@conference {921, title = {Locally optimal invariant detector for testing equality of two power spectral densities}, booktitle = { IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)}, year = {2018}, address = {Calgary, Canada}, abstract = {
This work addresses the problem of determining whether two multivariate random time series have the same power spectral density
(PSD), which has applications, for instance, in physical-layer security and cognitive radio. Remarkably, existing detectors for this
problem do not usually provide any kind of optimality. Thus, we study here the existence under the Gaussian assumption of optimal
invariant detectors for this problem, proving that the uniformly most powerful invariant test (UMPIT) does not exist. Thus, focusing on
close hypotheses, we show that the locally most powerful invariant test (LMPIT) only exists for univariate time series. In the multivariate
case, we prove that the LMPIT does not exist. However, this proof suggests two LMPIT-inspired detectors, one of which outperforms
previously proposed approaches, as computer simulations show.
}, keywords = {cognitive radio, winter}, author = {David Ram{\'\i}rez and Daniel Romero and Javier V{\'\i}a and R. L{\'o}pez-Valcarce and Ignacio Santamar{\'\i}a} }