pith. sign in

arxiv: 2604.18986 · v1 · submitted 2026-04-21 · 💻 cs.IT · math.IT

A Tight Channel-Capacity Lower Bound for the Simultaneous Wireless Information and Power Transfer Integrated Receiver

Konstantinos Ntontin , Symeon Chatzinotas This is my paper

Pith reviewed 2026-05-10 02:24 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords SWIPTintegrated receiverchannel capacity lower boundSchottky diodeTaylor expansiongamma distributionprobability transition matrixnonlinear rectification
0
0 comments X

The pith

A gamma-distributed input with a fourth-order Taylor expansion of the Schottky diode curve yields a tight lower bound on channel capacity for the integrated SWIPT receiver.

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

The paper develops a channel-capacity lower bound for simultaneous wireless information and power transfer that uses an integrated receiver rather than the more common separate architecture. It approximates the channel probability transition matrix in closed form by expanding the Schottky diode current-voltage curve to fourth order. Numerical checks show that a gamma input distribution produces a noticeably tighter bound than Rayleigh or uniform inputs. The same checks indicate that retaining the fourth-order term raises the estimated capacity relative to the usual second-order simplification.

Core claim

The paper supplies a closed-form tight approximation to the probability transition matrix of the integrated receiver channel by applying the fourth-order Taylor expansion to the current-voltage characteristic of the Schottky diode used for rectification. With this approximation the authors demonstrate that a gamma input distribution produces a tight lower bound on capacity, outperforming Rayleigh and uniform distributions, and that the fourth-order term produces a higher capacity value than the second-order model.

What carries the argument

The closed-form approximation to the channel probability transition matrix obtained from the fourth-order Taylor expansion of the Schottky diode current-voltage curve.

If this is right

  • A gamma input distribution yields a tighter capacity lower bound than Rayleigh or uniform distributions.
  • Retaining the fourth-order term in the diode expansion increases the predicted capacity relative to the second-order model.
  • The closed-form transition matrix enables explicit computation of information-theoretic limits for integrated receivers.
  • System designers can use the bound to evaluate joint rate and harvested-power performance without full nonlinear simulation.

Where Pith is reading between the lines

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

  • Device engineers could apply the same expansion technique to other nonlinear rectifiers to obtain capacity bounds for different hardware.
  • The gap between second-order and fourth-order predictions suggests that higher-order terms may be needed when input power varies over wide ranges.
  • If the bound proves tight in hardware tests, it could serve as a design tool for selecting modulation and power-splitting ratios in integrated SWIPT nodes.

Load-bearing premise

The fourth-order Taylor expansion of the Schottky diode current-voltage characteristic remains accurate over the voltage range and input power levels relevant to the integrated receiver operation.

What would settle it

Direct measurement of the output voltage statistics produced by a gamma-distributed input applied to a real Schottky diode at typical SWIPT power levels, compared against the probabilities predicted by the fourth-order approximation, would show whether the derived lower bound is tight.

Figures

Figures reproduced from arXiv: 2604.18986 by Konstantinos Ntontin, Symeon Chatzinotas.

Figure 2
Figure 2. Figure 2: Components of the SWIPT separate receiver architecture: a) [PITH_FULL_IMAGE:figures/full_fig_p001_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: SWIPT architecture with separate information and energy [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: SWIPT integrated receiver. The fact that in the SWIPT integrated receiver the output of the rectifier not only supplies the battery, but it is also the information signal to be decoded, creates fundamental differences with respect to the well-studied separate receiver architecture of [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: System model. We consider the system model presented in [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: R ∞ 0 |Fnccs(x) − Fnormal(x)| 2 dx vs. s for k = 2. Fnormal(x)| 2dx quickly goes to 0 as s increases. Proposition 1: p(yDC |u) is approximated as p(yDC |u) ∼= 1 q 2πσ2 yDC exp(− (yDC − µyDC ) 2 2σ 2 yDC ), (8) where µyDC = a4σ 2 u (1 + (2a4µu + a2) 2 4a4σ 2 u ) − a 2 2 4a4 σ 2 yDC = 2(a4σ 2 u ) 2 (1 + 2(2a4µu + a2) 2 4a4σ 2 u ) + Prec (9) [PITH_FULL_IMAGE:figures/full_fig_p003_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: illustrates the channel capacity vs. GLNA curves for the approximate expression based on the Blahut-Arimoto algorithm, our proposed lower bound based on the gamma distribution, two lower bounds based on the uniform and Rayleigh distributions of the same mean with the gamma distribution and, finally, a lower bound that considers only the 2nd- order term of the Taylor approximation. As we observe from [PITH… view at source ↗
read the original abstract

