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Enhanced Secure Wireless Information and Power Transfer via Intelligent Reflecting Surface
Weiping Shi, Xiaobo Zhou, Linqiong Jia, Yongpeng Wu, Feng Shu, Jiangzhou Wang
TL;DR
The paper studies how to maximize EHR harvested power in secure IRS-aided MISO SWIPT while satisfying secrecy-rate and IRS phase-shift constraints. It jointly optimizes AP beamforming and IRS phases using SDR and lower-complexity SCA methods, with the proposed schemes approximately doubling harvested power versus methods without IRS and SCA nearly matching SDR at much lower complexity.
Problem
Secure SWIPT needs IRS-assisted optimization of harvested power while preserving secrecy under coupled, non-convex beamforming and phase-shift constraints.
Source: §I · pp. 1–2Method
The paper uses SDR-based alternating optimization with Gaussian randomization, then develops an SCA-based alternating algorithm with semi-closed-form IRS phase updates.
Source: §I · p. 2, B. Proposed low-complexity SCA method · p. 4, C. Complexity Analysis · p. 4Results
The proposed SDR and SCA methods approximately double harvested power versus existing methods without IRS at the same secrecy rate, while SCA nearly matches SDR with much lower complexity.
Source: C. Complexity Analysis · p. 4, §IV · p. 5, §V · p. 5Takeaways & Limitations
IRS phase optimization provides a new degree of freedom and diversity gain for improving secure SWIPT harvested power, with SCA offering a lower-complexity alternative to SDR.
Source: §IV · p. 5, §V · p. 5
Abstract
from arXiv · showhide
In this paper, secure wireless information and power transfer with intelligent reflecting surface (IRS) is proposed for a multiple-input single-output (MISO) system. Under the secrecy rate (SR) and the reflecting phase shifts of IRS constraints, the secure transmit beamforming at access point (AP) and phase shifts at IRS are jointly optimized to maximize the harvested power of energy harvesting receiver (EHR). Due to the non-convexity of optimization problem and coupled optimization variables, firstly, we convert the optimization problem into a semidefinite relaxation (SDR) problem and a sub-optimal solution is achieved. To reduce the high-complexity of the proposed SDR method, a low-complexity successive convex approximation (SCA) technique is proposed. Simulation results show the power harvested by the proposed SDR and SCA methods approximately double that of the existing method without IRS given the same SR. In particular, the proposed SCA achieves almost the same performance as the proposed SDR but with a much lower complexity.
I. INTRODUCTION
The paper addresses secure IRS-aided SWIPT by jointly optimizing AP beamforming and IRS phase shifts to maximize EHR harvested power under secrecy and phase-shift constraints. It proposes SDR and lower-complexity SCA solutions for the resulting non-convex problem.
Related work
- Prior IRS studies optimize received power, energy efficiency, or secrecy rate, while prior secure SWIPT work does not address the IRS-aided setting.Existing SWIPT approaches also face limited wireless power-transfer range because of severe path loss.Source: §I · p. 1
Research gap and objective
- Secure IRS-aided SWIPT is formulated to maximize EHR harvested power while maintaining secure transmission in an AP–information receiver–EHR system with an eavesdropper.The HPMP jointly optimizes secure transmit beamforming and IRS phase shifts.Source: §I · p. 1
Optimization challenge
- The HPMP is non-convex because of the secure-rate and uni-modular phase-shift constraints and the coupling between beamforming and IRS variables.The paper therefore uses alternating optimization to address the coupled design.Source: §I · pp. 1–2
Proposed methods
- SDR-based alternating optimization with Gaussian randomization obtains a sub-optimal solution after transforming the problem into a tractable matrix formulation.The paper then proposes SCA-based alternating optimization to reduce the SDR method’s high complexity.Source: §I · p. 2
Expected outcome
- The proposed SDR and SCA algorithms harvest higher power than conventional schemes without IRS under the same secure-transmission requirement.The SCA method is designed as the lower-complexity alternative.Source: §I · p. 2
II. SYSTEM MODEL
The system is an IRS-assisted downlink MISO SWIPT network in which an AP transmits confidential information to Bob while an EHR and EVE receive the reflected broadcast signal. The model defines the channels, IRS reflection coefficients, rates, secrecy rate, and harvested power used in the optimization.
