Results 1  10
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32
Performance of statistical tests for singlesource detection using random matrix theory
 IEEE Transactions on Information Theory
, 2011
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Asymptotic Behaviour of Random Vandermonde Matrices with Entries on the Unit Circle
, 2008
"... Abstract—Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, or sparse sampling theory, just ..."
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Cited by 24 (10 self)
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Abstract—Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, or sparse sampling theory, just to name a few. Within this framework, we extend classical freeness results on random matrices with i.i.d. entries and show that Vandermonde structured matrices can be treated in the same vein with different tools. We focus on various types of matrices, such as Vandermonde matrices with and without uniform phase distributions, as well as generalized Vandermonde matrices. In each case, we provide explicit expressions of the moments of the associated Gram matrix, as well as more advanced models involving the Vandermonde matrix. Comparisons with classical i.i.d. random matrix theory are provided, and deconvolution results are discussed. We review some applications of the results to the fields of signal processing and wireless communications. Index Terms—Vandermonde matrices, Random Matrices, deconvolution, limiting eigenvalue distribution, MIMO.
On the condition number distribution of complex wishart matrices
, 2010
"... Abstract—This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multipleinput m ..."
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Cited by 20 (1 self)
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Abstract—This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multipleinput multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and noncentral Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closedform expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semicorrelated Rayleigh fading and Ricean fading. Index Terms—MIMO systems, complex Wishart matrices, condition number, joint eigenvalue distribution.
On the performance of spectrum sensing algorithms using multiple antennas
 IEEE Trans. Wireless Communications
, 2010
"... Abstract—In recent years, some spectrum sensing algorithms using multiple antennas, such as the eigenvalue based detection (EBD), have attracted a lot of attention. In this paper, we are interested in deriving the asymptotic distributions of the test statistics of the EBD algorithms. Two EBD algorit ..."
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Cited by 6 (2 self)
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Abstract—In recent years, some spectrum sensing algorithms using multiple antennas, such as the eigenvalue based detection (EBD), have attracted a lot of attention. In this paper, we are interested in deriving the asymptotic distributions of the test statistics of the EBD algorithms. Two EBD algorithms using sample covariance matrices are considered: maximum eigenvalue detection (MED) and condition number detection (CND). The earlier studies usually assume that the number of antennas (K) and the number of samples (N) are both large, thus random matrix theory (RMT) can be used to derive the asymptotic distributions of the maximum and minimum eigenvalues of the sample covariance matrices. While assuming the number of antennas being large simplifies the derivations, in practice, the number of antennas equipped at a single secondary user is usually small, say 2 or 3, and once designed, this antenna number is fixed. Thus in this paper, our objective is to derive the asymptotic distributions of the eigenvalues and condition numbers of the sample covariance matrices for any fixed K but large N, from which the probability of detection and probability of false alarm can be obtained. The proposed methodology can also be used to analyze the performance of other EBD algorithms. Finally, computer simulations are presented to validate the accuracy of the derived results.
Performance analysis of some eigenbased hypothesis tests for collaborative sensing
 in IEEE 15th Workshop on Statistical Signal Processing (SSP’09
, 2009
"... In this contribution, we provide a theoretical study of two hypothesis tests allowing to detect the presence of an unknown transmitter using several sensors. Both tests are based on the analysis of the eigenvalues of the sampled covariance matrix of the received signal. The Generalized Likelihood Ra ..."
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Cited by 6 (1 self)
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In this contribution, we provide a theoretical study of two hypothesis tests allowing to detect the presence of an unknown transmitter using several sensors. Both tests are based on the analysis of the eigenvalues of the sampled covariance matrix of the received signal. The Generalized Likelihood Ratio Test (GLRT) derived in [1] is analyzed under the assumption that both the number K of sensors and the length N of the observation window tend to infinity at the same rate: K/N → c ∈ (0, 1). The GLRT is compared with a test based on the condition number used which is used in cognitive radio applications. Using results of random matrix theory for spiked models and tools of Large Deviations, we provide the error exponent curve associated with both test and prove that the GLRT outperforms the test based on the condition number. I.
