Performance Analysis of Linear Detection under Noise-Dependent Fast-Fading Channels

Almutasem Bellah Enad; Hadi Sarieddeen; Hakim Jemaa; Jihad Fahs; Tareq Y. Al-Naffouri

REVIEW 2 major objections 5 minor 30 references

Performance Analysis of Linear Detection under Noise-Dependent Fast-Fading Channels

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A correlated channel and noise pair changes the zero-forcing symbol error rate by a factor (1−|λ|²) at high SNR.

desk verdict Solid niche SER analysis for ZF with correlated noise, but the detector is mislabeled as ML and the conditional mean of the effective noise is ignored. read the letter →

arxiv 2507.05897 v1 pith:BARVYSNF submitted 2025-07-08 eess.SP

Almutasem Bellah Enad , Jihad Fahs , Hadi Sarieddeen , Hakim Jemaa , Tareq Y. Al-Naffouri This is my paper · ORCID

classification eess.SP

keywords zero-forcingdetectionsymbolerrorratechannel-noisecorrelationRayleighfadingeffectivenoisecopulaasymptoticanalysisQAM

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 tries to establish that when the fading channel and the additive noise are statistically dependent, the usual independence-based SER analysis overestimates detection error, and that a zero-forcing detector's SER can be computed exactly from the distribution of the effective noise Z = n/h. For Rayleigh fading with jointly Gaussian channel and noise, it derives the SER in Eq. (8) and a high-SNR closed form in Eq. (14) in which channel-noise correlation scales the error rate by (1−|λ|²). This matters because emerging links such as terahertz systems, RIS-aided links, and hardware-impaired receivers can have noise that depends on the channel, and the result turns an otherwise intractable ratio distribution into a usable performance formula. The framework also extends to arbitrary dependence through copulas, giving a route to SER analysis when only marginal distributions and a dependence structure are known.

What carries the argument

The central object is the effective noise Z = n/h after zero-forcing inversion, whose PDF for correlated complex Gaussians is the ratio distribution in Eq. (7), cited from [30]. This density carries the entire argument: inserting it into the decision-region integral Eq. (2) gives the SER, and its quadratic-term asymptotics as σ → 0 produce the closed form in Eq. (14). For dependence beyond the joint-Gaussian model, a bivariate copula density, specifically the Frank copula in Eq. (22), builds the joint PDF of |h| and |n|, and Eq. (23) integrates over fades to give the effective-noise PDF.

What would settle it

Generate or measure a channel-noise pair whose joint statistics are known to deviate from the jointly Gaussian model, such as noise whose variance depends nonlinearly on |h|, then compare the measured zero-forcing SER with Eq. (8); a systematic mismatch at fixed λ would falsify the claim. A concrete test is a testbed that injects noise with power proportional to a nonlinear function of channel gain and then estimates the empirical effective-noise PDF to check whether Eq. (7) is the right density.

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Extended reading notes

Core claim

For a SISO Rayleigh fading channel with zero-mean circular complex Gaussian channel h and noise n having correlation coefficient λ, the effective noise after ZF inversion is Z = n/h, whose PDF is the ratio distribution in Eq. (7). Using this density in the decision-region integral gives the semi-analytical SER expression in Eq. (8) for M-QAM under ML detection. At high SNR this reduces to Eq. (14), where the only effect of correlation is the multiplicative factor Λ = σ²(1−|λ|²)/π, equivalent to a correlation gain of 10 log10(1−|λ|²) dB over the independent case. When λ = 0, the framework recovers the standard Rayleigh fading SER benchmark, and when λ ≠ 0, the independence assumption is shown to overestimate the error rate, with the overestimation reaching about 16 dB at SER 10⁻³ for |λ| near 1 for both 4-QAM and 16-QAM. For non-Gaussian dependence, a Frank copula constructs the joint PDF of |h| and |n|, leading to the effective-noise PDF in Eq. (23), and the SER follows from Eqs. (1)–(2).

