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Optimal Resource Allocation in Full-Duplex Wireless-Powered Communication Network

Hyungsik Ju, Rui Zhang

arXiv:1403.2580v3cs.IT

TL;DR

The paper addresses resource allocation in wireless-powered networks while reducing the time cost of separate downlink energy transfer and uplink information transmission. It proposes simultaneous full-duplex operation with joint time and power optimization, finding advantages over half-duplex operation under effective self-interference cancellation and stringent peak-power constraints.

  • Problem

    Wireless-powered networks need resource allocation approaches that avoid the limited operation time and practical burdens of fixed battery sources while improving throughput through full-duplex operation.

  • Method

    The paper designs an FD-WPCN protocol for simultaneous downlink WET and uplink TDMA WIT, then jointly optimizes time and H-AP power allocations under perfect and imperfect SIC, with HD-WPCN as a baseline.

  • Results

    FD-WPCN is more beneficial than HD-WPCN when self-interference is effectively cancelled, the user population is sufficiently large, or the H-AP peak-power constraint is more stringent than its average-power constraint.

  • Takeaways & Limitations

    Full-duplex H-AP operation can improve wireless-powered network throughput when interference cancellation and operating conditions favor simultaneous energy transfer and information reception.

Abstract

from arXiv · show

This paper studies optimal resource allocation in the wireless-powered communication network (WPCN), where one hybrid access-point (H-AP) operating in full-duplex (FD) broadcasts wireless energy to a set of distributed users in the downlink (DL) and at the same time receives independent information from the users via time-division-multiple-access (TDMA) in the uplink (UL). We design an efficient protocol to support simultaneous wireless energy transfer (WET) in the DL and wireless information transmission (WIT) in the UL for the proposed FD-WPCN. We jointly optimize the time allocations to the H-AP for DL WET and different users for UL WIT as well as the transmit power allocations over time at the H-AP to maximize the users' weighted sum-rate of UL information transmission with harvested energy. We consider both the cases with perfect and imperfect self-interference cancellation (SIC) at the H-AP, for which we obtain optimal and suboptimal time and power allocation solutions, respectively. Furthermore, we consider the half-duplex (HD) WPCN as a baseline scheme and derive its optimal resource allocation solution. Simulation results show that the FD-WPCN outperforms HD-WPCN when effective SIC can be implemented and more stringent peak power constraint is applied at the H-AP.

I. INTRODUCTION

The paper applies full-duplex operation to WPCNs so the H-AP can transfer energy and receive information simultaneously, then develops resource-allocation methods and compares FD with HD operation. It addresses both perfect and imperfect self-interference cancellation and studies when FD is more beneficial.

  • Motivation and protocol: FD-WPCN enables simultaneous downlink WET and uplink WIT over the same band, while users transmit independently through TDMA and harvest energy when not transmitting.The H-AP operates in FD mode, whereas users remain in time-division HD mode for implementation simplicity.
  • Resource allocation: The paper jointly optimizes H-AP transmit power and time allocations for downlink WET and users’ uplink WIT to maximize weighted sum-rate under total-time, average-power, and peak-power constraints.The optimization characterizes rate trade-offs among users through nonnegative rate weights.
  • Perfect SIC: With perfect SIC, the FD-WPCN weighted-sum-rate maximization problem is convex and admits a closed-form optimal time and power allocation solution.The perfect-SIC case is treated as the ideal benchmark for the allocation design.
  • Imperfect SIC: With imperfect SIC, the FD-WPCN problem is generally non-convex, so an iterative algorithm uses the no-self-interference optimum as an initial point to obtain a locally optimal solution.The algorithm alternately updates time and power allocations until the weighted sum-rate cannot be further improved.
  • HD baseline and comparison: The HD-WPCN baseline jointly considers time and power allocation under average and peak H-AP power constraints, unlike the prior constant-power formulation.The comparison indicates that FD is more beneficial when self-interference is effectively cancelled and/or the H-AP peak-power constraint is more stringent.

