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Joint Active and Passive Beamforming Optimization for Intelligent Reflecting Surface Assisted SWIPT under QoS Constraints

Qingqing Wu, Rui Zhang

arXiv:1910.06220v2cs.ITeess.SP

TL;DR

The paper studies how to minimize AP transmit power in a multiple-IRS SWIPT system while satisfying individual SINR and harvested-energy QoS constraints. It jointly optimizes AP precoders and IRS phase shifts using a penalty-based iterative method and a lower-complexity parallel algorithm, with simulations validating IRS-enabled WPT range extension and transmit-power saving.

  • Problem

    The paper addresses non-convex QoS-constrained joint active and passive beamforming for IRS-assisted SWIPT, where individual IU SINR and EU energy-harvesting requirements must be met.

  • Method

    The paper jointly optimizes AP transmit precoders and multiple-IRS phase shifts, transforming QoS constraints for a penalty-based algorithm and exploiting local IRS coverage for parallel optimization.

  • Results

    Simulation results validate IRS effectiveness for WPT range extension and transmit-power saving under SWIPT, while the penalty-based algorithm achieves the best performance among compared schemes and handles discrete phase shifts.

  • Takeaways & Limitations

    IRS deployment can reduce the number of transmit antennas required while enabling transmit-power saving and WPT range extension under SWIPT.

Abstract

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Intelligent reflecting surface (IRS) is a new and revolutionizing technology for achieving spectrum and energy efficient wireless networks. By leveraging massive low-cost passive elements that are able to reflect radio-frequency (RF) signals with adjustable phase shifts, IRS can achieve high passive beamforming gains, which are particularly appealing for improving the efficiency of RF-based wireless power transfer. Motivated by the above, we study in the paper an IRS-assisted simultaneous wireless information and power transfer (SWIPT) system. Specifically, a set of IRSs are deployed to assist in the information/power transfer from a multi-antenna access point (AP) to multiple single-antenna information users (IUs) and energy users (EUs), respectively. We aim to minimize the transmit power at the AP via jointly optimizing its transmit precoders and the reflect phase shifts at all IRSs, subject to the quality-of-service (QoS) constraints at all users, namely, the individual signal-to-interference-plus-noise ratio (SINR) constraints at IUs and energy harvesting constraints at EUs. However, this optimization problem is non-convex with intricately coupled variables, for which the existing alternating optimization approach is shown to be inefficient as the number of QoS constraints increases. To tackle this challenge, we first apply proper transformations on the QoS constraints and then propose an efficient iterative algorithm by applying the penalty-based method. Moreover, by exploiting the short-range coverage of IRSs, we further propose a low-complexity algorithm by optimizing the phase shifts of all IRSs in parallel.

I. INTRODUCTION

The paper motivates IRS-assisted SWIPT as a low-cost way to improve communication and wireless power transfer, then formulates QoS-constrained joint active and passive beamforming as an unresolved optimization problem. It proposes penalty-based and parallel algorithms to reduce AP transmit power while satisfying individual information and energy requirements.

  • Motivation: IoT growth motivates scalable wireless networks providing ubiquitous connectivity and perpetual energy supply.The number of IoT devices is anticipated to rise from about 7 billion in 2018 to 22 billion by 2025.
  • Motivation: Long-distance wireless power transfer is a bottleneck because energy users require substantially more received power than information users.Massive MIMO improves WPT efficiency through array and beamforming gains, but introduces high complexity, energy consumption, and hardware cost.
  • IRS opportunity: IRSs use many low-cost passive elements with adjustable phase shifts to reconfigure propagation channels and obtain fine-grained three-dimensional passive beamforming gains.Unlike active beamforming or relaying, IRSs do not amplify or regenerate signals, yielding lower hardware cost, energy consumption, and interference contamination.
  • IRS opportunity: IRS deployment can compensate long-distance RF attenuation, establish nearby energy-harvesting zones, and extend WPT coverage for SWIPT and battery-free IoT networks.Prior IRS-assisted SWIPT work considered weighted sum-power or weighted sum-rate optimization, rather than individual QoS requirements.
  • Problem and contribution: Because alternating optimization becomes inefficient and can get trapped at undesired suboptimal solutions as QoS constraints increase, the paper proposes transformed-constraint penalty-based and parallel IRS phase-shift algorithms.The parallel method exploits the short-range or local coverage of IRSs; numerical results report transmit-power savings while meeting QoS requirements and gains over heuristic benchmarks.
  • Problem and contribution: This paper addresses QoS-constrained joint active and passive beamforming, minimizing AP transmit power subject to individual IU SINR and EU energy-harvesting constraints.The problem has not previously been addressed in the cited literature and is more challenging than weighted aggregate objectives.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The paper models an IRS-assisted SWIPT system with multiple IRSs helping a multi-antenna AP serve single-antenna information and energy users. It formulates effective channels, signal models, QoS measures, and practical channel and reflection assumptions.

