Intelligent Reflecting Surface Aided MIMO Broadcasting for Simultaneous Wireless Information and Power Transfer

Arumugam Nallanathan; Cunhua Pan; Hong Ren; Jiangzhou Wang; Kezhi Wang; Lajos Hanzo; Maged Elkashlan

REVIEW 4 major objections 5 minor 46 references

Intelligent Reflecting Surface Aided MIMO Broadcasting for Simultaneous Wireless Information and Power Transfer

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A passive reflecting surface can nearly double the operating range of wireless energy harvesting.

desk verdict The paper's real contribution is a new problem instance and a plausible BCD-style algorithm, but Theorem 4's proof is not valid as written because it concatenates block KKT systems with different dual multipliers for the same constraint. read the letter →

arxiv 1908.04863 v4 pith:ROHKPW6R submitted 2019-08-13 eess.SP

Cunhua Pan , Hong Ren , Kezhi Wang , Maged Elkashlan , Arumugam Nallanathan , Jiangzhou Wang , Lajos Hanzo This is my paper · ORCID

classification eess.SP

keywords intelligentreflectingsurfacesimultaneouswirelessinformationandpowertransferMIMObroadcastingweightedsumratemaximizationblockcoordinatedescentphaseshiftoptimizationenergyharvestingpassivebeamforming

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that placing an intelligent reflecting surface (a reconfigurable passive mirror) near energy-harvesting receivers lets a base station deliver both data and power more effectively than broadcasting without it. It formulates the design as maximizing the weighted sum rate of information receivers subject to a minimum harvested-power requirement, and solves it by alternating between optimizing base-station precoding and IRS phase shifts. The paper proves each subproblem converges to a Karush-Kuhn-Tucker point and that the overall alternating algorithm converges to a KKT point of the original non-convex problem. Simulations show the harvested-power target can be met at much larger distances with an IRS, with the weighted sum rate also improving by up to about 10 bit/s/Hz.

What carries the argument

The engine is the WMMSE reformulation of weighted sum rate, which turns the rate objective into a block-friendly form, followed by block coordinate descent. With phase shifts fixed, the precoding subproblem is handled by successive convex approximation of the energy-harvesting constraint plus a Lagrangian dual/bisection search; with precoders fixed, the phase-shift subproblem is recast as a quadratic program under a unit-modulus constraint and solved by majorization-minimization with a price-based bisection for the energy constraint. The unit-modulus phase vector $\varphi$ and the equivalent channels $H_{b,k}+H_{r,k}\Phi Z$ carry the passive beamforming effect.

What would settle it

Run the same scenario with channel estimation errors of the magnitude produced by current two-stage IRS channel estimators; if the weighted-sum-rate or harvested-power advantage over no-IRS shrinks toward zero, or the 5.5-to-9 m range extension disappears, the central claim is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that jointly optimizing the base station's transmit precoding matrices and the IRS's passive phase shift matrix can satisfy a fixed harvested-power requirement at energy receivers while maximizing the weighted sum rate of information receivers, and that doing so expands the energy receivers' operating range. The design problem is solved by a block coordinate descent algorithm that alternates between a convexified precoding update and a phase-shift update; each subproblem provably reaches a KKT point, and the overall algorithm provably converges to a KKT point of the original problem. In simulation, the IRS lifts the maximum energy-receiver distance from about 5.5 m (no IRS) to about 9 m with 40 reflecting elements, and yields up to about 10 bit/s/Hz higher weighted sum rate than a no-IRS baseline.

Load-bearing premise

The base station knows all channels perfectly, and the authors state that this makes the results an upper bound.

