23 research outputs found
Cooperative Spectrum Sensing based on the Limiting Eigenvalue Ratio Distribution in Wishart Matrices
Recent advances in random matrix theory have spurred the adoption of
eigenvalue-based detection techniques for cooperative spectrum sensing in
cognitive radio. Most of such techniques use the ratio between the largest and
the smallest eigenvalues of the received signal covariance matrix to infer the
presence or absence of the primary signal. The results derived so far in this
field are based on asymptotical assumptions, due to the difficulties in
characterizing the exact distribution of the eigenvalues ratio. By exploiting a
recent result on the limiting distribution of the smallest eigenvalue in
complex Wishart matrices, in this paper we derive an expression for the
limiting eigenvalue ratio distribution, which turns out to be much more
accurate than the previous approximations also in the non-asymptotical region.
This result is then straightforwardly applied to calculate the decision
threshold as a function of a target probability of false alarm. Numerical
simulations show that the proposed detection rule provides a substantial
performance improvement compared to the other eigenvalue-based algorithms.Comment: 7 pages, 2 figures, submitted to IEEE Communications Letter
On the Performance of Spectrum Sensing Algorithms using Multiple Antennas
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.Comment: IEEE GlobeCom 201
Eigenvalue Ratio Detection Based on Exact Moments of Smallest and Largest Eigenvalues
Detection based on eigenvalues of received signal covariance matrix is currently one of the most effective solution for spectrum sensing problem in cognitive radios. However, the results of these schemes always depend on asymptotic assumptions since the close-formed expression of exact eigenvalues ratio distribution is exceptionally complex to compute in practice. In this paper, non-asymptotic spectrum sensing approach to approximate the extreme eigenvalues is introduced. In this context, the Gaussian approximation approach based on exact analytical moments of extreme eigenvalues is presented. In this approach, the extreme eigenvalues are considered as dependent Gaussian random variables such that the joint probability density function (PDF) is approximated by bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. In this context, the definition of Copula is cited to analyze the extent of the dependency between the extreme eigenvalues. Later, the decision threshold based on the ratio of dependent Gaussian extreme eigenvalues is derived. The performance analysis of our newly proposed approach is compared with the already published asymptotic Tracy-Widom approximation approach
SPECTRUM SENSING USING CYCLIC PREFIX IN COGNITIVE RADIO WIRELESS SYSTEM
The rapid growth of wireless communications has made the problem of spectrum utilization ever more critical. The increasing diversity (voice, short message, Web & multimedia) and demand of high quality-of-service (QoS) applications have resulted in overcrowding of the allocated (officially sanctioned) spectrum bands, leading to significantly reduced levels of user satisfaction. The concepts of GLRT algorithm and substantial improvement over the U-GLRT algorithm are explained. This paper presents a model which uses efficient CP method for CR in Wireless Systems. Primary signal has been detected in the OFDM transmission with both the CPCC and MP–based C-GLRT algorithms greatly outperform energy detection in multi path environment has been implemented using software design. The signal model in our analysis is to efficiently exploit the correlation among the transmitted signals due to the presence of CP. Proposed method of cognitive radio takes two steps of implementation .first named as MP based is to detect the noise and de-noise the signal and the second is cp based in which the signals are identified based on the cyclic prefix
Performance Analysis of Multi-Antenna Hybrid Detectors and Optimization with Noise Variance Estimation
In this paper, a performance analysis of multi-antenna spectrum sensing techniques is carried out. Both well known algorithms, such as Energy Detector (ED) and eigenvalue based detectors, and an eigenvector based algorithm, are considered. With the idea of auxiliary noise variance estimation, the performance analysis is extended to the hybrid approaches of the considered detectors. Moreover, optimization for Hybrid ED under constant estimation plus detection time is performed. Performance results are evaluated in terms of Receiver Operating Characteristic (ROC) curves and performance curves, i.e., detection probability as a function of the Signal-to-Noise Ratio (SNR). It is concluded that the eigenvector based detector and its hybrid approach are able to approach the optimal Neyman-Pearson performance
Phase transitions in the condition number distribution of Gaussian random matrices
We study the statistics of the condition number
(the ratio between
largest and smallest squared singular values) of Gaussian random
matrices. Using a Coulomb fluid technique, we derive analytically and for large
the cumulative and tail-cumulative
distributions of . We find that these
distributions decay as and , where is the Dyson index of the ensemble. The left
and right rate functions are independent of and
calculated exactly for any choice of the rectangularity parameter
. Interestingly, they show a weak non-analytic behavior at
their minimum (corresponding to the average condition
number), a direct consequence of a phase transition in the associated Coulomb
fluid problem. Matching the behavior of the rate functions around
, we determine exactly the scale of typical fluctuations
and the tails of the limiting distribution of
. The analytical results are in excellent agreement with numerical
simulations.Comment: 5 pag. + 7 pag. Suppl. Material. 3 Figure
On the probability that all eigenvalues of Gaussian, Wishart, and double Wishart random matrices lie within an interval
We derive the probability that all eigenvalues of a random matrix lie
within an arbitrary interval ,
, when is a real or complex finite dimensional Wishart,
double Wishart, or Gaussian symmetric/Hermitian matrix. We give efficient
recursive formulas allowing the exact evaluation of for Wishart
matrices, even with large number of variates and degrees of freedom. We also
prove that the probability that all eigenvalues are within the limiting
spectral support (given by the Mar{\v{c}}enko-Pastur or the semicircle laws)
tends for large dimensions to the universal values and for
the real and complex cases, respectively. Applications include improved bounds
for the probability that a Gaussian measurement matrix has a given restricted
isometry constant in compressed sensing.Comment: IEEE Transactions on Information Theory, 201