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Green 5G Heterogeneous Networks through Dynamic Small-Cell Operation

Shijie Cai, Yueling Che, Lingjie Duan, Jing Wang, Shidong Zhou, Rui Zhang

arXiv:1601.01453v2cs.ITmath.IT

TL;DR

Massive small-cell deployments can increase total 5G power consumption, motivating dynamic SBS operation to reduce HetNet power. The paper proposes location-based and joint location-and-density-based schemes, reporting less than 1% performance loss versus the optimal operation for the latter.

  • Problem

    Massive small-cell deployment can increase total 5G power consumption, making HetNet power minimization an important research problem.

    Source: §I · p. 2

  • Method

    The paper dynamically changes SBS on/off states while keeping the MBS active, using distance-based deactivation for uniform users and joint location-and-density decisions for nonuniform users.

    Source: A. Network Model · p. 5, §VI · p. 24

  • Results

    Less than 1% performance loss versus the optimal one is reported for the proposed operation algorithm.

    Source: §I · p. 3

  • Takeaways & Limitations

    The proposed small-cell operation scheme can save total HetNet power consumption.

    Source: §I · p. 3

Abstract

from arXiv · show

Traditional macro-cell networks are experiencing an upsurge of data traffic, and small-cells are deployed to help offload the traffic from macro-cells. Given the massive deployment of small-cells in a macro-cell, the aggregate power consumption of small-cells (though being low individually) can be larger than that of the macro-cell. Compared to the macro-cell base station (MBS) whose power consumption increases significantly with its traffic load, the power consumption of a small-cell base station (SBS) is relatively flat and independent of its load. To reduce the total power consumption of the heterogeneous networks (HetNets), we dynamically change the operating states (on and off) of the SBSs, while keeping the MBS on to avoid any service failure outside active small-cells. First, we consider that the wireless users are uniformly distributed in the network, and propose an optimal location-based operation scheme by gradually turning off the SBSs closer to the MBS. We then extend the operation problem to a more general case where users are non-uniformly distributed in the network. Although this problem is NP-hard, we propose a joint location and user density based operation scheme to achieve near-optimum (with less than 1\% performance loss in our simulations) in polynomial time.

I. INTRODUCTION

The paper studies dynamic SBS on/off operation to minimize total HetNet power and proposes schemes for uniformly and non-uniformly distributed users.

I. INTRODUCTION

  • Because MBS power rises with load while SBS power is nearly load-independent, offloading can save MBS power but increase aggregate SBS power.The paper notes that massive small-cell deployment can increase total HetNet power.Source: §I · p. 2
  • The paper optimizes SBS on/off states to minimize total HetNet power while meeting users’ service requirements, keeping the MBS active for seamless coverage.The MBS remains on to avoid service failure outside active small-cells.Source: §I · p. 2
  • For uniformly distributed users, an optimal location-based algorithm minimizes power by selecting SBS operation states according to their distance from the MBS.The uniform case assumes identical user densities in small-cells and the macro-cell.Source: §I · p. 3
  • For non-uniform users, the power-minimization problem is NP-hard; a location-and-density-based algorithm finds a near-optimal SBS configuration in polynomial time.The user density varies across small-cells and the macro-cell.Source: §I · p. 3
  • The proposed scheme incurs less than 1% performance loss versus optimal, saves more total HetNet power than two benchmarks, and can lower MBS power as traffic rises.The benchmarks are no SBS on/off adaptation and probability-based SBS adaptation.Source: §I · p. 3
  • Earlier work overlooked small-cell operation’s effect on total HetNet power; small-cell-only studies – also did not account for users needing macro-cell service after deactivation.The paper therefore considers both cell types’ power patterns and load balancing.Source: §I · p. 4

II. SYSTEM MODEL · A. Network Model · B. Power Consumption Models

The system model represents a single macro-cell with dynamically switchable small-cells and combines user assignment with load-dependent MBS and load-independent SBS power models to define HetNet consumption.

