Source-linked AI summary
User Cooperation in Wireless Powered Communication Networks
Hyungsik Ju, Rui Zhang
TL;DR
The paper asks how user cooperation can address unfairness from the doubly near-far problem in wireless powered communication networks. It proposes a two-user cooperative harvest-then-transmit protocol and jointly optimizes time and power allocations for weighted sum-rate maximization. Analytical results and simulations show improved throughput and desired user fairness compared with noncooperative operation.
Problem
The doubly near-far problem causes unfair rate allocation, and how cooperation can overcome it while improving throughput and fairness remains unknown.
Method
The paper lets the nearer user use part of its harvested energy and uplink time to relay the farther user, then jointly optimizes time and power allocations for weighted sum-rate.
Results
Analytical results and simulations show that the proposed user cooperation scheme improves achievable throughput over the baseline without cooperation.
Takeaways & Limitations
User cooperation can improve throughput while achieving desired user fairness in the studied two-user WPCN.
Abstract
from arXiv · showhide
This paper studies user cooperation in the emerging wireless powered communication network (WPCN) for throughput optimization. For the purpose of exposition, we consider a two-user WPCN, in which one hybrid access point (H-AP) broadcasts wireless energy to two distributed users in the downlink (DL) and the users transmit their independent information using their individually harvested energy to the H-AP in the uplink (UL) through time-division-multiple-access (TDMA). We propose user cooperation in the WPCN where the user which is nearer to the H-AP and has a better channel for DL energy harvesting and UL information transmission uses part of its allocated UL time and DL harvested energy to help to relay the far user's information to the H-AP, in order to achieve more balanced throughput optimization. We maximize the weighted sum-rate (WSR) of the two users by jointly optimizing the time and power allocations in the network for both wireless energy transfer in the DL and wireless information transmission and relaying in the UL. Simulation results show that the proposed user cooperation scheme can effectively improve the achievable throughput in the WPCN with desired user fairness.
I. INTRODUCTION
The paper addresses unfair rate allocation in WPCNs caused by the doubly near-far problem by introducing user cooperation and jointly optimizing network resources. The proposed scheme uses the near user’s harvested energy and uplink time to relay the far user’s information, improving throughput and fairness over a noncooperative baseline.
- Motivation: The WPCN’s doubly near-far problem gives far users less harvested downlink energy while requiring more uplink power for comparable communication performance.This leads to unfair rate allocations when sum-throughput is maximized.
- Motivation: Prior work improved fairness by assigning shorter uplink information-transmission time to near users and longer time to far users.
- Contribution: The paper studies whether user cooperation can overcome the doubly near-far problem while improving network throughput and user fairness.
- System and protocol: In the two-user WPCN, an H-AP broadcasts energy in the downlink, and users transmit independently harvested-energy-powered information in the uplink via TDMA.
- Cooperation protocol: The better-connected near user spends part of its uplink time and harvested energy relaying the far user’s information before transmitting its own information.
- Optimization: The scheme maximizes the two users’ weighted sum-rate by jointly optimizing downlink energy-transfer and uplink information-transmission time and power allocations.
- Results: Analytical results and simulations show throughput gains over the baseline scheme without user cooperation.
II. SYSTEM MODEL
The system model is a two-user WPCN with one H-AP, downlink wireless energy transfer, and uplink information transmission using harvested energy. User U2 is nearer to the H-AP and cooperates by relaying U1’s information.
- Network model: The network contains one H-AP and two users, with the H-AP supplying downlink energy while users replenish operational and communication energy from received signals.
- Topology assumptions: U2 is assumed nearer to the H-AP than U1, with D10 ≥ D20, and U2 can more conveniently decode U1’s information under D12 ≤ D10.
- Channel model: The model uses reciprocal downlink and reversed uplink channels with power gains h10, h20, and h12 that incorporate distance attenuation, shadowing, and fading.
- Channel model: Channels are block-based quasi-static flat-fading, remaining constant during each block while varying across blocks; the H-AP knows the relevant channel gains perfectly.
- Protocol: The protocol extends harvest-then-transmit operation to user cooperation over the same frequency band.
UL WIT
During each block, the H-AP first wirelessly powers the users, after which U1 transmits and U2 relays U1 before sending its own information. Time and power allocations determine the achievable rates under energy constraints.
- Transmission protocol: The block begins with a downlink wireless-energy-transfer phase lasting τ0T, followed by uplink transmissions organized according to the cooperation protocol.
- U1 transmission: U1 transmits its information during τ1T using harvested energy, and both the H-AP and U2 decode the received signal.
- U2 cooperation: U2 uses the remaining uplink time first to relay U1’s decoded information and then to transmit its own information.
- Energy constraints: U2’s combined relay and own-information transmission energy cannot exceed η2E2, while users use fixed portions ηi of harvested energy for uplink operation.
- Rate formulation: The optimization represents time allocations as τ = [τ0, τ1, τ21, τ22] and uplink powers as P = [P1, P21, P22] to characterize achievable user rates.
III. OPTIMAL TIME AND POWER ALLOCATIONS IN WPCN WITH USER COOPERATION
The paper reformulates joint time and power allocation as a time-allocation problem, then solves the resulting convex optimization using Lagrange duality. User cooperation enlarges achievable throughput regions relative to the noncooperative baseline, with larger far-user gains as path-loss severity increases.
