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Full-Duplex Wireless-Powered Communication Network with Energy Causality
Xin Kang, Chin Keong Ho, Sumei Sun
TL;DR
The paper studies time allocation in a full-duplex wireless-powered network where future harvested energy cannot support earlier transmissions and later users’ harvesting depends on preceding transmission times. It formulates STM and TTM problems, derives efficient solution strategies, and investigates suboptimal allocation and scheduling. The STM problem is convex with a closed-form, linear-complexity solution strategy, while TTM admits an optimal two-step algorithm and sum throughput is non-decreasing with the number of users.
Problem
The paper addresses time allocation in a full-duplex wireless-powered network with energy causality and coupling between users’ harvesting and transmission times.
Method
The paper formulates STM and TTM optimization problems, derives solution algorithms, and investigates suboptimal time allocation schemes and user scheduling.
Results
STM is proved convex with a closed-form linear-complexity solution strategy, while TTM has an optimal two-step algorithm and sum throughput is non-decreasing with user count.
Takeaways & Limitations
The proposed full-duplex protocol supports simultaneous downlink wireless power transfer and uplink TDMA communication, with different scheduling strategies needed for STM and TTM.
Abstract
from arXiv · showhide
In this paper, we consider a wireless communication network with a full-duplex hybrid access point (HAP) and a set of wireless users with energy harvesting capabilities. The HAP implements the full-duplex through two antennas: one for broadcasting wireless energy to users in the downlink and one for receiving independent information from users via time-division-multiple-access (TDMA) in the uplink at the same time. All users can continuously harvest wireless power from the HAP until its transmission slot, i.e., the energy causality constraint is modeled by assuming that energy harvested in the future cannot be used for tranmission. Hence, latter users' energy harvesting time is coupled with the transmission time of previous users. Under this setup, we investigate the sum-throughput maximization (STM) problem and the total-time minimization (TTM) problem for the proposed multi-user full-duplex wireless-powered network. The STM problem is proved to be a convex optimization problem. The optimal solution strategy is then obtained in closed-form expression, which can be computed with linear complexity. It is also shown that the sum throughput is non-decreasing with increasing of the number of users. For the TTM problem, by exploiting the properties of the coupling constraints, we propose a two-step algorithm to obtain an optimal solution. Then, for each problem, two suboptimal solutions are proposed and investigated. Finally, the effect of user scheduling on STM and TTM are investigated through simulations. It is also shown that different user scheduling strategies should be used for STM and TTM.
I. INTRODUCTION
The paper proposes a full-duplex wireless-powered communication network in which a dual-antenna HAP concurrently transfers energy downlink and collects TDMA uplink data, subject to energy causality. It formulates STM and TTM problems, derives optimal solution strategies, and shows that scheduling preferences differ between them.
- Energy causality: Each user can use only energy harvested before its transmission slot, so later users’ harvesting energy depends on earlier users’ transmission times.The constraint reflects supercapacitor self-discharge and potentially long delays between communication cycles.
- System model: The proposed full-duplex WPCN uses a dual-function HAP for concurrent downlink WPT and uplink information collection from multiple users.TDMA serves uplink transmissions, while downlink WPT continues during uplink communication.
- Optimization problems: The paper studies STM with fixed total time and TTM with per-user data requirements and minimized charging-plus-transmission time.These are identified as the two fundamental optimization problems for the proposed network.
- STM: The STM formulation is convex, admits a closed-form optimal time allocation, and can be computed by a linear-complexity algorithm.The paper also reports that STM throughput is non-decreasing as the number of users increases under the same total-time constraint.
- Scheduling: Simulations indicate that low-SNR users should transmit first for STM, whereas high-SNR users should transmit first for TTM.The paper therefore concludes that user scheduling should differ between the two optimization objectives.
- TTM: The TTM optimal solution may not be unique, but a two-step algorithm obtains an optimal time allocation by exploiting coupling constraints.Two suboptimal time-allocation schemes are also proposed for both STM and TTM.
II. SYSTEM MODEL
The system uses a full-duplex HAP with separate antennas for downlink wireless energy transfer and uplink information reception. Users harvest energy before their TDMA transmission slots, coupling later users’ available energy to earlier transmission times.
- Network architecture: The HAP uses one antenna for downlink wireless energy transfer and another for receiving uplink information.Uplink reception uses TDMA, while the HAP continuously broadcasts energy during the frame.
- Energy causality: Users harvest energy before, but not after, their transmission slots, so later users can harvest more energy.The model assumes no alternative energy source or battery storage, and harvested energy must be used within the frame.
