PaperlayerView exact revision on arXiv

Source-linked AI summary

Energy-Efficient Resource Allocation in OFDMA Systems with Hybrid Energy Harvesting Base Station

Derrick Wing Kwan Ng, Ernest S. Lo, Robert Schober

arXiv:1302.4721v1cs.IT

TL;DR

The paper addresses energy-efficient resource allocation for OFDMA downlink systems with hybrid energy-harvesting base stations. It develops asymptotically optimal offline optimization and a lower-complexity online iterative algorithm motivated by that solution. The proposed online method achieves close-to-optimal performance with fast convergence while using only causal system information.

  • Problem

    Resource allocation for hybrid energy-harvesting OFDMA base stations must accommodate time-varying energy availability, while prior results do not apply to this hybrid setting.

  • Method

    The paper combines time-sharing, fractional programming, and Lagrange dual decomposition for offline optimization, then uses the offline structure to design an online iterative algorithm.

  • Results

    The proposed online algorithm achieves close-to-optimal performance within a small number of iterations using only causal channel and energy-arrival information.

  • Takeaways & Limitations

    The offline solution provides a building block for practical online resource allocation in hybrid-energy OFDMA systems.

Abstract

from arXiv · show

We study resource allocation algorithm design for energy-efficient communication in an OFDMA downlink network with hybrid energy harvesting base station. Specifically, an energy harvester and a constant energy source driven by a non-renewable resource are used for supplying the energy required for system operation. We first consider a deterministic offline system setting. In particular, assuming availability of non-causal knowledge about energy arrivals and channel gains, an offline resource allocation problem is formulated as a non-convex optimization problem taking into account the circuit energy consumption, a finite energy storage capacity, and a minimum required data rate. We transform this non-convex optimization problem into a convex optimization problem by applying time-sharing and fractional programming which results in an efficient asymptotically optimal offline iterative resource allocation algorithm. In each iteration, the transformed problem is solved by using Lagrange dual decomposition. The obtained resource allocation policy maximizes the weighted energy efficiency of data transmission. Subsequently, we focus on online algorithm design. A stochastic dynamic programming approach is employed to obtain the optimal online resource allocation algorithm which requires a prohibitively high complexity. To strike a balance between system performance and computational complexity, we propose a low complexity suboptimal online iterative algorithm which is motivated by the offline optimization.

I. INTRODUCTION

The paper motivates energy-efficient OFDMA resource allocation for hybrid energy-harvesting base stations, where intermittent renewable energy and practical power constraints challenge existing approaches. It develops offline and online algorithms tailored to this setting.

  • System motivation: OFDMA supports flexible resource allocation by dividing a wideband channel into orthogonal narrowband subcarriers for multiple users.The downlink can assign different users to different subcarriers and adapt transmit power across them.
  • System motivation: Cellular base stations dominate network electricity consumption, motivating methods that improve wireless communication energy efficiency.The passages report approximately 60 billion kWh of annual cellular-network consumption, with 80% attributed to base stations.
  • Research gap: Existing energy-efficiency studies generally assume an ideal continuous power supply, which is overly optimistic for base stations lacking grid access.Remote deployments may instead rely on diesel generators or renewable harvesting, each introducing practical energy-supply constraints.
  • Research gap: Renewable energy availability varies over time, so a harvester-only base station may fail to maintain stable operation and guarantee QoS.The paper therefore motivates complementary energy sources for uninterrupted service.
  • Research gap: Prior energy-harvesting results focus on single-source or point-to-point narrowband systems and do not directly apply to hybrid-energy OFDMA networks.The paper identifies this mismatch as a motivation for new resource-allocation algorithms.
  • Contributions: This paper formulates offline resource allocation with non-causal information and uses fractional programming plus Lagrange dual decomposition to derive an iterative solution.The offline solution then serves as a building block for a practical online algorithm using only causal channel and energy-arrival information.
  • Contributions: The proposed online algorithm converges quickly and achieves close-to-optimal performance using only causal channel-state and energy-arrival information.The reported result concerns the algorithm’s performance and convergence rather than a specific numerical value.

II. OFDMA SYSTEM MODEL

The system is an OFDMA downlink with a base station serving multiple users over time-varying fading channels and hybrid energy sources. Channel changes and energy arrivals define epochs over which resource allocation is adapted.

  • The OFDMA network contains one base station, K single-antenna users, total bandwidth B, nF subcarriers, and transmission duration T.
  • The base station adapts power and subcarrier allocation policies L times during the transmission period.
  • The received-link model includes transmitted symbols, link power, small-scale fading, path loss, shadowing, and additive Gaussian noise.
  • Time-varying fading and energy sources: Harvested energy is buffered in a battery, while a constant traditional source supplies additional operating energy; events are channel-gain or battery-level changes, and epochs separate successive events.
  • Time-varying fading and energy sources: Energy arrives randomly at the harvester according to a Poisson counting process, with exponentially distributed inter-arrival times and harvested energy amounts Eb.