  • A. System Model: Multiple IRSs assist SWIPT from an M-antenna AP to single-antenna information users and energy users.
  • A. System Model: Each information or energy user is assigned one individual information or energy beam, with separate precoders and corresponding signals.
  • A. System Model: Information signals are i.i.d. zero-mean unit-variance CSCG variables, whereas energy signals are arbitrary random signals subject to radiation regulations.
  • A. System Model: The model uses TDD, channel reciprocity, uplink-based CSI acquisition, perfect AP channel knowledge, and quasi-static flat fading.
  • A. System Model: Each IRS reflection matrix uses element amplitudes β_n and phase shifts θ_n, with idealized β_n = 1 to maximize signal reflection.
  • A. System Model: The received information-user SINR and energy-user RF power characterize the system’s information and harvesting performance.
  • A. System Model: Multiple distributed IRS effective channels can be represented using an equivalent larger IRS, while separated IRSs yield sparse channel vectors because of limited coverage.
  • A. System Model: Energy-beam interference is assumed cancellable at information users because the known energy waveforms are available to both the AP and receivers.

B. Problem Formulation

The paper minimizes AP transmit power by jointly designing AP precoders and IRS phase shifts under individual information-user SINR and energy-user harvesting constraints. The resulting problem is non-convex and difficult for conventional alternating optimization as QoS constraints multiply.

  • B. Problem Formulation: The objective is to minimize total AP transmit power through joint optimization of transmit precoders and all IRS phase shifts.
  • B. Problem Formulation: The QoS requirements specify minimum SINR γ_i for each information user and minimum RF receive power E_j for each energy user.
  • B. Problem Formulation: Information beams may alone satisfy energy-harvesting constraints after jointly optimizing IRS phases and information beams, potentially eliminating dedicated energy beams.
  • B. Problem Formulation: The formulation couples transmit precoders and IRS phase shifts non-convexly within the QoS constraints, preventing standard globally optimal solution methods.
  • B. Problem Formulation: Alternating optimization iteratively fixes one variable block while optimizing the other, but becomes inefficient with more QoS constraints and can reach undesired suboptimal solutions.
  • B. Problem Formulation: The paper proposes reformulating QoS constraints and applying a penalty-based algorithm to obtain efficiently computable, high-quality suboptimal solutions.

III. PENALTY-BASED ALGORITHM

The proposed solution uses a two-layer penalty framework: block coordinate descent solves a penalized inner problem, while an outer loop updates the penalty coefficient. QoS reformulation separates constraints across users and enables efficient block updates.

  • III. PENALTY-BASED ALGORITHM: The algorithm has an inner block-coordinate-descent layer and an outer penalty-coefficient update layer, iterating until convergence.
  • III. PENALTY-BASED ALGORITHM: Introducing auxiliary variables transforms the SINR and energy-harvesting constraints so that different user constraints become fully decoupled and exclusive.
  • III. PENALTY-BASED ALGORITHM: The reformulated equality constraints remain coupled with precoders and phase shifts, so their quadratic violations are incorporated into the objective as penalty terms.
  • III. PENALTY-BASED ALGORITHM: The penalty coefficient ρ controls equality-constraint violations; decreasing it progressively reduces transmit power while enforcing the constraints within a prescribed accuracy.
  • III. PENALTY-BASED ALGORITHM: A sufficiently large initial ρ provides a good starting point, whereas an excessively small initialization can let penalty terms dominate and diminish the original objective.
  • III. PENALTY-BASED ALGORITHM: For fixed ρ, the non-convex penalized problem is partitioned into precoders, IRS phase shifts, and auxiliary variables, which are optimized alternately.
  • III. PENALTY-BASED ALGORITHM: The block-coordinate iterations continue until the objective’s fractional decrease falls below ε_1 or the maximum iteration count is reached.

B. Inner Layer: Block Coordinate Descent Algorithm for Solving (P3)

The inner layer updates precoders, IRS phases, and auxiliary variables in separate blocks. Phase updates use elementwise unit-modulus optimization, while auxiliary-variable subproblems separate across users and admit efficient convex or dual solutions.

