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Base Station Sleeping and Resource Allocation in Renewable Energy Powered Cellular Networks

Jie Gong, John S. Thompson, Sheng Zhou, Zhisheng Niu

arXiv:1305.4996v1cs.IT

TL;DR

The paper addresses how cellular networks with energy-harvesting BSs can minimize average grid power while meeting blocking-probability QoS requirements using statistical traffic and energy information. It transforms the problem into a weighted optimization and solves it with a two-stage DP algorithm that first selects BS states and then allocates active resources. The proposed method achieves near-optimal performance while substantially reducing computational complexity; for K = 1 and ptarget = 1.25%, it reduces grid power by about 50% versus the BS on-off algorithm.

  • Problem

    The paper asks how to allocate BS on-off states and active resources using statistical traffic and harvested-energy information while minimizing grid power under blocking-probability QoS constraints.

  • Method

    The constrained problem is converted into a weighted combination of grid power consumption and blocking probability, then solved with two-stage DP for BS states and per-BS resource allocation.

  • Results

    Near-optimal performance is achieved with greatly reduced computational complexity; for K = 1 and ptarget = 1.25%, grid power consumption falls by about 50% versus the BS on-off algorithm.

  • Takeaways & Limitations

    Separating BS on-off adaptation from active-subcarrier allocation provides close-to-optimal energy savings with lower computational complexity.

Abstract

from arXiv · show

We consider energy-efficient wireless resource management in cellular networks where BSs are equipped with energy harvesting devices, using statistical information for traffic intensity and harvested energy. The problem is formulated as adapting BSs' on-off states, active resource blocks (e.g. subcarriers) as well as power allocation to minimize the average grid power consumption in a given time period while satisfying the users' quality of service (blocking probability) requirements. It is transformed into an unconstrained optimization problem to minimize a weighted sum of grid power consumption and blocking probability. A two-stage dynamic programming (DP) algorithm is then proposed to solve this optimization problem, by which the BSs' on-off states are optimized in the first stage, and the active BS's resource blocks are allocated iteratively in the second stage. Compared with the optimal joint BSs' on-off states and active resource blocks allocation algorithm, the proposed algorithm greatly reduces the computational complexity, while at the same time achieves close to the optimal energy saving performance.

I. INTRODUCTION

The paper studies cellular resource allocation with energy-harvesting BSs using long-term traffic and harvested-energy statistics, targeting lower grid power while preserving users’ QoS. It formulates a weighted optimization and proposes a two-stage DP method for multi-cell BS operation.

  • Motivation: Energy-harvesting cellular networks must jointly account for traffic profiles, users’ QoS requirements, and renewable-energy availability when allocating wireless resources.The paper motivates network-level allocation because existing work largely focuses on link-level analysis.
  • Problem setting: The paper uses statistical information about traffic intensity and harvested energy to optimize resource allocation under uncertain energy arrivals.This avoids relying on energy-arrival profiles known completely in advance.
  • Problem formulation: The system combines renewable sources with grid power so reliable grid supply can satisfy service requirements while renewable energy reduces grid consumption.The optimization targets average grid power while maintaining users’ QoS through blocking-probability constraints.
  • Problem formulation: The optimization adjusts BS on-off states and resource-block allocation in a downlink multi-cell network with energy-harvesting equipment.The paper extends preliminary single-cell results to the multi-cell case.
  • Optimization method: The constrained grid-power problem is transformed into minimizing a weighted combination of grid consumption and blocking probability, solvable with dynamic programming.Blocking probability is analyzed jointly with BS states and harvested-energy profiles.
  • Optimization method: The proposed two-stage DP determines BS on-off states first and then optimizes per-BS resource allocation to reduce computational complexity.Its performance is evaluated against the optimal DP and heuristic algorithms through simulations.

II. SYSTEM MODEL

The system divides a fixed operational period into time slots and models each BS as jointly powered by harvested energy and the grid. It controls BS activation and subcarrier counts while allowing sleep modes and energy reservation across slots.

