GLRT for Reconfigurable Intelligent Surface aided Spectrum Sensing

Nikhilsingh Parihar; Praful Mankar; Sachin Chaudhari

REVIEW 4 major objections 5 minor 14 references

A GLRT that jointly estimates the unknown primary-to-RIS channel and transmit power, then configures a grouped RIS to maximize the estimated gain, is claimed to outperform energy detection under correlated noise and few observations.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-07-31 23:52 UTC pith:GWIYOVXY

load-bearing objection The GLRT math is largely sound, but the paper's own parameter choices violate the identifiability condition its estimator needs, so the ROC claims are not yet supported. the 4 major comments →

arxiv 2607.23277 v1 pith:GWIYOVXY submitted 2026-07-25 eess.SP math.STstat.TH

GLRT for Reconfigurable Intelligent Surface aided Spectrum Sensing

Nikhilsingh Parihar , Praful Mankar , Sachin Chaudhari This is my paper

classification eess.SP math.STstat.TH MSC 94A1362F0362H15

keywords spectrum sensingreconfigurable intelligent surfacegeneralized likelihood ratio testenergy detectioncorrelated noisemaximum likelihood estimationbeyond-diagonal RIScognitive radio

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper studies spectrum sensing for cognitive radio with a reconfigurable intelligent surface (RIS) helping the secondary user hear the primary user. Its key move is to remove the usual assumption that the channel between the primary user and the RIS is known. It splits the RIS into groups, estimates each group's channel and the primary transmit power by maximum likelihood from whitened received data, then chooses the RIS phase matrix in closed form to maximize the gain of the estimated channel. With that optimized surface, it builds a GLRT decision statistic from the dominant generalized eigenvalue of a data matrix pencil. In simulated ROC curves, this GLRT consistently beats an energy detector at the same false-alarm rate, and the gap is largest under correlated noise and few observations, exactly the regime where energy detection struggles.

Core claim

The paper claims that with grouped, sequential activation of RIS elements, the unknown primary-to-RIS channel and transmit power can be estimated on the fly: per group, the channel estimate is the dominant generalized eigenvector of the pencil formed by the whitened sample covariance and the effective sensing matrix, and the power estimate is the corresponding excess eigenvalue. These estimates feed a closed-form RIS phase design Φ* = U_G~ U_h^H that maximizes the norm of the estimated reflected channel through the von Neumann trace inequality. The resulting GLRT statistic is T(λ̂_max − 1 − ln λ̂_max), where λ̂_max is the dominant generalized eigenvalue under the optimally configured RIS. Th

What carries the argument

The central mechanism is the grouped beyond-diagonal RIS with sequential activation. Partitioning the L elements into G blocks makes the estimation problem low-dimensional enough for ML: each block's effective matrix A_g = W G_g Φ_g is N × L_bar, so the unknown channel is identifiable only when each group has at most N elements. The mathematical load is carried by two closed forms: the ML estimates as a generalized eigenvector/eigenvalue problem, derived via matrix determinant and Woodbury identities, and the phase-optimization solution Φ* = U_G~ U_h^H obtained from the von Neumann trace inequality. These reduce the whole detection problem to a scalar generalized-eigenvalue test statistic wi

Load-bearing premise

The load-bearing premise, stated by the paper in Section II as needing L ≤ N, is that each group's effective matrix is identifiable: per group, the number of active RIS elements must not exceed the number of receive antennas, and the training data must come from an active primary user. If either requirement fails — e.g., the default N=8, L=512, G=16 gives 32 elements per group — the estimated channel and the RIS phase built from it are not tied to the true channel.