II. SYSTEM MODEL

The system contains one full-duplex H-AP and K distributed users sharing a frequency band for downlink wireless energy transfer and uplink wireless information transmission. Users lack embedded energy sources and therefore replenish energy from the H-AP’s downlink signal.

  • Network configuration: The network has one H-AP and K users, with a two-antenna H-AP and one antenna per user, operating over the same frequency band.Users are assumed to be sufficiently separated from one another.
  • Energy model: The H-AP has a stable energy supply, whereas user terminals have no embedded energy sources and must harvest energy from received downlink signals.This harvested energy supports the users’ uplink transmissions.

A. FD-WPCN

FD-WPCN enables simultaneous downlink wireless energy transfer and uplink information transmission through full-duplex operation at the H-AP. The protocol divides each block into a dedicated power slot and user-specific slots, while accounting for self-interference and resource constraints.

  • FD operation: The H-AP uses separate antennas to broadcast energy in the DL and receive user information in the UL simultaneously over the same bandwidth.The effective loopback channel after analog SIC models residual self-interference at the H-AP.
  • Transmission protocol: Each block contains K + 1 slots: a dedicated DL-WET slot followed by K slots combining DL WET with TDMA UL WIT.The dedicated power slot ensures energy delivery even when K = 1.
  • Transmission protocol: During each user’s UL slot, the H-AP continues broadcasting energy while that user transmits information, whereas users cannot harvest energy while transmitting.Other users harvest energy during slots in which they do not transmit, and inter-user received UL energy is treated as negligible.
  • Rate model: User rates depend on slot durations, H-AP transmit powers, harvested-energy efficiency, channel gains, residual self-interference, noise, and the practical SINR gap.The achievable rate depends on the product of the user’s uplink and downlink channel power gains.
  • Self-interference model: The model incorporates analog and digital SIC, finite receiver dynamic range, quantization noise, and channel-estimation error in the residual self-interference.Residual self-interference power is modeled as proportional to the H-AP transmit power in the relevant slot.

B. HD-WPCN

HD-WPCN uses a harvest-then-transmit protocol with orthogonal downlink energy transfer and uplink information transmission. The H-AP transmits energy only in the first slot, followed by TDMA uplink slots for the users.

  • HD protocol: In HD-WPCN, DL energy is broadcast only during slot 0, while slots 1 through K are reserved for TDMA UL information transmission.Neither the H-AP nor the users transmit and receive simultaneously in the half-duplex protocol.
  • Rate and power model: The H-AP uses one DL-WET transmit power P in slot 0, and each user’s UL achievable rate is determined by the resulting harvested energy and its allocated transmission time.The rate expression is given in bits/second/Hz for each user.
  • Power constraints: The H-AP’s HD transmit power satisfies P = min(Pavg/τ0, Ppeak), jointly enforcing average and peak power constraints.The constraint depends on the duration of the dedicated energy-transfer slot.

III. OPTIMAL TIME AND POWER ALLOCATION IN FD-WPCN

The paper formulates FD-WPCN resource allocation as weighted-sum-rate maximization over slot durations and H-AP transmit powers. It evaluates ideal perfect-SIC operation separately from the practical finite-self-interference case.

  • Problem formulation: The FD-WPCN optimization maximizes the weighted sum-rate of all users’ UL information transmission through joint time and power allocation.The formulation includes the stated time, power, and block-level constraints.
  • Problem formulation: Nonnegative user weights ωi determine the rate trade-offs among users and characterize different weighted-throughput operating points.Changing the weights changes the relative importance assigned to users in the objective.
  • SIC cases: The analysis first considers perfect SIC, represented by γ = 0, and then studies finite residual self-interference with γ > 0.The two cases correspond to ideal and practical FD-WPCN operation.

A. FD-WPCN with Perfect SIC

With perfect SIC, the FD-WPCN weighted sum-rate problem is transformed into a jointly time-and-energy allocation problem that is convex and admits an optimal allocation procedure. The resulting allocation favors energy transmission during weaker users’ slots and information transmission during stronger users’ slots, subject to peak-power constraints.