System architecture
- The network contains an AP with M antennas, an IRS with N reflecting units, single-antenna Bob and EHR, and a single-antenna eavesdropper.The AP transmits a confidential message toward Bob with IRS assistance.Source: §II · p. 2, Figure 1 · p. 2
Signal model
- The transmit beamforming vector w carries Bob’s confidential message under the AP power constraint, while received signals at Bob, EVE, and EHR include their respective channels and noise.The model assumes quasi-static fading and complex AWGN at the receivers.Source: §II · p. 2
IRS model
- The IRS reflection matrix uses phase shifts θ_n and amplitudes β_n, with β_n=1 assumed in this paper.The phase shifts determine the reflected signal configuration.Source: §II · p. 2
Rate and harvesting model
- Bob’s and EVE’s achievable rates define the secrecy rate, while the EHR harvests power from the information beam.The paper explicitly uses the broadcast nature of wireless channels to carry energy with the information signal.Source: §II · p. 2
Energy harvesting
- The harvested-power expression scales the received signal power by the harvesting efficiency ζ.The efficiency parameter appears directly in the EHR harvested-power model.Source: §II · p. 2
III. PROBLEM FORMULATION AND PROPOSED SOLUTION
The paper maximizes EHR harvested power by jointly designing AP beamforming and IRS phase shifts while enforcing a minimum secrecy rate and IRS phase constraints. Because the resulting HPMP is non-convex and variables are coupled, it is solved iteratively after a matrix reformulation.
Problem formulation
- The optimization maximizes EHR harvested power subject to a minimum secrecy rate, AP power budget, and IRS phase-shift constraints.The channel state information of all receivers is assumed available at the AP and IRS.Source: §III · p. 2
Non-convexity
- The HPMP is non-convex because its objective and constraints are non-convex and the beamforming vector w is coupled with the IRS matrix Θ.The objective is convex with respect to each variable separately, motivating alternating optimization.Source: §III · p. 2
Solution strategy
- Alternating optimization fixes one design variable while updating the other to address the coupled beamforming and phase-shift problem.The paper applies this alternating and iterative manner to the reformulated problem.Source: §III · pp. 2–3
Matrix reformulation
- Introducing u and v represents the IRS phase shifts in an augmented vector, while the associated matrix formulation encodes the phase constraints as unit-modulus conditions.The reformulation converts the original variables into a form suitable for subsequent optimization.Source: §III · p. 3
A. Proposed SDR-based alternating optimization method
The SDR-based method lifts beamforming and IRS variables into matrix variables, relaxes their rank-one constraints, and alternates between two semidefinite programs. Gaussian randomization then recovers a high-quality sub-optimal solution.
SDR formulation
- Dropping rank(W)=1 and rank(V)=1 yields an SDR of the matrix-formulated optimization problem.Here, W=ww^H and V=vv^H represent the lifted beamforming and IRS variables.Source: A. Proposed SDR-based alternating… · p. 3
Alternating optimization
- With either IRS phases or beamforming fixed, the relaxed problem decomposes into two standard semidefinite programs solvable by CVX.This decomposition enables alternating optimization over the coupled variables.Source: A. Proposed SDR-based alternating… · p. 3
Rank recovery
- Gaussian randomization recovers rank-one candidates and produces a high-quality sub-optimal solution for the original problem.The randomization addresses the rank-one constraints omitted by the SDR.Source: A. Proposed SDR-based alternating… · p. 3
Convergence
- The SDR-based alternating objective is non-decreasing across iterations and therefore converges to a locally optimal solution.The convergence statement applies to the relaxed alternating procedure.Source: A. Proposed SDR-based alternating… · p. 3
B. Proposed low-complexity SCA method
The proposed SCA-based alternating optimization method reduces the complexity of jointly optimizing transmit beamforming and IRS phase shifts under the secure SWIPT problem's non-convex constraints. It uses first-order approximations and bisection search to obtain a sub-optimal solution with guaranteed convergence.
