Terahertz channel power and BER performance in rain

Chen Yao; Da Li; Fei Song; Guohao Liu; Hong Liang; Jiabiao Zhao; Jiacheng Liu; Jianjun Ma; Jiayuan Cui; Mingxia Zhang

Terahertz channel power and BER performance in rain

T0 review · 5 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper claims that a 220-230 GHz terahertz link in rain keeps a strong line-of-sight path—Rician K-factors stay above 40 dB—so rain mostly costs power, not coherence.

desk verdict New 220-230 GHz rain dataset is worth a look, but the high-K-factor claim needs a noise-floor calibration before it can carry the 'no multipath' conclusion. read the letter →

arxiv 2412.03916 v2 pith:247P7MCF submitted 2024-12-05 physics.app-ph

Yuheng Song , Jiayuan Cui , Guohao Liu , Jiabiao Zhao , Mingxia Zhang , Jiacheng Liu , Da Li , Peian Li

show 4 more authors

Chen Yao Fei Song Hong Liang Jianjun Ma

This is my paper · ORCID

classification physics.app-ph

keywords terahertzcommunicationsrainattenuationRicianK-factorbiterrorrateMiescatteringraindropsizedistributionQAMmodulation

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

The paper is trying to establish that rain does not destroy the basic usability of terahertz links in the 220-230 GHz band: it attenuates the signal but leaves a strong line-of-sight path, so the channel stays Rician with K-factors above 40 dB and inter-symbol interference stays small. If true, this matters because it separates rain's effect into a power-budget problem—solvable by transmit power, adaptive modulation, and frequency choice—rather than a waveform-coherence problem. The authors support this with outdoor measurements over 54 meters under natural rain and with a paired theoretical analysis using ITU-R and Mie-scattering attenuation models, plus BER calculations for QAM and other modulations.

What carries the argument

The Rician K-factor—the ratio of line-of-sight power to scattered multipath power—fitted to one-minute cumulative distribution functions of received SNR is the quantity that carries the claim that rain does not add significant multipath. Supporting machinery includes the ITU-R power-law attenuation model and Mie-scattering attenuation computed with exponential raindrop size distributions, with the ITU and Joss-Drizzle models bracketing the measured loss. A K-factor formula extended with rain rate and path-loss exponent then feeds a 16-QAM bit-error-rate expression under Rician fading.

What would settle it

Install a disdrometer along the exposed part of the path and compare its one-minute raindrop size distributions with the station rain rate during the same storms; if measured attenuation systematically falls outside the ITU-R upper and Joss-Drizzle lower bounds when the local distribution is used, the prediction-range claim fails.

Watch

Extended reading notes

Core claim

The paper reports that over a 54 m outdoor path at 220, 225, and 229 GHz, rain lowers received SNR but leaves the channel Rician with K-factors above 40 dB, meaning the line-of-sight component dominates and multipath-induced inter-symbol interference is negligible. Measured rain attenuation falls between the ITU-R prediction (upper bound) and the Joss-Drizzle Mie-scattering prediction (lower bound), while power loss at equal rain rates varies because raindrop size distribution changes. In BER terms, 16-QAM matches BPSK and 2-PAM under strong LOS fading, 2-FSK is worst, a 41.5 m link at 20 dBm stays near BER $2\times10^{-7}$ up to 50 mm/hr, and a 1 km link needs 40 dBm to stay below the forward-error-correction threshold for rain rates below about 30 mm/hr. Higher frequencies show more humidity sensitivity than lower ones, so the paper concludes that adaptive modulation and lower-THz frequency planning are the practical levers.

Load-bearing premise

The results assume the rain rate reported by the nearby weather station matches what actually falls on the 54-meter path during each one-minute measurement; if local rain differs, the attenuation-versus-rate curves and the constant-rate variability conclusion shift.

Editorial extensions

If this is right

At 220-230 GHz over tens of meters, rain-induced multipath is weak enough that inter-symbol interference is not the limiting factor in rain.
Measured attenuation falls between the ITU-R upper bound and the Joss-Drizzle lower bound, giving a prediction range rather than a single value for link budgets.
16-QAM achieves the same BER as BPSK and 2-PAM under the strong line-of-sight channel, so higher spectral efficiency is available in rain without a BER penalty.
At 1 km, 20 dBm transmit power fails the FEC threshold in rain, while 40 dBm sustains reliable BER for rain rates below about 30 mm/hr.
Higher THz frequencies are more sensitive to humidity, so lower-frequency channels offer greater environmental resilience in rainy conditions.

