On Energy Harvesting of Hybrid TDMA-NOMA Systems

Alister G. Burr; Haitham Al-Obiedollah; Jie Tang; Kanapathippillai Cumanan; Octavia A. Dobre; Yogachandran Rahulamathavan; Zhiguo Ding

REVIEW 3 major objections 6 minor 29 references

On Energy Harvesting of Hybrid TDMA-NOMA Systems

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read By having users split each received signal into information and energy branches and serving grouped users with NOMA inside TDMA slots, the paper claims minimum transmit power falls below TDMA's while meeting the same rate and…

desk verdict A reasonable problem and a standard SCA template, but the printed rate constraints do not enforce the minimum rate, so the headline power savings over TDMA are not established. read the letter →

arxiv 1908.08719 v1 pith:F3MWZHDP submitted 2019-08-23 eess.SP

Haitham Al-Obiedollah , Kanapathippillai Cumanan , Alister G. Burr , Jie Tang , Yogachandran Rahulamathavan , Zhiguo Ding , Octavia A. Dobre This is my paper · ORCID

classification eess.SP

keywords hybridTDMA-NOMAenergyharvestingSWIPTpowersplittingminimizationsuccessiveconvexapproximationnon-orthogonalmultipleaccesswirelesstransfer

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 tries to establish that a hybrid TDMA-NOMA downlink with simultaneous wireless power and information transfer can serve users at guaranteed data rates and harvested power using less transmit power than conventional TDMA. The reason this would matter is that wireless networks could harvest part of their energy from the same radio signal that carries data, easing battery and environmental pressures in dense deployments. The paper formulates the joint choice of transmit powers and receiver power-splitting ratios as a nonconvex minimization of total base-station power, solves it with successive convex approximation, and uses simulations over 500 channel realizations to support the claim that the hybrid scheme is more power-efficient.

What carries the argument

The central object is the power-splitting SIC SINR model combined with a successive convex approximation reformulation. Each nonconvex rate constraint $t_i\log_2(1+\mathrm{SINR}_{j,i})\ge R_{\min}$ is replaced in OP1 by slack variables $\vartheta_{j,i}$, $\theta_{j,i}$, $\alpha^d_{j,i}$, and $\chi_{j,i}$ linked by constraints (14a)--(14c) and (19)--(21), with bilinear products linearized by first-order Taylor expansions around the previous iterate. This machinery turns the joint power-allocation and power-splitting design into a sequence of convex subproblems; the paper treats the converged point of that sequence as the solution of the original minimization.

What would settle it

Run OP1 for a single two-user group with $C=1$ and fixed channel gains, then evaluate the returned allocation against the original formulas: $R_{j,1}=t_1\log_2(1+\mathrm{SINR}_{j,1})$ using (6) and $P_{j,1}=\eta(1-\beta_{j,1})|h_{j,1}|^2(p_{1,1}^2+p_{2,1}^2)$. If the slack variables satisfy the printed constraints while the true rate or harvested power drops below $R_{\min}$ or $P_{\min}$, the power-saving comparison is settled by the surrogate rather than by the original problem.

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Extended reading notes

Core claim

The paper's central claim is that in a single-antenna downlink, dividing users into groups, serving each group in its own time slot with power-domain NOMA, and letting every receiver split the received signal between information decoding and energy harvesting yields a lower minimum transmit power than the TDMA-only schedule under the same constraints. The decisive mechanism is that the NOMA superposition signal contributes to the harvested power at each user, $P_{j,i}=\eta(1-\beta_{j,i})|h_{j,i}|^2\sum_s p_{s,i}^2$, while SIC keeps the information branch decodable. The paper reports simulations in which the hybrid scheme's required transmit power stays below TDMA's over the tested range of minimum harvested-power requirements.

Load-bearing premise

The load-bearing premise is that the convex chain that replaces the rate constraint actually enforces the promised minimum rate rather than just a slack bound; in the printed version the step $\theta \ge 2^{\vartheta}$ omits the time-slot duration $t_i$, and if that omission is not harmless the reported transmit powers are below what the original problem truly requires.