- Uplink transmission: Each user transmits in an allocated TDMA slot, with no mutual user interference.The HAP uses successive interference cancellation to decode and subtract the downlink energy signal before information detection.
- Optimization objectives: The paper studies sum-throughput maximization under a fixed total time and total-time minimization for users with required uplink data.These are formulated as the two principal optimization problems for the proposed network.
III. SUM-THROUGHPUT MAXIMIZATION
The sum-throughput problem allocates harvesting and uplink transmission time under energy-causality and total-time constraints. Its throughput formulation is established as a convex optimization problem through concavity of user throughput functions.
- Problem formulation: The sum-throughput objective is the total system throughput T(τ), optimized over nonnegative harvesting and transmission durations.The formulation uses τ = [τ0, · · · , τK]^T and a normalized total time of T = 1.
- Convexity analysis: Each user throughput function Ti(τ) is concave in the nonnegative time-allocation vector τ.The proof establishes negative semidefiniteness of the Hessian, including its diagonal and off-diagonal entries.
- Convexity analysis: Problem 1 is a convex optimization problem because its objective is concave and its constraints are affine.The paper reaches this conclusion by summing the concave user-throughput functions and applying standard convex-optimization conditions.
- Optimality property: The optimal time allocation exhausts the available total time.The proof uses the fact that the objective increases with the harvesting duration τ0.
B. Optimal Solution
The paper derives the STM solution through KKT conditions and a sequential closed-form computation involving the Lambert W-function. The resulting two-pass algorithm scales favorably as users are added, while sum throughput is non-decreasing in user count.
- Optimal solution: The STM optimum is obtained by solving the KKT conditions under strong duality.Slater’s condition applies because a strictly positive feasible time allocation exists with total duration below one.
- Optimal solution: The auxiliary variables xi are computed sequentially in closed form using the Lambert W-function, then converted into optimal time allocations.Each ci depends only on previously computed auxiliary values, enabling a forward computation followed by reverse time allocation.
- Algorithm: The proposed computation is a two-pass algorithm: sequentially compute xi, then compute τi in reverse order.When extending from K to K + 1 users, only the second pass needs to be rerun.
- Algorithm: The algorithm has good scalability because adding a user does not require recomputing earlier sequential auxiliary values.The first pass remains unchanged for existing users because each xi depends only on preceding values.
- User count: Sum throughput is non-decreasing as the number of users increases under the same total-time constraint.The proof adds a new user while assigning it zero transmission time, preserving the previous feasible allocation and throughput.
IV. TOTAL-TIME MINIMIZATION
The total-time problem minimizes charging and transmission time while satisfying each user’s data requirement. The paper analyzes its coupled constraints and uses their monotonic and geometric properties to obtain an optimal solution.
- Problem formulation: The TTM problem minimizes the completion time for charging and transmitting all users’ required data.The formulation constrains all time variables to be nonnegative and assumes Di > 0 for every user.
- Optimality property: The Kth constraint holds with equality at the optimal solution.The proof uses that x log(1 + c/x) increases with x, allowing the final transmission time to be adjusted until the constraint is tight.
- Coupled constraints: Each user’s harvesting time is coupled with the transmission times of all preceding users, making the optimization difficult to solve.This coupling is the central structural feature analyzed before constructing the solution method.
- Constraint properties: The function Vi(τi) is strictly decreasing in transmission time τi.The result relies on positive required data Di and supports the subsequent constraint analysis.
- Geometric interpretation: The ith constraint is represented geometrically by a line and a curve, with the shaded region denoting feasibility.For Ci below its critical value there is no intersection; for Ci above it, there are two intersection points.
B. Optimal Solution
The paper derives an optimal solution for total-time minimization using constraint properties and an efficient two-step computation. The solution may be non-unique when K ≥ 2, whereas it is unique when K = 1.
- B. Optimal Solution: The optimal solution of Problem 2 is obtained at the largest k satisfying the stated constraint condition.The computation first identifies this largest k, then solves for the remaining C_i and τ_i values.
- B. Optimal Solution: The constraint analysis considers cases where the (K−1)th constraint is either satisfied or violated, adjusting C_K or τ_K accordingly.Choosing the smaller feasible root in Case 1 preserves feasibility for remaining constraints, while Case 2 requires increasing C_K.
- B. Optimal Solution: Algorithm 3 efficiently computes an optimal time allocation for Problem 2 after k is found.The algorithm outputs τ*_0 through τ*_K.
- B. Optimal Solution: When K ≥ 2, the optimal time allocation of Problem 2 may not be unique.For K = 2, any allocation on a specified feasible line can be optimal under the stated conditions.