II. SYSTEM MODEL

  • The two-tier HetNet places M SBSs within one macro-cell and switches their operation to offload MBS traffic and save aggregate network power.Source: §II · p. 5

A. Network Model

  • Each SBS is centered in a radius-Rs coverage area within the MBS’s radius-R0 area, with R0 > Rs > 0.The MBS is located at the origin, and each SBS location xm lies within the macro-cell.Source: A. Network Model · p. 5
  • Each SBS is either active to serve offloaded data or sleeping to save power, while the MBS stays active for seamless control coverage and to avoid service failure.Users in active small-cells are served by their SBSs, while users outside them are served by the MBS.Source: A. Network Model · pp. 5–6
  • The model assigns separate carriers to the MBS and SBSs and assumes active-SBS interference is controlled for QoS; a shared-spectrum extension would require MBS–SBS interference control.Source: A. Network Model · p. 6
  • Independent homogeneous PPPs model users in each SBS coverage area with density λm and in the MBS coverage area with density λ0.These assumptions make users uniform within each area but allow their densities to differ across areas.Source: A. Network Model · p. 6
  • The user model permits non-identical densities across cells, including hotspots, while the access rule serves all users through active SBSs or the MBS.Source: A. Network Model · p. 6

B. Power Consumption Models

  • The total-power model sums active-SBS consumption and MBS consumption, whose transmit power depends on the MBS traffic load and SBS operation modes.The number of active small-cells is determined by the SBS mode vector.Source: B. Power Consumption Models · p. 7
  • In a practical macro-cell containing hundreds or thousands of small cells, 100 active SBSs consume more power than an MBS; SBS active and sleeping powers are modeled as load-independent constants, typically 10W and 3W.Source: B. Power Consumption Models · p. 7

C. Derivation of MBS Transmit Power P t(θ) · 1) MBS Transmit Power to Each Individual User:

For a given SBS operation mode, the section derives the MBS transmit power by determining the power needed for each user’s QoS and aggregating over users. The resulting power is expressed as a product of traffic and power-efficiency factors.

C. Derivation of MBS Transmit Power P t(θ)

1) MBS Transmit Power to Each Individual User:

  • A user’s QoS is met when the probability its rate falls below b bits/sec is at most ε; equal bandwidth sharing assigns each of K users W/K.The derivation uses Shannon’s formula and the outage threshold to find the minimum received power, then inversely obtains the required transmit power.Source: 1) MBS Transmit Power to Each… · p. 8
  • Equal bandwidth sharing is used for simplicity, while the analysis can also be applied similarly to unequal bandwidth sharing.The passage gives the unequal-bandwidth-sharing scheme in as an example.Source: 1) MBS Transmit Power to Each… · p. 8
  • The required transmit power for an individual user increases with its distance from the MBS and with the number of users K.The channel model includes distance-dependent path loss with exponent α, a fixed loss D below reference distance r0, and independent unit-mean exponential Rayleigh fading.Source: 1) MBS Transmit Power to Each… · pp. 8–9
  • Under the PPP user-location model, the number of macro-cell users K is Poisson with mean equal to the average users in the MBS coverage area, and user distances are i.i.d. given K.Summing individual-user powers and taking expectations over K and the distances yields the total MBS power for operation mode θ.Source: 1) MBS Transmit Power to Each… · p. 9
  • The derivation obtains an explicit expression for total MBS transmit power by evaluating the expected individual-user power under the Poisson user count.The expectation over user distances is evaluated for fixed K before taking the outer expectation over K.Source: 1) MBS Transmit Power to Each… · p. 9
  • The MBS transmit power is the product of a traffic factor for the area outside active small-cells and a power-efficiency factor representing average transmit power per user.The traffic factor grows exponentially with MBS traffic load, motivating SBS activation to offload traffic while accounting for SBS power consumption.Source: 1) MBS Transmit Power to Each… · pp. 9–10

III. SMALL-CELL DYNAMIC OPERATION FOR UNIFORMLY DISTRIBUTED USERS · A. Problem Formulation for Uniformly Distributed Users · B. Optimal Operation Modes of SBSs

For uniformly distributed users, the section formulates HetNet power minimization through dynamic SBS on/off operation and develops a location-based solution. It also examines how user density affects the operation decision.

III. SMALL-CELL DYNAMIC OPERATION FOR UNIFORMLY DISTRIBUTED USERS

  • The section assumes identical user density across the macro-cell and all small-cells, and examines user density’s impact on SBS operation decisions.It specifically notes that the trend of threshold m1 is studied in relation to macro-cell user density.Source: §III · p. 10, B. Optimal Operation Modes of SBSs · p. 13

A. Problem Formulation for Uniformly Distributed Users

  • The objective is to minimize total power consumed by the MBS and all SBSs, subject to a maximum allowable MBS transmit-power level.The formulation derives the uniform-user power expressions by setting λ0 = λ1 = · · · = λM.Source: A. Problem Formulation for Uniformly… · pp. 10–11
  • If traffic exceeds what the MBS can support even with all SBSs active, the problem is infeasible; admission control is mentioned but its details are out of scope.Admission control would allow only users for whom the MBS required transmit power remains within its maximum.Source: A. Problem Formulation for Uniformly… · p. 11
  • The location-based policy turns off SBSs in order of increasing distance from the MBS, avoiding an exhaustive search over 2^M operation combinations.The formulation proposes this gradual deactivation method to avoid computational complexity that grows exponentially with the number of SBSs.Source: B. Optimal Operation Modes of SBSs · p. 11, A. Problem Formulation for Uniformly… · p. 11