Load-bearing premise

The channel h and noise n are jointly zero-mean circular complex Gaussian with a fixed correlation coefficient λ, so the effective noise Z = n/h has the specific density in Eq. (7); if the physical dependence differs from this joint-Gaussian form, the derived SER formulas do not apply.

Editorial extensions

If this is right

When |λ| is nonzero, ignoring channel-noise correlation overstates the SER; at |λ| ≈ 1 the error is overestimated by about 16 dB at SER 10⁻³ for both 4-QAM and 16-QAM.
At high SNR, the correlation gain is exactly 10 log10(1−|λ|²) dB, so even modest correlation yields a measurable improvement in detection reliability.
Setting λ = 0 recovers the standard Rayleigh fading SER benchmark, showing the framework generalizes existing results rather than replacing them.
The copula branch allows the same SER computation when the joint distribution of channel and noise is specified only through marginals and a dependence parameter.

Reading between the lines

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

If real hardware noise (phase noise, nonlinearities, interference) produces dependence that is not joint-Gaussian, the copula branch would be needed; this suggests measuring the empirical copula of h and n in THz and RIS testbeds to see which dependence model actually fits.
The same ratio-of-Gaussians machinery could be extended to MMSE detection or to MIMO ZF, where the effective noise is a more complex ratio, although the paper only treats the SISO case.
A testable extension is to inject noise whose variance is a nonlinear function of channel gain and check whether the (1−|λ|²) scaling still predicts the measured SER, which would reveal how far the idealized joint-Gaussian model reaches.

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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 derives a semi-analytical SER for SISO ZF detection when the fading and noise are jointly Gaussian and possibly correlated. The main result, Eq. (8), follows from a known ratio-of-Gaussians PDF, and the independent-case recovery plus the simulation matches give me confidence the algebra is right. The closed-form high-SNR term Λ = σ^2(1−|λ|^2)/π is a clean summary of the correlation effect. For a niche problem (THz, RIS, hardware-impaired links) this is a useful tool.

The real problem is the ML label. Section II says the receiver is ML and that conditioned on h the effective noise is Gaussian with variance σ^2/|h|^2. That is only true when the conditional mean is zero. Under the joint Gaussian model, E[n|h] = λ(σ_n/σ_h)h, so Z = n/h has conditional mean λ(σ_n/σ_h)e^{j arg h}, which is not zero. The correct ML decision regions after ZF would be shifted by that mean. The paper ignores this and integrates against fixed, h-independent Voronoi regions. So Eq. (8) is the SER of a mismatched fixed nearest-neighbor ZF detector, not ML. The simulations use fixed slicing, so they validate the fixed detector. This is not fatal — relabel the detector and the math stands — but it is load-bearing for the claimed contribution. The asymptotic analysis in Eq. (14) survives because the shift decays relative to the noise variance at high SNR.

Other issues are minor. The correlation gain sign in the text is backwards (10 log10(1−|λ|^2) is a loss relative to independence, not a gain — though the SER expression correctly shows SER decreases with |λ|). The asymptotic closed form is derived for 4-QAM but Fig. 1b legend may show it for 16-QAM as well; the paper should be explicit. The abstract overclaims generality ("wide range of channel and noise models") when the actual work is one joint-Gaussian model plus a copula extension.

The citation pattern looks fine; the ratio PDF is credited to [30] and the textbook benchmark to [4]. No fitting, no free parameters. This is honest work.

Who is this for? Someone doing link budgets for systems where noise is correlated with the channel — THz front-ends, RIS with phase noise, hardware-impaired receivers. A careful referee could get value from it, but it needs a revision to fix the detector label and the conditional-mean oversight before publication. I'd send it to review with that expectation.

Referee Report

2 major / 5 minor

Summary. This paper develops an analytical framework for the symbol error rate (SER) of zero-forcing (ZF) detection in a SISO Rayleigh fading channel when the additive Gaussian noise and the channel coefficient are statistically dependent. The key step is to use the known density of the ratio Z = n/h for correlated complex Gaussian variables (Eq. (7) from [30]) and integrate it over the standard QAM decision regions, yielding the semi-analytical expression in Eq. (8). At high SNR the authors derive a closed-form asymptotic for 4-QAM, Eq. (14), which exhibits the dependence on 1-|lambda|^2, and an improved finite-SNR approximation for the independent case, Eq. (20). A Frank-copula extension for the case where only the marginal magnitudes are known is given in Eq. (23). Monte Carlo simulations in Section V are reported to match the theoretical curves.