- B. Optimal Solution: When K = 1, the optimal time allocation of Problem 2 is unique.The paper states that the unique allocation is given by the corresponding closed-form expression.
V. SUBOPTIMAL TIME ALLOCATION
The paper proposes suboptimal time-allocation schemes for STM and TTM to assess optimization benefits and develop lower-complexity methods with near-optimal performance.
- V. SUBOPTIMAL TIME ALLOCATION: Two suboptimal time-allocation schemes are proposed for the sum-throughput maximization and total-time minimization problems.The schemes are intended for both performance comparison and lower-complexity operation.
- V. SUBOPTIMAL TIME ALLOCATION: The schemes examine whether optimization improves system performance.
- V. SUBOPTIMAL TIME ALLOCATION: The schemes aim to achieve near-optimal performance with lower complexity.
A. Sum-throughput maximization
The STM formulation is established as a convex optimization problem, enabling an efficient optimal time-allocation strategy. Equal-time and fixed-TDMA schemes are also examined as suboptimal alternatives.
- A. Sum-throughput maximization: Two suboptimal STM schemes allocate equal time to users, either including the initial charging slot or optimizing that slot separately.The fixed-TDMA scheme keeps τ0 as an optimization variable while equalizing user transmission times.
- A. Sum-throughput maximization: The STM objective is concave in the initial charging time τ0, so the resulting Problem 3 is a convex optimization problem.The concavity follows from the user-level function and preservation of concavity under summation.
- A. Sum-throughput maximization: The optimal STM solution can be calculated with a subgradient method because the problem has one optimization variable.The cited passage notes that implementation details are omitted.
B. Total-time minimization
The TTM section develops equal-time and tangent-point allocation schemes and uses the coupling constraints to determine feasible charging time. A throughput-versus-HAP-power figure is also included.
- B. Total-time minimization: The TTM analysis considers equal-time allocation, assigning the same duration to each user and the initial charging slot.Under this restriction, the problem is simplified subject to each user's throughput requirement.
- B. Total-time minimization: The tangent-point scheme chooses user durations from the tangent-point construction used to derive the optimal TTM solution.The scheme is explicitly inspired by the graphic method for Problem 2.
- B. Total-time minimization: The initial charging time τ0 is selected as the smallest value satisfying all coupling constraints and can be found by bisection search.This follows because the left-hand side of each constraint is monotonic increasing in τ0.
VI. NUMERICAL RESULTS
Simulations evaluate assumptions, user scheduling, throughput, and time-allocation strategies. Throughput increases with HAP transmit power and user count, while optimal allocation becomes more valuable in larger or higher-power settings.
- A. Simulation setup: The simulations assume unit receiver noise power, identical unit harvesting efficiency and data demand, i.i.d. Rayleigh fading, and averages over 1000 channel realizations.
- 1) Effect of the user scheduling:: Increasing-order SNR scheduling, serving the lowest-SNR user first, outperforms decreasing-order scheduling for throughput.
- 1) Effect of the user scheduling:: The throughput gap between scheduling schemes increases with PH, indicating that scheduling matters more at higher HAP transmit power.
- 2) Optimal Vs. Suboptimal Time Allocation: Optimal time allocation always outperforms equal time allocation, and their throughput gap widens as PH increases.
- 2) Optimal Vs. Suboptimal Time Allocation: Throughput increases with the number of users under both optimal and equal time allocation; at K = 10, their gap reaches 1.
C. Total-time minimization
The total-time results compare scheduling and time-allocation strategies in the full-duplex wireless-powered network. Decreasing-order SNR scheduling performs slightly better, while tangent-point allocation closely approaches the optimum and total time falls as PH increases.
- C. Total-time minimization: For total-time minimization, decreasing-order SNR scheduling performs better than increasing-order scheduling, although the gap is quite small.
- C. Total-time minimization: Poor-SNR users determine overall collection time because they require longer charging and transmission periods, whereas good-SNR users finish quickly.
- C. Total-time minimization: Total collection time decreases as PH increases, and the scheduling gap also decreases with increasing PH.
- 2) Optimal Vs. Suboptimal Time Allocation: Optimal time allocation always outperforms tangent-point allocation, whose performance gap is very small.
- The paper models a full-duplex HAP that transfers downlink wireless power while receiving TDMA uplink information from energy-harvesting users.
- STM is convex with a closed-form, linear-complexity solution, while TTM admits an optimal two-step algorithm exploiting coupling constraints.
- Sum throughput is non-decreasing in the number of users, and simulations show that STM and TTM require different scheduling strategies.