Editorial extensions

If this is right

Placing the IRS near the energy receivers, rather than midway between base station and receivers, is the configuration that yields the large range extension reported in the simulations.
The number of reflecting elements $M$ is a direct performance knob: with 40 elements the energy-receiver working distance grows from 5.5 m to 9 m, and the weighted sum rate grows with $M$.
IRS location matters through the path-loss exponent of the IRS links; when that exponent rises to 3, most of the weighted-sum-rate gain over no-IRS disappears, so obstacle-free siting is part of the design.
A quick feasibility check can tell an operator whether an energy-harvesting target can be met at all under the transmit power limit before running the full optimization.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the perfect-CSI assumption is relaxed with a realistic channel-estimation error model, the range-extension numbers should be treated as upper bounds; the authors themselves flag robust design as future work.
The same alternating pattern—convexify the energy-harvesting constraint, optimize phase shifts by majorization-minimization, and price the constraint—applies to other IRS design problems with non-convex unit-modulus and coupling constraints, such as secrecy-rate or latency-constrained designs.
A testable next step is to replace the linear energy-harvesting model with a nonlinear rectifier model; the optimal precoding and phase-shift split may shift toward concentrating power in the rectifier's sensitive region.
Because the block coordinate descent loop converges to a KKT point rather than a global optimum, comparing it to a global solver on small instances would show how much performance is left on the table.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: the paper has a real problem instance — WSR maximization for IRS-assisted SWIPT MIMO with EH constraints — and the algorithm is a sensible assembly of WMMSE, SCA, MM, and pricing. The subproblem derivations are mostly careful, and the simulations are internally consistent. But the sharpest claim, Theorem 4, is not proven as written.

The stress-test note is right. Appendix D takes a KKT point for the F block with multiplier mu* on the EH constraint and a KKT point for the phase block with multiplier nu* on the same constraint, then declares the concatenation to be the KKT conditions of the original problem. In the original KKT system, a single multiplier must appear in both stationarity equations. Nothing shows mu* = nu*. For block coordinate methods with coupled constraints, coordinatewise stationarity does not imply joint stationarity; the example in the note (max x + 2y s.t. x^2 + y^2 >= 1, x,y >= 0) demonstrates the failure mode cleanly. So the convergence-to-KKT claim is unsupported.

Other soft spots are smaller. Algorithm 3's step 1 terminates when J(0) <= Qhat, which is the wrong side of the inequality; that looks like a straightforward typo. Theorem 1 and Lemma 3 are deferred to 'similar to' references; acceptable if the referenced arguments truly carry over, but Lemma 3's monotonicity underlies the bisection and should be stated. The paper also assumes perfect CSI and a linear EH model, which the authors acknowledge gives an upper bound; that limits the practical reach of the range-extension numbers but does not undercut the algorithmic framework.

Credit where due: the WMMSE reformulation, the SCA lower bound on the EH constraint, the MM bounding for the phase objective, and the price-based global optimality argument for the subproblem are all standard tools applied carefully. The simulations use sensible benchmarks and the complexity accounting is explicit. The self-citations are heavy but the cited prior work is genuinely relevant.

The audience is researchers in IRS/RIS and SWIPT resource allocation. They get a useful algorithm and a clean problem formulation. The paper deserves serious refereeing, but a referee should push for a repaired proof of Theorem 4 — either a true joint-KKT argument or a weaker but honest convergence statement.

Referee Report

4 major / 5 minor

Summary. This paper considers an intelligent reflecting surface (IRS) aided multiuser MIMO simultaneous wireless information and power transfer (SWIPT) system. A multi-antenna base station serves multiple multi-antenna information receivers (IRs) while guaranteeing a weighted sum harvested-power constraint for energy receivers (ERs), with the IRS deployed in the vicinity of the ERs. The authors formulate the weighted sum rate (WSR) maximization problem over transmit precoding matrices and the IRS phase-shift matrix, subject to the transmit power budget, the energy-harvesting (EH) constraint, and unit-modulus phase constraints. They propose a block coordinate descent (BCD) algorithm based on the WMMSE reformulation: the precoding subproblem is solved by successive convex approximation with a bisection-search dual method, and the phase-shift subproblem by an MM method combined with a price-based bisection method. They prove convergence of the subroutines and claim that the BCD algorithm converges to a KKT point of the original problem (Theorem 4). A feasibility-checking algorithm is also presented. Simulations over a Rician/Rayleigh fading scenario with four ERs and two IRs demonstrate that the IRS significantly improves the harvested power and WSR relative to no-IRS and fixed-phase benchmarks, and that the BCD algorithm converges quickly.