SCA-based AO algorithm
- The SCA-based AO algorithm uses first-order Taylor approximations for beamforming and phase-shift subproblems, then solves the resulting convex subproblem with CVX.The beamforming step applies a global lower-bound approximation, while the phase-shift step uses an equivalent formulation and bisection search.Source: B. Proposed low-complexity SCA method · pp. 3–4
- The phase-shift update sets u(µ) = e^j arg(d+µf), with µ obtained by bisection from the complementary slackness condition.The relevant constraint function is monotone increasing in µ, enabling the search.Source: B. Proposed low-complexity SCA method · p. 4
- The algorithm alternates between optimizing w with SCA and updating θ through the phase-shift solution until the relative harvested-power change falls below ǫ.Each iteration updates the harvested-power measure Er(t) and checks the convergence criterion.Source: B. Proposed low-complexity SCA method · p. 4
Convergence
- The objective value is non-decreasing after each iteration and has a finite upper bound, so Algorithm 1 is guaranteed to converge.The monotonicity follows from applying first-order Taylor expansions in the objective function.Source: B. Proposed low-complexity SCA method · p. 4
C. Complexity Analysis
The complexity analysis contrasts the SDR-based and SCA-based alternating optimization algorithms. Although SCA uses two levels of iteration, its highest-order complexity is cubic rather than eighth-order in the antenna and IRS dimensions.
Complexity expressions
- The SDR-based AO complexity includes the number D of alternating iterations, while the SCA-based expression includes maximum alternating iterations L and SCA iteration counts L1 and L2.The SCA expression also accounts for bisection through log2((λmax − λmin)/ε).Source: C. Complexity Analysis · p. 4
Complexity comparison
- The SCA-based AO algorithm has highest-order complexity M^3 and N^3 FLOPS, compared with M^8 and N^8 FLOPS for the SDR-based AO algorithm.The paper concludes that SCA is much less complex, especially for massive IRS or massive MIMO scenarios.Source: C. Complexity Analysis · p. 4
IV. SIMULATION AND DISCUSSION
Simulations evaluate harvested EHR power under convergence, secrecy-rate, and IRS-size variations. The proposed methods converge rapidly, approximately double harvested power versus the conventional no-IRS scheme, and show similar performance between SCA and SDR.
IV. SIMULATION AND DISCUSSION
- Within about ten iterations, both proposed alternating-optimization methods converge to their power ceilings for SR values of 1bps/Hz and 3bps/Hz.After convergence, both methods improve harvested power over the initial phases.Source: §IV · p. 4, Figure 2 · p. 4
- Approximately doubled harvested power is achieved by both proposed methods versus the conventional scheme under the same secrecy-rate setting.The comparison is reported for N = 50, with IRS-assisted methods outperforming both the no-IRS and random-phase-shifts schemes.Source: §IV · p. 5, Figure 3 · p. 5
- For N = 50, harvested power decreases as SR increases, while SCA approaches SDR when SR<4bps/Hz and is slightly worse when SR>4bps/Hz.Increasing the number of AP antennas also improves harvested EHR power.Source: §IV · pp. 4–5, Figure 3 · p. 5
- With SR = 1bps/Hz, harvested EHR power increases gradually as the number of IRS reflecting elements N increases.The proposed methods remain better than existing methods, whereas random phase shifts provide only a minor improvement over no IRS.Source: §IV · p. 5, Figure 4 · p. 5
V. CONCLUSION
The paper investigates secure transmit beamforming and IRS phase shifting to maximize harvested EHR power in a secure IRS-assisted MISO-SWIPT network. SDR and SCA alternating algorithms address the non-convex problem, with SCA achieving SDR-level performance at much lower complexity.
V. CONCLUSION
- The proposed SCA method achieves the same performance as SDR with much lower complexity, while both methods double harvested power compared with existing methods.These results concern secure IRS-assisted MISO-SWIPT optimization of harvested EHR power.Source: §V · p. 5