PaperlayerView exact revision on arXiv

Source-linked AI summary

Wireless Information and Power Transfer: Energy Efficiency Optimization in OFDMA Systems

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

arXiv:1303.4006v2cs.IT

TL;DR

The paper addresses energy-efficient resource allocation for OFDMA wireless information-and-power-transfer systems with power-splitting receivers. It formulates continuous- and discrete-ratio cases as non-convex problems and develops iterative algorithms using fractional programming and dual decomposition. Simulations report excellent performance and expose trade-offs among energy efficiency, wireless power transfer, and multiuser diversity.

  • Problem

    Energy-efficient OFDMA resource allocation is challenging because power, subcarrier, and splitting variables form a jointly non-convex problem with integer subcarrier assignment.

  • Method

    The paper formulates continuous- and discrete-power-splitting allocation problems and solves them with iterative fractional-programming, dual-decomposition, and relaxation-based algorithms.

  • Results

    Simulation results show excellent performance for both proposed suboptimal algorithms and reveal trade-offs among energy efficiency, wireless power transfer, and multiuser diversity.

  • Takeaways & Limitations

    Hybrid information-and-energy-harvesting receivers provide better system energy efficiency than pure information receivers in the reported baseline comparison.

Abstract

from arXiv · show

This paper considers orthogonal frequency division multiple access systems with simultaneous wireless information and power transfer. We study the resource allocation algorithm design for maximization of the energy efficiency of data transmission. In particular, we focus on power splitting hybrid receivers which are able to split the received signals into two power streams for concurrent information decoding and energy harvesting. Two scenarios are investigated considering different power splitting abilities of the receivers. In the first scenario, we assume receivers which can split the received power into a continuous set of power streams with arbitrary power splitting ratios. In the second scenario, we examine receivers which can split the received power only into a discrete set of power streams with fixed power splitting ratios. In both scenarios, we formulate the corresponding algorithm design as a non-convex optimization problem which takes into account the circuit power consumption, the minimum data rate requirements of delay constrained services, the minimum required system data rate, and the minimum amount of power that has to be delivered to the receivers. Subsequently, by exploiting fractional programming and dual decomposition, suboptimal iterative resource allocation algorithms are proposed to solve the non-convex problems. Simulation results illustrate that the proposed iterative resource allocation algorithms approach the optimal solution within a small number of iterations and unveil the trade-off between energy efficiency, system capacity, and wireless power transfer.

I. INTRODUCTION

The paper studies OFDMA downlink systems where hybrid receivers split received signals between information decoding and energy harvesting. It motivates energy-efficient resource allocation under limited mobile-device energy and practical receiver constraints.

  • I. INTRODUCTION: OFDMA divides frequency-selective spectrum into orthogonal narrowband subcarriers, enabling user multiplexing and flexible resource allocation.The system serves multiple receivers while supporting quality-of-service requirements.
  • I. INTRODUCTION: Limited battery capacity and rising data-rate demands motivate energy-efficient communication for mobile networks.Transmitter and receiver operation contributes to increasing energy consumption.
  • I. INTRODUCTION: Power-splitting receivers divide received power into streams for simultaneous information decoding and energy harvesting.The paper assumes passive splitting without additional power consumption, loss, or signal-processing noise.
  • I. INTRODUCTION: The modeled OFDMA downlink uses single-antenna transceivers, quasi-static block fading, nF subcarriers, and receiver feedback for channel gains.Received signals include transmitted data, multipath fading, path loss, shadowing, antenna noise, and co-channel interference modeled as AWGN.
  • I. INTRODUCTION: Receivers harvest energy to replenish rechargeable batteries while retaining fixed circuit consumption independent of harvested power.Hybrid operation includes information decoding and energy harvesting from the received radio signals.

III. RESOURCE ALLOCATION - CONTINUOUS SET OF POWER SPLITTING RATIOS

The continuous-ratio formulation maximizes weighted energy efficiency, defined as delivered bits per consumed Joule, while accounting for transmission, circuit, amplifier, and harvested-energy terms. Its structure supports quasi-concavity analysis and reveals that interference can contribute usable energy.