Contrary to the vast majority of works on simultaneous wireless information and power transfer that provide information-theoretic limits for the separate receiver architecture, in this work we focus on the integrated receiver and provide a channel-capacity lower bound. Towards this, we provide a closed-form tight approximation for the probability transition matrix of the channel by leveraging the 4th-order Taylor expansion of the current-voltage characteristic curve of a Schottky diode used for rectification. Numerical results reveal that the consideration of the gamma distribution as an input distribution leads to a tight channel-capacity lower bound, in contrast to other input distributions, such as the Rayleigh and uniform ones. Furthermore, the results reveal that the consideration of the 4th order term in the Taylor expansion leads to a notably higher capacity with respect to the overly simplified 2nd order term-based model.

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

1 major / 1 minor

Summary. The manuscript derives a closed-form approximation to the transition probability matrix of the SWIPT integrated receiver channel by applying a fourth-order Taylor expansion to the I-V characteristic of a Schottky diode. This approximation is then used to evaluate mutual information under gamma, Rayleigh, and uniform input distributions, yielding the claims that the gamma distribution produces a tight capacity lower bound and that the fourth-order model yields notably higher capacity values than the second-order truncation.

Significance. If the fourth-order approximation is shown to be accurate in the relevant operating regime, the work supplies a useful analytic framework for capacity analysis of hardware-efficient integrated receivers, which are more practical than separate architectures. The closed-form transition probabilities and the numerical comparison across input distributions constitute a concrete contribution that could guide signal design in SWIPT systems.

major comments (1)
  1. [Numerical results and abstract] The assertions that the gamma distribution produces a 'tight' lower bound and that the fourth-order expansion produces 'notably higher' capacity than the second-order model rest on the accuracy of the Taylor approximation. The manuscript provides no direct comparison of the approximated transition probabilities (or resulting mutual-information values) against those generated by the exact exponential diode model over the voltage and input-power ranges appearing in the numerical results. Without such validation or an accompanying error analysis, it is impossible to confirm that the reported ordering of distributions and capacity gains are properties of the true channel rather than truncation artifacts.
minor comments (1)
  1. [Abstract] The abstract states that the fourth-order expansion is used but supplies neither the underlying channel assumptions nor any quantitative indication of approximation accuracy.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and for recognizing the potential utility of our analytic framework for integrated SWIPT receivers. We address the major comment below.

read point-by-point responses

  1. Referee: [Numerical results and abstract] The assertions that the gamma distribution produces a 'tight' lower bound and that the fourth-order expansion produces 'notably higher' capacity than the second-order model rest on the accuracy of the Taylor approximation. The manuscript provides no direct comparison of the approximated transition probabilities (or resulting mutual-information values) against those generated by the exact exponential diode model over the voltage and input-power ranges appearing in the numerical results. Without such validation or an accompanying error analysis, it is impossible to confirm that the reported ordering of distributions and capacity gains are properties of the true channel rather than truncation artifacts.

    Authors: We agree that explicit validation against the exact exponential diode model is necessary to rigorously support the claims of tightness and capacity gains. The fourth-order Taylor expansion is a standard modeling choice in the SWIPT literature for the low-power regime of Schottky diodes, and our numerical results use input-power and voltage ranges consistent with typical hardware parameters where the approximation is expected to hold. Nevertheless, to directly address the concern, the revised manuscript will add a dedicated subsection (or figure) that compares the fourth-order approximated transition probabilities and mutual-information values against those obtained from the exact exponential I-V model, for the gamma, Rayleigh, and uniform input distributions over the exact ranges used in the original numerical results. We will also include quantitative error metrics (e.g., average relative error) to confirm that the observed ordering and gains are preserved under the exact model. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation uses independent physical approximation to compute MI lower bound

full rationale

The paper starts from the physical I-V curve of the Schottky diode and applies a standard 4th-order Taylor expansion to obtain a closed-form approximation to the channel transition probabilities. These probabilities are then inserted into the mutual-information expression for chosen input distributions (gamma, Rayleigh, uniform) to produce numerical lower bounds on capacity. This chain contains no self-definitional steps, no parameters fitted to capacity values, no load-bearing self-citations, and no imported uniqueness theorems; the reported ordering and improvement over the 2nd-order model are direct consequences of the explicit approximation and the chosen inputs, not tautological reductions to the inputs themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The derivation rests on the domain assumption that a fourth-order Taylor polynomial adequately captures the diode nonlinearity for the relevant operating regime; no free parameters are introduced beyond those already fixed by the diode physics and the chosen input distribution family.