Reading between the lines

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

If K-factors stay above 40 dB across rain rates, receiver equalizers for terahertz links could be far simpler than those for multipath-dominated bands; the paper does not design equalizers, but its Rician fits point in that direction.
The observed constant-rate power spread implies link margins should be set by raindrop-size-distribution variability, not just the rain-rate reading, since a margin built only on a single attenuation curve would miss the spread at fixed rain rates.
A natural extension is to measure 140 GHz and 220-230 GHz in the same storms to test the paper's frequency-sensitivity conclusion directly, rather than comparing to a separate earlier 140 GHz study.
The BER model sets the critical rain rate at 50 mm/hr; in regions with more extreme rain, the predicted operating window for 1 km links would close faster, so that threshold should be validated locally before deployment.

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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

The thing to know: this is a straightforward measurement paper with a useful new dataset at 220-230 GHz, but the central claim that rain leaves the Rician K-factor above 40 dB needs a noise-floor calibration before it can carry the 'no multipath, no ISI' conclusion. The BER analysis is a simulation, not a measurement.

What is new: a 54 m outdoor channel at 220, 225, and 229 GHz, with rain rates up to 25 mm/hr, and CDF-based fits to Rician and Weibull distributions. That frequency/path combination is genuinely new. The attenuation data falls between the ITU-R upper bound and the Joss-Drizzle lower bound, and the paper sensibly presents this as a prediction range rather than forcing a single model. The observation that power loss varies at constant rain rate, attributed to raindrop size distribution, is consistent with earlier work and worth having documented at these frequencies.

What is soft: First, the K-factors above 40 dB imply received power fluctuations of order 0.02 dB; the paper does not report a static-channel calibration, noise floor, or sensor resolution, so the fitted K may reflect sensor noise rather than rain multipath. The stress-test note is right that this is load-bearing. Second, Eq. (5) defines a K-factor scaling with distance and rain rate but never defines alpha_c, and Rc=50 mm/hr is manually selected. The BER curves in Figs. 6 and 7 are consequences of that assumed form, so calling them predictions overstates what is known. Third, the claim of QAM superiority is overstated: BPSK, 2-PAM, and 4-QAM give identical BER, and the paper simply moves on to 16-QAM. Also, in two of the rain cases the Weibull fit has slightly higher R2 than Rician, so the statement that Rician performed relatively better is not uniformly supported. Minor, but the paper should acknowledge it.

The measurements appear carefully done within their scope, and the paper is candid about limitations. The issues are addressable with a calibration run and a clearer description of the K-factor formula. I would send this to peer review — the dataset deserves scrutiny, and the K-factor question can be settled with proper calibration.

For your reading group, worth a look if anyone works on THz link budgets; otherwise it's a pass.

Referee Report

5 major / 5 minor

Summary. The paper reports an outdoor terahertz channel measurement campaign at 220, 225, and 229 GHz over a 54 m line-of-sight path during rain and clear weather. The authors analyze the cumulative distribution functions of the received power, fit Rician and Weibull distributions, and infer Rician K-factors of 40–50 dB, concluding that rain-induced multipath and inter-symbol interference are negligible. They compare measured rain attenuation with the ITU-R P.838-3 model and Mie scattering predictions for several raindrop size distributions, finding the measurements bounded above by ITU-R and below by the Joss-Drizzle model. A bit error rate (BER) analysis is then carried out using a Rician fading model with an assumed K-factor formula, comparing modulation schemes and evaluating the effects of rain rate, temperature, humidity, and frequency. The central conclusions are that rain mainly attenuates the LoS component without strong multipath, QAM performs well in rain, and lower THz frequencies are more resilient.

Significance. If the central claims hold, the paper provides valuable experimental evidence on THz propagation in rain at 220–230 GHz, a frequency range of direct relevance to 6G backhaul and access links. The finding that Rician K-factors remain above 40 dB would support the use of simple LoS channel models and adaptive modulation in rainy conditions, and the attenuation bounds with respect to ITU-R and Mie models are practically useful for link budgeting. The paper also benefits from a real outdoor measurement campaign with co-located meteorological data. However, the significance is conditional on the K-factor extraction being physically meaningful, and on the BER model parameters being justified; these are the points of concern in the major comments.

major comments (5)

