pith. sign in

arxiv: 1907.11647 · v1 · pith:SAWXZ2GZnew · submitted 2019-07-25 · 📡 eess.SP · cs.SY· eess.SY

Analysis of RF Energy Harvesting in Uplink-NOMA IoT-based Network

Zhou Ni , Ziru Chen , Qinbo Zhang , Chi Zhou This is my paper

Pith reviewed 2026-05-24 16:35 UTC · model grok-4.3

classification 📡 eess.SP cs.SYeess.SY
keywords IoTNOMAenergy harvestinguplinkPoisson point processthroughputinterferenceRF
0
0 comments X

The pith

An optimal duration T for the downlink energy harvesting phase maximizes total uplink NOMA throughput within a defined harvesting circle.

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

The paper models a cellular IoT network where base stations and devices follow Poisson point processes, dividing each time slot into a downlink energy harvesting phase of duration T and an uplink NOMA data transmission phase. Devices inside a fixed energy harvesting circle collect enough RF energy from all base station transmissions to support their uplink, while inter-cell interference is included in the throughput calculation. The objective is to choose T to maximize the aggregate uplink throughput inside the circle, with analysis of the probability mass function for the number of devices in the circle. Simulations confirm an optimal T exists and show that higher base station density reduces throughput due to interference.

Core claim

Within the energy harvesting circle, the total uplink throughput achieved by NOMA transmissions reaches a maximum at a specific value of the harvesting phase duration T, and base station density must be chosen so that devices inside the circle experience relatively low interference with only small probability of circle overlaps.

What carries the argument

The energy harvesting circle, a region in which every IoT device harvests sufficient RF energy from base station transmissions to enable NOMA uplink, with T varied to maximize aggregate throughput under PPP interference.

If this is right

  • Dense base station deployment decreases total throughput because of increased interference.
  • The probability mass function for the number of IoT devices inside the circle matches Monte Carlo results.
  • Inter-cell interference must be accounted for when computing uplink throughput under the PPP model.
  • Energy harvesting circles should overlap only with low probability to maintain performance.

Where Pith is reading between the lines

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

  • Network planning could treat base station density as a tunable parameter to balance harvested energy against interference levels.
  • The fixed-circle approach implies that protocols adapting the circle radius to local device density might further improve throughput.
  • Validation of the device-count PMF supports using the same stochastic geometry tools for related metrics such as outage probability.

Load-bearing premise

The energy harvesting circle is well-defined and fixed such that all IoT devices inside it harvest sufficient energy for NOMA transmission.

What would settle it

A simulation or calculation in which total uplink throughput inside the circle increases or decreases monotonically with T across a range of base station densities, showing no interior maximum.

Figures

Figures reproduced from arXiv: 1907.11647 by Chi Zhou, Qinbo Zhang, Zhou Ni, Ziru Chen.

Figure 1
Figure 1. Figure 1: Illustration of the system setup and the two sub-slots (Energy harvest, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: PMF of UEs in circle. The system throughput with changed T can be calculated according to equation (6). From this equation, we can find that the total data rate of the whole system is related to the information transmission time and inter-cell interference. In Fig.4, we show that with same energy harvesting time T, smaller λb can reach up to a higher system throughput compared with larger BS density. This … view at source ↗
Figure 2
Figure 2. Figure 2: Relation between r and λb. In Fig.3, we show the accuracy of our equation (5) who gives the PMF of how many UEs in the circle. Then we need to compare the analysis result with simulation result to make sure that they can match with each other. In this simulation, we randomly distribute the BSs and UEs following the PPP. Then one typical cell is extracted from all the cells to present other cells. Therefore… view at source ↗
Figure 4
Figure 4. Figure 4: System throughput with changed [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Compare throughput with and without inter-cell interference. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