  • Problem transformation: The original joint time-and-power problem is transformed using E_i = τ_iP_i, where E_i denotes H-AP energy broadcast during slot i.This conversion changes the average-power constraint into a sum-energy constraint while retaining the peak-power constraint E_i − Ppeakτ_i ≤ 0.
  • Convex formulation: For perfect SIC, each user’s achievable-rate function is jointly concave in time and energy, making the transformed weighted sum-rate problem convex.The convex formulation can be solved through Lagrangian duality after the variable transformation.
  • Solution procedure: The optimal solution is obtained by maximizing the Lagrangian over time and energy for fixed dual variables, then updating the dual variables with a subgradient-based method.The time and energy variables are iteratively optimized, while the ellipsoid method can update the two dual variables.
  • Solution procedure: The resulting algorithm has total time complexity O(K), because only two dual variables are updated regardless of the number of users.The per-iteration steps involving time and energy allocations scale linearly with K.
  • Infinite peak-power case: When Ppeak → ∞, optimal operation uses a zero-duration dedicated WET slot with unbounded power, and the FD-WPCN reduces to a TDMA uplink with constant user energy Pavg.In this limit, its weighted sum-rate is equivalent to that of a conventional K-user TDMA network and also corresponds to HD-WPCN with τ_0 → 0.
  • Finite peak-power behavior: For finite peak power, energy is concentrated in weaker users’ slots, while stronger users receive more UL transmission time and may have no simultaneous DL energy transmission.With Ppeak = 2Pavg, 97% of energy is broadcast during the first eight slots; with Ppeak = 5Pavg, 93% is broadcast during the first six slots.

B. FD-WPCN with Finite SI

With imperfect self-interference cancellation, the weighted sum-rate problem is generally non-convex, so the paper develops an iterative algorithm initialized by the perfect-SIC solution. The resulting procedure alternates time and power updates and has total complexity O(K^2).

  • Finite residual self-interference makes the weighted sum-rate problem generally non-convex and prevents efficient globally optimal solution.
  • The algorithm initializes time and power allocations with the optimal no-self-interference solution, then alternately updates time and power until the weighted sum-rate no longer improves.
  • The time-update subproblem is convex and is solved using Lagrangian duality and an ellipsoid method over the dual variables.
  • The power update uses gradient projection over the feasible set defined by average and peak power constraints.
  • O(K^2) is the total time complexity of the finite-self-interference algorithm.

IV. OPTIMAL TIME AND POWER ALLOCATION IN HD-WPCN

The paper derives optimal joint time and power allocation for the HD-WPCN baseline, whose H-AP transmits at peak power. It analyzes how the allocation and rate-region advantage depend on peak power, channel quality, user weights, and the number of users.

  • The HD-WPCN optimization is generally non-convex because its objective and average-power constraint are non-convex.
  • The optimal HD-WPCN H-AP transmit power is always P*=Ppeak, regardless of the optimal time allocation.
  • When Ppeak=∞, the optimal H-AP WET time is zero while its transmit power tends to infinity with τ0*P*→Pavg.
  • User WIT time increases with channel parameter αi or weight ωi.
  • For finite Ppeak, increasing DL WET time can reduce WSR because lost UL WIT time outweighs the harvested-energy gain.
  • With finite peak power, FD-WPCN has a larger achievable rate region than HD-WPCN, especially when Ppeak=2Pavg; the gap decreases as Ppeak increases.

V. SIMULATION RESULTS

The simulations compare FD- and HD-WPCNs under fading channels while varying average power, residual self-interference, user count, and peak-to-average power ratio. FD performance depends strongly on cancellation quality and becomes more favorable with more users or tighter peak-power limits.