Significance. If the expressions are read as applying to a fixed minimum-distance ZF detector, the paper contributes a useful semi-analytical tool: it avoids Monte Carlo integration over the fading distribution, requires no fitted parameters, recovers the textbook independent Rayleigh-fading result when lambda=0, and quantifies the effect of channel-noise correlation through the factor (1-|lambda|^2). This is relevant to systems where hardware impairments or interference couple the noise to the channel, such as THz and RIS links. The main mathematical derivation is compact and the simulation agreement is a genuine verification. However, the paper overstates the result by calling the detector ML; this is a correctness issue in the interpretation of Eq. (8), and the asymptotic expressions are only valid for 4-QAM unless extended.

major comments (2)

[Section II and Eq. (8)] The detector whose SER is computed is not the ML detector described in the text. Under the jointly Gaussian model, E[n|h] = lambda (sigma_n/sigma_h) h, so the effective noise Z = n/h has conditional mean lambda (sigma_n/sigma_h) e^{j arg h} and conditional variance (1-|lambda|^2) sigma_n^2 / |h|^2. Consequently, the conditional distribution of Z given h is Gaussian with a nonzero, h-dependent mean, and the true ML decision regions are the constellation Voronoi regions shifted by that mean; they are not the fixed regions D_k used in Eq. (8). Equation (8) integrates the unconditional density (7) over fixed regions and therefore gives the SER of a fixed nearest-neighbor (minimum-distance) ZF detector that ignores the conditional shift. The Monte Carlo results in Section V validate this fixed-detector calculation, not the ML claim. The authors should either relabel the detector as fixed minimum-distance ZF throughout, or re-derive the SER with h-dependent shifted regions; the Section II statement that the effective noise has variance sigma^2/|h|^2 is also incorrect for lambda != 0, since the variance should be multiplied by 1-|lambda|^2. This is load-bearing because the paper's central claim concerns which detector's SER Eq. (8) represents.
[Section IV-A and Fig. 1] The asymptotic expression (14) and the improved approximation (20) are derived explicitly for 4-QAM (M=4) with quadrant decision regions and a corner symbol at (alpha_1, beta_1). The figures, however, appear to display these curves for both 4-QAM and 16-QAM. For 16-QAM, interior, edge, and corner symbols have different decision regions, and the regions are not the four quadrants, so Eqs. (14) and (20) do not apply without modification. The authors should either restrict these curves to 4-QAM or provide the corresponding 16-QAM derivations, and the figure legends should state which modulation each curve is for.

minor comments (5)

[Section IV-A, after Eq. (14)] The 'correlation gain' formula 10 log10(1 - |lambda|^2) dB has the wrong sign; for |lambda| > 0 this quantity is negative, so taken literally it is a loss, whereas the text correctly describes a reduction in required SNR. The intended horizontal shift is -10 log10(1 - |lambda|^2) dB.
[Eq. (9)] The constant Lambda is written with lambda^2 instead of |lambda|^2; since lambda is complex, the magnitude should be used consistently.
[Fig. 1 legends] The legends do not make clear which curves correspond to 4-QAM and which to 16-QAM, especially for the 'Asymptotic Eq(14)' and 'Aprox Eq(20)' entries; please clarify.
[Eq. (23)] The argument of f_{W_r,W_i} is printed as (w_r, w_r) in the text; it should be (w_r, w_i).
[Section V] The simulation procedure for generating correlated (h,n) pairs is not described for either the correlation model or the Frank-copula model, and the reported Monte Carlo standard error range is given without the SER levels to which it applies, so the numerical results are not fully reproducible as written.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: Eq. (8) and Eq. (14) follow from the externally derived ratio PDF [30] with no fitted parameters; the Section II ML/fixed-slicing mismatch is a correctness caveat, not a circularity.