Internet of Things (IoT) systems in general consist of a lot of devices with massive connectivity. Those devices are usually constrained with limited energy supply and can only operate at low power and low rate. In this paper, we investigate a cellular-based IoT system combined with energy harvesting and NOMA. We consider all base stations (BS) and IoT devices follow the Poisson Point Process (PPP) distribution in a given area. The unit time slot is divided into two phases, energy harvesting phase in downlink (DL) and data transmission phase in uplink (uplink). That is, IoT devices will first harvest energy from all BS transmissions and then use the harvested energy to do the NOMA information transmission. We define an energy harvesting circle within which all IoT devices can harvest enough energy for NOMA transmission. The design objective is to maximize the total throughput in uplink within the circle by varying the duration T of energy harvesting phase. In our work, we also consider the inter-cell interference in the throughput calculation. The analysis of Probability Mass Function (PMF) for IoT devices in the energy harvesting circle is also compared with simulation results. It is shown that the BS density needs to be carefully set so that the IoT devices in the energy harvesting circle receive relatively smaller interference and energy circles overlap only with a small probability. Our simulations show that there exists an optimal T to achieve the maximum throughput. When the BSs are densely deployed consequently the total throughput will decrease because of the interference.

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

3 major / 1 minor

Summary. The paper models a cellular IoT network with RF energy harvesting in the downlink from all BSs (modeled as PPP) followed by uplink NOMA transmission. It defines a fixed-radius energy harvesting circle inside which all devices are assumed to harvest sufficient energy during duration T for NOMA uplink; the PMF of the number of devices inside this circle is derived and validated by simulation; total uplink throughput (accounting for inter-cell interference) is maximized over T via simulation, showing an optimal T exists, while BS density must be chosen to keep interference low and limit circle overlap.

Significance. If the fixed-circle approximation can be shown to introduce only small error, the work supplies simulation-supported design guidelines for time allocation between energy harvesting and NOMA uplink in dense IoT deployments, together with the observation that excessive BS density harms throughput via interference. The explicit comparison of the derived PMF against Monte-Carlo results is a concrete strength.

major comments (3)
  1. [Abstract / energy harvesting circle definition] Abstract and the section defining the energy harvesting circle: the radius is stated to be chosen so that every device inside harvests enough energy for NOMA transmission, yet the harvested energy at a random location is itself a random sum over the PPP of BS locations and fading; no derivation is supplied showing how the deterministic radius is obtained from the energy threshold, path loss, and BS density, nor is the resulting conditioning error on the throughput and optimal-T claim quantified.
  2. [Throughput analysis and optimization] Throughput maximization over T: the central claim that an optimal T exists is supported only by simulation search; because the throughput expression inside the circle (with inter-cell interference) is not given in closed form as a function of T, it is unclear whether the reported optimum is robust or merely an artifact of the fixed-circle conditioning.
  3. [BS density and interference discussion] BS-density conclusion: the statement that BS density must be set carefully so devices receive smaller interference and circles overlap only with small probability is presented as a design insight, but it rests on the same unquantified fixed-circle approximation; without an error analysis or comparison against a random energy-sufficient point process, the load-bearing interference claim cannot be assessed.
minor comments (1)
  1. [Abstract] Abstract contains minor grammatical issues (e.g., 'constrained with limited energy supply') that should be polished for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below, indicating the revisions we will incorporate.

read point-by-point responses

  1. Referee: [Abstract / energy harvesting circle definition] Abstract and the section defining the energy harvesting circle: the radius is stated to be chosen so that every device inside harvests enough energy for NOMA transmission, yet the harvested energy at a random location is itself a random sum over the PPP of BS locations and fading; no derivation is supplied showing how the deterministic radius is obtained from the energy threshold, path loss, and BS density, nor is the resulting conditioning error on the throughput and optimal-T claim quantified.

    Authors: We agree that harvested energy is random and that the deterministic radius constitutes an approximation. The radius in the manuscript was selected using the expected harvested energy (averaged over BS locations in the PPP and Rayleigh fading) to meet the NOMA transmission threshold under the given path-loss model and BS density. We will add an explicit derivation of this radius choice to the system model section. We will also include new simulation results that quantify the conditioning error by comparing fixed-circle throughput against per-device energy-sufficiency checks, confirming the approximation error remains small in the evaluated regimes. revision: yes

  2. Referee: [Throughput analysis and optimization] Throughput maximization over T: the central claim that an optimal T exists is supported only by simulation search; because the throughput expression inside the circle (with inter-cell interference) is not given in closed form as a function of T, it is unclear whether the reported optimum is robust or merely an artifact of the fixed-circle conditioning.