  • System configuration: The cellular system contains B BSs, each jointly powered by an energy-harvesting device and the power grid over T time slots.The operational period may be, for example, 24 hours.
  • Battery assumption: The model assumes an infinite-capacity battery because harvested energy is generally insufficient for reliable network operation and battery overflow is unlikely.This is presented as an approximation for real systems with finite batteries.
  • Power model: Active-mode BS consumption combines a constant power term with radio-frequency-related power, while sleep consumption and reactivation power are approximated as negligible or low.The constant term includes baseband processing, conversion, and cooling components.
  • Resource allocation: The network decides which BSs are active and how many of the N orthogonal subcarriers each active BS uses.The RF power is modeled as a linear function of active-subcarrier count.
  • Energy management: Harvested energy can be reserved for later time slots by reducing active subcarriers or switching a BS into sleep mode.This balances resource use across the operational timeline.
  • Sleep modes: Deep sleep turns a BS completely off for a slot, with users in the sleeping cell served by neighboring BSs.The model treats deep-sleep power consumption as negligible.
  • Sleep modes: Opportunistic sleep lets an active BS turn off during part of its active period when available energy is insufficient.The model assigns opportunistic sleep a power consumption of P_S.

B. Traffic Model

The traffic model represents users by rate classes and geographic regions, with Poisson arrivals and corresponding service rates. It links active BS states and resource allocation to achievable rates and blocking probability under long-timescale channel assumptions.

  • Traffic and network model: Users are grouped into K rate classes and M disjoint regions, with class-region arrivals modeled by Poisson processes.Each class k has data-rate requirement Rk, and arrivals in region m have rate λmk with service rate µmk.
  • Traffic and network model: Traffic intensity is computed from the class-region arrival and service rates and represented for each time slot by an M × K traffic matrix.The traffic profile is treated as constant within each slot but may vary across slots.
  • Association and resource allocation: Each region’s traffic is served by the BS with the largest signal strength, and users are assigned to serving BSs after active/sleep states are fixed.Resource allocation then assigns active subcarriers to users to meet their data-rate requirements.
  • Blocking probability: A newly arriving user is blocked when available subcarriers cannot satisfy the required rate, making blocking probability a QoS metric linked to traffic load and opportunistic sleep.High traffic causes service blocking, while opportunistic sleep can also block newly arrived users.
  • Channel model: The channel model averages small-scale fading and large-scale shadowing over realizations, so the analysis mainly focuses on pathloss effects and averaged interference.Achievable transmission rate is determined from SINR and the number of active subcarriers.

A. Service Blocking Probability

Service blocking probability measures whether traffic exceeds a BS’s available normalized bandwidth. The paper approximates its calculation across heterogeneous user classes and locations, then tunes it through BS activation and subcarrier allocation.

  • Admission condition: A BS admits users only when their total normalized bandwidth requirement does not exceed its available capacity.The admission condition is expressed as zb ≤ 1, with blocking occurring when a newly arriving user violates that condition.
  • Blocking calculation: Because direct integration over all possible user quantities and locations is difficult, the paper extends Erlang’s approximation to the multi-class, multi-area setting.The approximation averages users’ bandwidth requirements over possible positions before applying Erlang’s formula.
  • Blocking calculation: The approximation assumes users in an area have the same bandwidth requirement when calculating blocking with Erlang’s formula.This assumption simplifies the spatially varying rate calculation.
  • Blocking calculation: The service blocking probability is evaluated over active-user states that satisfy the bandwidth constraint and identifies states in which an arriving user is blocked.The formulation accounts for user classes, regions, and their normalized bandwidth requirements.
  • Control variables: Service blocking can be tuned by changing BS working states and the number of active subcarriers, while opportunistic sleep introduces an additional sleep-related blocking mechanism.The service-blocking analysis considers an always-active BS before relating overall blocking to sleep behavior.

1) Case 1:

The formulation jointly adapts BS states, resource allocation, and sleep ratios over time using traffic and harvested-energy profiles. It minimizes average grid power while imposing a weighted blocking-probability requirement.

  • 1) Case 1:: When harvested energy is insufficient for required consumption, grid power is needed; otherwise, the battery can supply the required power without grid input.The opportunistic sleep ratio is related to the available input power and grid-power condition.
  • 1) Case 1:: The optimization uses traffic and harvested-energy profiles that are constant within each slot but may vary across slots.Traffic is represented by an M × K matrix, while harvested power is represented for the BSs by a vector.
  • 1) Case 1:: The decision variables are BS on-off states, resource allocation, and opportunistic sleep ratios for every time slot.These controls determine BS availability and active resource usage over the planning period.
  • 1) Case 1:: The objective minimizes average grid power consumption while satisfying a weighted blocking-probability constraint over the predefined period.The weighting factor can emphasize QoS during particular times, such as peak-load periods.