full rationale

The derivation chain is self-contained and externally anchored: the effective-noise PDF in Eq. (7) is quoted from reference [30] (Li and He, IEEE Communications Letters 2019), which is not the present authors' work; Eq. (8) is the definitional integral of that PDF over the decision regions, with no fitted parameter; Eq. (14) follows from Eq. (8) by a standard dominant-term asymptotic analysis, giving the multiplicative factor Lambda = sigma^2 (1-|lambda|^2)/pi; and the lambda=0 limit recovers the textbook benchmark [4, eq. 8.107] through Eqs. (5)-(6), as confirmed in Fig. 1a. No quantity is fitted to the SER curves: the correlation coefficient lambda in Fig. 1b and the Frank-copula parameter theta in Fig. 1c are model inputs, and the Monte Carlo simulations draw from the same model, so the agreement verifies the integration and the asymptotics rather than fitting a prediction. The paper's self-citations ([3], [8], [16], [17]) are motivational background and carry no load in the derivation, so per the hard rules they do not raise the score. Flagged for the record per the reviewing rule: Section II states 'the effective noise is Gaussian with variance sigma~^2 = sigma^2/|h|^2 (for a given h)' and 'the ML decision boundaries ... are determined by the minimum distance rule,' omitting the conditional mean E[n|h] = lambda (sigma_n/sigma_h) h implied by the paper's own jointly Gaussian model; consequently Eq. (8), which integrates the unconditional ratio density against h-independent regions, is the SER of a fixed nearest-neighbor ZF detector rather than of the claimed ML detector. This is a correctness/model-claim mismatch, not a circular reduction: Eq. (8) does not reduce to its inputs, the simulations use the same fixed detector so the match is internally consistent, and since the omitted shift is O(sigma), the high-SNR result Eq. (14) is unaffected. The circularity score is therefore 1.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No free parameters are fitted to data. The correlation coefficient λ and copula parameter θ are model inputs chosen for simulation, not estimated from measurements. The main axioms are the joint Gaussianity of channel and noise, perfect CSI, the ratio PDF from [30], and the Frank copula example. No invented entities.

assumptions (5)

domain assumption Channel h and noise n are jointly zero-mean circular complex Gaussian with correlation coefficient λ.
Section II states 'we assume that h and n are jointly Gaussian', which is the basis for the ratio PDF in Eq. (7).
domain assumption Perfect channel state information at the receiver.
Section II assumes perfect CSI, which justifies ZF inversion and Gaussian decision regions conditional on h.
standard math The PDF of the ratio of two correlated complex Gaussians is given by Eq. (7), taken from reference [30].
Eq. (7) is cited from Li and He, IEEE Comm. Lett. 2019, and is the core analytical input.
domain assumption Minimum-distance decision regions are treated as ML decision regions.
Section II defines decision regions by the minimum distance rule, but under correlation the effective noise has a nonzero conditional mean, which would shift ML boundaries.
ad hoc to paper Frank copula models the dependence between |h| and |n| in the copula-based extension.
Section IV-B introduces the Frank copula density in Eq. (22) as an example; it is not required for the core Gaussian-correlation result.

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Cite this review

Pith. "Pith review of Performance Analysis of Linear Detection under Noise-Dependent Fast-Fading Channels." pith.science (2026). https://pith.science/paper/BARVYSNF

@misc{pith2026250705897,
  author       = {Pith},
  title        = {Pith review of: Performance Analysis of Linear Detection under Noise-Dependent Fast-Fading Channels},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BARVYSNF}},
  note         = {Machine review of arXiv:2507.05897}
}

read the original abstract

This paper presents a performance analysis framework for linear detection in fast-fading channels with possibly correlated channel and noise. The framework is both accurate and adaptable, making it well-suited for analyzing a wide range of channel and noise models. As such, it serves as a valuable tool for the design and evaluation of detection algorithms in next-generation wireless communication systems. By characterizing the distribution of the effective noise after zero-forcing filtering, we derive a semi-analytical and asymptotic expression for the symbol error rate under Rayleigh fading and channel-dependent additive circular complex Gaussian noise. The proposed approach demonstrates excellent agreement with integration-based benchmarks as confirmed by numerical simulations thus validating its accuracy. The framework is flexible and can be extended to various channel and noise models, offering a valuable tool for the design and analysis of detection algorithms in next-generation communication systems.