[Section 3.1, Table 2] The claim that the Rician distribution 'performed relatively better' is not consistently supported by the reported R² values. For example, at 220 GHz with 8 mm/hr rain, the Weibull fit has R²=0.9961 versus Rician R²=0.9953, and at 229 GHz with 23 mm/hr rain, Weibull R²=0.9976 versus Rician R²=0.9960. The paper should justify the Rician choice, perhaps with a formal goodness-of-fit test that accounts for the differing number of parameters, or explicitly acknowledge that the two distributions are statistically indistinguishable for several rows of Table 2. This is load-bearing because the K-factors and the 'minimal multipath' conclusion derive from the Rician fit.
[Section 2 and Section 3.1] The measurement system's noise floor, power sensor resolution, and static-channel calibration are not reported. At K-factors of 40–50 dB, the relative power standard deviation from multipath is on the order of sqrt(2/K) ≈ 0.02 dB, which is extremely small. If the measured power CDF spread is dominated by sensor noise, slow drift, or atmospheric scintillation rather than by rain-induced multipath, the fitted K-factor would not be a valid indicator of multipath severity. The authors should provide a noise-floor measurement, a static (no-rain) calibration run, and an estimate of the achievable dynamic range to demonstrate that the K-factors are resolved by the measurement system.
[Section 4, Eq. (5)] The proposed K-factor formula is under-specified. The exponent denoted α in Eq. (5) is not clearly defined; the text first introduces α as a path loss exponent in the formula for path loss, but it is not stated whether the same α is used in the K-factor formula. The parameters K0 and Rc (set to 50 mm/hr) are selected ad hoc rather than derived from the measurement data. Since this formula is used to generate the BER predictions in Figs. 6 and 7, the quantitative BER results are not reproducible and their sensitivity to the free parameters is unknown. The authors should derive the distance and rain-rate dependence of K from the measurements, or clearly present the BER analysis as an illustrative scenario with a sensitivity study over the free parameters.
[Section 4, Fig. 7(a)] The BER-versus-frequency predictions rely on an atmospheric absorption model that is not described or referenced. The statement that clear-weather operation is limited to 350 GHz and rainy operation to 300 GHz depends on the specific gaseous absorption model used (e.g., ITU-R P.676 or a line-by-line model), which is not identified. Without specifying the absorption model and its parameters, the frequency-dependent BER thresholds and the recommendation for lower-frequency planning are not verifiable. The model should be named, and its sensitivity to humidity and temperature should be discussed.
[Section 2 and Section 3.2, Fig. 4] The rain rate used in the attenuation comparison is taken from a China Meteorological Administration station described only as 'proximate' to the campus. The distance between the station and the 54 m channel, and the spatial uniformity of rain along the 41.5 m exposed path, are not quantified. If the station rain rate differs from the path-average rain rate, the attenuation-versus-rain-rate curves in Fig. 4 and the conclusion that measurements fall between the ITU-R and J-D bounds could be biased. The authors should report the station distance and, if possible, provide an uncertainty estimate for the rain rate along the channel.

minor comments (5)

[Section 3.2, Eq. (2)] The Mie scattering formula in Eq. (2) is garbled; the constant 3.3429 and the integration variable are not clearly defined. Please rewrite the equation in standard notation and specify the units of the extinction efficiency and raindrop radius.
[Section 4, Fig. 5] The text states that QAM has 'superior BER performance,' but the simulation results show that BPSK, 2-PAM, and 4-QAM have identical BER under the Rician channel. The claim should be softened to 'comparable BER with higher spectral efficiency' to avoid overstatement.
[Section 4, Fig. 7 caption] The caption says 'linear K-factor is calculated by for Eq. (5),' which is a typo; it should read 'calculated by Eq. (5).'
[Table 2] The table header contains the typo 'Ricain'; it should be 'Rician.'
[Throughout] There are numerous typographical and grammatical errors (e.g., 'the influence of rain-induced fading on power profile and bit error performances remains poorly understood,' 'this impact it not so obvious'). A thorough language edit is recommended.

Circularity Check

1 steps flagged · score 3.0 of 10

The attenuation and high-K conclusions rest on self-contained measurements, but the BER section's 'confirmation' of negligible ISI simply re-imports the measured K=46 dB and so is circular, though not load-bearing for the central claim.

fitted input called prediction [Section 4, paragraph beginning 'To further investigate the BER performance...' (near Fig. 7(a))]
"It should also be note that the presence of Rician fading introduces fluctuations of the predicted BER curves, but this impact it not so obvious and can be negligible. This confirms our previous conclusion that the ISI caused by multipath scattering is negligible under rainy conditions."