Significance. The paper addresses a timely problem and provides a plausible algorithmic framework that appears to work numerically. The WMMSE transformation, the SCA lower bound for the nonconvex EH constraint, and the MM bounding of the phase objective are sensible, and the simulation results support the qualitative claim that IRS deployment extends the ER operating range and improves WSR. The claimed guarantees, especially Theorem 4's assertion of KKT convergence for the BCD algorithm, are central to the paper's theoretical contribution and are not established by the arguments given. The paper also acknowledges the perfect-CSI assumption as a limitation, which is appropriate. If the convergence claims are corrected or appropriately weakened, the algorithmic and numerical contributions would be of interest to the SWIPT and IRS communities. The provided proofs for the subproblem algorithms are mostly standard when given; the omitted proofs and the flawed concatenation in Appendix D are the main obstacles.

major comments (4)

[Appendix D, Theorem 4] The proof of Theorem 4 concatenates the KKT stationarity and complementary slackness equations of the F-block (D.3)-(D.5), with dual variable μ* for the energy-harvesting constraint, and those of the phase block (C.5), (C.6), (C.8), with dual variable ν* for the same constraint. The KKT conditions of Problem (8) require a single multiplier ξ for constraint (8c), and that same ξ must multiply the gradient of the constraint in both stationarity equations. The authors do not prove μ* = ν*, and the concatenated equations are therefore not a valid KKT system. Block-coordinate methods with coupled constraints can converge to points that satisfy each block's KKT conditions with different multipliers but do not satisfy the joint KKT conditions, so this gap is a load-bearing error in the central convergence claim.
[Section III-C, Algorithm 3] Step 1 of Algorithm 3 states: 'Calculate J(0). If J(0) ≤ Qhat, terminate; otherwise go to step 2.' Since the linearized EH constraint (43) requires J(p) ≥ Qhat, the termination condition is inverted: when J(0) < Qhat, the candidate φ(0) is infeasible and the bisection step should be invoked; when J(0) ≥ Qhat, the solution should be returned. As written, the algorithm may terminate with an infeasible phase vector, which propagates to Algorithm 4 and undermines the feasibility guarantee in Theorem 3.
[Section III-C, Lemma 3] The monotonicity of J(p) is load-bearing because Algorithm 3 relies on it for the bisection search, yet the proof is omitted with the statement 'similar to Lemma 1 and thus omitted.' Lemma 1's proof concerns the value function of a convex optimization problem with a linear perturbation; J(p) is the value of a linear function evaluated at the global maximizer of a nonconvex unit-modulus problem, so the argument does not transfer directly. The claim is not obviously true for this nonconvex problem, and a complete proof is required.
[Section III-B, Theorem 1] The proof of Theorem 1 is omitted ('similar to [44]'). Because Algorithm 2's SCA treatment of the nonconvex EH constraint differs from the setting of [44], and because Theorem 1 is used as a premise in the proof of Theorem 4, the convergence of the F-block to a KKT point needs a self-contained proof or a precise argument explaining why the proof of [44] covers the present problem.

minor comments (5)

[Equation (7)] The left-hand side uses the subscript i in Q_i, although the quantity is defined for the l-th ER (Q_l); please unify the notation.
[Algorithm 2, Step 1] The initialization statement 'initialize the precoding matrices F(0) from Section 2' should read 'Section IV' (the feasibility-check section).
[Section V, Fig. 3 description] The text describing Fig. 3 uses 'xEH' whereas the figure and the rest of the text use 'xER'; please use one notation consistently.
[Caption of Fig. 3] The caption contains a typo ('Havested Power'); correct it to 'Harvested Power'.
[Notation, Section I] The notation 'A*' and 'A⋆' for the conjugate operator and converged solution, respectively, may be confusing; consider using more standard notation such as A^H for conjugate transpose and A^* for converged value, or a clearer distinction.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central WMMSE/SCA/MM/BCD derivation is self-contained; only a minor self-citation in an omitted subproblem proof, which is not load-bearing.

full rationale

The paper's derivation chain is not circular. Problem (8) is reformulated via the WMMSE equivalence in (12) using standard external references [33] and [39]; the F-block and phase-block algorithms are derived in-line with SCA, dual decomposition, MM, and a price-based search. There is no fitting of parameters to external data, and no fitted quantity is renamed as a prediction: the Section V results are simulations generated from the stated channel model, not independent predictions forced by calibrated inputs. The paper does contain heavy self-citation (e.g., [24], [28], [32], [33], [40], [41], [44]), but these citations are for established proof techniques and prior algorithmic methods, not for the target result. The one flagged omission is Theorem 1, whose proof is delegated to the authors' own [44]: 'The proof is similar to that of [44] and hence it is omitted for simplicity.' This is a completeness concern, but not circularity: [44] is an externally published convergence proof for a different objective, and the F-subproblem updates are independently derived in this paper; the citation does not presuppose Theorem 1 or Theorem 4. The Appendix D issue of concatenating block KKT conditions with distinct dual variables (mu* and nu* for the same EH constraint) is a correctness risk, not a circularity: the claim does not become equivalent by definition to the paper's inputs. Overall, no central step reduces the claimed result to its own assumptions, so the circularity score is low.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities or fitted parameters. The derivation rests on standard WMMSE theory and on three domain assumptions: perfect CSI, linear energy harvesting, and single-reflection dominance. All are explicitly stated in the system model.