Figures

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Works this paper leans on

30 extracted references · 26 canonical work pages

[30]

On the ratio of two correlated complex ga ussian random variables,

Y . Li and Q. He, “On the ratio of two correlated complex ga ussian random variables,” IEEE Commun. Lett. , vol. 23, no. 12, pp. 2172–2176, 2019

work page 2019
[4]

M. K. Simon and M.-S. Alouini, Digital communication over fading channels. John Wiley & Sons, 2005, vol. 95

work page 2005
[1]

White paper on broadband connectivity in 6G,

N. Rajatheva, I. Atzeni, E. Bjornson, A. Bourdoux, S. Buz zi, J.-B. Dore, S. Erkucuk, M. Fuentes, K. Guan et al. , “White paper on broadband connectivity in 6G,” arXiv preprint arXiv:2004.14247 , 2020

arXiv 2004
[2]

Towards 6G MIMO: Massive spatial multiplexing, dense arra ys, and interplay between electromagnetics and processing,

E. Björnson, C.-B. Chae, R. W. Heath Jr, T. L. Marzetta, A. Mezghani, L. Sanguinetti, F. Rusek, M. R. Castellanos, D. Jun, and Ö. T. Demir, “Towards 6G MIMO: Massive spatial multiplexing, dense arra ys, and interplay between electromagnetics and processing,” arXiv preprint arXiv:2401.02844, 2024

arXiv 2024
[3]

An overview of signal processing techniques for terahertz communication s,

H. Sarieddeen, M.-S. Alouini, and T. Y . Al-Naffouri, “An overview of signal processing techniques for terahertz communication s,” Proceedings of the IEEE , vol. 109, no. 10, pp. 1628–1665, 2021

work page 2021
[5]

Goldsmith, Wireless Communication

A. Goldsmith, Wireless Communication. Cambridge University Press, August 2005

work page 2005
[6]

Fifty years of MIMO detection: The r oad to large-scale MIMOs,

S. Y ang and L. Hanzo, “Fifty years of MIMO detection: The r oad to large-scale MIMOs,” IEEE Commun. Surveys Tuts. , vol. 17, no. 4, pp. 1941–1988, 2015

work page 1941
[7]

Massive MI MO detection techniques: A survey,

M. A. Albreem, M. Juntti, and S. Shahabuddin, “Massive MI MO detection techniques: A survey,” IEEE Commun. Surveys Tuts. , vol. 21, no. 4, pp. 3109–3132, 2019

work page 2019

Show all 30 references

[8]

Bridging the complexity gap in Tbps-achieving THz- band baseband processing,

H. Sarieddeen, H. Jemaa, S. Tarboush, C. Studer, M.-S. Al ouini, and T. Y . Al-Naffouri, “Bridging the complexity gap in Tbps-achieving THz- band baseband processing,” IEEE Wireless Commun. , 2024, in press

2024
[9]

J. G. Proakis and M. Salehi, Digital communications . McGraw-hill, 2008

2008
[10]

D. T. Se and P . Viswanath, Fundamentals of wireless communication . Cambridge, United Kingdom: Cambridge University Press, 20 05
[11]

A new, simple and exact result for calculatin g the probability of error for two-dimensional signal constellations,

J. Craig, “A new, simple and exact result for calculatin g the probability of error for two-dimensional signal constellations,” in Proc. IEEE MILCOM, 1991, pp. 571–575 vol.2

1991
[12]

