REVIEW 3 major objections 5 minor 8 references
Multi-Antenna Relaying and Reconfigurable Intelligent Surfaces: End-to-End SNR and Achievable Rate
T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash
Pith's one-line read This report claims that end-to-end SNR and achievable rate for relay- and RIS-aided links can be written in one unified set of formulas, covering half-duplex/full-duplex operation, DF/AF protocols, and two RIS scattering regimes, so the…
desk verdict Handy formula summary for relay and RIS links, but the RIS half rests on textbook path-loss laws that are never derived or validated; fine as a reference, not as a research paper. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central objects are the SNR expressions built from MRC/MRT combining vectors at the relay and destination, the variable-gain AF relay gain that yields the harmonic SNR combination, and the RIS phase-shift matrix Φ whose entries are chosen to co-phase the direct and reflected signals. These are combined with two path-loss laws taken from textbook propagation theory: the sum-distance law for anomalous reflection and the product-distance law for diffuse scattering. The machinery does the work of converting channel and distance parameters into a single end-to-end SNR for each system, which then feeds directly into the Shannon rate formulas and the optimal power-allocation derivations.
What would settle it
A controlled free-space experiment with a RIS whose element size is large relative to the wavelength could settle the matter: fix the transmitter and receiver such that dSR+dRD is constant while dSR and dRD vary, and measure the reflected power. If the power scales as 1/(dSR+dRD)^2, the sum-distance law in equation (31) holds; if it scales as 1/($dSR^{2}$ $dRD^{2}$), the product-distance law in equation (32) holds; if neither, the RIS SNR expressions are not predictive.
Extended reading notes
Core claim
The report establishes a common framework in which the end-to-end SNR of a relay link is expressed through MRC/MRT combining, with the AF case following the harmonic form γ1γ2/(γ1+γ2+1) and the DF case following a min of the two hops; the RIS link is expressed through a co-phased sum of the direct and reflected signals, giving a squared-sum SNR formula. For each of the four relaying protocols, the paper provides closed-form or quadratic-solution expressions for the optimal source and relay powers that maximize achievable rate. For the RIS, two limiting cases are considered: anomalous reflection, where the received power scales with the sum-distance law PL(dSR+dRD), and diffuse scattering, where it scales with the product-distance law PL(dSR)PL(dRD). The rate formulas are the Shannon logarithms of these SNRs, with the half-duplex factor 1/2 where applicable.
Load-bearing premise
The RIS SNR and rate formulas are only as good as the two textbook path-loss models they rely on: the sum-distance law for large RIS elements and the product-distance law for small RIS elements, and the paper does not test either model against measurements.
Editorial extensions
If this is right
- If the formulas are correct, relay and RIS systems can be compared under identical channel and power budgets using the expressions in Tables I and II, without re-deriving either system's SNR from scratch.
- The optimal power-allocation formulas for HD-DF and HD-AF relaying give ready-to-use source/relay power splits, which could be applied immediately in system-level studies of relay deployment.
- The FD formulas show that the rate penalty of full-duplex operation disappears as the number of transmitted symbols grows, but the SINR is degraded by residual loop-back self-interference and concurrent source transmission; the paper's expressions quantify that trade-off.
- For RIS, the two limiting path-loss models produce different rate predictions, so knowing which scattering regime applies in practice determines whether RIS-assisted links should be modeled with a sum-distance or a product-distance decay.
- The unified framework can serve as the departing point for comparing relay and RIS performance in specific deployment scenarios, such as millimeter-wave blockage relief.
Reading between the lines
- A natural extension the paper does not explore is a hybrid relay-RIS architecture, where the RIS provides a reflected-path boost to the relay link; the unified SNR forms would need to be re-derived because the reflected and relayed signals would combine coherently at the destination.
- The two RIS path-loss laws are taken from classical specular-reflection and radar backscattering theory; if measurements on real RIS prototypes show a different distance dependence, the RIS rows of Tables I and II would need to be revised, which would change any relay-versus-RIS comparison that uses these formulas.