The BER curves were computed with the Rician K-factor fixed at 46 dB, 'obtained from the measurements' (Section 4: 'The K-factor used in the analysis is the average K-factor value of 46 dB obtained from the measurements'). In a Rician model, K=46 dB means the diffuse component is 46 dB below the LoS component by definition, so the predicted BER fluctuation is negligible by construction. The sentence then uses that constructed negligibility to 'confirm' the earlier no-ISI conclusion, which itself was inferred from the same measured high K-factors in Section 3.1. Thus the confirmation is not an independent check; it is the input parameter being reported back as a conclusion. This is a minor circular confirmation, not the source of the central attenuation/K-factor finding.

full rationale

The paper's central derivation is largely self-contained. The attenuation-versus-rain-rate comparison uses the authors' own outdoor measurements against standard ITU-R and Mie-scattering models, and the K-factors in Table 2 are fit directly to the measured CDFs rather than imported from prior work. No load-bearing self-citation chain is present: earlier work by the corresponding author is cited for background (rainfall introduces fast fading, reference [29]) and for the choice Rc = 50 mm/hr (reference [58]), but the central attenuation and high-K conclusions would stand without those citations. The one genuine circular passage is in Section 4, where the claimed 'confirmation' of negligible ISI is produced by inserting the measured K = 46 dB into a Rician BER formula and observing that the resulting fluctuations are small. That is the fitted parameter re-stated as a result, and it does not independently corroborate the multipath conclusion from Section 3.1. Because this circular confirmation is not the basis for the headline attenuation and high-K findings, the circularity is partial rather than central. Other issues raised by the data, such as Weibull sometimes fitting better than Rician in Table 2, the lack of a power-sensor noise-floor calibration for resolving very high K-factors, and the representativeness of the CMA rain-rate reading, are correctness and measurement concerns, not circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central attenuation and multipath claims rely on the measured data and standard scattering models, but the BER predictions depend on an ad hoc K-factor formula with unspecified exponent and a chosen threshold. The paper also assumes the meteorological station's rain rate is representative of the channel and that one-minute windows are stationary, both of which are plausible but unverified.

free parameters (3)

K0(d0) = 46 dB (average of measured K-factors at 41.5 m)
Used as the reference K-factor in Eq. (5) for all BER predictions; it is an average over measurements at various rain rates and frequencies, not a fixed physical constant.
alpha_c (exponent in K(d) formula) = Not specified in the paper
The exponent in K(d) = K0 * (d/d0)^alpha_c * (1 - R/Rc) is introduced but never given a numeric value or derived from the measurements, making the BER predictions non-reproducible.
Rc (critical rain rate) = 50 mm/hr
Chosen as an extreme rain threshold and inserted into Eq. (5); no fitting to data or physical justification is provided.

assumptions (4)

domain assumption Rain rate at the China Meteorological Administration station represents the conditions along the 54 m channel path.
The paper correlates power loss with rain rate recorded at a nearby station (Section 2, Fig. 3-4), but local rain intensity and raindrop size distribution can vary over short distances.
domain assumption The channel is stationary within each one-minute measurement window, so a single CDF fit is meaningful for a given rain rate.
Measurements are time-limited to one minute, but rain rate and drop size distribution change continuously, as the paper itself notes in Section 3.2.
domain assumption Gaseous absorption can be neglected when comparing rain attenuation because temperature and humidity were similar in clear and rainy conditions.
The theoretical model in Section 3.2 omits gaseous absorption; this is acceptable for differential loss but not for absolute attenuation, and the paper does not quantify the error.
domain assumption The Rician fading model with a single average K-factor is adequate for BER calculations.
The BER analysis in Section 4 uses K = 46 dB for all conditions, despite the K-factor varying with rain rate (Table 2), which could underestimate fading in heavy rain.

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Cite this review

Pith. "Pith review of Terahertz channel power and BER performance in rain." pith.science (2026). https://pith.science/paper/247P7MCF

@misc{pith2026241203916,
  author       = {Pith},
  title        = {Pith review of: Terahertz channel power and BER performance in rain},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/247P7MCF}},
  note         = {Machine review of arXiv:2412.03916}
}

read the original abstract

Terahertz (THz) communications have emerged as a promising technology for 6G networks due to their potential for achieving terabit-per-second data rates. However, the impact of rainfall on THz channel characteristics remains incompletely understood, particularly regarding power attenuation mechanisms and bit error rate (BER) performance. This article presents a systematic measurement-based and theoretical investigation of line-of-sight (LoS) THz channel behavior under rainfall conditions, methodically examining both power attenuation mechanisms and bit error rate (BER) performance. Our experimental campaign, conducted at frequencies of 220-230 GHz over a 54-meter outdoor channel, is complemented by analytical frameworks incorporating ITU-R and Mie scattering models. The study reveals that while rain induces significant power attenuation, multipath scattering effects remain minimal, with Rician K-factors maintaining high values. Notably, we observe substantial variations in power loss under constant rain rates, attributed to dynamic changes in raindrop size distribution. Comparative analysis demonstrates superior BER performance of Quadrature Amplitude Modulation (QAM) in rainfall conditions, while revealing increased environmental sensitivity at higher frequencies. These findings underscore the necessity for adaptive modulation schemes and strategic frequency planning in future THz communication systems.

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Reviewed August 11, 2026 · model on record in the stance chip above.