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arxiv: 1907.11866 · v1 · pith:2EXDNDDHnew · submitted 2019-07-27 · 💻 cs.NI

Energy Beamforming for Wireless Information and Power Transfer in Backscatter Multiuser Networks

Wenyuan Ma , Wei Wang , Tao Jiang This is my paper

Pith reviewed 2026-05-24 15:04 UTC · model grok-4.3

classification 💻 cs.NI
keywords energy beamformingbackscatter communicationwireless power transferinformation transfermultiuser networkschannel state informationmax-min optimizationachievable rate
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The pith

Energy beamforming with estimated backscatter channel info maximizes the minimum rate across tags while meeting energy needs.

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

The paper develops an energy beamforming approach for backscatter networks that handles both wireless power delivery and data transmission at the same time. It casts the design as a max-min problem that lifts the worst-case tag's achievable rate under a total energy limit, using only estimated backscatter channel state information. Closed-form expressions are given for the energy harvesting rate at each tag and for a lower bound on the ergodic rate. Simulations show the method beats prior beamforming schemes and comes close to the performance obtained with perfect channel knowledge. The result matters for building fair, reliable low-power backscatter systems where exact channel data is unavailable.

Core claim

The authors formulate energy beamforming as a max-min optimization that maximizes the minimum achievable rate over all tags subject to an energy constraint, derive the closed-form energy harvesting rate, obtain a lower bound on the ergodic achievable rate, and demonstrate through numerical evaluation that the resulting scheme significantly outperforms existing energy beamforming methods while remaining comparable to beamforming that assumes perfect CSI.

What carries the argument

The max-min optimization problem that maximizes the smallest achievable rate across tags subject to the energy constraint, using estimated backscatter channel state information together with the derived closed-form harvesting rate and ergodic-rate lower bound.

If this is right

  • User fairness is enforced because the optimization explicitly protects the tag with the lowest rate.
  • The closed-form harvesting rate allows the energy constraint to be enforced without iterative search.
  • The ergodic-rate lower bound supports analytical design even when exact rate expressions are intractable.
  • Performance close to perfect-CSI beamforming shows that estimation errors do not destroy the gains.
  • The scheme jointly optimizes energy and information, avoiding separate designs that ignore one or the other.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could be extended to time-varying channels by updating the estimates periodically without redesigning the entire optimization.
  • In dense deployments the fairness focus might reduce overall network throughput, suggesting a tunable fairness parameter as a follow-on study.
  • Because the method works with estimated CSI, it fits naturally into protocols that already perform channel sounding for backscatter tags.
  • The same max-min structure might apply to other joint power-and-data problems such as simultaneous wireless information and power transfer without backscatter.

Load-bearing premise

The estimated backscatter channel state information is accurate enough that the closed-form expressions and numerical gains remain valid under real conditions.

What would settle it

A hardware testbed measurement of the minimum tag rate achieved by the proposed beamformer versus prior schemes, using the same estimated CSI that would be available in the field, to check whether the reported gains disappear.

Figures

Figures reproduced from arXiv: 1907.11866 by Tao Jiang, Wei Wang, Wenyuan Ma.

Figure 1
Figure 1. Figure 1: A WPBC network with energy beamforming. only depends on the forward channel (i.e., transmitter-to￾tag), while the achievable rate at the reader depends on the backscatter channel (i.e., transmitter-to-tag-to-receiver). As a consequence, energy beamforming that only maximizes harvested energy cannot guarantee the achievable rate to retain reliable communications. Likewise, energy beamforming that only maxim… view at source ↗
Figure 2
Figure 2. Figure 2: Maximal minimum achievable rate vs. R for three schemes. 0 200 400 600 800 1000 Number of Antennas 10-5 10-4 10-3 10-2 10-1 Energy Harvesting Rate (Watt) E.B. with BS-CSI: User1 E.B. with BS-CSI: User2 E.B. with P-CSI: User1 E.B. with P-CSI: User2 O.T. without E.B.: User1 O.T. without E.B.: User2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Energy harvesting rate vs [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

Wirelessly powered backscatter communication (WPBC) has been identified as a promising technology for low-power communication systems, which can reap the benefits of energy beamforming to improve energy transfer efficiency. Existing studies on energy beamforming fail to simultaneously take energy supply and information transfer in WPBC into account. This paper takes the first step to fill this gap, by considering the trade-off between the energy harvesting rate and achievable rate using estimated backscatter channel state information (BS-CSI). To ensure reliable communication and user fairness, we formulate the energy beamforming design as a max-min optimization problem by maximizing the minimum achievable rate for all tags subject to the energy constraint. We derive the closed-form expression of the energy harvesting rate, as well as the lower bound of the ergodic achievable rate. Our numerical results indicate that our scheme can significantly outperform state-of-the-art energy beamforming schemes. Additionally, the proposed scheme achieves performance comparable to that obtained via beamforming with perfect CSI.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes an energy beamforming design for wirelessly powered backscatter communication (WPBC) multiuser networks that jointly considers energy harvesting and information transfer under estimated backscatter channel state information (BS-CSI). It formulates a max-min optimization problem to maximize the minimum ergodic rate across tags subject to an energy constraint, derives a closed-form expression for the energy harvesting rate and a lower bound on the ergodic achievable rate, and presents numerical results claiming significant outperformance over state-of-the-art schemes as well as performance comparable to perfect-CSI beamforming.