- Optimization reformulation: Joint time and power allocation is reformulated as a time-allocation-only problem by introducing variables for U2’s relaying and own-transmission durations.The reformulation uses t21 and t22 to represent portions of harvested energy allocated to relaying U1’s information and transmitting U2’s own information.
- Solution method: At the optimum, all available frame time is allocated across downlink energy transfer and uplink transmission or relaying.The cited optimality conditions require t21 + t22 = τ0 and justify reallocating unused time to improve U2’s rate without reducing U1’s rate.
- Optimization reformulation: The transformed problem is convex because its objective and relevant rate functions are concave while the constraints are affine.The formulation also satisfies Slater’s condition, enabling solution through Lagrange duality.
- Solution method: The dual solution is obtained by minimizing the dual function over nonnegative multipliers, after which the optimal time allocation and corresponding power allocation are recovered.An iterative optimization and subgradient-based multiplier update procedure, such as the ellipsoid method, is described for solving the problem.
- Throughput evaluation: The cooperative throughput region is always larger than the noncooperative region, while the far-user throughput gain reaches 1.33, 1.92, and 3.60 for α = 2, 2.5, and 3.The noncooperative scheme is a special case obtained by setting τ21 = 0 and P21 = 0; the gain increases as the doubly near-far problem becomes more severe.
- Throughput evaluation: As κ increases, more time is allocated to U2 for its own transmission and relaying because U2 experiences greater signal attenuation.The reported increase in τ22 reflects the need for additional time to maximize common throughput when U2 moves farther from the H-AP.
IV. SIMULATION RESULT
Simulations compare user cooperation with a no-cooperation baseline under fixed and fading-channel setups. Cooperation yields higher common throughput, with gains depending on transmit power, κ, and α.
- Simulation setup: Under practical fading, Rayleigh channel gains are exponentially distributed with unit mean.The setup uses the same other system parameters as in earlier figures.
- Transmit-power comparison: At α = 2 and κ = 0.5, cooperation produces notably higher maximum average common-throughput than the baseline, especially as P0 increases.The comparison is against optimized time allocation without user cooperation.
- κ and α effects: With cooperation, common-throughput first increases with κ and then decreases beyond a threshold, while the throughput-maximizing threshold increases with α.Figure 7 uses α = 2, 2.5, and 3.
- Common-throughput comparison: The maximum common-throughput with cooperation is always larger than without cooperation.This comparison is reported for varying κ at P0 = 30 dBm.
V. CONCLUSION
The paper jointly optimizes cooperation and resource allocation in a two-user WPCN to improve throughput while achieving desired fairness. Convex reformulation and simulations show that cooperation improves both throughput and user fairness, while future work broadens the considered setups.
- Conclusion: The two-user WPCN jointly exploits user cooperation and time-and-power allocation to maximize network throughput and achieve desired fairness.The design addresses the doubly near-far problem.
- Conclusion: The maximum weighted sum-rate is characterized through problem reformulation and convex-optimization tools.
- Conclusion: Extensive simulations comparing throughput regions and maximum common-throughput show that cooperation improves throughput and user fairness.The comparison includes WPCNs with and without user cooperation.
- Future work: Future work considers extending the results beyond the present setup to more than two users, alternative relaying schemes, and other performance metrics.
PROOF OF LEMMA 3.1
The proof establishes concavity of the relevant rate expressions by applying a supporting lemma to their dependence on the time-allocation variables.
- Proof of Lemma 3.1: The proof invokes a lemma asserting that a function g(x, y) is jointly concave for nonnegative variables.
- Proof of Lemma 3.1: The rate functions R1(t) and R2(t) depend on elements of t and have the same form as the concave function used in the lemma.The time vector includes τ0, τ1, τ21, τ22, t21, and t22.
- Proof of Lemma 3.1: Therefore, the relevant rate functions are concave functions of the time-allocation vector t.
PROOF OF LEMMA A.1
The proof represents the Hessian of g(x1, x2) using its entries and shows that it is negative semi-definite, establishing joint concavity in x1 and x2.
- The Hessian ∇2g(x1, x2) is represented as the matrix [di,j] for i, j ∈ {1, 2}.
- For an arbitrary real vector v = [v1, v2]T, the Hessian-based quadratic form is evaluated to establish its definiteness.
- ∇2g(x1, x2) is negative semi-definite.
- Therefore, g(x1, x2) is jointly concave in x1 and x2, completing Lemma A.1.
PROOF OF PROPOSITION 3.1
The proof establishes convexity and derives optimality conditions for (P2), then obtains the relevant variables through quadratic and monotonic-function relationships.
- (P2) is a convex optimization problem satisfying the conditions required for global optimality through its necessary and sufficient conditions.
- The optimization variables satisfy the time-allocation equality τ∗0 + τ∗1 + τ∗21 + τ∗22 = 1.
- The proof assumes λ∗2 > 0 except when no harvested energy at U2 is used for uplink wireless information transmission.
- λ∗1 = 0 occurs only when τ∗0 = t∗21 = t∗22 = 0, meaning the H-AP transfers no energy.
- After algebraic manipulation, the stationarity condition becomes the quadratic equation az1^2 + bz1 + c = 0.
- The proof also derives τ∗0 = τ∗1 from the relevant optimality relation.
- Because f(z) is monotonically increasing, the corresponding equations yield unique z∗21 and z∗22 and then t∗21 and t∗22.