M-P SK and M-QAM BER computation using signal-space concepts,

J. Lu, K. B. Letaief, J. C.-I. Chuang, and M. L. Liou, “M-P SK and M-QAM BER computation using signal-space concepts,” IEEE Trans. Commun. , vol. 47, pp. 181–184, 1999. [Online]. Available: https://api.semanticscholar.org/CorpusID:5295560

1999
[13]

Ergodic capacity and symbol error rate of distributed massive MIMO systems over Rayleig h- Inverse Gaussian fading channels using ZF detectors,

B. B. Pradhan and L. P . Roy, “Ergodic capacity and symbol error rate of distributed massive MIMO systems over Rayleig h- Inverse Gaussian fading channels using ZF detectors,” Physical Communication, vol. 38, p. 100906, 2020. [Online]. Available: https://doi.org/10.1016/j.phyc...

2020
[14]

Analytical SER performance bound of M- QAM MIMO system with ZF-SIC receiver,

J. Xu, X. Tao, and P . Zhang, “Analytical SER performance bound of M- QAM MIMO system with ZF-SIC receiver,” in Proc. IEEE Int. Conf. Commun. (ICC) , 2008, pp. 5103–5107

2008
[15]

Average SEP-optimal precoding for correlated massive MIMO with ZF detection: An asymptotic an alysis,

Z. Dong, J.-K. Zhang, and H. Chen, “Average SEP-optimal precoding for correlated massive MIMO with ZF detection: An asymptotic an alysis,” IEEE Trans. Commun. , vol. 67, no. 4, pp. 2807–2821, 2019

2019
[16]

GRAND for fad ing channels using pseudo-soft information,

H. Sarieddeen, M. Médard, and K. R. Duffy, “GRAND for fad ing channels using pseudo-soft information,” in Proc. IEEE Global Conmun. Conf. (GLOBECOM) , 2022, pp. 3502–3507

2022
[17]

Performance analysis of outdoor THz links under mixture gamma fading with misalignment,

H. Jemaa, S. Tarboush, H. Sarieddeen, M.-S. Alouini, an d T. Y . Al- Naffouri, “Performance analysis of outdoor THz links under mixture gamma fading with misalignment,” IEEE Wireless Commun. Lett. , vol. 28, no. 11, pp. 2668–2672, 2024

2024
[18]

Performance analysis of terahertz com munications in random fog conditions with misalignment,

O. S. Badarneh, “Performance analysis of terahertz com munications in random fog conditions with misalignment,” IEEE Wireless Commun. Lett., vol. 11, no. 5, pp. 962–966, 2022

2022
[19]

Analytical performance assessment of THz wireless systems,

A.-A. A. Boulogeorgos, E. N. Papasotiriou, and A. Alexi ou, “Analytical performance assessment of THz wireless systems,” IEEE Access, vol. 7, pp. 11 436–11 453, 2019

2019
[20]

Copula theory and its applications,

P . Bickel, P . Diggle, S. Fienberg, U. Gather, I. Olkin, a nd S. Zeger, “Copula theory and its applications,” in Proc. W orkshop, Warsaw, Poland, 2009, pp. 25–26

2009
[21]

R. B. Nelsen, An introduction to copulas . Springer, 2006

2006
[22]

Copula models for wireless fading and the ir impact on wireless diversity combining,

J. A. Ritcey, “Copula models for wireless fading and the ir impact on wireless diversity combining,” in Proc. Asilomar Conf. Signals, Systems and Computers (Asilomar) , 2007, pp. 1564–1567

2007
[23]

Communications meets copula modeling: Non-standard depe ndence features in wireless fading channels,

G. W. Peters, T. A. Myrvoll, T. Matsui, I. Nevat, and F. Se ptier, “Communications meets copula modeling: Non-standard depe ndence features in wireless fading channels,” in Proc. IEEE Global Conf. on Signal and Inform. Process. (GlobalSIP) , 2014, pp. 1224–1228

2014
[24]

On the capacity of mimo correlated nakagami- m fading channels using copula,

M. H. Gholizadeh, H. Amindavar, and J. A. Ritcey, “On the capacity of mimo correlated nakagami- m fading channels using copula,” EURASIP J. on Wireless Commun. and Netw. , vol. 2015, pp. 1–11, 2015. [Online]. Available: https://api.semanticscholar.org/CorpusID:2265071