    Authors: A closed-form throughput expression as a function of T is intractable because T simultaneously affects harvested energy (hence the random number of eligible devices), uplink transmission duration, and the NOMA success probabilities under PPP interference. Numerical optimization via simulation is therefore the appropriate method, consistent with standard practice in stochastic-geometry analyses of IoT networks. To demonstrate robustness, we will augment the results with additional curves of throughput versus T across a range of BS and device densities, explicitly discussing the influence of the fixed-circle model on the location of the optimum. revision: partial

  3. Referee: [BS density and interference discussion] BS-density conclusion: the statement that BS density must be set carefully so devices receive smaller interference and circles overlap only with small probability is presented as a design insight, but it rests on the same unquantified fixed-circle approximation; without an error analysis or comparison against a random energy-sufficient point process, the load-bearing interference claim cannot be assessed.

    Authors: The design guideline follows from the observed trade-off between higher BS density (more harvested energy but stronger uplink interference and greater circle overlap probability). We will revise the discussion to state the reliance on the fixed-circle model explicitly and will add simulation results that vary BS density while reporting both throughput and empirical overlap probability. These results will support the interference claim under the model used in the paper. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on PPP modeling and simulation

full rationale

The paper defines the energy harvesting circle as the region enabling sufficient energy harvest for NOMA transmission under PPP distributions for BSs and devices. It derives PMF and throughput expressions (including inter-cell interference) conditioned on this region, then uses numerical simulation to identify an optimal harvesting duration T that maximizes uplink throughput. No quoted equation or step reduces a claimed prediction or result to an input parameter by construction, nor does any load-bearing premise rest solely on self-citation. The analysis remains self-contained against the stated stochastic geometry assumptions and simulation benchmarks, with the circle definition serving as a modeling choice rather than a tautological fit.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on standard domain assumptions from stochastic geometry and introduces the energy harvesting circle as a modeling simplification without independent empirical grounding beyond the simulation comparison.

free parameters (2)
  • Energy harvesting circle radius
    Chosen or derived so devices inside harvest enough energy for NOMA; directly affects which devices contribute to throughput.
  • Harvesting duration T
    Varied to maximize throughput; the optimum is located via analysis or simulation.
axioms (2)
  • domain assumption Base stations and IoT devices are distributed as independent homogeneous Poisson point processes
    Invoked to model random locations and enable analytical expressions for interference and harvested energy.
  • domain assumption Each time slot is strictly divided into a downlink energy harvesting phase and an uplink data transmission phase
    Modeling choice that enables separate analysis of energy collection and NOMA transmission.

pith-pipeline@v0.9.0 · 5813 in / 1402 out tokens · 43490 ms · 2026-05-24T16:35:04.279982+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

  1. [1]

    Noma with imperfect sic implementation,

    T. Manglayev, R. C. Kizilirmak, Y . H. Kho, N. Bazhayev, and I. Lebedev, “Noma with imperfect sic implementation,” in IEEE EUROCON 2017- 17th International Conference on Smart Technologies . IEEE, 2017, pp. 22–25

    work page 2017

  2. [2]

    Stochastic geometry based performance study on 5g non-orthogonal multiple access scheme,

    Z. Zhang, H. Sun, R. Q. Hu, and Y . Qian, “Stochastic geometry based performance study on 5g non-orthogonal multiple access scheme,” in 2016 IEEE Global Communications Conference (GLOBECOM) . IEEE, 2016, pp. 1–6

    work page 2016

  3. [3]

    Power allocation for a downlink non-orthogonal multiple access system,

    C.-L. Wang, J.-Y . Chen, and Y .-J. Chen, “Power allocation for a downlink non-orthogonal multiple access system,” IEEE wireless com- munications letters , vol. 5, no. 5, pp. 532–535, 2016

    work page 2016

  4. [4]

    Analyzing non-orthogonal multiple access (noma) in downlink poisson cellular networks,

    K. S. Ali, H. ElSawy, A. Chaaban, M. Haenggi, and M.-S. Alouini, “Analyzing non-orthogonal multiple access (noma) in downlink poisson cellular networks,” in 2018 IEEE International Conference on Commu- nications (ICC) . IEEE, 2018, pp. 1–6

    work page 2018

  5. [5]

