Paper accepted in IEEE Transactions on Signal Processing

The paper "Testing Equality of Multiple Power Spectral Density Matrices", co-authored by D. Ramirez, D. Romero, J. Via, R. Lopez-Valcarce and I. Santamaría, has been accepted for publication in the IEEE Transactions on Signal Processing.

Abstract: This work studies the existence of optimal invariant detectors for determining whether P multivariate processes have the same power spectral density (PSD). 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 (UMPIT), 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 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 one LMPIT-inspired detector, which outperforms previously proposed detectors.