axioms (1)
  • domain assumption The current-voltage characteristic of the Schottky diode admits a sufficiently accurate fourth-order Taylor expansion around the bias point.
    Invoked to obtain the closed-form transition probability matrix.

pith-pipeline@v0.9.0 · 5437 in / 1274 out tokens · 45099 ms · 2026-05-10T02:24:38.012334+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

  1. [1]

    Fundamentals of wireless information and power transfer: From rf energy harvester models to signal and system designs,

    B. Clerckx, R. Zhang, R. Schober, D. W. K. Ng, D. I. Kim, and H. V . Poor, “Fundamentals of wireless information and power transfer: From rf energy harvester models to signal and system designs,”IEEE Journal on Selected Areas in Communications, vol. 37, no. 1, pp. 4–33, 2019

    work page 2019

  2. [2]

    Wireless power transfer for future networks: Signal processing, ma- chine learning, computing, and sensing,

    B. Clerckx, K. Huang, L. R. Varshney, S. Ulukus, and M.-S. Alouini, “Wireless power transfer for future networks: Signal processing, ma- chine learning, computing, and sensing,”IEEE Journal of Selected Topics in Signal Processing, vol. 15, no. 5, pp. 1060–1094, 2021

    work page 2021

  3. [3]

    Wireless information and energy transfer in the era of 6g communica- tions,

    C. Psomas, K. Ntougias, N. Shanin, D. Xu, K. Mayer, N. M. Tran, L. Cottatellucci, K. W. Choi, D. I. Kim, R. Schober, and I. Krikidis, “Wireless information and energy transfer in the era of 6g communica- tions,”Proceedings of the IEEE, vol. 112, no. 7, pp. 764–804, 2024

    work page 2024

  4. [4]

    Waveform optimization for swipt with nonlinear energy harvester modeling,

    B. Clerckx, “Waveform optimization for swipt with nonlinear energy harvester modeling,” inWSA 2016; 20th International ITG Workshop on Smart Antennas, 2016, pp. 1–5

    work page 2016

  5. [5]

    Ultra-low power receivers for iot applications: A review,

    D. D. Wentzloff, A. Alghaihab, and J. Im, “Ultra-low power receivers for iot applications: A review,” in2020 IEEE Custom Integrated Circuits Conference (CICC), 2020, pp. 1–8

    work page 2020

  6. [6]

    Ambient iot connectivity topologies: Technology enablers, applications, and challenges,

    A. Al-nahari, J. Liao, R. Jäntti, D. Mishra, D.-T. Phan-Huy, and Y . Zhou, “Ambient iot connectivity topologies: Technology enablers, applications, and challenges,”IEEE Internet of Things Magazine, pp. 1–8, 2025

    work page 2025

  7. [7]

    Wireless information and power transfer: Architecture design and rate-energy tradeoff,

    X. Zhou, R. Zhang, and C. K. Ho, “Wireless information and power transfer: Architecture design and rate-energy tradeoff,”IEEE Transac- tions on Communications, vol. 61, no. 11, pp. 4754–4767, 2013

    work page 2013

  8. [8]

    Toward efficient integration of information and energy reception,

    S. A. Tegos, P. D. Diamantoulakis, K. N. Pappi, P. C. Sofotasios, S. Muhaidat, and G. K. Karagiannidis, “Toward efficient integration of information and energy reception,”IEEE Transactions on Communica- tions, vol. 67, no. 9, pp. 6572–6585, 2019

    work page 2019

  9. [9]

    Wireless information and power transfer for iot: Pulse position modulation, integrated receiver, and experimental validation,

    J. Kim and B. Clerckx, “Wireless information and power transfer for iot: Pulse position modulation, integrated receiver, and experimental validation,”IEEE Internet of Things Journal, vol. 9, no. 14, pp. 12 378– 12 394, 2022

    work page 2022

  10. [10]