- The paper's assumption of perfect CSI at the relay and destination is an upper bound; a practical extension would incorporate channel estimation error into the SNR expressions, which would reduce the achievable rates and likely alter the optimal power allocations.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper is a technical report that compiles end-to-end signal-to-noise ratio (SNR) and achievable rate expressions for wireless systems assisted by multiple-antenna relays and by reconfigurable intelligent surfaces (RISs). For relays, it covers half-duplex and full-duplex operation under decode-and-forward and amplify-and-forward protocols, including maximal-ratio combining and transmission, self-interference modeling, and optimal power allocation between the source and the relay. For RISs, it considers two limiting regimes, anomalous reflection and diffuse scattering, with corresponding path-loss approximations. All final expressions are collected in two summary tables.
Significance. If corrected and used with appropriate caveats, the report provides a useful unified reference for comparing relay-based and RIS-based communication systems. Its strengths are the systematic treatment of four relaying modes with closed-form power-allocation solutions, the explicit inclusion of the direct link and self-interference, and the concise tabular presentation. However, the RIS SNR and rate formulas rest on two path-loss scaling laws that are asserted from a general propagation textbook without validation for RIS, and the derivation of the half-duplex DF combined SNR contains an incorrect intermediate combining-vector expression. These issues must be fixed before the report can be considered a reliable reference.
major comments (3)
- [II-A-1-a, Eq. (10)] The MRC combining vector in Eq. (10) omits the path-loss and power coefficients of the two branches. With w_D^MRC defined as [h_SD, ||h_RD||]^H / ||[h_SD, ||h_RD||]||, the combined SNR obtained from Eq. (9) is not the sum of the per-branch SNRs in Eq. (11); the correct weights must be proportional to [sqrt(pS PL(dSD)) h_SD, sqrt(pR PL(dRD)) ||h_RD||]^H. Please correct the definition or explain the intended normalization so that Eq. (11) follows.
- [II-B, Eqs. (31)-(32)] The RIS SNR formulas rely on two path-loss scaling laws: the sum-distance law PL(dSR+dRD) for anomalous reflection and the product-distance law PL(dSR)PL(dRD) for diffuse scattering, both taken from Ref. [8, p.12] without derivation or a statement of their domain of validity in terms of element size, surface area, wavelength, and near/far-field distances. Since these approximations are the only part of the RIS analysis that is not derived, the authors should justify them with a derivation or with references to RIS-specific propagation models, and they should explicitly state that all RIS SNR and rate expressions inherit these assumptions.
- [II-A-2-b, Eq. (26)] The end-to-end FD-AF SINR in Eq. (26) is stated after some algebraic manipulations without any derivation. This is the most involved SINR expression in the paper and is central to the FD-AF rate result in Section III-A-2-b. Please provide the derivation or a reference to a source that contains it.
minor comments (5)
- [Abstract and Section I] The text says amplify-and-forward (FD) in the abstract and in the system model; the acronym should be AF.
- [Abstract] The phrase well as should be as well as.
- [Section I] The sentence with pS and pR we denoted should read with pS and pR we denote.
- [Section II-A-2, Eq. (19)] The symbols s'' and \bar{s} are used in Eq. (19) but are not explicitly defined; please define them.
- [Tables I and II] The tables would be easier to read if equations were numbered consistently and if the notation for the MRC/MRT weights matched the main text.
Circularity Check
No significant circularity: the relay and RIS SNR/rate expressions are derived from explicit signal models and standard textbook path-loss laws, with no fitted parameter or self-citation chain doing the work.
full rationale
The report is a compilation of standard end-to-end SNR and achievable-rate expressions. The relay formulas (Eqs. (2), (5), (8), (11), (14), (18), (21), (24), (26)) follow directly from the stated signal models, MRC/MRT combining vectors, and variable-gain definitions; no parameter is fitted to a subset of data and then renamed as a prediction. The power-allocation results in Section III are obtained by explicit maximization (first-order conditions) of the derived rate expressions, so they are mathematical consequences rather than circular inputs. The RIS section derives Eq. (30) from co-phasing of the direct and reflected signals, which is a standard application of the triangle inequality, not an imported conclusion. The two RIS path-loss variants, Eqs. (31) and (32), rest on the sum-distance law and product-distance law cited to the external textbook [8, p. 12]; these are assumptions about the free-space propagation scaling, not consequences of the paper's own results, and they are not fitted from the same data the paper later 'predicts.' The in-text citations to the authors' prior RIS papers [2], [3] are used only as background references for the concept of reconfigurable intelligent surfaces and the generalized Snell's law; they are not invoked as uniqueness theorems or as substitutes for the SNR/rate derivations. Thus, the central claim of the paper—providing unified end-to-end SNR and rate formulas—is self-contained with respect to its own derivation chain. Any concern that the RIS path-loss laws may be inaccurate is a modeling-validity issue, not a circularity issue.