Editorial extensions

If this is right

For the simulated system, the hybrid TDMA-NOMA design satisfies the same minimum rate per user and minimum harvested power with lower base-station transmit power than TDMA.
As the minimum harvested-power requirement grows, both schemes need more transmit power, but the hybrid scheme's interference-assisted harvesting keeps its power lower.
The SCA algorithm converges in a small number of iterations for the tested parameters, so the design is computationally practical for the ten-user, five-group setup.
The grouping strategy pairs the strongest user with the weakest so that SIC differences are large, which the paper argues is needed for practical NOMA.

Reading between the lines

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

The paper fixes two users per group; because harvested power scales with total received power, larger groups would likely make the energy constraint easier to satisfy, though at additional SIC decoding burden, and testing $K_i>2$ would show whether the power advantage grows.
The time slots are fixed at $T/C$; allowing unequal slot lengths would add a degree of freedom that could trade per-user rate against harvesting time, a direct extension of the same problem.
The rate surrogate in (14c) would need to be scaled by the slot duration to strictly enforce $R_{\min}$; rerunning the reported simulations with $\theta \ge 2^{R_{\min}/t_i}$ would test how much of the power saving is robust to the surrogate gap.
Before the algorithm can be reimplemented, a value or rule for the multiplier $\gamma$ in (21a) must be supplied, since the printed linearized bound leaves it unspecified.

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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 takes on a sensible problem — jointly allocating power and power-splitting ratios for a hybrid TDMA-NOMA system with SWIPT to minimize transmit power under rate and harvested-power constraints — and the broad SCA approach is a reasonable template. The system model is clearly set out, the SIC ordering is conventional, and the simulation setup is standard. But the way the rate constraints are written does not actually enforce the minimum rate, so the comparison against TDMA cannot be trusted as printed.

What is genuinely new is the specific combination: hybrid TDMA-NOMA plus SWIPT plus a P-Min formulation solved with SCA. That is a legitimate extension of prior NOMA resource-allocation work, including the authors' own. The problem statement OPP is well posed, and the grouping heuristic is sensible. The paper is not circular; it is solving a new combination of known ingredients.

Where it falls apart: the rate constraint chain in Eqs. (14a)–(14c) and OP1. Because R_j,i = t_i log2(1+SINR_j,i), enforcing R_j,i ≥ Rmin requires log2(1+SINR) ≥ Rmin/t_i. The chain only enforces log2(1+SINR) ≥ ϑ and then, at best, ϑ ≥ Rmin. With t_i < 1, the actual rate can be as low as t_i Rmin, below the stated requirement. For the simulations' t_i = 0.2 and Rmin = 0.1, the SINR target is understated by about 7.6 dB. That is a load-bearing flaw, not a typo.

There are also internal inconsistencies in OP1 as printed. The variable set Γ includes p, r, β, ϱ, ρ, α, but the constraints include (14c), (20), and (21a), which use ϑ, θ, χ, and an undefined multiplier γ. Even allowing for typos, a reader cannot reproduce the algorithm as stated. The TDMA comparison uses the same SCA chain, so the relative power gap is also suspect.

Credit where due: the paper is clearly written, the literature is cited appropriately, and the authors are not overclaiming beyond the reported simulation. The central idea is salvageable. With the rate constraint corrected to θ ≥ 2^(Rmin/t_i) and OP1 fully specified, the result could be a modest but useful incremental contribution to NOMA-SWIPT resource allocation. As it stands, the main claim is not supported.

I would reject the current version. The flaw is central but fixable, so a serious editor could send it to peer review rather than desk reject — a reviewer will likely catch the same issue and the authors can repair it. But my own verdict on this manuscript is clear: not acceptable without major revision.

Referee Report

3 major / 6 minor

Summary. The paper proposes a hybrid TDMA-NOMA downlink system with simultaneous wireless power and information transfer (SWIPT). Users are divided into groups, each served in a dedicated time slot using power-domain NOMA, and each user splits its received signal between information decoding and energy harvesting. The authors formulate a non-convex power minimization problem with minimum rate and minimum harvested-power constraints per user, and propose an iterative successive convex approximation (SCA) algorithm to jointly optimize the power allocations and power-splitting ratios. Simulation results compare the required transmit power of the proposed hybrid scheme with that of a conventional TDMA system and report a transmit-power advantage for the hybrid scheme.

