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.

%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
%C Calgary, Canada
%G eng
%0 Journal Article
%J IEEE Trans. Signal Processing
%D 2018
%T Testing equality of multiple power spectral density matrices
%A David Ramírez
%A Daniel Romero
%A Javier Vía
%A R. López-Valcarce
%A Ignacio Santamaría
%K winter
%B IEEE Trans. Signal Processing
%V 66
%P 6268-6280
%8 12/2018
%G eng
%N 23
%R 10.1109/TSP.2018.2875884
%0 Conference Paper
%B IEEE Statistical Signal Processing Workshop (SSP 2012)
%D 2012
%T Detection of Gaussian signals in unknown time-varying channels
%A Daniel Romero
%A Javier Vía
%A R. López-Valcarce
%A Ignacio Santamaría
%K cognitive radio
%K dynacs
%K spectrum sensing
%X Detecting the presence of a white Gaussian signal distorted by a noisy time-varying channel is addressed by means of three different detectors. First, the generalized likelihood ratio test (GLRT) is found for the case where the channel has no temporal structure, resulting in the well-known Bartlett’s test. Then it is shown that, under the transformation group given by scaling factors, a locally most powerful invariant test (LMPIT) does not exist. Two alternative approaches are explored in the low signal-to-noise ratio (SNR) regime: the first assigns a prior probability density function (pdf) to the channel (hence modeled as random), whereas the second assumes an underlying basis expansion model (BEM) for the (now deterministic) channel and obtains the maximum likelihood (ML) estimates of the parameters relevant for the detection problem. The performance of these detectors is evaluated via Monte Carlo simulation.

%B IEEE Statistical Signal Processing Workshop (SSP 2012)
%I IEEE
%C Ann Arbor, MI
%8 08/2012
%G eng
%R 10.1109/SSP.2012.6319858
%0 Journal Article
%J IEEE Trans. on Signal Processing
%D 2011
%T Detection of Rank-P Signals in Cognitive Radio Networks With Uncalibrated Multiple Antennas
%A David Ramírez
%A Gonzalo Vázquez-Vilar
%A R. López-Valcarce
%A Javier Vía
%A Ignacio Santamaría
%K cognitive radio
%K dynacs
%K spectrum sensing
%X Spectrum sensing is a key component of the Cognitive Radio paradigm. Typically, primary signals have to be detected with uncalibrated receivers at signal-to-noise ratios (SNRs) well below decodability levels. Multiantenna detectors exploit spatial independence of receiver thermal noise to boost detection performance and robustness. We study the problem

of detecting a Gaussian signal with rank-P unknown spatial

covariance matrix in spatially uncorrelated Gaussian noise with

unknown covariance using multiple antennas. The generalized

likelihood ratio test (GLRT) is derived for two scenarios. In the

first one, the noises at all antennas are assumed to have the same (unknown) variance, whereas in the second, a generic diagonal noise covariance matrix is allowed in order to accommodate calibration uncertainties in the different antenna frontends. In the latter case, the GLRT statistic must be obtained numerically, for which an efficient method is presented. Furthermore, for asymptotically low SNR, it is shown that the GLRT does admit a closed form, and the resulting detector performs well in practice. Extensions are presented in order to account for unknown temporal correlation in both signal and noise, as well as frequency-selective channels.

%B IEEE Trans. on Signal Processing
%V 59
%P 3764-3774
%8 08/2012
%G eng
%N 8
%R 10.1109/TSP.2011.2146779
%0 Conference Paper
%B IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
%D 2011
%T Multiantenna detection under noise uncertainty and primary user's spatial structure
%A David Ramírez
%A Gonzalo Vázquez-Vilar
%A R. López-Valcarce
%A Javier Vía
%A Ignacio Santamaría
%K cognitive radio
%K generalized likelihood ratio test (GLRT)
%K spectrum sensing
%B IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
%I IEEE
%C Prage, Czech Republic
%P 2948-2951
%8 May
%G eng
%0 Conference Paper
%B IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
%D 2010
%T Multiantenna spectrum sensing: detection of spatial correlation among time-series with unknown spectra
%A David Ramírez
%A Javier Vía
%A Ignacio Santamaría
%A R. López-Valcarce
%A L. L. Scharf
%K cognitive radio
%K coherence spectrum
%K generalized likelihood ratio test
%K Hadamard ratio
%K multiple-channel signal detection
%B IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
%C Dallas, TX
%G eng