What would settle it

Reproduce the detection experiment under the paper's stated default parameters N=8, L=512, G=16, giving 32 RIS elements per group against 8 antennas. The matrix A_g^H A_g is singular, so the generalized-eigenvalue MLE in (9) is not well-defined; if the detector still shows a large ROC gain over energy detection, the gain cannot come from the paper's estimation theory. Conversely, run the full two-phase procedure with only noise present during training and check that the resulting phase yields no better detection than random phases.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

If the claim holds, RIS-aided spectrum sensing no longer requires perfect knowledge of the primary-to-RIS channel, removing the main practical obstacle in previous RIS-sensing designs.
The closed-form phase design lets the hardware switch from estimation mode to sensing mode without iterative optimization, keeping sensing latency short.
Working on whitened data makes the detector specifically effective in correlated-noise environments, where energy detectors need very long observation windows to stabilize their threshold.
The groupwise estimation trick caps the required training dimension: sensing with large RISs is feasible as long as each group stays small enough, but the per-group element count must respect the identifiability limit.

Where Pith is reading between the lines

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

If the estimation phase runs while the primary user is silent, the estimates are noise-driven and the phase solution aligns to noise; a robust design would need a coarse pre-detection trigger or a known pilot, which the paper does not describe.
The identifiability condition L_bar ≤ N is load-bearing; the paper's default simulation parameters (N=8, L=512, G=16) appear to violate it with 32 elements per group, so the claimed ROC gains may not be supported by the MLE theory unless the figure used a compliant grouping.
A natural next experiment is to inject an explicit channel-estimation error model and measure how the optimal-phase GLRT degrades; since the phase is a rotation that aligns to the estimate, small angular errors in the channel estimate could disproportionately hurt the beamforming gain.
The grouped-estimation plus closed-form-phase front-end is agnostic to the downstream test, so it could equally serve maximum-eigenvalue or other covariance-based detectors, making the grouping and phase design the more portable contribution than the GLRT itself.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

The GLRT math is largely sound, but the paper's own parameter choices violate the identifiability condition its estimator needs, so the ROC claims are not yet supported.

read the letter

The genuinely new thing here is combining GLRT with a grouped beyond-diagonal RIS for spectrum sensing under correlated noise and unknown PU-RIS channel. That is a real gap: prior work either assumes the channel is known or only handles white noise. The derivations in Appendices A and B are algebraically correct for the models they address, and the group-wise ML formulation is a sensible way to deal with large RISs. The ED analysis is standard and clean. Credit where it is due: the paper is not sloppy in its math, and the statistical approach is coherent.

The soft spots are real, but mostly fixable. First, the identifiability constraint. The paper motivates grouping by saying L <= N is impractical, but it never states the per-group condition Lbar <= N that its own generalized eigenvalue problem requires. The default simulation parameters (L=512, G=16, N=8) give Lbar=32 > N, which makes A_g^H A_g singular. Fig. 3's caption says L=16, and Fig. 2 uses G=8 so Lbar=N=64. The text and figures do not agree. If the authors actually ran with Lbar > N, both the ML estimator in (9) and the GLRT statistic in (20) are not well-defined because the matrix pencil is singular. This is a load-bearing inconsistency, not a cosmetic one.

Second, the rank-one claim in Section IV is simply wrong for N > 1. \tilde{G}^H \tilde{G} is not rank-one in general; the maximum effective gain is sigma_max^2(\tilde{G}) ||h||^2, not the product of two single eigenvalues. This affects the ED analysis and the phase-optimization derivation, and should be corrected.

Third, the two-phase protocol assumes the PU is transmitting during Phase 1. If the PU is silent, the ML estimates are noise-dominated and the "optimal" RIS matrix is uninformative. The paper never specifies how the SU knows the PU is active, nor what fallback exists if Phase 1 sees only noise. That is an acknowledged circularity in the framework, and it needs an explicit statement or a workaround.

The core statistical ideas are sound, and the GLRT derivation is correct under the proper rank condition. The paper deserves a serious referee, but the authors must fix the parameter constraints and reconcile the simulation setup before the claimed detection gains are credible. I would send it to review with a clear request for these revisions, not desk-reject it.