  • B. Inner Layer: Block Coordinate Descent Algorithm for Solving (P3): With phases and auxiliary variables fixed, AP transmit precoders are optimized through the corresponding simplified subproblem.
  • B. Inner Layer: Block Coordinate Descent Algorithm for Solving (P3): The unconstrained auxiliary-variable subproblem is a convex quadratic minimization problem, while the general SINR case becomes a one-constraint non-convex QCQP.
  • B. Inner Layer: Block Coordinate Descent Algorithm for Solving (P3): With precoders and auxiliary variables fixed, IRS phases are represented as unit-modulus variables u_n = e^jθ_n and optimized under those constraints.
  • B. Inner Layer: Block Coordinate Descent Algorithm for Solving (P3): Although the phase subproblem is non-convex, each phase is updated while the other N −1 phases remain fixed, and the process repeats to convergence.
  • B. Inner Layer: Block Coordinate Descent Algorithm for Solving (P3): For a fixed phase coordinate, the objective is linear in u_n, yielding a closed-form optimal phase update.
  • B. Inner Layer: Block Coordinate Descent Algorithm for Solving (P3): Auxiliary variables separate into K_I + K_E independent subproblems, each containing only one SINR or energy-harvesting constraint.
  • B. Inner Layer: Block Coordinate Descent Algorithm for Solving (P3): Under Slater’s condition, the one-constraint QCQP has zero duality gap and can be solved efficiently using Lagrange duality and bisection.
  • B. Inner Layer: Block Coordinate Descent Algorithm for Solving (P3): The SINR auxiliary solution uses a dual variable λ_i constrained below one, with monotonicity enabling efficient recovery of primal and dual variables.

C. Outer Layer: Update Penalty Coefficient

The algorithm gradually decreases the penalty coefficient to enforce the equality constraints, trading improved performance against additional outer-layer iterations.

  • C. Outer Layer: Update Penalty Coefficient: The penalty coefficient ρ is gradually decreased to enforce the equality constraints in the converged solution.The penalty term becomes larger as ρ decreases, helping guarantee equality constraints.
  • C. Outer Layer: Update Penalty Coefficient: A larger scaling factor c can achieve better performance but requires more outer-layer iterations.

D. Convergence Analysis and Computational Complexity

Algorithm 1 alternates updates of precoders, phase shifts, and auxiliary variables within penalty-based inner and outer loops. Its objective is non-increasing and bounded, yielding convergence to a stationary point, while complexity is explicitly characterized.

  • D. Convergence Analysis and Computational Complexity: The penalty coefficient decreases until the equality-constraint violation ξ falls below the predefined accuracy ϵ2.
  • D. Convergence Analysis and Computational Complexity: For any ρ, block coordinate descent produces a non-increasing objective, while the objective is bounded below.
  • D. Convergence Analysis and Computational Complexity: The proposed algorithm is guaranteed to converge to a stationary point of (P1).

IV. ALTERNATIVE LOW-COMPLEXITY ALGORITHM

The alternative algorithm separates IRS phase-shift design from AP precoder optimization by exploiting IRSs’ short-range coverage. It optimizes different IRSs in parallel, significantly reducing phase-shift complexity while retaining the proposed QoS-oriented subproblem structure.

  • IV. ALTERNATIVE LOW-COMPLEXITY ALGORITHM: Algorithm 1 may require successive optimization of all IRS phase shifts, motivating a low-complexity alternative.
  • IV. ALTERNATIVE LOW-COMPLEXITY ALGORITHM: The alternative separates phase-shift and transmit-precoder design, assuming each user mainly receives reflected signals from its nearest IRS.The assumption is motivated by IRSs’ short-range or local coverage and their deployment sufficiently far apart to avoid complicated inter-IRS interference management.
  • IV. ALTERNATIVE LOW-COMPLEXITY ALGORITHM: Users are associated with their closest IRS, whose phase shifts are optimized by solving a unit-modulus subproblem for the associated users.
  • IV. ALTERNATIVE LOW-COMPLEXITY ALGORITHM: The phase shifts of different IRSs can be optimized in parallel, after which effective channels are constructed and AP precoders are optimized.
  • IV. ALTERNATIVE LOW-COMPLEXITY ALGORITHM: The phase-shift complexity of Algorithm 2 is significantly reduced compared with Algorithm 1 because of the separate design.The overall complexity is given as O(I0N + IinnIout(M^3 + M^2(KI + KE) + (K^2KIKE)log2(1/ϵ3))).

A. Convergence of Algorithm 1

The simulations examine Algorithm 1’s convergence and IRS-aided wireless power transfer under specified user and channel setups. The reported results show satisfaction of QoS-related equality constraints and reduced transmit-power requirements with IRS assistance.

  • A. Convergence of Algorithm 1: With KE = 4, KI = 4, E0 = 5 µW, and γ0 = 20 dB, Fig. 3 evaluates equality-constraint violation and Algorithm 1 convergence.
  • A. Convergence of Algorithm 1: 10−7: increasing outer-layer iterations eventually satisfies the equality constraints within the predefined accuracy.This indicates that Algorithm 1 obtains a solution satisfying all user QoS constraints in (P1).
  • A. Convergence of Algorithm 1: The transmit power required at the AP converges quickly under different setups.
  • A. Convergence of Algorithm 1: As outer-layer iterations increase, or equivalently as ρ decreases, the required AP transmit power increases.A smaller ρ imposes a larger penalty on equality-constraint violations, generally requiring more transmit power to reduce the penalty term.
  • B. IRS-aided WPT: The IRS-aided WPT study compares alternating optimization, fixed phase shifts, and no IRS under LoS-dominated and rich-scattering environments.