B. Optimal Operation Modes of SBSs

  • Under the optimal operation mode, if an SBS is turned off, every SBS closer to the MBS is also turned off.This ordering follows because the MBS consumes less power serving users in small-cells closer to it.Source: B. Optimal Operation Modes of SBSs · p. 12
  • Turning off each successive SBS saves a constant Δp at that SBS, while the resulting MBS power increase grows with the SBS index in distance order.Deactivation stops when the next SBS offers no net power saving, or when the MBS transmit-power limit is reached.Source: B. Optimal Operation Modes of SBSs · p. 12
  • With SBSs sorted from nearest to farthest, the location-based algorithm gradually deactivates them and has computational complexity that increases linearly with the number of SBSs.The algorithm returns the operation modes subject to the stopping thresholds.Source: B. Optimal Operation Modes of SBSs · pp. 12–13

C. Impact of User Density in Small-Cell Operation

Under uniformly distributed users with no transmit-power constraint, the section establishes macro-user density thresholds that determine whether all SBSs are off or all are on. It also examines how network conditions affect these thresholds and the desirability of using small-cells.

IV. SMALL-CELL DYNAMIC OPERATION FOR NON-UNIFORMLY DISTRIBUTED USERS · A. Problem Formulation for Non-Uniformly Distributed Users · B. Computation Complexity of Problem (P2)

The section extends small-cell operation to non-uniform user densities, formulating a power-minimization problem that accounts for both SBS locations and coverage-area densities. It shows the problem is NP-hard and motivates an efficient suboptimal approach.

A. Problem Formulation for Non-Uniformly Distributed Users

  • (P2) minimizes total HetNet power using the MBS transmit power T(θ)Z(θ), subject to the MBS transmit-power constraint T(θ)Z(θ) ≤ P_t^max.The paper names this formulation problem (P2).Source: A. Problem Formulation for… · p. 15
  • Unlike (P1), (P2) depends on both SBS distances to the MBS and user densities in their coverage areas, so Proposition 1 no longer holds.The non-uniform case is therefore more difficult to solve optimally than (P1).Source: A. Problem Formulation for… · p. 15

IV. SMALL-CELL DYNAMIC OPERATION FOR NON-UNIFORMLY DISTRIBUTED USERS

  • For non-uniform user distributions, the proposed efficient suboptimal method jointly considers SBS distances to the MBS and coverage-area user densities.The section introduces the method for solving the problem sub-optimally in general.Source: A. Problem Formulation for… · p. 15, §IV · p. 15

B. Computation Complexity of Problem (P2)

C. Dynamic Operations of SBSs under Special Cases · D. Dynamic Operations of SBSs for General Case

The special cases assign optimal SBS on/off modes according to user-density thresholds; for the general case, Algorithm 2 combines location and density to select SBS operation modes.

C. Dynamic Operations of SBSs under Special Cases

D. Dynamic Operations of SBSs for General Case

V. SIMULATION RESULTS · A. Near-Optimal Performance of Algorithm 2

For non-uniform user distributions, simulations show Algorithm 2 incurs less than 1% performance loss relative to the optimum across macro-cell user densities; similar performance is reported for Algorithm 1 with uniform users.

V. SIMULATION RESULTS

  • The simulations focus on the general case of non-uniformly distributed users and evaluate Algorithm 2; the MBS maximum power is set to 40 W [5].Source: §V · p. 20
  • For uniformly distributed users, Algorithm 1 is reported to have similar performance, so its results are omitted for brevity.Source: §V · p. 20
  • The planned scheme comparisons include SBS operation without on/off adaptation and probability-based SBS on/off adaptation.The section also says it will examine the individual power consumption of the MBS and SBSs; no comparison outcomes are supplied here.Source: §V · pp. 20–21

A. Near-Optimal Performance of Algorithm 2

B. Comparison with Benchmark Schemes · C. Power Consumption of MBS and All SBSs · VI. CONCLUSION

Dynamic SBS operation reduces HetNet power while preserving the MBS, with decisions based on SBS location for uniformly distributed users and on location and user density for non-uniform users. The paper also compares the proposed scheme with benchmarks and examines how MBS and SBS power change with macro-cell user density.