Referee Report

4 major / 5 minor

Summary. The paper studies RIS-aided spectrum sensing under correlated Gaussian noise, proposing a generalized likelihood ratio test (GLRT) that estimates the unknown PU-RIS channel and PU transmit power, then optimizes the RIS phase shifts to maximize the estimated effective channel gain. A group-wise estimation scheme is introduced to handle large RISs, and an energy detector (ED) with optimized RIS is also analyzed. Numerical ROC results claim that the proposed GLRT outperforms ED, especially at low SNR and under correlated noise. The appendices provide algebraic derivations of the ML estimates and the GLRT statistic.

Significance. If the technical gaps are repaired, the paper would be a useful contribution: it extends RIS-aided sensing to unknown PU-RIS channels, considers correlated noise, and provides closed-form GLRT and ED statistics together with a grouped processing strategy for large RISs. The algebraic derivations in Appendices A and B are a strength, and the GLRT statistic is self-contained rather than a fitted quantity. However, the manuscript currently contains load-bearing errors and missing assumptions: the rank-one claim in Section IV is false for N>1, the identifiability condition for the per-group ML estimator is not respected by the default simulation parameters, and the two-phase framework presupposes PU activity during parameter estimation without specifying a training protocol. These issues must be addressed before the claimed detection improvements can be considered supported.

major comments (4)

[Section IV, Eq. (17)] The statement that "\tilde G^H \tilde G and \hat h\hat h^H are rank-one matrices" is false for N>1. With the paper's N=8, \tilde G is 8×L, so \tilde G^H \tilde G has rank at most 8, not 1. The correct maximized value of J is λ_max(\tilde G^H \tilde G)λ_h, where λ_max is the largest eigenvalue. The phase solution in (16) can still achieve this bound if λ_{\tilde G} is redefined as the largest eigenvalue, but as written Eq. (17) and the subsequent ED moment expressions in Section V.B inherit the error. Please correct the rank argument and propagate the fix.
[Section III, Eq. (9) and Section VI defaults] The ML estimator in Eq. (9) is a generalized eigenvalue problem that is well-posed only if A_g = W G_g Φ_g has full column rank, i.e., \bar L = L/G ≤ N. The paper only imposes L ≤ N in Section II, not the per-group condition. The stated default parameters N=8, L=512, G=16 give \bar L = 32 > N, so A_g^H A_g is singular and the "dominant generalized eigenvector" is undefined. Figure 2 uses G=8 (\bar L=64=N), while Figure 3's caption states L=16; the simulation settings are inconsistent. All experiments supporting the claimed ROC gains must use \bar L ≤ N and report G and L explicitly for each figure.
[Section II, two-phase framework] Phase 1 'channel estimation and RIS configuration' uses the signal model in Eq. (2b), which assumes the PU is active (H1). The paper never states how the SU knows the PU is active during this phase, nor what happens if Phase 1 is run while the PU is silent. Under H0, the estimates from (9)–(12) are noise-dominated, \hat h is essentially arbitrary, and the optimized phase matrix in (16) is not aligned to the true channel. The detection gains reported in Figs. 3–4 are therefore unsupported unless the authors explicitly define a training protocol with a known PU-active interval or otherwise justify the H1 assumption during estimation.
[Section V, Eq. (20)] The detection model in Eq. (18b) uses the full matrix A⋆ = √ν W G Φ⋆ with L columns, whereas estimation is performed group-wise with \bar L ≤ N. For L > N, which is the default scenario (L=512, N=8), C = A⋆^H A⋆ is singular, and the generalized eigenvalue problem in Eq. (20) is not well-defined without restricting to the range of A⋆^H. Appendix B's maximization of Eq. (39) subject to h^H C h = 1 is ill-posed for singular C. The manuscript should either define the effective rank and domain for the GLRT statistic or perform Phase 2 detection group-wise and combine the per-group statistics.

minor comments (5)