  • III. RESOURCE ALLOCATION - CONTINUOUS SET OF POWER SPLITTING RATIOS: The continuous-ratio scenario optimizes system energy efficiency over power allocation, subcarrier allocation, and power-splitting policies.The derived solution also benchmarks discrete-ratio receivers and guides selection of discrete splitting levels.
  • III. RESOURCE ALLOCATION - CONTINUOUS SET OF POWER SPLITTING RATIOS: The signal model assumes perfect receiver-side CSI and treats received interference on each subcarrier as AWGN.These assumptions simplify capacity and resource-allocation modeling.
  • III. RESOURCE ALLOCATION - CONTINUOUS SET OF POWER SPLITTING RATIOS: The model accounts for harvested energy from information signals, interference signals, and antenna noise.Receiver efficiency ηk converts received radio signals into stored electrical energy.
  • III. RESOURCE ALLOCATION - CONTINUOUS SET OF POWER SPLITTING RATIOS: Power dissipation includes transmitter circuit power, receiver circuit power, and power-amplifier consumption, while harvested terms reduce net consumption.The amplifier inefficiency factor ε captures drain efficiency and output backoff effects.
  • III. RESOURCE ALLOCATION - CONTINUOUS SET OF POWER SPLITTING RATIOS: Weighted energy efficiency measures the total average bits successfully conveyed to receivers per Joule of consumed energy.The numerator is weighted system capacity and the denominator is total system power dissipation.
  • III. RESOURCE ALLOCATION - CONTINUOUS SET OF POWER SPLITTING RATIOS: Weighted energy efficiency is quasi-concave in the power-allocation variables, enabling analysis of a transformed resource-allocation problem.Strong interference can act as an energy source and facilitate system energy savings.

B. Optimization Problem Formulation

The optimization formulation maximizes energy efficiency subject to power, rate, splitting, and energy-transfer constraints. Practical receiver limits include common harvesting ratios across subcarriers and passive splitting behavior.

  • B. Optimization Problem Formulation: The optimization seeks optimal power, subcarrier, and power-splitting policies under constraints C1–C12.The policies jointly determine transmission allocation and receiver operation.
  • B. Optimization Problem Formulation: Constraints impose minimum receiver power transfer, transmitter power limits, grid-supplied power limits, and minimum system data rate.Pmax reflects power-amplifier hardware limits, while Rmin guarantees the desired system data rate.
  • B. Optimization Problem Formulation: Power-splitting ratios have lower and upper bounds that represent limited receiver splitting capability.The information-decoding ratio is bounded separately, with its upper bound set to 1.
  • B. Optimization Problem Formulation: The passive splitting constraint prevents extra power gain, and the harvesting ratio is constrained to be identical across subcarriers for each receiver.This common-ratio assumption avoids the complexity of an adaptive frequency-selective passive splitter.
  • B. Optimization Problem Formulation: The formulation avoids explicitly imposing some cross-subcarrier information-splitting equalities because they can be deduced when multiple subcarriers serve the same receiver.Including them initially would make efficient solution development more cumbersome.

C. Solution of the Optimization Problem

The paper tackles a non-convex resource-allocation problem by transforming energy efficiency, approximating the transformed objective, and relaxing subcarrier assignment. Dinkelbach iterations and dual decomposition yield tractable algorithms, with close-to-optimal behavior supported under the stated approximations.