2015
[25]

Performance analysis over co rre- lated/independent ﬁsher-snedecor F fading multiple access channels,

F. R. Ghadi and W.-P . Zhu, “Performance analysis over co rre- lated/independent ﬁsher-snedecor F fading multiple access channels,” IEEE Trans. V eh. Technol., vol. 71, no. 7, pp. 7561–7571, 2022

2022
[26]

Cop ula-based modeling of RIS-assisted communications: Outage probabil ity analysis,

I. Trigui, D. Shahbaztabar, W. Ajib, and W.-P . Zhu, “Cop ula-based modeling of RIS-assisted communications: Outage probabil ity analysis,” IEEE Commun. Lett. , vol. 26, no. 7, pp. 1524–1528, 2022

2022
[27]

E. E. Elsayed, “Investigations on OFDM UA V -based free- space optical transmission system with scintillation mitigation for opt ical wireless communication-to-ground links in atmospheric turbulence ,” Optical and Quantum Electronics, vol. 56, no. 837, 2024

2024
[28]

S. A. Kassam, Signal Detection in Non-Gaussian Noise . New Y ork: Springer-V erlag, 1988

1988
[29]

Gradshteyn, I

I. Gradshteyn, I. Ryzhik, D. Zwillinger, and V . Moll, Table of Integrals, Series, and Products , 8th ed. Rensselaer Polytechnic Institute, USA and Tulane University, Department of Mathematics: Academi c Press, 2014

2014

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [30]

On the ratio of two correlated complex ga ussian random variables,

Y . Li and Q. He, “On the ratio of two correlated complex ga ussian random variables,” IEEE Commun. Lett. , vol. 23, no. 12, pp. 2172–2176, 2019

work page 2019

[2] [4]

M. K. Simon and M.-S. Alouini, Digital communication over fading channels. John Wiley & Sons, 2005, vol. 95

work page 2005

[3] [1]

White paper on broadband connectivity in 6G,

N. Rajatheva, I. Atzeni, E. Bjornson, A. Bourdoux, S. Buz zi, J.-B. Dore, S. Erkucuk, M. Fuentes, K. Guan et al. , “White paper on broadband connectivity in 6G,” arXiv preprint arXiv:2004.14247 , 2020

arXiv 2004

[4] [2]

Towards 6G MIMO: Massive spatial multiplexing, dense arra ys, and interplay between electromagnetics and processing,

E. Björnson, C.-B. Chae, R. W. Heath Jr, T. L. Marzetta, A. Mezghani, L. Sanguinetti, F. Rusek, M. R. Castellanos, D. Jun, and Ö. T. Demir, “Towards 6G MIMO: Massive spatial multiplexing, dense arra ys, and interplay between electromagnetics and processing,” arXiv preprint arXiv:2401.02844, 2024

arXiv 2024

[5] [3]

An overview of signal processing techniques for terahertz communication s,

H. Sarieddeen, M.-S. Alouini, and T. Y . Al-Naffouri, “An overview of signal processing techniques for terahertz communication s,” Proceedings of the IEEE , vol. 109, no. 10, pp. 1628–1665, 2021

work page 2021

[6] [5]

Goldsmith, Wireless Communication

A. Goldsmith, Wireless Communication. Cambridge University Press, August 2005

work page 2005

[7] [6]

Fifty years of MIMO detection: The r oad to large-scale MIMOs,

S. Y ang and L. Hanzo, “Fifty years of MIMO detection: The r oad to large-scale MIMOs,” IEEE Commun. Surveys Tuts. , vol. 17, no. 4, pp. 1941–1988, 2015

work page 1941

[8] [7]

Massive MI MO detection techniques: A survey,

M. A. Albreem, M. Juntti, and S. Shahabuddin, “Massive MI MO detection techniques: A survey,” IEEE Commun. Surveys Tuts. , vol. 21, no. 4, pp. 3109–3132, 2019

work page 2019