1) AP Transmit Power versus AP-EU Distance:

IRS deployment reduces AP transmit power and extends the WPT operating range, while the proposed Algorithm 1 outperforms alternating optimization and fixed-phase benchmarks. LoS AP–IRS channels are more effective than Rayleigh-fading channels under the same average path loss.

  • AP Transmit Power versus AP-EU Distance:: IRS deployment alleviates transmit-power decay with distance and extends the WPT operating range without compromising EU RF receive-power targets.Without IRS, transmit power increases drastically as EUs move farther from the AP.
  • AP Transmit Power versus AP-EU Distance:: Beyond 7 m, EUs cannot meet the harvesting constraint without IRS at about 6 W, whereas LoS IRS deployment makes 12 m feasible.The IRS compensates distance-dependent path loss through aperture and beamforming gains near EUs.
  • AP Transmit Power versus AP-EU Distance:: Under the same average AP–IRS path loss, LoS channels require much less transmit power than Rayleigh-fading channels because rank-deficient LoS channels induce stronger effective-channel correlation.The stronger correlation renders WPT more efficient.
  • AP Transmit Power versus AP-EU Distance:: As the number of EUs increases, the performance gap widens and alternating optimization suffers considerable loss, while Algorithm 1 remains superior to the compared benchmarks.The number of EUs also represents the number of QoS constraints in this comparison.
  • AP Transmit Power versus AP-EU Distance:: IRS deployment reduces the number of energy beams required by aligning effective EU channels, simplifying AP transmitter design.LoS AP–IRS deployment needs only one energy beam in all considered cases; more reflecting elements also reduce beam requirements under Rayleigh fading.

1) AP Transmit Power versus Number of Reflecting Elements:

Increasing IRS reflecting elements improves SWIPT performance, although discrete phase shifts and separate information–energy beam design incur losses relative to the proposed joint design. IRS gains become especially useful at higher EU energy targets.

  • AP Transmit Power versus Number of Reflecting Elements:: Discrete phase shifts lose performance relative to continuous phase shifts because reflected signals become misaligned, but still outperform systems without IRS.This demonstrates benefits even with low-cost coarse phase shifters.
  • AP Transmit Power versus Number of Reflecting Elements:: The separate information–energy beam design suffers considerable performance loss compared with the proposed joint design.The performance gap decreases as the IRS aperture becomes larger because joint precoders can better serve IUs despite increased energy leakage.
  • AP Transmit Power versus Number of Reflecting Elements:: As the EU RF receive-power target increases, IRS deployment produces more evident transmit-power reductions.At small targets, information-beam energy leakage is often sufficient; at high targets, IRS path-loss compensation is more useful.
  • AP Transmit Power versus Number of Reflecting Elements:: With IRS, dedicated energy beams provide much smaller savings because optimized IRS phase shifts can make information-beam leakage sufficient for EU harvesting constraints.This weakens the need for dedicated energy beams and can simplify AP beamforming and IU receiver design.
  • AP Transmit Power versus Number of Reflecting Elements:: Deploying IRS around EUs improves effective EU channel gains, reducing transmit power allocated to dedicated energy beams in most cases.The effect is attributed to the additional IRS beamforming gain.

3) AP Transmit Power versus Number of IUs:

Increasing the number of IUs can make IU interference the SWIPT bottleneck, reducing the benefit of IRSs deployed only around EUs. A second IRS around IUs and the low-complexity parallel algorithm address broader multi-hotspot settings.

  • AP Transmit Power versus Number of IUs:: With IRS around EUs, dedicated energy beams yield negligible additional transmit-power reduction, especially as the number of IUs increases.This is consistent with the observation that optimized information-beam leakage often satisfies EU harvesting constraints.
  • AP Transmit Power versus Number of IUs:: As the number of IUs increases, IRS gains around EUs decrease because more severe multiuser interference makes IUs the performance bottleneck.IRS deployment around EUs alone is no longer sufficient when IU demand becomes dominant.
  • AP Transmit Power versus Number of IUs:: When IU counts or SINR targets are high, additional IRS deployment around IUs may be needed.The paper identifies this as a practical boundary for IRS deployment focused only on EUs.
  • AP Transmit Power versus Number of IUs:: The paper jointly optimizes AP transmit precoders and multiple-IRS phase shifts under IU SINR and EU harvesting constraints using two algorithms.The penalty-based algorithm targets performance, while the second algorithm balances performance and computational complexity.
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