    Optimal pulse energy modulation for swipt sys- tems with integrated receivers,

    A. Gkekas, V . E. Galanopoulou, O. G. Karagiannidis, S. A. Tegos, and P. D. Diamantoulakis, “Optimal pulse energy modulation for swipt sys- tems with integrated receivers,”IEEE Communications Letters, vol. 29, no. 5, pp. 1028–1031, 2025

    work page 2025

  11. [11]

    In- tegrated swipt receivers: Circuit analysis and performance evaluation,

    E. Demarchou, Z. Bin Ashraf, B. Smida, C. Psomas, and I. Krikidis, “In- tegrated swipt receivers: Circuit analysis and performance evaluation,” IEEE Transactions on Communications, vol. 73, no. 11, pp. 10 345– 10 359, 2025

    work page 2025

  12. [12]

    On the capacity-achieving distribution of the discrete-time noncoherent and partially coherent awgn channels,

    M. Katz and S. Shamai, “On the capacity-achieving distribution of the discrete-time noncoherent and partially coherent awgn channels,”IEEE Transactions on Information Theory, vol. 50, no. 10, pp. 2257–2270, 2004

    work page 2004

  13. [13]

    On the capacity of the block-memoryless phase-noise channel,

    G. Durisi, “On the capacity of the block-memoryless phase-noise channel,”IEEE Communications Letters, vol. 16, no. 8, pp. 1157–1160, 2012

    work page 2012

  14. [14]

    On phase noise channels at high snr,

    A. Lapidoth, “On phase noise channels at high snr,” inProceedings of the IEEE Information Theory Workshop, 2002, pp. 1–4

    work page 2002

  15. [15]

    Optimizing constellations for single-subcarrier intensity-modulated optical systems,

    J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Transactions on Information Theory, vol. 58, no. 7, pp. 4645– 4659, 2012

    work page 2012

  16. [16]

    Upper-bounding the capacity of optical im/dd channels with multiple-subcarrier modulation and fixed bias using trigonometric moment space method,

    R. You and J. Kahn, “Upper-bounding the capacity of optical im/dd channels with multiple-subcarrier modulation and fixed bias using trigonometric moment space method,”IEEE Transactions on Informa- tion Theory, vol. 48, no. 2, pp. 514–523, 2002

    work page 2002

  17. [17]

    Capacity bounds for power- and band-limited optical intensity channels corrupted by gaussian noise,

    S. Hranilovic and F. Kschischang, “Capacity bounds for power- and band-limited optical intensity channels corrupted by gaussian noise,” IEEE Trans. on Information Theory, vol. 50, no. 5, pp. 784–795, 2004

    work page 2004

  18. [18]

    On the capacity of free-space optical intensity channels,

    A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,”IEEE Transactions on Information Theory, vol. 55, no. 10, pp. 4449–4461, 2009

    work page 2009

  19. [19]

    Capacity bounds for wireless optical in- tensity channels with gaussian noise,

    A. A. Farid and S. Hranilovic, “Capacity bounds for wireless optical in- tensity channels with gaussian noise,”IEEE Transactions on Information Theory, vol. 56, no. 12, pp. 6066–6077, 2010

    work page 2010

  20. [20]

    When to use optical amplification in noncoherent transmission: An information- theoretic approach,

    K. Keykhosravi, E. Agrell, M. Secondini, and M. Karlsson, “When to use optical amplification in noncoherent transmission: An information- theoretic approach,”IEEE Transactions on Communications, vol. 68, no. 4, pp. 2438–2445, 2020

    work page 2020

  21. [21]

    Computation of channel capacity and rate-distortion func- tions,

    R. Blahut, “Computation of channel capacity and rate-distortion func- tions,”IEEE Transactions on Information Theory, vol. 18, no. 4, pp. 460–473, 1972

    work page 1972

  22. [22]

    J. G. Proakis,Digital Communications, 4th ed. New York: McGraw- Hill, 2001, iSBN-13: 978-0072321111

    work page 2001

  23. [23]

    Waveform design for wireless power transfer,

    B. Clerckx and E. Bayguzina, “Waveform design for wireless power transfer,”IEEE Transactions on Signal Processing, vol. 64, no. 23, pp. 6313–6328, 2016

    work page 2016