  • C. Solution of the Optimization Problem: The problem is jointly non-convex because power, subcarrier, and splitting variables interact, while subcarrier assignment is integer-valued.Exhaustive search or branch-and-bound would be computationally infeasible even for small systems.
  • C. Solution of the Optimization Problem: Fractional programming converts the energy-efficiency objective into a subtractive form U(P,S,ρ)−qUTP(P,S,ρ).The transformed formulation has the same optimal resource-allocation policy under the theorem’s conditions.
  • C. Solution of the Optimization Problem: Dinkelbach iterations solve a parameterized inner problem, with convergence to optimal energy efficiency guaranteed when each inner problem is solved.The transformed objective remains nonnegative for parameters generated by the algorithm.
  • C. Solution of the Optimization Problem: Time-sharing relaxation replaces Boolean subcarrier selection with values in [0,1] and introduces auxiliary variables for transmitted power and information-splitting allocation.The relaxed selection variable represents a time-sharing factor across receivers.
  • C. Solution of the Optimization Problem: The high-SINR capacity approximation satisfies Ci,k≥C̃i,k and becomes asymptotically tight at high SINR, producing a suboptimal solution to the original problem.Simulations are reported to show close-to-optimal performance in high-SINR conditions.
  • C. Solution of the Optimization Problem: The approximated transformed problem is a concave maximization over a convex feasible set after relaxation.This follows from joint concavity of the transformed objective and convexity of the stated constraints.

F. Dual Problem Formulation

The resource allocation problem is recast through a Lagrangian with multipliers representing power-transfer, transmit-power, and system constraints. Boundary constraints are handled through KKT conditions before forming the dual problem.

  • F. Dual Problem Formulation: The Lagrangian is constructed for the primal resource allocation problem (11).
  • F. Dual Problem Formulation: The multiplier vector w corresponds to individual minimum required power-transfer constraints.
  • F. Dual Problem Formulation: λ represents the maximum transmit-power constraint, while β accounts for the power-use constraint.
  • F. Dual Problem Formulation: Boundary constraints C6, C7, C9, and C10 are incorporated through KKT conditions when deriving the allocation solution.
  • F. Dual Problem Formulation: The dual problem is defined from the Lagrangian of the primal formulation.
  • F. Dual Problem Formulation: The resulting dual formulation retains the allocation variables P, S, and ρ inside the Lagrangian maximization.

G. Dual Decomposition Solution

Dual decomposition solves the transformed resource allocation problem through parallel subproblems and iterative multiplier updates. The resulting policies allocate subcarriers by marginal benefit and power through water-filling while enforcing rate and power-transfer requirements.

  • The dual problem is decomposed into parallel inner subproblems and an outer master minimization solved iteratively.
  • For a given Dinkelbach parameter q, KKT conditions produce power allocation and power-splitting policies for each subcarrier and receiver.
  • The power allocation solution is multilevel water-filling.
  • A receiver is selected on a subcarrier when it provides the maximum marginal benefit to the system.
  • Higher receiver priority or stricter individual rate requirements increase the allocator’s preference for serving that receiver.
  • The relaxed subcarrier allocation remains Boolean, so time sharing does not occur in the resulting allocation policy.
  • The multiplier updates enforce system rate, individual rate, and minimum power-transfer requirements.
  • With sufficiently small step sizes, iterative solution of the concave approximated problem is guaranteed to obtain its primal optimum.

IV. RESOURCE ALLOCATION DESIGN - DISCRETE SET OF POWER SPLITTING RATIOS

For receivers restricted to discrete power-splitting ratios, the formulation represents each ratio as an operating mode and jointly selects modes, subcarriers, powers, and harvesting contributions. Dinkelbach-based optimization addresses the fractional objective, while discrete variables create additional complexity.

  • Discrete receivers use N distinct power-splitting ratios for energy harvesting and information decoding.
  • Discrete power-splitting variables make the optimization disjoint and may require exhaustive search whose space grows as N^2KnF.
  • Each power-splitting mode is treated as a receiver operating mode with a corresponding equivalent SINR.
  • Subcarrier selection and operating-mode selection are combined by augmenting the optimization variables.
  • System capacity and power consumption account for information-signal harvesting, interference harvesting, and antenna-noise harvesting.
  • The formulation includes transmit-power allocation, binary subcarrier allocation, and power-splitting-ratio selection for energy harvesting.
  • The fractional objective is transformed into subtractive form and solved iteratively using the Dinkelbach method.