1) Energy Harvesting Source:

The energy-harvesting source is modeled through battery and power constraints that enforce causality, finite storage, and limits on energy drawn from the traditional source.

  • The harvested-energy and non-renewable-source portions of transmit power are distinguished for each user and subcarrier.
  • The power-amplifier inefficiency factor ε accounts for the power consumed relative to RF power radiated.For ε = 10, 100 Watts are consumed for every 10 Watts radiated.
  • Energy drawn from the harvester cannot exceed currently stored energy, and battery storage cannot exceed Emax.
  • A small-capacity battery may cause energy overflow when incoming harvested energy exceeds available storage.
  • The traditional source imposes a cumulative energy-draw limit of PNt Joules by time t.

III. OFFLINE RESOURCE ALLOCATION AND SCHEDULING DESIGN

The offline design assumes non-causal knowledge of energy arrivals and channel gains and maximizes weighted energy efficiency under system capacity, energy, allocation, and QoS constraints.

  • The offline algorithm assumes non-causal knowledge of energy arrivals and channel gains.
  • Weighted energy efficiency balances weighted delivered data against total system energy consumption, including signal-processing and power-amplifier energy.
  • The policy variables comprise energy-source-specific transmit powers and subcarrier allocation decisions.
  • The optimization includes a minimum system data rate Rmin as a QoS constraint and a maximum transmit-power limit Pmax.
  • The model permits individual user data-rate requirements through additional constraints.

C. Transformation of the Objective Function

The offline fractional optimization is converted into a tractable time-sharing formulation and solved iteratively across event-defined epochs. The resulting method is asymptotically optimal for sufficiently many subcarriers and has epoch-constant optimal policies.

  • Objective transformation: The original optimization is non-convex because its objective is fractional and its subcarrier-allocation constraint is combinatorial.
  • Objective transformation: Dinkelbach iterations solve the transformed problem for successive q values.
  • Objective transformation: Fractional programming replaces the ratio objective with the subtractive form U(P,S) − qUTP(P,S) while preserving the optimal allocation policy.
  • Optimality and complexity: Exhaustive search for the exact combinatorial solution has complexity O(KnF), making it computationally infeasible when users and subcarriers are large.
  • Time-sharing and epoch structure: Time-sharing relaxes binary subcarrier assignments to values in [0,1], yielding a jointly concave transformed problem solvable through dual methods.
  • Time-sharing and epoch structure: The optimal offline policy remains constant within each epoch, where epochs are formed by channel changes and energy arrivals.
  • Optimality and complexity: The relaxed solution is asymptotically optimal for large numbers of subcarriers, and the resulting allocation can still satisfy binary subcarrier assignment.

E. Dual Problem Formulation

The transformed problem is solved through Lagrange dual decomposition, separating subcarrier-level allocation from a master dual problem. The resulting KKT-based policy allocates subcarriers by marginal benefit and balances harvested and non-renewable energy use.

  • E. Dual Problem Formulation: The dual formulation incorporates the equality constraint directly, so ν is not an optimization variable in the dual problem.Boundary constraints C7 and C9 are absorbed into the KKT conditions used to derive the optimal solution.
  • E. Dual Problem Formulation: The allocation accounts for causality, battery capacity, minimum data rate, source constraints, and subcarrier usage through associated multipliers.The multipliers γ, β, ρ, µ, ν, ψ, and η correspond to the stated energy, battery, rate, equality, and allocation constraints.
  • F. Dual Decomposition and Subproblem Solution: Lagrange dual decomposition splits the dual problem into inner subcarrier subproblems and an outer master dual problem.The inner loop contains nF similarly structured subproblems, while the outer loop solves the master problem iteratively.
  • F. Dual Decomposition and Subproblem Solution: Each subcarrier subproblem is solved for fixed Lagrange multipliers using standard optimization techniques and KKT conditions.The resulting power allocation is described as a multi-level water-filling scheme with potentially different user water levels.
  • F. Dual Decomposition and Subproblem Solution: Harvested transmit power lowers the water level used to determine non-renewable transmit power and reduces energy drawn from the non-renewable source.The policy does not necessarily consume all available renewable energy in every epoch when maximizing weighted energy efficiency.
  • F. Dual Decomposition and Subproblem Solution: The subcarrier is assigned to the user providing the largest marginal benefit on that subcarrier and event.Because marginal benefit includes fairness, the selected user need not maximize instantaneous system throughput.
  • F. Dual Decomposition and Subproblem Solution: The source-power solution follows KKT conditions because the relevant Lagrangian is affine in harvested transmit power.The feasible solution is characterized by vertices induced by the associated constraints.
  • F. Dual Decomposition and Subproblem Solution: When harvested energy is insufficient to supply the required circuit energy, the base station also draws energy from the non-renewable source.This occurs when the residual battery energy is below the circuit-power requirement.