B. Optimal DP Algorithm

The optimal DP formulation uses battery energy as its state and BS states, active subcarriers, and sleep ratios as actions, solving the weighted objective by backward induction. Its exponential scaling motivates a lower-complexity two-stage algorithm.

  • Performance benchmark: The optimal DP solution can characterize a lower-bound curve of minimum average grid power for target blocking probabilities.Any achievable grid-power and blocking-probability pair lies above this curve, although not every curve value is guaranteed to be attainable.
  • Performance benchmark: If a suitable β produces the target blocking probability, the weighted optimization recovers the constrained optimum; otherwise, selecting the largest feasible blocking-probability point gives a suboptimal result.This limitation arises because the target may not correspond to a point generated by the weighted formulation.
  • Optimal DP formulation: The DP state is the vector of battery energy levels at the beginning of each time slot.Energy evolves between slots subject to available harvested energy and consumption constraints.
  • Optimal DP formulation: DP actions include BS working states, the number of active subcarriers, and sleep ratios, with per-stage cost combining grid power and blocking probability.The cost-to-go minimizes the current slot’s cost together with the costs of following slots.
  • Optimal DP formulation: Backward induction from slot T to slot 1 yields the minimum cost, represented by the initial cost-to-go value J1(0).The per-slot subproblems are solved recursively.
  • Complexity and proposed reduction: Both action and state spaces grow exponentially with the number of BSs, making the optimal DP computationally difficult for large networks.The paper therefore proposes a two-stage optimization algorithm to reduce state and action space dimensions.

C. Two-stage DP Algorithm

The two-stage DP algorithm first optimizes BS on-off states, then iteratively allocates active subcarriers and power for each active BS. This decomposition substantially reduces the DP state and action spaces relative to the original joint optimization.

  • First stage: The first stage optimizes BS working states while assuming active BSs use all N subcarriers and require no opportunistic sleeping.The second stage then adjusts subcarrier numbers and power allocation.
  • Complexity reduction: The first-stage action space is 2^B, and the maximum next-slot state space falls from (NNϕ + 1)^B to 2^B.The reduced problem can therefore be solved by standard DP with much lower complexity than the original DP.
  • Second stage: The second stage separately updates each BS’s resource allocation using other BSs’ current allocations until the solution stops changing.Subcarrier adaptation changes interference, so per-BS allocations remain coupled during iteration.
  • Complexity reduction: The complete two-stage procedure reduces each slot’s action space from (NNϕ + 1)^B to 2^B BNNϕ.Algorithm 1 summarizes the resulting optimization procedure.

D. Heuristic Algorithms

The paper compares low-complexity two-stage heuristics for BS sleeping and resource-block utilization against DP-based optimization. These heuristics use current traffic and energy conditions but do not guarantee QoS performance.

  • Overview: The proposed low-complexity heuristic algorithms also operate in two stages, first selecting BS on-off states and then tuning per-BS resource allocation.The second-stage choices include active subcarriers and opportunistic sleep ratios.
  • BS on-off policies: The non-sleep policy keeps all BSs active, while the threshold-based sleep policy selects active BSs from traffic thresholds subject to a minimum coverage requirement.The non-sleep policy serves as a traditional-network baseline.
  • Resource-block policies: Resource-block policies activate all blocks, set their number proportional to traffic intensity, or additionally account for available power.The joint traffic-energy-aware policy reflects that outages can result from insufficient wireless resources or insufficient power.
  • Complexity and QoS: The heuristic algorithms depend only on current-slot traffic and energy conditions, making their complexity much lower than DP, but QoS performance is not guaranteed.Their grid-power handling uses available grid power to satisfy requirements when possible.

V. NUMERICAL SIMULATIONS

The numerical study evaluates the proposed methods using macro-BS energy and LTE channel models in single-cell and sectorized multi-cell settings. It examines QoS-resource allocation relationships and the performance of the two-stage algorithm.

  • Simulation setup: The simulations use the EARTH macro-BS energy-consumption model and a 3GPP LTE channel model.The macro-cell parameters include P0 = 712.2W, ∆P = 15.96, Pmax = 40W, and R = 1000m.
  • Evaluation scope: The study first evaluates QoS and resource allocation in a single cell, then extends the simulation to sectorized multi-cell networks.The extension is used to study the two-stage algorithm’s performance.