Significance. If the proposed algorithm were correct, the paper would provide a useful design framework for energy-harvesting NOMA systems and a quantitative comparison against a TDMA baseline. The system model is clearly presented, the SWIPT formulation is standard, and the comparison with TDMA is a natural evaluation. However, the central claim in the conclusion rests entirely on the correctness of the SCA reformulation, and that reformulation contains several load-bearing errors, detailed below, which mean the numerical results in Section IV do not currently establish the claimed transmit-power advantage.

major comments (3)

[Section III.B, Eqs. (14a)-(14c) and OP1 (25)] The rate constraint is not enforced with the time-sharing factor t_i. The chain in (14a)-(14c) together with r_{j,i} >= Rmin in (25b) imposes log2(1+SINR_{j,i}) >= Rmin, but the actual rate is R_{j,i} = t_i log2(1+SINR_{j,i}) with t_i = T/C < 1. Consequently, a point feasible for the surrogate can have R_{j,i} as low as t_i Rmin, which is below the required minimum rate. The correct surrogate requires theta_{j,i} >= 2^{Rmin/t_i} (or equivalently vartheta_{j,i} >= Rmin/t_i). In addition, OP1 omits (14a) and does not link r_{j,i} to theta_{j,i} or vartheta_{j,i}; the variable set Gamma in (25) does not contain theta or vartheta, so the chain is incomplete as printed.
[Section III.B, Eq. (21a)] The multiplier gamma in (21a) is undefined. It is not introduced in the text, is not included in the optimization variable set Gamma, and is not listed as a simulation parameter. Since (21) is used in OP1, the feasible set actually implemented in simulations is unspecified; if gamma is not equal to 1, the constraint is not equivalent to (17). The authors must either remove gamma or define it explicitly and justify its value.
[Section III.B, Eqs. (19) and (23)] The first-order Taylor linearization of beta p^2 (and similarly of (1-beta)p^2) is not a valid SCA lower bound. The function f(beta,p) = beta p^2 has an indefinite Hessian, so its linearization is not a global underestimator; for example, at (beta0,p0)=(1,1), the linearization at (beta,p)=(4,0.5) equals 3 while f equals 1. Therefore the constraint (19) >= alpha can be satisfied while the original constraint (18) is violated. This means the SCA may return points that are infeasible for OPP, and the claimed equivalence of OP1 and OPP is not established. A different convex underestimator or a proof of conservativeness over the domain is needed.

minor comments (6)

[Abstract] The abstract says 'we employ successive interference cancellation to overcome these non-convexity issues'; this should be 'successive convex approximation' (SCA), not SIC.
[Section III.B, Eq. (25)] The variable set Gamma lists r_{j,i}, while the derivation uses vartheta_{j,i} as the rate slack variable; the relationship between r_{j,i} and vartheta_{j,i} is never defined, which makes OP1 difficult to interpret.
[Section II.A, Eq. (13a)] The grouping notation in (13a) mixes two indexing conventions and is difficult to follow; an explicit example for the simulated case K=10, C=5 would clarify the proposed grouping strategy.
[Section IV, Fig. 3] Figure 3 contains an inset whose axes and meaning are not described in the caption; please add an explanation.
[Section III, Algorithm 1] The stopping threshold mu in Algorithm 1 is not given a value in Section IV, so the convergence results in Fig. 4 are not fully reproducible.
[References] Reference [28] is cited as 'Accepted IEEE Trans. Commun. 2019' without volume, pages, or DOI; please complete the reference.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the TDMA-NOMA vs TDMA comparison is generated from two independent optimization formulations, not from fitted inputs or self-citation.