G. Solution of the Master Dual Problem

The master dual problem updates Lagrange multipliers by gradient iterations after solving the decomposed subproblems. Under suitable step sizes, the resulting procedure converges to the primal solution, while the offline policy remains an asymptotic benchmark requiring non-causal information.

  • G. Solution of the Master Dual Problem: The master minimization problem finds γ, β, ρ, µ, and ψ for a given resource allocation using gradient updates.The dual function is differentiable, and the update equations use iteration indices and positive step sizes.
  • G. Solution of the Master Dual Problem: Updated Lagrange multipliers are used to solve the subproblems by updating resource allocation policies.Updating η is unnecessary because it has the same value for all users and does not affect subcarrier allocation.
  • G. Solution of the Master Dual Problem: The transformed problem is jointly concave and satisfies Slater’s constraint qualification, supporting zero duality gap.This establishes equivalence between the dual optimum and the primal optimum for the transformed problem.
  • G. Solution of the Master Dual Problem: The master and subproblem iterations converge to the solution when the step sizes satisfy the infinite travel condition.The convergence statement is given for the relaxed primal optimum under the specified step-size condition.
  • G. Solution of the Master Dual Problem: The asymptotically optimal offline algorithm requires non-causal channel-gain and energy-arrival knowledge that may be unavailable in practice.Its performance serves as an upper bound for online schemes, and its structure informs online algorithm design.
  • G. Solution of the Master Dual Problem: The proposed online algorithms address causality by using only causal energy-arrival and channel-gain information.The online formulation reflects that current observations are available, whereas future channel and energy-arrival information is not.

IV. ONLINE RESOURCE ALLOCATION AND SCHEDULING DESIGN

The online design first formulates an expected weighted-energy-efficiency problem and solves it optimally with dynamic programming. Because dynamic programming scales poorly, a lower-complexity event-driven iterative algorithm adapts the offline structure using causal information.

  • Online problem formulation: The online problem uses only causal energy-arrival and channel-state information because future observations are unavailable when policies are computed.The formulation therefore adopts a statistical approach based on random energy arrivals and channel gains.
  • Optimal online algorithm: The optimal online policy maximizes expected weighted energy efficiency and is obtained through Bellman equations and backward induction.The policy depends on channel state and battery energy and is implemented over discretized time intervals.
  • Suboptimal online algorithm: The online optimization applies fractional-objective transformation and solves the resulting jointly concave problem by dual decomposition.The battery energy available in each epoch summarizes prior channel fluctuations, energy arrivals, consumption, and harvesting.
  • Suboptimal online algorithm: Dynamic programming becomes impractical because the search space grows exponentially with the number of users and subcarriers.The paper identifies the resulting computational complexity and memory requirement as the reason for introducing a suboptimal method.
  • Suboptimal online algorithm: The proposed suboptimal algorithm is event-driven, triggering computation when fading levels or energy arrivals change.It requires only causal system information and statistics of the system.
  • Suboptimal online algorithm: The suboptimal online algorithm is inspired by the asymptotically optimal offline algorithm and uses statistical average epoch lengths.The offline epoch-length knowledge is unavailable under causality, so the online method uses an estimated average event duration.
  • Suboptimal online algorithm: The tractable suboptimal formulation omits the battery-overflow constraint, discharging energy that exceeds storage capacity.The performance loss relative to the optimal formulation is evaluated in simulation.
  • Suboptimal online algorithm: The online power and subcarrier solutions share the offline policy’s preference for harvested energy before non-renewable energy.Non-renewable energy is used when harvested energy cannot achieve the maximum weighted energy efficiency; the online parameter q uses average epoch length.

V. RESULTS AND DISCUSSIONS

The evaluation studies the proposed resource-allocation methods in a simulated micro-cell OFDMA system under specified channel, energy-harvesting, and circuit-power assumptions. Figure 3 examines iterative convergence using average weighted energy efficiency across different transmit-power allowances.