Significance. If the central performance claims hold, the work supplies closed-form expressions and a lower-bound-based max-min formulation that enable efficient beamforming design balancing energy and rate in WPBC systems, which could benefit low-power IoT deployments. The explicit derivation of the energy harvesting rate and the lower bound on ergodic rate are analytical strengths that support reproducible optimization; the numerical demonstration of gains relative to existing schemes would constitute a useful incremental contribution if the bound tightness is confirmed.

major comments (2)
  1. [Formulation section] Formulation section: the max-min problem is solved by optimizing the derived lower bound on ergodic rate (obtained via standard inequalities on the mutual information expression involving estimated BS-CSI) rather than the true ergodic rate; because the beamforming vectors are chosen to maximize this bound, the reported optimality and gains are valid only to the extent the bound is tight under the channel estimation error model and SNR regimes considered.
  2. [Numerical results section] Numerical results section: the claims that the scheme 'significantly outperform[s] state-of-the-art energy beamforming schemes' and 'achieves performance comparable to that obtained via beamforming with perfect CSI' rest on the lower-bound optimization; the manuscript does not report the gap between the optimized lower bound and Monte-Carlo estimates of the true ergodic rate for the final beamformers, leaving open the possibility that the observed gains are artifacts of bound looseness rather than genuine improvements.
minor comments (2)
  1. [Abstract and Numerical results section] The abstract and numerical results section should explicitly state the channel estimation error variance model and the specific parameter values (e.g., SNR ranges, number of antennas, tag count) used to generate the performance curves.
  2. Notation for the estimated BS-CSI and the energy harvesting rate expression could be introduced with a short table or consistent symbols to improve readability across the derivation and simulation sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the insightful comments on our manuscript. We provide point-by-point responses to the major comments below and will incorporate revisions as indicated.

read point-by-point responses

  1. Referee: [Formulation section] Formulation section: the max-min problem is solved by optimizing the derived lower bound on ergodic rate (obtained via standard inequalities on the mutual information expression involving estimated BS-CSI) rather than the true ergodic rate; because the beamforming vectors are chosen to maximize this bound, the reported optimality and gains are valid only to the extent the bound is tight under the channel estimation error model and SNR regimes considered.

    Authors: We agree that our optimization is based on the lower bound of the ergodic rate rather than the exact expression, which is intractable. This is a standard technique in wireless communication literature for designing beamformers under channel uncertainty. The bound is obtained via standard inequalities and we believe it is tight in the operating regimes of interest. In the revision, we will add a sentence in the formulation section to clarify this point and note the implications for the optimality claims. revision: yes

  2. Referee: [Numerical results section] Numerical results section: the claims that the scheme 'significantly outperform[s] state-of-the-art energy beamforming schemes' and 'achieves performance comparable to that obtained via beamforming with perfect CSI' rest on the lower-bound optimization; the manuscript does not report the gap between the optimized lower bound and Monte-Carlo estimates of the true ergodic rate for the final beamformers, leaving open the possibility that the observed gains are artifacts of bound looseness rather than genuine improvements.

    Authors: We acknowledge that the manuscript would benefit from explicitly showing the difference between the lower bound and the true ergodic rate. We will perform additional Monte-Carlo simulations in the revised version to evaluate the true ergodic rate achieved by our beamforming design and compare it to the lower bound, as well as to the perfect CSI benchmark. This will substantiate that the bound is tight and the reported gains are valid. revision: yes

Circularity Check

0 steps flagged

No circularity: derivations of closed-form EH rate and rate lower bound are independent of simulation outcomes

full rationale

The paper derives a closed-form energy harvesting rate expression and a lower bound on ergodic rate directly from the estimated BS-CSI channel model and standard bounding techniques (e.g., Jensen-type inequalities on mutual information). These expressions are then inserted into the max-min optimization formulation. Numerical results merely evaluate the resulting beamformers against baselines; they do not feed back into or redefine the closed-form expressions or bounds. No self-citations, fitted parameters renamed as predictions, or ansatzes smuggled via prior work appear in the derivation chain. The central claims therefore remain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard wireless communication assumptions about channel estimation accuracy and the validity of ergodic rate bounding techniques; no new entities are introduced and no free parameters are explicitly fitted in the abstract description.

axioms (1)
  • domain assumption Estimated backscatter CSI is sufficiently accurate for the optimization and performance claims to hold.
    The paper explicitly uses estimated BS-CSI as the basis for beamforming design.

pith-pipeline@v0.9.0 · 5698 in / 1169 out tokens · 29746 ms · 2026-05-24T15:04:55.649739+00:00 · methodology

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Reference graph

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