[Section VI, Figs. 2 and 3] The parameter settings are inconsistent: the default text gives N=8, L=512, G=16; Fig. 2 says G=8; Fig. 3 caption says L=16. Please unify the notation and state exactly which (N,L,G,\bar L) pair is used in each curve.
[Section V.B, Eq. (28)] Eq. (28) contains a stray factor 'G' in γ_ED = G μ_0 + σ_0 Q^{-1}(P_FA). The ED statistic in Eq. (23) does not involve the number of groups, and the threshold should be μ_0 + σ_0 Q^{-1}(P_FA).
[Section II, group-wise activation] When only one RIS group is active, the phase-shift matrix Φ_g has zeros outside the group indices and is not unitary on the full L×L space. The unitary constraint (15b) should be stated for the active \bar L×\bar L block; otherwise the model is ambiguous.
[Throughout] There are minor typos and grammar issues, e.g., 'V on Neumann' (Von Neumann), 'SU have control' (has), and 'SG g=1 Ig' (union symbol). A careful proofreading pass is needed.
[Section V] The text mentions a tradeoff between detection performance and computational complexity, but no complexity analysis is given. A short discussion of the cost of the generalized eigen-decomposition and the group-wise estimation would improve the paper.

Circularity Check

0 steps flagged

No self-referential derivation; the GLRT statistic is self-contained. Minor self-citations and an H1-training assumption are limitations, not circular reductions.

full rationale

The central derivation chain is not circular. The ML estimates (9)-(13) are obtained by maximizing the H1 log-likelihood (8)/(33), and the GLRT statistic in (20)/(40) is the resulting generalized-eigenvalue likelihood ratio; it is not a fitted parameter renamed as a prediction. The RIS phase solution (16) is derived in the text via von Neumann's trace inequality, so the citation to [14] is not load-bearing. The only self-citation used in a derivation is [13, Theorem 1] in (29) for the distribution of lambda_h when deconditioning the ED detection probability; this is a baseline-analysis step and is not load-bearing for the paper's central GLRT-versus-ED comparison, which is evaluated numerically. The two-phase protocol in Section II does, however, implicitly assume that Phase-1 estimation data are generated under H1: equation (7) defines the covariance under H1, and under H0 the estimator (9) has no signal component, making the optimized RIS (16) uninformative. This is a genuine operational/identifiability limitation, as is the parameter inconsistency (default L=512, G=16 gives \bar{L}=32>N=8, while (9) requires \bar{L}\le N; Fig. 3 uses L=16). These are correctness and robustness defects, not circular reductions: no equation in the derivation is equivalent by construction to its own input, and the test statistic does not reduce to the Phase-1 estimates.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 0 invented entities

No constants are fitted to data in the proposed method; the estimators are ML and the detectors are threshold-based with thresholds chosen from target P_FA. The central claim rests instead on modeling assumptions: known noise covariance, known G, identifiability of h_g (Lbar<=N), Gaussian signaling, an imported eigenvalue distribution from [13], and an H1 training phase. The identifiability and training-phase assumptions are the most fragile and are not validated in the paper.

axioms (6)

domain assumption Noise covariance R_n is known exactly and used to whiten the received signal (W = R_n^{-1/2}, Eq. 5).
The whitening and all subsequent estimates/detectors assume R_n is available; if R_n is unknown or estimated, the GLRT statistic and ED analysis change.
domain assumption The PU-RIS channel h is constant over the sensing interval and the RIS-SU channel G is known at the SU with a dominant LoS component.
Section II states slow flat fading and known G; the ML estimator and phase optimization require G known and h fixed across T_g observations.
ad hoc to paper The active-group matrix A_g = W G_g Phi_g has full column rank (equivalently Lbar <= N) so that the generalized eigenvalue problem (9) is well-posed and h_g is identifiable.
The paper states the L<=N constraint in Section II; the MLE (9) is undefined for null-space components if A_g is rank deficient, yet the default simulation parameters violate this (Lbar=32>N=8).
standard math The transmitted primary symbols are complex Gaussian with unknown variance sigma_x^2, making the received vector Gaussian.
The Gaussian likelihood (8) and the CLT-based ED analysis rely on this distributional model.
domain assumption The distribution of lambda_h needed in the ED detection probability (29) is imported from [13, Theorem 1] without re-derivation.
The paper uses the authors' prior result for the eigenvalue distribution; if [13] is incorrect or its conditions do not match this setup, the ED curve is wrong.
ad hoc to paper A training/estimation phase exists in which the PU is active (H1), so the ML estimates and RIS phase optimization are meaningful.
Section II's two-phase framework estimates h_g and sigma_x^2 before detection; under H0 these estimates describe noise, the phase solution is arbitrary, and the claimed RIS gain is not obtained. The paper does not discuss this.