Assumptions & free parameters
assumptions (4)
- domain assumption Perfect instantaneous CSI at relay and destination
- domain assumption Residual self-interference modeled as Rician
- domain assumption RIS path-loss models: sum-distance and product-distance laws
- domain assumption Noise variance model N0 = -174 + 10log10(BW) + NF (dBm)
Cite this review
Pith. "Pith review of Multi-Antenna Relaying and Reconfigurable Intelligent Surfaces: End-to-End SNR and Achievable Rate." pith.science (2026). https://pith.science/paper/G6PRP4OP
@misc{pith2026190807967,
author = {Pith},
title = {Pith review of: Multi-Antenna Relaying and Reconfigurable Intelligent Surfaces: End-to-End SNR and Achievable Rate},
year = {2026},
howpublished = {\url{https://pith.science/paper/G6PRP4OP}},
note = {Machine review of arXiv:1908.07967}
}
read the original abstract
In this report, we summarize the end-to-end signal-to-noise ratio and the rate of half-duplex, full-duplex, amplify-and-forward, and decode-and-forward relay-aided communications, and well as the signal-to-noise ratio and the rate of the emerging technology known as reconfigurable intelligent surfaces.
Figures
Reference graph
Works this paper leans on
-
[1]
M. Dohler and Y . Li, Cooperative communications: Hardware, channel and PHY , Wiley-Blackwell, Feb. 2010
work page 2010
-
[2]
Smart radio environments empowered by reconfigurable AI meta-surfaces: An idea whose time has come
M. Di Renzo et al. , “Smart radio environments empowered by reconfigurable AI meta-surfaces: An idea whose time has come”, EURASIP J. Wireless Commun. Net. , vol. 129, 20 pages, May 2019
work page 2019
-
[3]
Wireless communications through reconfigurable intelligent surfaces
E. Basar, M. Di Renzo, J. de Rosny, M. Debbah, M.-S. Alouini, and R. Zhang, “Wireless communications through reconfigurable intelligent surfaces”, IEEE Access , to appear, Aug. 2019. [Online]. Available: https://arxiv.org/pdf/1906.09490.pdf
arXiv 2019
-
[4]
Goldsmith, Wireless communications, Cambridge New York: Cambridge University Press, 2005
A. Goldsmith, Wireless communications, Cambridge New York: Cambridge University Press, 2005
work page 2005
-
[5]
Hybrid full-duplex/half-duplex relaying with transmit power adaptation
T. Riihonen, S. Werner, and R. Wichman, “Hybrid full-duplex/half-duplex relaying with transmit power adaptation”, IEEE Trans. Wireless Commun., vol. 10, no. 9, pp. 3074-3085, Sep. 2011
work page 2011
-
[6]
In-band full-duplex relaying: A survey, research issues and challenges
G. Liu, F. R. Yu, H. Ji, V . C. M. Leung, and X. Li, “In-band full-duplex relaying: A survey, research issues and challenges”, IEEE Commun. Surveys Tuts. , vol. 17, no. 2, pp. 500-524, 2nd Quart. 2015
work page 2015
-
[7]
Experiment-driven characterization of full-duplex wireless systems
M. Duarte, C. Dick, and A. Sabharwal, “Experiment-driven characterization of full-duplex wireless systems”, IEEE Trans. Wireless Commun., vol. 11, no. 12, pp. 4296-4307, Dec. 2012
work page 2012
-
[8]
F. P. Fontán and P. M. Espiñeira, Modelling the wireless propagation channel: A simulation approach with MATLAB , John Wiley & Sons, 2008
work page 2008
Reviewed August 14, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.