 4 and Nb = 37.
  • A. Validation of the Analysis: Throughput increases with both backhaul capacity and cache capacity, and cache capacity has a sharper effect when β is small.This indicates that caching boosts throughput more efficiently when inter-cell interference is reduced.

B. When EE Benefits from Caching?

Caching improves energy efficiency only under favorable hardware and network conditions, and its benefit depends non-monotonically on cache capacity. The largest gains occur with stringent backhaul, low interference, skewed popularity, and pico-BS deployment.

  • When EE Benefits from Caching?: EE may not benefit from BS caching when cache power consumption is high relative to backhaul power consumption.With the same NfF, the condition is more prone to fail when content size F is larger.
  • Impact of Cache Capacity: 575% and 250% are the maximal EE gains over not caching for Nf = 5000 when β = 0 and β = 1, respectively.For larger catalogs, EE first increases and then decreases with normalized cache capacity.
  • Impact of Content Popularity: 350% is the EE gain from optimized caching over not caching when content popularity skew is δ = 1.The optimal cache capacity decreases as δ increases, while EE at a fixed cache capacity increases with δ.
  • Impact of User Density: 230% is the EE gain from caching when the user-density-to-BS-density ratio is around one.EE eventually saturates as throughput becomes limited by inter-cell interference, but it increases more sharply when caching is enabled.
  • Where to Cache: Pico networks achieve higher EE than macro networks because caching relieves pico backhaul congestion while backhaul power is a large energy component.Under β = 1, pico throughput increases with cache capacity while macro throughput does not; under β = 0, both increase with cache capacity.
  • User Association: Distributed caching raises EE when β = 0 but lowers it when β = 1 because users may associate with non-nearest BSs that create stronger interference.With shadowing, EE is slightly lower but the main EE-cache relationship remains unchanged.

APPENDIX A PROOF OF LEMMA 1

The appendix approximates average achievable rates under noise-limited and interference-limited regimes, using distributional assumptions and asymptotic approximations. These approximations support the rate expression used in the analysis.

  • Rate approximation: The approximation uses Gamma-distributed beamforming gains and a uniform-user distance distribution.The channel gain follows G(N_t−K_b+1, 1), while the user-distance term is characterized through its probability density function.
  • Approximation conditions: The high-SINR approximation omits the term 1 inside the logarithm, while the Digamma function is approximated by ln n.The Digamma approximation is stated to be accurate when N_t−K_b+1 > 1.
  • Rate approximation: The derivation treats noise-limited and interference-limited networks separately according to the relative interference and noise powers.The noise-limited case assumes βPI_k ≪ σ^2, whereas the interference-limited case assumes βPI_k ≫ σ^2.
  • Validation: Simulations in Section V-A show that the approximation in (A.5) is accurate for all β ∈ [0, 1].
  • Rate interpretation: The resulting expression treats R̄_e(K_b) as the average achievable rate of a cell-edge user with unlimited backhaul capacity.This rate corresponds to a base station serving K_b users.

APPENDIX B PROOF OF THE CONSTANT Φ WHEN Nb →∞

The appendix shows that the interference constant Φ depends on the path-loss exponent and the number of base stations, not the cell radius, and converges as network density grows. It also establishes a large-network approximation for comparing cache-miss rates with backhaul capacity.

  • Dependence of Φ: After coordinate normalization and averaging over small-scale fading, Φ depends only on α and N_b, not on the cell radius D.
  • Large-network behavior: For α > 2, Φ increases with N_b and converges as N_b →∞, so it has an upper bound.
  • Cache-miss rate: The derivation uses exponential channel-power variables whose sum over cache-miss users follows G(K_b−K_c, 1).
  • Backhaul comparison: For large N_b, the local-BS distance r_kb dominates the comparison between aggregate cache-miss rate and C_bh.
  • Validation: The resulting approximation is reported to be accurate through simulations in Section V-A.
  • Backhaul comparison: When C_bh ≤ (K_b−K_c)R̄_e(K_b), the throughput expression switches between the cache-miss transmission rate and the backhaul capacity.
  • Large-network behavior: When interference powers are i.i.d., the aggregate interference per base station approaches N_bE{I_k} as N_b grows.This follows from the law of large numbers.
  • Proof conclusion: Combining the derived cases proves Lemma 2.

APPENDIX D PROOF OF PROPOSITION 1

The appendix proves the condition for caching to improve energy efficiency by comparing the no-cache baseline with caching. It shows that failure to gain EE from one cached content implies failure for any larger cache size.

  • Baseline comparison: The no-caching energy efficiency is obtained by setting N_c=0 and p_h=0 in the general EE expression.
  • Caching condition: If caching one content cannot improve EE, then caching any N_c > 1 contents cannot improve EE either.
  • Caching condition: Therefore, the derived inequality is the condition determining whether caching can increase network EE.
  • Proof conclusion: The proof obtains the proposition by rewriting the condition as equation (27).

APPENDIX F PROOF OF COROLLARY 4

The appendix analyzes how the EE threshold varies with base-station density and establishes the transmit power that maximizes network EE. The density results distinguish the threshold itself from its product with density.

  • Base-station density: With fixed area-related density scaling, the threshold η_0 decreases as N_b increases when α > 2.
  • Base-station density: The product η_0N_b increases with N_b under the same scaling.
  • Power model: The average circuit power is p_aP_cca+(1−p_a)P_cci, while the average cache power is w_caηN_fF.
  • Transmit power: The network EE increases below P_0 and decreases above P_0, making P_0 the optimal transmit power.
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