A. Optimization Problem Formulation

The discrete-ratio problem is relaxed using time-sharing variables and reformulated into a jointly concave optimization problem. This enables dual decomposition while preserving mode-selection constraints and their physical meanings.

  • A. Optimization Problem Formulation: The discrete-ratio optimization problem is reformulated for solution in each iterative step.
  • A. Optimization Problem Formulation: Constraints C7 and C9 are relaxed so subcarrier-mode variables can represent time-sharing factors.
  • A. Optimization Problem Formulation: The auxiliary variable ˜P^n_i,k represents actual transmitter power under a selected mode and time-sharing condition.
  • A. Optimization Problem Formulation: The reformulation preserves binary mode-selection behavior and ensures only one power-splitting mode is selected for each receiver.
  • A. Optimization Problem Formulation: The relaxed problem with the approximated objective is jointly concave and satisfies Slater’s constraint qualification.
  • PCT + KPCR +: Dual decomposition uses scalar and vector Lagrange multipliers associated with the reformulated constraints.

B. Dual Decomposition Solution

The dual decomposition solution derives resource allocation policies for power, power splitting, and subcarrier assignment under fixed Lagrange multipliers. Gradient updates then iteratively refine the multipliers, with selected updates omitted when they do not affect allocation decisions.

  • Policy derivation: For fixed Lagrange multipliers, the procedure obtains power allocation, power splitting, and subcarrier allocation policies for each receiver, mode, and subcarrier.The policies are derived through dual decomposition and an iterative procedure.
  • Policy derivation: The power allocation has a multi-level water-filling interpretation and is performed separately for each power splitting mode.This distinguishes the discrete-mode allocation from the corresponding continuous-ratio formulation.
  • Policy derivation: The mode-selection variables are binary even though time-sharing relaxation is used to facilitate algorithm design.
  • Multiplier updates: Because the dual function is differentiable, the Lagrange multipliers are updated using a gradient method for fixed primal allocations.The update equations are specified for the current power, splitting, and allocation variables.
  • Multiplier updates: Updating ζ_i and ϕ_i is unnecessary because these multipliers do not affect power-splitting mode selection or subcarrier allocation.

V. RESULTS

The simulations evaluate convergence and energy-efficiency behavior under varying interference, transmit-power limits, and receiver counts. The proposed algorithms converge rapidly, while energy-efficiency gains depend on receiver number, interference, and the feasible power-splitting set.

  • Simulation setup: With discrete power splitting, the implementation uses five ratios: ρ^E_i,k ∈ {0, 0.25, 0.5, 0.75, 1}.Unmet minimum rate or power-transfer requirements cause the corresponding channel realization’s energy efficiency and capacity to be set to zero.
  • Simulation setup: The average energy efficiency is computed using (7) and averaged over 100000 independent realizations of multipath fading and path-loss attenuation.
  • Convergence and optimality: After only 5 iterations, both proposed algorithms achieve over 95% of the upper-bound energy-efficiency value across all considered scenarios.The convergence speed is invariant to the interference levels σ².
  • Energy efficiency versus transmit power: As P_max increases, energy efficiency first rises rapidly and then saturates when P_max > 18 dBm in the small-receiver, moderate-interference case.The algorithms balance energy efficiency against system power consumption.
  • Energy efficiency versus transmit power: Proposed algorithm I outperforms algorithm II because continuous power-splitting ratios provide a larger feasible solution set than discrete ratios.
  • Energy efficiency versus transmit power: Strong interference can supply harvestable energy but still impair energy efficiency because its harvesting gain cannot compensate for the associated capacity loss.
  • Energy efficiency versus receiver count: At P_max = 25 dBm, energy-harvesting gains over baseline II increase with receiver count and interference power.With more receivers, more RF energy can be harvested; stronger interference both adds energy and tends to saturate SINR.
  • Energy efficiency versus receiver count: More received power is assigned to energy harvesting when interference makes additional information decoding provide little channel-capacity gain, reducing total system energy consumption.