  • The simulations use 1MHz bandwidth, user distances uniformly distributed from 5m to 10m, pathloss exponents αD=αU=2, and independent unit-mean Rayleigh fading.
  • With K=10, Ppeak=2Pavg, and ϕ=−60dB, FD-WPCN’s average sum-rate exceeds HD-WPCN’s for sufficiently low average power, but not for Pavg≥25dBm.
  • With ϕ=−80dB, imperfect-SIC FD-WPCN approaches perfect-SIC performance and outperforms HD-WPCN.
  • With ϕ=−40dB, imperfect-SIC FD-WPCN’s average sum-rate is always below HD-WPCN’s.
  • For ϕ=−60dB, FD-WPCN is below HD-WPCN when K<5 but above it when K≥5, while both systems’ sum-rates increase with K.
  • At K=10 and Pavg=20dBm, FD-WPCN’s gain over HD-WPCN is larger at small Ppeak/Pavg and diminishes as the ratio increases.

VI. CONCLUSION

The paper formulates FD-WPCN resource allocation with simultaneous downlink energy transfer and uplink information transmission, considering both perfect and finite self-interference. It compares the resulting FD scheme with an optimized HD baseline and identifies conditions favoring FD operation.

  • The proposed FD-WPCN jointly allocates WET and WIT time and H-AP transmit power to maximize users’ weighted sum-rate.
  • Perfect-SIC FD-WPCN admits an optimal allocation, whereas finite self-interference is handled through a locally optimal iterative solution.
  • The optimal allocation exploits available multiuser channel diversity in the hybrid network.
  • FD H-AP operation is more beneficial than HD operation when self-interference is effectively cancelled, user count is sufficiently large, or peak power is relatively restrictive.

APPENDIX C PROOF OF COROLLARY 3.1

The proof establishes the optimal allocation for problem (P2) as the H-AP peak-power limit tends to infinity by reducing the system to TDMA cases.

  • Proof by cases: The proof uses separate cases for zero and positive user-energy allocations to complete Corollary 3.1.The argument considers each user i = 1, …, K.
  • Proof by cases: If one user receives zero energy, the system becomes equivalent to a (K − 1)-user TDMA network excluding that user.The remaining users consume constant transmission energy, with user Uj's channel given by αj.
  • Proof by cases: When all users receive positive energy, FD-WPCN becomes equivalent to a K-user TDMA network with constant user energy and channel αi.The corresponding allocation has E∗0 = Pavg and τ∗0 = 0.
  • Optimality conclusion: Because the achievable rate region of a (K − 1)-user TDMA network is contained in that of a K-user TDMA network, the all-user allocation is optimal.Thus, (τ∗i, E∗i) with E∗0 = Pavg and τ∗0 = 0 solves problem (P2) when Ppeak →∞.

APPENDIX E PROOF OF PROPOSITION 3.2

The proof derives Proposition 3.2 by maximizing the Lagrangian over individual time variables and applying monotonicity, feasibility, convexity, and KKT conditions.

  • Lagrangian maximization: For fixed λ, µ, and P^(k−1), the Lagrangian is maximized by independently maximizing each individual term L^(F−SI)i(τi, λ, µ).The cases i = 0 and i = 1, …, K are handled separately.
  • Lagrangian maximization: The monotonicity of f̄(zi) determines the solution of the scalar equation for each user’s nonzero time allocation.f̄(zi) is monotonically increasing and has minimum value −CiP^(k−1).
  • Feasibility: A nonzero user allocation together with τ̄0 = 1 violates the sum-time constraint, so the feasible solution must satisfy the stated time relation.This follows from the scalar optimality condition and the constraint structure.
  • Power and time allocation: The maximum WSR uses P∗ = Ppeak because increasing transmit power increases the rate, while additional DL-WET time decreases WSR for fixed harvested energy.The resulting allocation sets τ∗ according to the derived optimal time solution.
  • Optimality conditions: After fixing the peak-power allocation, the modified problem is convex with strong duality, so its optimum satisfies the KKT conditions and yields (57) and (58).The variables are changed using the optimal Lagrange multiplier and the corresponding transformed quantities.
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