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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
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