pith-pipeline@v1.3.0-alltime-deepseek · 8647 in / 20710 out tokens · 190204 ms · 2026-07-31T23:52:10.490733+00:00 · methodology

0 comments

read the original abstract

Spectrum sensing (SS) is crucial for realising cognitive radio networks, where the secondary user (SU) needs to detect the presence of a primary user (PU) in order to utilise the spectrum. However, the ability of detection is influenced by unknown propagation environment factors such as multipath fading, correlated noise, transmission power of PU, etc. This paper investigates reconfigurable intelligent surfaces (RIS)-aided SS under correlated noise conditions using a generalised likelihood ratio test (GLRT) and energy detector (ED) frameworks. We first derive maximum likelihood estimates of the unknown channel state and transmit power, and employ these estimates to construct the GLRT-based test statistic using the signal received with an optimally configured RIS. The RIS phase shift matrix is optimally determined to maximise the gain of the estimated channel. Besides, the detection and false alarm probabilities of ED with optimally configured RIS are also derived. The numerical receiver output characteristics (ROC) demonstrate that the proposed GLRT achieves superior detection probability compared to ED, particularly under correlated noise and limited number of observations.

Figures

Figures reproduced from arXiv: 2607.23277 by Nikhilsingh Parihar, Praful Mankar, Sachin Chaudhari.

**Figure 3.** Figure 3: shows the ROC curves of the proposed GLRT and ED detectors for SNR equal to 0, −4 and −8 dB. It can be observed from the figure that the GLRT consistently outperforms the ED for all SNRs. This is because the GLRT exploits the estimated channel state and PU transmission power information to accurately characterize the likelihood function with the optimally configured RIS, whereas ED uses only information … view at source ↗

**Figure 2.** Figure 2: shows the MSE performance of the proposed groupwise ML estimator for PU–RIS channel estimate hˆ for different numbers of observations T ∈ {40, 100, 500, 1000}. Here, the number of RIS elements L = 512 are grouped into G = 8 groups of size L¯ = N = 64. The graph shows that the MSE decreases monotonically with increasing SNR and increasing the number of observations T, as expected. This verifies that the p… view at source ↗

**Figure 4.** Figure 4: Probability of Detection versus the noise correlation coefficient. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

discussion (0)

Reference graph

Works this paper leans on

14 extracted references

[1]

Active RIS vs. Passive RIS: Which will prevail in 6G?

Z. Zhang, L. Dai, X. Chen, C. Liu, F. Yang, R. Schober, and H. V . Poor, “Active RIS vs. Passive RIS: Which will prevail in 6G?”IEEE Transactions on Communications, 2023

2023
[2]

Ra- dio localization and mapping with reconfigurable intelligent surfaces: Challenges, opportunities, and research directions,

H. Wymeersch, J. He, B. Denis, A. Clemente, and M. Juntti, “Ra- dio localization and mapping with reconfigurable intelligent surfaces: Challenges, opportunities, and research directions,”IEEE V ehicular Technology Magazine, 2020

2020
[3]

Radar target detection aided by reconfigurable intelligent surfaces,

S. Buzzi, E. Grossi, M. Lops, and L. Venturino, “Radar target detection aided by reconfigurable intelligent surfaces,”IEEE Signal Processing Letters, 2021

2021
[4]

Enhancing spectrum sensing via re- configurable intelligent surfaces: Passive or active sensing and how many reflecting elements are needed?