C. Average System Capacity versus Maximum Allowed Transmit Power

Average system capacity scales with the transmit-power allowance below 18 dBm, then saturates as energy-efficiency optimization limits further transmit-power increases. The results also show trade-offs among capacity, interference, receiver count, harvested power, and energy efficiency.

  • Below 18 dBm, the proposed algorithms’ average system capacities scale with the maximum transmit power allowance Pmax.
  • At Pmax ≥18 dBm, capacity gains from increasing Pmax begin to saturate because further transmit power can increase energy consumption more than capacity.
  • Baseline II gains capacity over the other algorithms at low transmit-power allowances because it uses no power splitting and maximizes each subcarrier’s SINR.
  • Baseline I exceeds the other algorithms in capacity at Pmax ≥18 dBm by radiating all available power, but this higher capacity comes with lower energy efficiency.
  • For proposed algorithm II with K = 3 receivers, harvested power saturates in the high-transmit-power regime because transmit power stops increasing and average interference remains unchanged.
  • Increasing interference power raises harvested power and can improve energy efficiency, while increasing receiver count raises capacity through multiuser diversity but may reduce energy efficiency when circuit consumption dominates.

APPENDIX

The appendix establishes that the weighted energy-efficiency objective is quasi-concave in the power allocation variables, using super-level sets and monotonicity analysis.

  • Definition: A strictly quasi-concave function has convex super-level sets, providing the definition used in the appendix.The proof considers the super-level set of g(x) as the basis for quasi-concavity.
  • Super-level sets: For ν < 0, the relevant super-level set is empty because U(P, S, ρ) and U_T^P(P, S, ρ) are positive.The appendix therefore characterizes L_α as an affine or concave set in this case.
  • Super-level sets: For ν > 0, concavity of the transformed expression makes L_ν a concave set, establishing strict quasi-concavity of the objective.The argument uses concavity of U(P, S, ρ) and affinity of U_T^P(P, S, ρ) with respect to power allocation.
  • Monotonicity: With a fixed subcarrier assignment, the objective is first monotonically non-decreasing and then monotonically non-increasing as P_i,k increases.The appendix analyzes the partial derivative with respect to P_i,k, including small- and large-power regimes.
  • Monotonicity: The large-power derivative analysis uses L’Hospital’s rule, supporting the conclusion that the objective eventually becomes monotonic non-increasing.Combining the low- and high-power analyses yields the stated quasi-concavity result.

B. Proof of Concavity of the Transformed Problem with Objective Function Approximation

The transformed problem becomes a concave maximization after approximating the objective: per-subcarrier concavity is preserved through perspective transformation and non-negative aggregation, while the feasible set is convex.

  • Per-subcarrier concavity: The proof first analyzes the concavity of the approximated utility function bU(P, S, ρ) on each subcarrier.The function is studied with respect to the optimization variables using a per-subcarrier representation.
  • Per-subcarrier concavity: The Hessian matrix of f_i,k(x_i,k) is negative semi-definite, so f_i,k(x_i,k) is jointly concave in its optimization variables.The conclusion follows from the signs of the Hessian eigenvalues.
  • Perspective transformation: Perspective transformation preserves concavity, making u_i,k(x_i,k) jointly concave in the transformed power and splitting variables.The transformation is u_i,k(x_i,k) = s_i,k f_i,k(x_i,k/s_i,k).
  • Aggregated objective: A non-negative weighted sum of the transformed per-subcarrier functions remains concave, while bU_T^P(P, S, ρ) is affine.These properties combine to establish joint concavity of the approximated objective expression.
  • Transformed problem: The expression bU(P, S, ρ) − q bU_T^P(P, S, ρ) is jointly concave, and the relaxed constraints define a convex feasible set.Therefore, the transformed problem with the approximated objective is a concave maximization problem.
Loading 1303.4006v2…