Locally Most Powerful Invariant Tests for Correlation and Sphericity of Gaussian Vectors

Ramírez, David; Vía, Javier; Santamarı́a, Ignacio; Scharf, Louis L.

doi:10.1109/tit.2012.2232705

Cited by 74 publications

(70 citation statements)

References 36 publications

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“…This test was proposed in [1] as an approximation of the GLRT for low values of the cross-correlation coefficients under H 1 and was recently shown to be a locally most powerful invariant test (LMPIT) for the correlation detection problem [23]. The asymptotic behavior ofη…”

Section: Introductionmentioning

confidence: 99%

Correlation Tests and Linear Spectral Statistics of the Sample Correlation Matrix

Mestre

Vallet

2017

IEEE Trans. Inform. Theory

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Abstract-Testing the independence of the entries of multidimensional Gaussian observations is a very important problem in statistics, with a number of applications in signal processing, radar, cognitive radio, seismography and multiple other fields. Typically, the problem is formulated as a binary hypothesis test, whereby the presence of correlation is declared when the value of a certain statistic is higher than a certain predetermined threshold. Most of the statistics for correlation tests are constructed from the sample correlation matrix (also known as sample coherence matrix in signal processing), which is defined as a power-normalized version of the sample covariance matrix. In this paper, correlation tests constructed from linear spectral statistics (LSS) of the sample correlation matrix are analyzed under the asymptotic framework where both sample size and observation dimension become large but comparable in magnitude. A Central Limit Theorem (CLT) is established on this class of statistics, which is valid for generally correlated Gaussian observations. Results show that LSS asymptotically fluctuate as Gaussian random variables under both hypotheses, with an asymptotic mean and variance that can be established for each particular test. In particular, this general CLT can be used to establish the asymptotic behavior of two of the most important correlation test statistics, namely the Generalized Likelihood Ratio Test (GLRT) and the Frobenius Norm Test (FNT), under both null and alternative hypotheses. As a by-product, it is established that LSS of sample covariance and sample correlation matrices have exactly the same first order behavior, but quite different asymptotic fluctuations in the second order regime. In both cases, the LSS asymptotically behave as Gaussian random variables, although with quite different asymptotic means and variances.

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Section: Introductionmentioning

confidence: 99%

Correlation Tests and Linear Spectral Statistics of the Sample Correlation Matrix

Mestre

Vallet

2017

IEEE Trans. Inform. Theory

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“…Thus for the case that the number of samples per antenna L is large enough we could use a truncated form of (34) with the most relevant coefficients ψ mM,k , which has lower computational complexity compared to (34), as,…”

Section: Remarkmentioning

confidence: 99%

On the Performance of Hadamard Ratio Detector-Based Spectrum Sensing for Cognitive Radios

Sedighi

Taherpour

Sala-Alvarez

et al. 2015

IEEE Trans. Signal Process.

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We consider the problem of multiantenna spectrum sensing in Cognitive Radios (CRs) when the receivers are assumed to be uncalibrated across the antennas. The performance of the Hadamard Ratio Detector (HRD) is analyzed in such a scenario. Specifically, we first derive the exact distribution of the HRD statistic under the null hypothesis, which leads to an elaborate but closed-form expression for the false-alarm probability. Then, we derive a simpler and tight closed-form approximation for both the false-alarm and detection probabilities by using a moment-based approximation of the HRD statistical distribution under both hypotheses. Finally, the accuracy of the obtained results is verified by simulations.

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“…This idea, proposed in [12] and already used in [13] to derive the generalized likelihood ratio test (GLRT), allows us to cast the detection problem as a test for the covariance structure of the observations. Using Wijsman's theorem [14][15][16], in this paper we obtain the locally most powerful invariant test (LMPIT), which is the best invariant detector for low signalto-noise ratios. The use of Wijsman's theorem provides an alternative way to derive the LMPIT without the need for obtaining the maximal invariant statistic.…”

Section: Introductionmentioning

confidence: 99%

An asymptotic LMPI test for cyclostationarity detection with application to cognitive radio

Ramírez

Schreier

Vía

et al. 2015

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We propose a new detector of primary users in cognitive radio networks. The main novelty of the proposed detector in comparison to most known detectors is that it is based on sound statistical principles for detecting cyclostationary signals. In particular, the proposed detector is (asymptotically) the locally most powerful invariant test, i.e. the best invariant detector for low signal-to-noise ratios. The derivation is based on two main ideas: the relationship between a scalar-valued cyclostationary signal and a vector-valued wide-sense stationary signal, and Wijsman's theorem. Moreover, using the spectral representation for the cyclostationary time series, the detector has an insightful interpretation, and implementation, as the broadband coherence between frequencies that are separated by multiples of the cycle frequency. Finally, simulations confirm that the proposed detector performs better than previous approaches.

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Locally Most Powerful Invariant Tests for Correlation and Sphericity of Gaussian Vectors

Cited by 74 publications

References 36 publications

Correlation Tests and Linear Spectral Statistics of the Sample Correlation Matrix

Correlation Tests and Linear Spectral Statistics of the Sample Correlation Matrix

On the Performance of Hadamard Ratio Detector-Based Spectrum Sensing for Cognitive Radios

An asymptotic LMPI test for cyclostationarity detection with application to cognitive radio

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