  • Simulation setup: The simulations evaluate the proposed resource allocation and scheduling algorithms in a micro-cell system with radius 500 m.The setup uses nF = 128 subcarriers, a 2.5 GHz carrier frequency, and 5 MHz system bandwidth.
  • Channel model: The channel model uses i.i.d. Rayleigh fading, the 3GPP urban path-loss model, and the LTE extended pedestrian A power-delay profile.Users are uniformly distributed between the reference distance and cell boundary.
  • Simulation setup: The default system requires Rmin = 5 Mbits/s over T = 10 seconds, with Pmax varied by case study.The circuit power is PC = 40 dBm, while the battery has Emax = 500 J and initial energy E0 = 0 J.
  • Energy model: Each energy epoch supplies 5 J, corresponding to an energy-harvesting rate of 5λE Joule/s.The harvested-energy preference parameter is set to φ = 0.01.
  • Simulation setup: The battery-capacity and energy-arrival values are illustrative rather than universal system settings.In practice, battery capacity should scale with energy-arrival rates and cell size.
  • Convergence evaluation: Figure 3 plots average weighted energy efficiency in bit-per-Joule against iteration count for different Pmax values.The figure uses K = 5 users, PN = 50 dBm, and an energy-harvesting base station.
  • Evaluation metric: Weighted energy efficiency counts successfully decoded weighted bits divided by total energy consumption, averaged over small-scale fading.Channel realizations failing the minimum-rate requirement receive zero weighted energy efficiency and average capacity.

A. Convergence of Proposed Iterative Algorithm

The proposed suboptimal online iterative algorithm converges quickly and achieves performance close to offline and optimal online benchmarks. Its energy-efficiency and capacity behavior varies with harvesting rate, non-renewable supply, and transmit-power limits.

  • Convergence: Within 5 iterations, the algorithm reaches above 83% and 90% of the weighted energy efficiency of the asymptotically optimal offline and optimal online algorithms, respectively.The inner loop also converges within 5 iterations per event.
  • Convergence: Around 5 × 5 × Z total iterations are required on average for convergence, where Z is the average number of events during T seconds.
  • Energy harvesting rate: The proposed suboptimal algorithm has performance close to the benchmark algorithms across energy-harvesting-rate regimes.It approaches the benchmarks at both low and high harvesting rates.
  • Energy harvesting rate: At low harvesting rates, limited harvested energy makes the base station rely mainly on the non-renewable source.At high harvesting rates, harvested energy becomes effectively continuous, reducing the value of future-arrival knowledge.
  • Non-renewable supply: Higher maximum non-renewable energy supply improves average weighted energy efficiency, but returns diminish at high harvesting rates.A small non-renewable supply is preferable when the harvester can collect large amounts of energy.
  • System capacity: With Pmax = 23 dBm, capacity gains from higher harvesting rates quickly saturate because radiated RF power remains limited.For Pmax = 33 dBm, capacity approaches a constant in the high-harvesting-rate regime.

C. Energy Efficiency versus Number of Users

As the number of users increases, the proposed suboptimal online and asymptotically optimal offline algorithms scale with similar slopes. The online algorithm exploits multiuser diversity, while larger transmit-power allowances provide diminishing energy-efficiency returns.

  • Computational boundary: The optimal online algorithm is omitted for large K because solving (37) has prohibitive computational complexity.
  • Scaling with users: The proposed suboptimal online and asymptotically optimal offline algorithms scale with the number of users with a similar slope.
  • Scaling with users: The proposed suboptimal online algorithm exploits multiuser diversity to enhance system performance.Multiuser diversity introduces an extra power/energy gain that can facilitate further energy savings.
  • Transmit-power allowance: Increasing Pmax from 33 dBm to 43 dBm yields diminishing weighted energy-efficiency returns because both schemes avoid consuming exceedingly large transmission energy.

VI. CONCLUSIONS

The paper develops offline and practical online resource-allocation algorithms for OFDMA systems with hybrid energy-harvesting base stations, accounting for circuit consumption, finite storage, and minimum data-rate requirements. The offline policy is asymptotically optimal under non-causal knowledge, while the online algorithm uses causal knowledge and achieves close-to-optimal performance with fast convergence.

  • The formulated hybrid-energy OFDMA problem includes circuit energy consumption, finite battery capacity, and a minimum system data-rate requirement.
  • The offline resource-allocation algorithm assumes non-causal channel-gain and energy-arrival knowledge and is asymptotically optimal.The offline solution is used as a building block for the online algorithm.
  • The proposed suboptimal online algorithm uses only causal system knowledge, converges within a small number of iterations, and achieves close-to-optimal performance.The reported online result concerns system energy efficiency and weighted energy efficiency of data transmission.
  • The conclusion identifies imperfect channel-state information and energy-related effects as topics for future work.
  • The transformed offline problem is a concave optimization problem with a convex feasible set.The objective is shown to be concave, while constraints C1-C9 span a convex feasible set.
  • A constant resource-allocation policy within each epoch achieves at least the same performance as a non-constant policy.This conclusion follows from the concavity of the per-subcarrier objective function.
Loading 1302.4721v1…