Testing Equality of Multiple Power Spectral Density Matrices Articles uri icon

publication date

  • December 2018

start page

  • 6268

end page

  • 6280

issue

  • 23

volume

  • 66

international standard serial number (ISSN)

  • 1053-587X

electronic international standard serial number (EISSN)

  • 1941-0476

abstract

  • This paper studies the existence of optimal invariant detectors for determining whether P multivariate processes have the same power spectral density. This problem finds application in multiple fields, including physical layer security and cognitive radio. For Gaussian observations, we prove that the optimal invariant detector, i. e., the uniformly most powerful invariant test, does not exist. Additionally, we consider the challenging case of close hypotheses, where we study the existence of the locally most powerful invariant test (LMPIT). The LMPIT is obtained in the closed form only for univariate signals. In the multivariate case, it is shown that the LMPIT does not exist. However, the corresponding proof naturally suggests an LMPIT-inspired detector that outperforms previously proposed detectors.

keywords

  • generalized likelihood ratio test (glrt); locally most powerful invariant test (lmpit); power spectral density (psd); toeplitz matrix; uniformly most powerful invariant test (umpit); time-series