H. Xie, D. Li, and B. Gu, “Enhancing spectrum sensing via re- configurable intelligent surfaces: Passive or active sensing and how many reflecting elements are needed?”IEEE Transactions on Wireless Communications, 2024

2024
[5]

Signal processing in cognitive radio,

J. Ma, G. Y . Li, and B. H. Juang, “Signal processing in cognitive radio,” Proceedings of the IEEE, 2009

2009
[6]

Blind cyclostationary spectrum sensing in cognitive radios,

W. M. Jang, “Blind cyclostationary spectrum sensing in cognitive radios,”IEEE Communications Letters, 2014

2014
[7]

Blind spectrum sensing using extreme eigenvalues for cognitive radio networks,

K. Bouallegue, I. Dayoub, M. Gharbi, and K. Hassan, “Blind spectrum sensing using extreme eigenvalues for cognitive radio networks,”IEEE Communications Letters, 2018

2018
[8]

Maximum eigenvalue detection: Theory and application,

Y . Zeng, C. L. Koh, and Y .-C. Liang, “Maximum eigenvalue detection: Theory and application,” inIEEE ICC, 2008

2008
[9]

GLRT approach for multi- antenna-based spectrum sensing under interference,

M. Lin, W. Wang, X. Hong, and W. Zhang, “GLRT approach for multi- antenna-based spectrum sensing under interference,”IEEE Communica- tions Letters, 2020

2020
[10]

Optimal GLRT-based robust spectrum sensing for MIMO cognitive radio networks with CSI uncertainty,

A. Patel, S. Biswas, and A. K. Jagannatham, “Optimal GLRT-based robust spectrum sensing for MIMO cognitive radio networks with CSI uncertainty,”IEEE Transactions on Signal Processing, 2016

2016
[11]

RIS-enhanced spectrum sensing: How many reflecting elements are required to achieve a detection probability close to 1?

J. Ge, Y .-C. Liang, S. Li, and Z. Bai, “RIS-enhanced spectrum sensing: How many reflecting elements are required to achieve a detection probability close to 1?”IEEE Transactions on Wireless Communications, 2022

2022
[12]

Active ris enhanced spectrum sensing for opportunistic cognitive radio networks,

J. Ge, Y .-C. Liang, and S. Sun, “Active ris enhanced spectrum sensing for opportunistic cognitive radio networks,” inIEEE GLOBECOM 2023, 2023

2023
[13]

Maximum eigenvalue detection based spectrum sensing in RIS-aided system with correlated fading,

N. Parihar, P. D. Mankar, and S. Chaudhari, “Maximum eigenvalue detection based spectrum sensing in RIS-aided system with correlated fading,” inIEEE VTC-Spring, 2024

2024
[14]

Capacity analysis of cascaded BD-RIS assisted MIMO systems,

M. S. S. Manasa, P. D. Mankar, and S. Vanka, “Capacity analysis of cascaded BD-RIS assisted MIMO systems,” 2025. APPENDIXA ML ESTIMATION OFh g ANDσ 2 x The log-likelihood function of the unknown parametersh g andσ 2 x for theg-th RIS group, given the sample covariance matrix ˆR˜y,g= 1 Tg ˜Yg ˜YH g , is given in (8) as Lg(hg, σ2 x) =−T g log|Σ ˜y,g| −Tg tr...

2025

[1] [1]

Active RIS vs. Passive RIS: Which will prevail in 6G?