    Uplink nonorthogonal multiple access in 5g systems,

    N. Zhang, J. Wang, G. Kang, and Y . Liu, “Uplink nonorthogonal multiple access in 5g systems,” IEEE Communications Letters , vol. 20, no. 3, pp. 458–461, 2016

    work page 2016

  6. [6]

    On user pairing in uplink noma,

    M. A. Sedaghat and R. R. M ¨uller, “On user pairing in uplink noma,” IEEE Transactions on Wireless Communications , vol. 17, no. 5, pp. 3474–3486, 2018

    work page 2018

  7. [7]

    Downlink non-orthogonal multiple access (noma) in poisson networks,

    K. S. Ali, M. Haenggi, H. ElSawy, A. Chaaban, and M.-S. Alouini, “Downlink non-orthogonal multiple access (noma) in poisson networks,” IEEE Transactions on Communications , vol. 67, no. 2, pp. 1613–1628, 2018

    work page 2018

  8. [8]

    A stochastic geometry analysis of energy harvesting in large scale wireless networks,

    Z. Chen, Z. Chen, L. X. Cai, Y . Cheng, and R. Gong, “A stochastic geometry analysis of energy harvesting in large scale wireless networks,” in 2018 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber , Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData) , J...

    work page 2018

  9. [9]

    Optimal beamforming design for simultaneous wireless information and power transfer in sustainable cloud-ran,

    Z. Chen, Z. Chen, L. X. Cai, and Y . Cheng, “Optimal beamforming design for simultaneous wireless information and power transfer in sustainable cloud-ran,” IEEE Transactions on Green Communications and Networking , vol. 2, no. 1, pp. 163–174, 2017

    work page 2017

  10. [10]

    Wireless-powered communications with non-orthogonal multiple ac- cess,

    P. D. Diamantoulakis, K. N. Pappi, Z. Ding, and G. K. Karagiannidis, “Wireless-powered communications with non-orthogonal multiple ac- cess,” IEEE Transactions on Wireless Communications , vol. 15, no. 12, pp. 8422–8436, 2016

    work page 2016

  11. [11]

    A hybrid approach for efficient wireless information and power transfer in green c- ran,

    X. Li, Z. Chen, A. Laha, Z. Chen, Y . Cheng, and L. X. Cai, “A hybrid approach for efficient wireless information and power transfer in green c- ran,” in 2018 IEEE 87th V ehicular Technology Conference (VTC Spring). IEEE, 2018, pp. 1–5

    work page 2018

  12. [12]

    Recursive waterfilling for wireless links with energy harvesting transmitters,

    P. He, L. Zhao, S. Zhou, and Z. Niu, “Recursive waterfilling for wireless links with energy harvesting transmitters,” IEEE Transactions on V ehicular Technology, vol. 63, no. 3, pp. 1232–1241, 2013

    work page 2013

  13. [13]

    Energy-throughput tradeoff in sustainable cloud-ran with energy harvesting,

    Z. Chen, Z. Chen, L. X. Cai, and Y . Cheng, “Energy-throughput tradeoff in sustainable cloud-ran with energy harvesting,” in 2017 IEEE International Conference on Communications (ICC) . IEEE, 2017, pp. 1–6

    work page 2017

  14. [14]

    A stochastic geometry analysis of inter-cell interference coordination and intra-cell diversity,

    X. Zhang and M. Haenggi, “A stochastic geometry analysis of inter-cell interference coordination and intra-cell diversity,” IEEE Transactions on Wireless Communications, vol. 13, no. 12, pp. 6655–6669, 2014

    work page 2014

  15. [15]

    Sinr-based k-coverage probability in cellular networks with arbitrary shadowing,

    H. P. Keeler, B. Błaszczyszyn, and M. K. Karray, “Sinr-based k-coverage probability in cellular networks with arbitrary shadowing,” in 2013 IEEE International Symposium on Information Theory . IEEE, 2013, pp. 1167–1171

    work page 2013

  16. [16]

    Joint uplink and downlink coverage analysis of cellular-based rf-powered iot network,

    M. A. Kishk and H. S. Dhillon, “Joint uplink and downlink coverage analysis of cellular-based rf-powered iot network,” IEEE Transactions on Green Communications and Networking , vol. 2, no. 2, pp. 446–459, 2017

    work page 2017