B. Comparison with Benchmark Schemes

C. Power Consumption of MBS and All SBSs

VI. CONCLUSION

  • For uniformly distributed users, optimal SBS operation is found by gradually deactivating SBSs according to their distance from the MBS.Source: §VI · p. 24
  • For non-uniform users, optimal operation is NP-hard, while the proposed near-optimal algorithm considers SBS locations and small-cell user density and has polynomial complexity.Source: §VI · p. 24
  • Future work would extend the single-macro-cell scenario to multiple macro-cells while accounting for interference from neighboring macro-cells.Source: §VI · p. 24

APPENDIX A PROOF OF THEOREM 1 · APPENDIX B PROOF OF PROPOSITION 1 · APPENDIX C PROOF OF LEMMA 1

The appendices derive Theorem 1’s transmit-power factorization, prove Proposition 1’s optimal distance ordering, and establish increasing successive power increments in Lemma 1.

APPENDIX A PROOF OF THEOREM 1

  • The expectation derivation assumes users are independently distributed and uniform within each area A_n.It averages over possible user locations and then over the Poisson-distributed user count K.Source: Appendix A · p. 24
  • Substituting (5) and (23) into (6), and using K’s Poisson mean μ = λ₀∥A₀∥ + Σ_{m:θₘ=0} λₘ∥Aₘ∥, yields Pₜ(θ) = Z(θ) · T(θ).Source: Appendix A · p. 24

APPENDIX B PROOF OF PROPOSITION 1

  • Proposition 1 rules out an optimal state that turns off a farther SBS m while keeping a closer SBS n on, where d_n < d_m.Swapping their states preserves T, lowers Z, and therefore lowers P_Het, contradicting optimality.Source: Appendix B · p. 25

APPENDIX C PROOF OF LEMMA 1

  • Lemma 1’s proof establishes h1(m) − h1(m − 1) > h1(m − 1) − h1(m − 2) > 0.It uses that h1 is increasing and convex.Source: Appendix C · p. 25
  • The proof also establishes h2(m) − h2(m − 1) ≥ h2(m − 1) − h2(m − 2) > 0.Source: Appendix C · p. 25
  • Combining the two facts yields ΔP_m > ΔP_{m−1}, the successive transmit-power increment inequality concluding Lemma 1.Source: Appendix C · p. 26

APPENDIX D PROOF OF THEOREM 2 · APPENDIX E PROOF OF PROPOSITION 2 · APPENDIX F PROOF OF COROLLARY 1

The appendices prove that optimal SBS deactivation proceeds from cells closer to the MBS, that at least one SBS remains active in the stated λ0 > λoff case, and that Corollary 1’s parameter properties follow from monotonicity arguments.

APPENDIX D PROOF OF THEOREM 2

  • The proof rules out stopping before m1 in Case 1 because further deactivation saves power, and stopping beyond m1 is not optimal.Source: Appendix D · p. 26
  • Theorem 2’s proof identifies the optimal stopping index as m1 or m2 across its two cases, so closer small-cells are deactivated first.The proof concludes that deactivation continues until the corresponding stopping index is reached.Source: Appendix D · p. 26

APPENDIX E PROOF OF PROPOSITION 2

  • The threshold in Proposition 2 can be obtained through bisection search.Source: Appendix E · p. 26
  • When λ0 > λoff, closing all SBSs is not optimal, so at least one SBS should remain active.Source: Appendix E · p. 27

APPENDIX F PROOF OF COROLLARY 1

  • The function h3 decreases with b and N0, and increases with ε.Source: Appendix F · p. 27
  • For W > 0, h4(W) and h5(W) have negative first derivatives; combined with (28), these results establish Corollary 1’s properties.Source: Appendix F · pp. 27–28

APPENDIX G PROOF OF PROPOSITION 4

The proof establishes a density-threshold rule for SBS operation: below the threshold, deactivating the SBS reduces HetNet power regardless of other SBS modes, and the high-density case follows by a similar argument.

APPENDIX G PROOF OF PROPOSITION 4

  • The threshold λoff_th(m) exists uniquely and can be found by bisection search.Source: Appendix G · p. 28
  • When λ_m < λoff_th(m), SBS m should always be turned off, regardless of the operation modes of other SBSs.The proof concludes that deactivation reduces HetNet power consumption.Source: Appendix G · p. 28
  • The high-user-density case is proved using a similar method to the low-density case and is omitted for brevity.Source: Appendix G · p. 28
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