A cooperative bayesian nonparametric framework for primary user activity monitoring in cognitive radio networks
 IEEE J. Sel. Areas Commun
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Asymptotics of eigenbased collaborative sensing
 Proc. IEEE Information Theory Workshop (ITW 2009
, 2009
"... Abstract—In this contribution, we propose a new technique for collaborative sensing based on the analysis of the normalized (by the trace) largest eigenvalues of the sample covariance matrix. Assuming that several base stations are cooperating and without the knowledge of the noise variance, the tes ..."
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Cited by 5 (0 self)
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Abstract—In this contribution, we propose a new technique for collaborative sensing based on the analysis of the normalized (by the trace) largest eigenvalues of the sample covariance matrix. Assuming that several base stations are cooperating and without the knowledge of the noise variance, the test is able to determine the presence of mobile users in a network when only few samples are available. Unlike previous heuristic techniques, we show that the test has roots within the Generalized Likelihood Ratio Test and provide an asymptotic random matrix analysis enabling to determine adequate threshold detection values (probability of false alarm). Simulations sustain our theoretical claims. I.
Theoretical Performance Analysis of Eigenvaluebased Detection
, 2009
"... In this paper we develop a complete analytical framework based on Random Matrix Theory for the performance evaluation of Eigenvaluebased Detection. While, up to now, analysis was limited to falsealarm probability, we have obtained an analytical expression also for the probability of missed detecti ..."
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Cited by 4 (0 self)
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In this paper we develop a complete analytical framework based on Random Matrix Theory for the performance evaluation of Eigenvaluebased Detection. While, up to now, analysis was limited to falsealarm probability, we have obtained an analytical expression also for the probability of missed detection, by using the theory of spiked population models. A general scenario with multiple signals present at the same time is considered. The theoretical results of this paper allow to predict the error probabilities, and to set the decision threshold accordingly, by means of a few mathematical formulae. In this way the design of an eigenvaluebased detector is made conceptually identical to that of a traditional energy detector. As additional results, the paper discusses the conditions of signal identifiability for single and multiple sources. All the analytical results are validated through numerical simulations, covering also convergence, identifiabilty and nonGaussian practical modulations.
The effect of noise correlation on fractional sampling based spectrum sensing
 in IEEE ICC
, 2013
"... Abstract—This paper considers a Fractional Sampling (FS) technique to enhance the Spectrum Sensing (SS) efficiency of a Cognitive Radio (CR) using a decision statistic based on asymptotic Random Matrix Theory (RMT). Firstly, the effect of noise correlation on eigenvalue based SS is studied analytica ..."
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Cited by 2 (2 self)
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Abstract—This paper considers a Fractional Sampling (FS) technique to enhance the Spectrum Sensing (SS) efficiency of a Cognitive Radio (CR) using a decision statistic based on asymptotic Random Matrix Theory (RMT). Firstly, the effect of noise correlation on eigenvalue based SS is studied analytically and by numerical evaluation. Secondly, new bounds for the Standard Condition Number (SCN) are proposed to enhance the SS efficiency in correlated noise scenarios. It is shown that proposed FS method can enhance SS efficiency up to certain FS rates at the expense of receiver complexity and no performance advantage is obtained if the FS rate is increased beyond this limit. As a result, a method for determining the operating point for the FS rate in terms of sensing performance and complexity is suggested.
Low Complexity Enhanced Hybrid Spectrum Sensing Architectures for Cognitive Radio Equipment
"... Abstract—Spectrum sensing enables detecting opportunities in licensed bands in order to access unused portions of the licensed spectrum. In this paper we propose two low complexity detectors based on a combination of two wellknown and complementary signal detection mechanisms: energy detection and ..."
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Cited by 1 (0 self)
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Abstract—Spectrum sensing enables detecting opportunities in licensed bands in order to access unused portions of the licensed spectrum. In this paper we propose two low complexity detectors based on a combination of two wellknown and complementary signal detection mechanisms: energy detection and monocycle detection, which exploits cyclostationarity property of the signals. In the first algorithm the monocycle detector iteratively corrects the thresholds of a double threshold energy detector, that will finally converge to the performance of the monocycle detector. The second algorithm uses the monocycle detector to directly estimate the noise level N0, which is used to fix the threshold of the radiometer. Simulation results conducted on different environments show promising performances of the proposed detectors especially in low SNR.