Z. Zhang, L. Dai, X. Chen, C. Liu, F. Yang, R. Schober, and H. V . Poor, “Active RIS vs. Passive RIS: Which will prevail in 6G?”IEEE Transactions on Communications, 2023

2023

[2] [2]

Ra- dio localization and mapping with reconfigurable intelligent surfaces: Challenges, opportunities, and research directions,

H. Wymeersch, J. He, B. Denis, A. Clemente, and M. Juntti, “Ra- dio localization and mapping with reconfigurable intelligent surfaces: Challenges, opportunities, and research directions,”IEEE V ehicular Technology Magazine, 2020

2020

[3] [3]

Radar target detection aided by reconfigurable intelligent surfaces,

S. Buzzi, E. Grossi, M. Lops, and L. Venturino, “Radar target detection aided by reconfigurable intelligent surfaces,”IEEE Signal Processing Letters, 2021

2021

[4] [4]

Enhancing spectrum sensing via re- configurable intelligent surfaces: Passive or active sensing and how many reflecting elements are needed?

H. Xie, D. Li, and B. Gu, “Enhancing spectrum sensing via re- configurable intelligent surfaces: Passive or active sensing and how many reflecting elements are needed?”IEEE Transactions on Wireless Communications, 2024

2024

[5] [5]

Signal processing in cognitive radio,

J. Ma, G. Y . Li, and B. H. Juang, “Signal processing in cognitive radio,” Proceedings of the IEEE, 2009

2009

[6] [6]

Blind cyclostationary spectrum sensing in cognitive radios,

W. M. Jang, “Blind cyclostationary spectrum sensing in cognitive radios,”IEEE Communications Letters, 2014

2014

[7] [7]

Blind spectrum sensing using extreme eigenvalues for cognitive radio networks,

K. Bouallegue, I. Dayoub, M. Gharbi, and K. Hassan, “Blind spectrum sensing using extreme eigenvalues for cognitive radio networks,”IEEE Communications Letters, 2018

2018

[8] [8]

Maximum eigenvalue detection: Theory and application,

Y . Zeng, C. L. Koh, and Y .-C. Liang, “Maximum eigenvalue detection: Theory and application,” inIEEE ICC, 2008

2008

[9] [9]

GLRT approach for multi- antenna-based spectrum sensing under interference,

M. Lin, W. Wang, X. Hong, and W. Zhang, “GLRT approach for multi- antenna-based spectrum sensing under interference,”IEEE Communica- tions Letters, 2020

2020

[10] [10]

Optimal GLRT-based robust spectrum sensing for MIMO cognitive radio networks with CSI uncertainty,

A. Patel, S. Biswas, and A. K. Jagannatham, “Optimal GLRT-based robust spectrum sensing for MIMO cognitive radio networks with CSI uncertainty,”IEEE Transactions on Signal Processing, 2016

2016

[11] [11]

RIS-enhanced spectrum sensing: How many reflecting elements are required to achieve a detection probability close to 1?

J. Ge, Y .-C. Liang, S. Li, and Z. Bai, “RIS-enhanced spectrum sensing: How many reflecting elements are required to achieve a detection probability close to 1?”IEEE Transactions on Wireless Communications, 2022

2022

[12] [12]

Active ris enhanced spectrum sensing for opportunistic cognitive radio networks,

J. Ge, Y .-C. Liang, and S. Sun, “Active ris enhanced spectrum sensing for opportunistic cognitive radio networks,” inIEEE GLOBECOM 2023, 2023

2023

[13] [13]

Maximum eigenvalue detection based spectrum sensing in RIS-aided system with correlated fading,

N. Parihar, P. D. Mankar, and S. Chaudhari, “Maximum eigenvalue detection based spectrum sensing in RIS-aided system with correlated fading,” inIEEE VTC-Spring, 2024

2024

[14] [14]

Capacity analysis of cascaded BD-RIS assisted MIMO systems,

M. S. S. Manasa, P. D. Mankar, and S. Vanka, “Capacity analysis of cascaded BD-RIS assisted MIMO systems,” 2025. APPENDIXA ML ESTIMATION OFh g ANDσ 2 x The log-likelihood function of the unknown parametersh g andσ 2 x for theg-th RIS group, given the sample covariance matrix ˆR˜y,g= 1 Tg ˜Yg ˜YH g , is given in (8) as Lg(hg, σ2 x) =−T g log|Σ ˜y,g| −Tg tr...

2025