assumptions (4)

domain assumption Perfect CSI at the BS for all links (BS-IRS, BS-IR, BS-ER, IRS-IR, IRS-ER).
Stated in Section II-A. The entire algorithm and the claimed performance gains depend on this assumption, and the paper acknowledges it produces an upper bound.
domain assumption Linear energy harvesting model: harvested power is proportional to total received RF power with efficiency eta.
Section II-A. The EH constraint (8c) and all range-extension simulations rely on this linear model, which does not capture nonlinear RF-to-DC conversion.
domain assumption Only single reflections at the IRS are significant; multiple reflections are ignored.
Section II-A: 'Due to absorption and diffraction, the signal power that has been reflected multiple times is ignored.' This yields the equivalent channel Hbar_k = Hb,k + Hr,k Phi Z.
standard math WMMSE equivalence: maximizing WSR is equivalent to optimizing the weighted MSE with optimal U and W.
Used in Section III-A to reformulate Problem (8) into (12). This is a known theorem from [39].

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Cite this review

Pith. "Pith review of Intelligent Reflecting Surface Aided MIMO Broadcasting for Simultaneous Wireless Information and Power Transfer." pith.science (2026). https://pith.science/paper/ROHKPW6R

@misc{pith2026190804863,
  author       = {Pith},
  title        = {Pith review of: Intelligent Reflecting Surface Aided MIMO Broadcasting for Simultaneous Wireless Information and Power Transfer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ROHKPW6R}},
  note         = {Machine review of arXiv:1908.04863}
}

read the original abstract

An intelligent reflecting surface (IRS) is invoked for enhancing the energy harvesting performance of a simultaneous wireless information and power transfer (SWIPT) aided system. Specifically, an IRS-assisted SWIPT system is considered, where a multi-antenna aided base station (BS) communicates with several multi-antenna assisted information receivers (IRs), while guaranteeing the energy harvesting requirement of the energy receivers (ERs). To maximize the weighted sum rate (WSR) of IRs, the transmit precoding (TPC) matrices of the BS and passive phase shift matrix of the IRS should be jointly optimized. To tackle this challenging optimization problem, we first adopt the classic block coordinate descent (BCD) algorithm for decoupling the original optimization problem into several subproblems and alternatively optimize the TPC matrices and the phase shift matrix. For each subproblem, we provide a low-complexity iterative algorithm, which is guaranteed to converge to the Karush-Kuhn-Tucker (KKT) point of each subproblem. The BCD algorithm is rigorously proved to converge to the KKT point of the original problem. We also conceive a feasibility checking method to study its feasibility. Our extensive simulation results confirm that employing IRSs in SWIPT beneficially enhances the system performance and the proposed BCD algorithm converges rapidly, which is appealing for practical applications.

Figures

Figures reproduced from arXiv: 1908.04863 by the authors.

**Figure 1.** An IRS-assisted SWIPT system. power transfer (SWIPT) is an appealing technique for future energy-hungry Internet-of-Things (IoTs) networks. Specifically, a base station (BS) with constant power supply will transmit wireless signals to a set of devices. Some devices intend to decode the information from the received signal, which are termed as information receivers (IRs), while the others will harvest the signal ener… view at source ↗

**Figure 2.** The simulated IRS-aided SWIPT MIMO communication scenario. [PITH_FULL_IMAGE:figures/full_fig_p023_2.png] view at source ↗

**Figure 3.** Maximum harvested power achieved by various schemes. [PITH_FULL_IMAGE:figures/full_fig_p023_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: WSR versus the number of phase shifters. [PITH_FULL_IMAGE:figures/full_fig_p024_5.png]

**Figure 7.** Figure 7: WSR versus the IRS-related path loss exponent [PITH_FULL_IMAGE:figures/full_fig_p025_7.png]

**Figure 9.** Figure 9: WSR versus the location of IR circle center [PITH_FULL_IMAGE:figures/full_fig_p026_9.png]

Discussion (0). Continue with ORCID to comment.

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