A. Single-Cell Case

The single-cell simulations characterize bandwidth- and energy-limited operating regions and evaluate DP and heuristic policies over daily traffic and renewable-energy profiles. The results show tradeoffs among blocking probability, grid consumption, and traffic-aware weighting.

  • Single-cell resource limits: When active subcarriers n < 300, blocking is mainly bandwidth-limited; when n ≥ 300, insufficient power prevents all active subcarriers from remaining on.These define the bandwidth-limited and energy-limited regions, respectively.
  • Single-cell resource limits: Each blocking-probability curve has a minimum-outage operating point, while equal blocking targets can require less than PIn in the bandwidth-limited region but all available PIn in the energy-limited region.The results therefore favor adapting subcarriers to traffic and available energy over relying on opportunistic sleeping.
  • Daily-profile evaluation: The DP evaluation uses T = 24 one-hour slots with a daily traffic profile and renewable-energy harvesting profile.The traffic intensity is λt = φtλmax with λmax = 10s^-1 and 0 < φt ≤ 1.
  • Policy comparison: The proposed DP-based algorithm is reported as the optimal solution for the evaluated tradeoff between average blocking probability and grid energy consumption.The traffic-aware DP optimization is performed before renewable-energy effects are included in the actual grid-consumption calculation.
  • Weighted blocking: Changing the weighting exponent produces different per-slot blocking profiles: with j = 2, the algorithm tends to increase blocking during low-traffic periods.The weighting factor emphasizes higher-traffic regimes when φt < 1.

B. 3-Sector Case

The 3-sector evaluation models sectorized multi-cell traffic and energy conditions, then compares BS sleeping and resource-allocation strategies through outage–grid-energy tradeoffs. The two-stage DP algorithm is close to optimal in asymmetric settings, while active-subcarrier adaptation offers limited benefit under symmetric traffic.

  • Model and settings: The sectorized model divides coverage into regions according to which BSs are active, with M = 2 for one active BS and M = 4 for two active BSs.Each region is served by an active BS, while sleep-BS coverage is reassigned to active BSs.
  • Single-user-class results: The two-stage DP algorithm performs close to the optimal DP algorithm and better than the BS on-off algorithm in the asymmetric single-user-class case.The comparison uses tradeoff curves between blocking probability and grid energy consumption.
  • Symmetric traffic: For symmetric traffic, the BS on-off and two-stage DP algorithms are close because active-subcarrier adaptation and opportunistic sleep adjustment provide little additional improvement.The reported explanation is that the blocking-probability increase from reducing radio resources exceeds the interference reduction under equal traffic.
  • Subcarrier adaptation: In asymmetric traffic, reducing active subcarriers at a low-traffic BS can reduce interference more than it reduces radio resources, helping approach the optimal bound.The opposite tradeoff occurs when all three BSs experience the same traffic, where keeping all subcarriers active is preferable.
  • Multiple user classes: With two user classes, the two-stage DP algorithm is no longer close to optimal when a low blocking probability is targeted under asymmetric traffic.The symmetric two-user-class case has performance similar to the K = 1 case, whereas the asymmetric case differs.

VI. CONCLUSION

The paper studies joint BS sleeping and resource allocation using long-term traffic and harvested-energy profiles. Its two-stage DP method achieves near-optimal performance in supported settings, reducing grid consumption and lowering complexity, while asymmetric traffic makes active-subcarrier adaptation especially useful.

  • Conclusion: The paper studies joint BS sleeping and resource allocation using average network traffic and harvested-energy profiles over a long-term period.The studied objective concerns network operation with renewable-energy-powered BSs.
  • Conclusion: The proposed two-stage DP algorithm achieves near-optimal performance when the first-stage BS on-off adaptation is optimal.This conclusion links the overall result to the quality of the first-stage state decision.
  • Conclusion: Under symmetric traffic, active-subcarrier adaptation does not significantly improve performance, so active BSs can use all subcarriers with sufficient power input.This simplification greatly reduces computational complexity while achieving the optimal solution in the stated scenario.
  • Conclusion: Under asymmetric traffic, active-subcarrier adaptation can effectively reduce interference while guaranteeing radio-resource requirements, improving performance.The conclusion contrasts asymmetric traffic with the symmetric-traffic simplification.
  • Conclusion: For K = 1 and ptarget = 1.25%, the two-stage DP algorithm reduces grid power consumption by about 50% compared with the BS on-off algorithm.The comparison is reported for the single-user-class case.
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