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Weighted Sum Power Maximization for Intelligent Reflecting Surface Aided SWIPT
Qingqing Wu, Rui Zhang
TL;DR
Far-field WPT efficiency limits the SWIPT rate-energy trade-off, motivating IRS assistance for stronger passive beamforming. The paper jointly optimizes AP precoding and IRS phases under IDR SINR constraints, and proves that information signals alone suffice while simulations show substantial gains.
Problem
SWIPT requires improved WPT efficiency because EHRs need much higher receive power than IDRs, limiting the rate-energy trade-off.
Method
The paper jointly optimizes AP transmit precoders and IRS phase shifts to maximize weighted EHR sum-power under individual IDR SINR constraints.
Results
Information signals alone suffice to achieve maximum weighted EHR sum-power with arbitrary user channels when at least one IDR is present, while IRS designs significantly improve the R-E trade-off.
Takeaways & Limitations
IRS deployment can drastically enlarge the SWIPT R-E trade-off, with strong AP-IRS LoS beneficial for harvested EHR energy.
Abstract
from arXiv · showhide
The low efficiency of far-field wireless power transfer (WPT) limits the fundamental rate-energy (R-E) performance trade-off of the simultaneous wireless information and power transfer (SWIPT) system. To address this challenge, we propose in this letter a new SWIPT system aided by the emerging intelligent reflecting surface (IRS) technology. By leveraging massive low-cost passive elements that are able to reflect the signals with adjustable phase shifts, IRS achieve a high passive beamforming gain, which is appealing for drastically enhancing the WPT efficiency and thereby the R-E trade-off of SWIPT systems. We consider an IRS being deployed to assist a multi-antenna access point (AP) to serve multiple information decoding receivers (IDRs) and energy harvesting receivers (EHRs). We aim to maximize the weighted sum-power received by EHRs via jointly optimizing the transmit precoders at the AP and reflect phase shifts at the IRS, subject to the individual signal-to-interference-plus-noise ratio (SINR) constraints for IDRs. Since this problem is non-convex, we propose efficient algorithms to obtain suboptimal solutions for it. In particular, we prove that it is sufficient to send information signals only at the AP to serve both IDRs and EHRs regardless of their channel realizations. Moreover, simulation results show significant performance gains achieved by our proposed designs over benchmark schemes.
I. INTRODUCTION
SWIPT faces a critical WPT-efficiency challenge because EHRs require much higher receive power than IDRs. The paper introduces IRS assistance to improve this trade-off and establishes that dedicated energy signals are unnecessary.
- EHRs may require tens of dB more receive power than IDRs, making WPT efficiency critical to improving SWIPT’s R-E trade-off.
- IRS elements use adjustable phase shifts to create high passive beamforming gains for improving WPT efficiency.IRS reflection is passive, generally noise-free, and full-duplex, without requiring transmit RF chains.
- The studied system uses an IRS to assist a multi-antenna AP serving multiple IDRs and EHRs in an energy charging zone.The IDRs are assumed unable to cancel interference from any AP-transmitted energy signals.
- Dedicated energy signals are unnecessary even with arbitrary user channels, provided that at least one IDR is present.The paper extends the corresponding result from conventional SWIPT and proposes efficient algorithms for the resulting non-convex problem.
A. System Model
The system models IRS-assisted SWIPT from a multi-antenna AP to single-antenna IDRs and EHRs using linear precoding and adjustable IRS reflection coefficients. Received IDR signals and EHR power depend on direct and IRS-reflected channels.
- An IRS with N reflecting elements assists an M-antenna AP serving sets of single-antenna IDRs and EHRs.Each receiver is assigned one dedicated information or energy beam under linear precoding.
- The AP is assumed to know all link CSI perfectly under a quasi-static flat-fading model for characterizing the optimal R-E trade-off.
- The IRS reflection matrix has adjustable amplitudes and phase shifts, with β_n=1 selected to maximize signal reflection.The effective receiver channels combine the AP-to-receiver direct link with the AP-to-IRS-to-receiver reflected link.
- IDRs cannot cancel energy-signal interference, which is therefore included in their SINR calculation.EHR received RF power is evaluated while ignoring noise power.
B. Problem Formulation
The paper formulates weighted sum-power maximization for EHRs subject to individual IDR SINR constraints. Joint AP-precoder and IRS-phase optimization is non-convex, and the necessity of dedicated energy beams is initially unresolved.
- The objective maximizes the weighted sum-power received by EHRs subject to individual SINR constraints for IDRs.Each nonnegative energy weight α_j represents the priority assigned to EHR j.
- The AP transmit precoders and IRS phase shifts are jointly optimized through their coupled effects on the objective and SINR constraints.
- The resulting optimization problem is non-convex and challenging to solve optimally.
- It remains unknown at formulation whether dedicated energy beams are necessary when at least one IDR is present.The question is whether v_j=0 for all EHRs can still achieve optimality.
III. SPECIAL CASE: IRS-AIDED WPT
For the EHR-only special case, the paper solves IRS-aided WPT by alternating optimization over energy precoders and IRS phases. The method converges because the objective is non-decreasing and bounded, with closed-form updates in each iteration.
- With no IDRs, the problem reduces to IRS-aided WPT involving only EHR energy delivery.
- Alternating optimization iteratively updates energy precoders and IRS phase shifts because fixing either block yields an efficiently solvable problem.
- For fixed IRS phases, all optimal EHR energy precoders align with the principal eigenvector of the weighted channel matrix S.Consequently, one common energy beam suffices for all EHRs without loss of optimality.
- When one EHR has a much larger weight, the AP should beam energy toward that EHR to maximize its received RF power.
- The alternating algorithm converges because its objective is non-decreasing and upper-bounded, and each iteration has a closed-form optimal update.
