Simple and Accurate Closed-Form Approximation of the Standard Condition Number Distribution with Application in Spectrum Sensing

Kobeissi, Hussein; Nafkha, Amor; Nasser, Youssef; Bazzi, Oussama; Louët, Yves

doi:10.1007/978-3-319-40352-6_29

Cited by 14 publications

(18 citation statements)

References 14 publications

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“…Given the normalized covariance matrix defined by Based on Y D , Eq. (49) in [23] provides a decision threshold function γ ∆ = f (N T , K, P f ), for measuring how many antennas on one subcarrier are required to achieve a certain probability of false alarm denoted by P f . Therefore, we could establish a single-subcarrier encoding (SSE) principle, finally encoding the number of detected signals into binary and Mary digits.…”

Section: A Energy Feature Extractionmentioning

confidence: 99%

Hierarchical 2-D Feature Coding for Secure Pilot Authentication in Multi-User Multi-Antenna OFDM Systems: A Reliability Bound Contraction Perspective

Ren

Ritcey

2019

IEEE Trans.Inform.Forensic Secur.

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Due to the publicly-known and deterministic characteristic of pilot tones, pilot authentication (PA) in multiuser multi-antenna OFDM systems is very suspectable to the jamming/nulling/spoofing behaviors. To solve this, we in this paper develop a hierarchical 2-D feature (H2DF) coding theory that exploits the hidden pilot signal features, i.e., the energy feature and independence feature, to secure pilot information coding which is applied between legitimate parties through a well-designed five-layer hierarchical coding (HC) model to achieve secure multiuser PA (SMPA). The reliability of SMPA is characterised using the identification error probability (IEP) of pilot encoding and decoding, with the exact closed-form upper and lower bounds. However, this phenomenon of nontight bounds brings about the risk of long-term instability in SMPA. Therefore, a reliability bound contraction (RBC) theory is developed to shrink the bound interval and practically, this is done by an easy-to-implement technique, namely, codebook partition within the H2DF code. In this process, a tradeoff between the upper and lower bounds of IEP is identified and a problem of optimal upper-lower bound tradeoff is formulated, with the objective of optimizing the cardinality of sub-codebooks such that the upper and lower bounds coincide. Solving this, we finally derive an exact closed-form expression for IEP, which realizes a stable and highly-reliable SMPA. Numerical results validate the stability and resilience of H2DF coding in SMPA.Index Terms-Physical-layer authentication, anti-attack, multiuser OFDM, channel training, hierarchical 2-D feature coding.

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Section: A Energy Feature Extractionmentioning

confidence: 99%

Hierarchical 2-D Feature Coding for Secure Pilot Authentication in Multi-User Multi-Antenna OFDM Systems: A Reliability Bound Contraction Perspective

Ren

Ritcey

2019

IEEE Trans.Inform.Forensic Secur.

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“…The bi-variate first order Taylor expansion of the function X = g(λ 1 , T n ) = λ 1 /T n about any point θ = (θ λ 1 , θ T n ) is written as [20]:…”

Section: Mean Of Sle Using λ 1 and T Nmentioning

confidence: 99%

“…where µ λ 1 , µ T n and µ X are respectively the means of the LE, the normalized trace and the SLE given by (12), (20) and (34) respectively. σ λ 1 and σ T n are respectively the standard deviations of the LE and the normalized trace and are the square root of (13) and (21) respectively.…”

Section: Deduction Of the Correlation Coefficient ρmentioning

confidence: 99%

On the Performance Analysis and Evaluation of Scaled Largest Eigenvalue in Spectrum Sensing: A Simple Form Approach

Kobeissi¹,

Nafkha²,

Nasser³

et al. 2017

EAI Endorsed Transactions on Cognitive Communications

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Scaled Largest Eigenvalue (SLE) detector stands out as the optimal single-primary-user detector in uncertain noisy environments. In this paper, we consider a multi-antenna cognitive radio system in which we aim at detecting the presence/absence of a Primary User (PU) using the SLE detector. By the exploitation of the distributions of the largest eigenvalue and the trace of the receiver sample covariance matrix, we show that the SLE could be modeled using the standard Gaussian function. Moreover, we derive the distribution of the SLE and deduce a simple yet accurate form of the probability of false alarm and the probability of detection. Hence, this derivation yields a very simple form of the detection threshold. Correlation coefficient between the largest eigenvalue and the trace is also considered as we derive a simple analytical expression. These analytical derivations are validated through extensive Monte Carlo simulations

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“…They are given by µ T W 2 = −1.7710868074, σ 2 T W 2 = 0.8131947928 and S T W 2 = 0.2240842036 respectively [25]. Accordingly, using (12), the mean, variance and skewness of λ H 0 1 are, respectively, given by: and using (15), the mean, variance and skewness of λ H 0 K are, respectively, given by: …”

Section: Central Moments Of λmentioning

confidence: 99%

“…Email: hussein.kobeissi.87@gmail.com signal covariance matrix and it utilises results from Random Matrix Theory (RMT) [4]. It detects the presence/absence of the PU by exploiting receiver diversity and includes the Largest Eigenvalue (LE) detector [5][6][7], the Scaled Largest Eigenvalue (SLE) detector [7][8][9] , and the Standard Condition Number (SCN) detector [5,[10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Approximation of the Standard Condition Number Detector for Large Multi-Antenna Cognitive Radio Systems

Kobeissi¹,

Nasser²,

Nafkha³

et al. 2017

EAI Endorsed Transactions on Cognitive Communications

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Standard condition number (SCN) detector is a promising detector that can work efficiently in uncertain environments. In this paper, we consider a Cognitive Radio (CR) system with large number of antennas (eg. Massive MIMO) and we provide an accurate and simple closed form approximation for the SCN distribution using the generalized extreme value (GEV) distribution. The approximation framework is based on the moment-matching method where the expressions of the moments are approximated using bi-variate Taylor expansion and results from random matrix theory. In addition, the performance probabilities and the decision threshold are considered. Since the number of antennas and/or the number of samples used in the sensing process may frequently change, this paper provides simple form decision threshold and performance probabilities offering dynamic and real-time computations. Simulation results show that the provided approximations are tightly matched to relative empirical ones.

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Simple and Accurate Closed-Form Approximation of the Standard Condition Number Distribution with Application in Spectrum Sensing

Cited by 14 publications

References 14 publications

Hierarchical 2-D Feature Coding for Secure Pilot Authentication in Multi-User Multi-Antenna OFDM Systems: A Reliability Bound Contraction Perspective

Hierarchical 2-D Feature Coding for Secure Pilot Authentication in Multi-User Multi-Antenna OFDM Systems: A Reliability Bound Contraction Perspective

On the Performance Analysis and Evaluation of Scaled Largest Eigenvalue in Spectrum Sensing: A Simple Form Approach

Asymptotic Approximation of the Standard Condition Number Detector for Large Multi-Antenna Cognitive Radio Systems

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