full rationale

The paper's central claim—that the hybrid TDMA-NOMA design requires less transmit power than conventional TDMA under identical rate and harvested-power constraints—is obtained by solving the P-Min problem OPP (12) through the SCA surrogate OP1 (25) and comparing it with the TDMA problem OP2 (28). The design variables (power allocations and splitting ratios) are optimization outputs, not calibrated constants; no parameter is fitted to the simulated curves and then re-labeled as a prediction. The citations to the authors' prior work [14,19,20] are used only to justify the SCA technique ('Note that SCA has been utilized to solve different non-convex optimization problem in the literature [19], [20], [14]'), not as a premise that forces the claimed advantage; no uniqueness theorem from the authors' prior work is invoked. There is a real correctness concern, but it is not circularity: the link between the slack variable r_{j,i} in OP1 (25b) and the actual rate R_{j,i}=t_i log2(1+SINR_{j,i}) is incomplete, because Eq. (14a) (R_{j,i}≥ϑ_{j,i}) is not carried into the constraint list of OP1 and the t_i factor is absent from the θ_{j,i}≥2^{ϑ_{j,i}} surrogate; Eq. (21a) also contains an undefined multiplier γ. If these surrogates are inexact, the reported transmit-power values may solve a relaxed or infeasible problem, but that is an equivalence/feasibility defect, not a derivation that reduces to its own inputs. The comparison itself is therefore not circular, and the circularity score is 0.

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

No new entities or fitted constants appear. The central claim rests on standard domain assumptions (perfect SIC, linear EH, known CSI) and on the correctness of the SCA surrogates, which is called into question by the missing time fraction and undefined γ.

assumptions (4)

domain assumption SIC is implemented with no errors at every user.
Stated in Section II-A after Eq. (5): 'we assume that SIC is implemented with no errors.' This is standard in NOMA analysis but unattainable in practice.
domain assumption Perfect channel state information is available at the base station and users.
The problem formulation and algorithm use fixed channel gains |h_{j,i}|^2 without uncertainty models. The paper does not discuss CSI acquisition errors.
domain assumption The energy harvester has a linear RF-to-DC conversion model.
Eq. (11) uses P = η(1-β)|h|^2 sum p^2 with constant efficiency η. Real energy harvesters are nonlinear, and this can change optimal splitting ratios.
ad hoc to paper The convex approximations in (19), (20), (21), (23) are faithful surrogates of the original non-convex constraints.
The paper relies on these approximations to claim that solving OP1 solves OPP. The derivation omits the time-sharing factor in the rate chain and uses an undefined γ in (21a), so this premise is not established.

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Cite this review

Pith. "Pith review of On Energy Harvesting of Hybrid TDMA-NOMA Systems." pith.science (2026). https://pith.science/paper/F3MWZHDP

@misc{pith2026190808719,
  author       = {Pith},
  title        = {Pith review of: On Energy Harvesting of Hybrid TDMA-NOMA Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F3MWZHDP}},
  note         = {Machine review of arXiv:1908.08719}
}

read the original abstract

In this paper, we investigate energy harvesting capabilities of non-orthogonal multiple access (NOMA) scheme integrated with the conventional time division multiple access (TDMA) scheme, which is referred to as hybrid TDMA-NOMA system. In a such hybrid scheme, users are divided into a number of groups, with the total time allocated for transmission is shared between these groups through multiple time slots. In particular, a time slot is assigned to serve each group, whereas the users in the corresponding group are served based on power-domain NOMA technique. Furthermore, simultaneous wireless power and information transfer technique is utilized to simultaneously harvest energy and decode information at each user. Therefore, each user splits the received signal into two parts, namely, energy harvesting part and information decoding part. In particular, we jointly determine the power allocation and power splitting ratios for all users to minimize the transmit power under minimum rate and minimum energy harvesting requirements at each user. Furthermore, this joint design is a non-convex problem in nature. Hence, we employ successive interference cancellation to overcome these non-convexity issues and determine the design parameters (i.e., the power allocations and the power splitting ratios). In simulation results, we demonstrate the performance of the proposed hybrid TDMA-NOMA design and show that it outperforms the conventional TDMA scheme in terms of transmit power consumption.

Figures

Figures reproduced from arXiv: 1908.08719 by the authors.

**Figure 2.** Information Decoding (ID) Stage: At this stage, the fraction of received signal p βj,i of rj,i is utilized to decode the information. Therefore, the signal split to the ID stage [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 2.** Illustration of splitting the received signal at [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

Figures from the paper (2 more)

**Figure 3.** Figure 3: The required transmit power versus different mini [PITH_FULL_IMAGE:figures/full_fig_p006_3.png]

**Figure 4.** Figure 4: The convergence of the SCA algorithm to solve [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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