IV. IRS-AIDED SWIPT: ENERGY BEAMFORMING OR NOT?
The paper shows that dedicated energy signals are unnecessary in the IRS-aided SWIPT system, even with arbitrary user channels. It develops an alternating optimization approach for the resulting non-convex joint precoding and phase-shift problem.
- IRS-Aided SWIPT: Energy Beamforming or Not?: The joint optimization of AP precoders and IRS phase shifts is non-convex, motivating an efficient alternating optimization algorithm.The algorithm alternates between information-precoder optimization and IRS phase-shift optimization.
- IRS-Aided SWIPT: Energy Beamforming or Not?: Dedicated energy signals are unnecessary for optimal weighted sum-power when at least one IDR is present, regardless of user-channel dependence.This extends the conventional SWIPT result beyond statistically independent channels.
- IRS-Aided SWIPT: Energy Beamforming or Not?: For fixed IRS phase shifts, the transmit precoders can be obtained from the semidefinite relaxation with the energy covariance set to zero.The resulting rank-one information covariance matrices allow recovery of the transmit precoders by eigenvalue decomposition.
- IRS-Aided SWIPT: Energy Beamforming or Not?: For fixed transmit precoders, the phase-shift subproblem is relaxed to a convex semidefinite program by dropping its rank-one constraint.Gaussian randomization can recover a feasible solution when the relaxed optimum is not rank one.
- IRS-Aided SWIPT: Energy Beamforming or Not?: The alternating algorithm converges because its objective is non-decreasing and upper-bounded, while each iteration admits a closed-form optimal subproblem solution.The algorithm stops when objective improvement falls below a threshold or the relaxed problem becomes infeasible.
V. NUMERICAL RESULTS
The numerical study evaluates the proposed designs under specified channel, receiver, and IRS settings, including AP–IRS distance variation. It uses a 4-antenna AP and 50 reflecting elements as default parameters.
- Numerical Results: The numerical evaluation sets the reference-distance signal attenuation to 30 dB for all channels.The simulations use distinct pathloss assumptions for AP–IRS, IRS-user, and AP-user links.
- Numerical Results: Fig. 2 plots EHR received sum-power against the AP–IRS distance r0.The figure examines how deployment distance relates to harvested sum-power.
- Numerical Results: The default setup uses σ2_i = −90 dBm, common IDR SINR target γ, unit EHR weights α_j = 1, M = 4, and N = 50.These parameters apply unless otherwise specified.
A. IRS-Aided WPT
For IRS-aided WPT, the proposed design improves EHR received sum-power relative to no-IRS and benchmark schemes. An LoS AP–IRS channel provides more harvested energy than a Rayleigh-fading AP–IRS channel in the evaluated setting.
- A. IRS-Aided WPT: Deploying the IRS around EHRs significantly improves their received sum-power over no-IRS and benchmark schemes in both AP–IRS channel cases.The comparison uses KE = 4 and a proposed design with M = 4.
- A. IRS-Aided WPT: The LoS AP–IRS channel enables EHRs to receive more RF energy than the Rayleigh-fading AP–IRS channel.The simulations model LoS by setting all elements of G to 1 and rich scattering by independent CN(0, 1) elements.
- A. IRS-Aided WPT: Rank-one AP–IRS channels can make one energy beam more effective because channel correlation among EHRs allows simultaneous energy harvesting.This contrasts with information transmission, where rank deficiency can increase multiuser interference.
B. IRS-Aided SWIPT
In the IRS-aided SWIPT setting with IDRs and EHRs, deploying the IRS significantly enlarges the achievable power–SINR region. A design using a dedicated energy beam performs worse than the proposed information-only design.
- B. IRS-Aided SWIPT: Deploying the IRS significantly enlarges the achievable power–SINR region for the SWIPT system.The comparison considers KI = 2 IDRs and KE = 2 EHRs.
- B. IRS-Aided SWIPT: Without compromising IDR SINR, the IRS greatly improves the RF power received by EHRs.The result is reported for the evaluated LoS-dominated AP–IRS deployment.
- B. IRS-Aided SWIPT: The benchmark with one dedicated energy beam suffers considerable performance loss compared with the proposed design.The paper attributes this to the result that dedicated energy signals should not be used in the considered system.
VI. CONCLUSION
The paper formulates weighted sum-power maximization for IRS-assisted SWIPT and develops suboptimal joint AP-precoding and IRS-phase algorithms. The design requires no dedicated energy signals and substantially enlarges the SWIPT R-E trade-off, with strong AP–IRS LoS benefiting harvested energy.
- The paper studies weighted sum-power maximization for an IRS-assisted SWIPT system.
- Efficient algorithms jointly optimize AP precoding and IRS phase shifts to obtain suboptimal solutions.
- Dedicated energy signals are unnecessary for general SWIPT systems with arbitrary user channels.
- The proposed IRS design drastically enlarges the SWIPT R-E performance trade-off relative to benchmark designs.
- Deploying the IRS in strong LoS with the AP benefits harvested EHR energy and the system R-E trade-off.
APPENDIX A: PROOF OF PROPOSITION 1
The proof establishes equivalence between formulations with and without dedicated energy covariance by constructing an equally effective solution using information beams only. It then invokes rank-one optimality for the information covariance matrices.
- The proof compares SDR1, which permits an energy covariance matrix, with SDR2, which fixes W_E = 0.
- Because SDR2 is a special case of SDR1, its optimal objective value cannot exceed that of SDR1.
- For any optimal SDR1 solution, the proof constructs a feasible SDR2 solution attaining the same weighted sum-power.
- When a SINR dual variable is positive, dummy information beams can replace energy beams without affecting the corresponding SINR constraint.
- The resulting equality of optimal values implies that only information signals are needed, and an optimal solution with rank-one information covariances exists.