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.

JF - IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
CY - Calgary, Canada
ER -
TY - JOUR
T1 - Testing equality of multiple power spectral density matrices
JF - IEEE Trans. Signal Processing
Y1 - 2018
A1 - David Ramírez
A1 - Daniel Romero
A1 - Javier Vía
A1 - R. López-Valcarce
A1 - Ignacio Santamaría
KW - winter
VL - 66
IS - 23
ER -
TY - CONF
T1 - Detection of Gaussian signals in unknown time-varying channels
T2 - IEEE Statistical Signal Processing Workshop (SSP 2012)
Y1 - 2012
A1 - Daniel Romero
A1 - Javier Vía
A1 - R. López-Valcarce
A1 - Ignacio Santamaría
KW - cognitive radio
KW - dynacs
KW - spectrum sensing
AB - 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.

JF - IEEE Statistical Signal Processing Workshop (SSP 2012)
PB - IEEE
CY - Ann Arbor, MI
ER -
TY - JOUR
T1 - Detection of Rank-P Signals in Cognitive Radio Networks With Uncalibrated Multiple Antennas
JF - IEEE Trans. on Signal Processing
Y1 - 2011
A1 - David Ramírez
A1 - Gonzalo Vázquez-Vilar
A1 - R. López-Valcarce
A1 - Javier Vía
A1 - Ignacio Santamaría
KW - cognitive radio
KW - dynacs
KW - spectrum sensing
AB - 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.

VL - 59
IS - 8
ER -
TY - CONF
T1 - Multiantenna detection under noise uncertainty and primary user's spatial structure
T2 - IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Y1 - 2011
A1 - David Ramírez
A1 - Gonzalo Vázquez-Vilar
A1 - R. López-Valcarce
A1 - Javier Vía
A1 - Ignacio Santamaría
KW - cognitive radio
KW - generalized likelihood ratio test (GLRT)
KW - spectrum sensing
JF - IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
PB - IEEE
CY - Prage, Czech Republic
ER -
TY - CONF
T1 - Multiantenna spectrum sensing: detection of spatial correlation among time-series with unknown spectra
T2 - IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Y1 - 2010
A1 - David Ramírez
A1 - Javier Vía
A1 - Ignacio Santamaría
A1 - R. López-Valcarce
A1 - L. L. Scharf
KW - cognitive radio
KW - coherence spectrum
KW - generalized likelihood ratio test
KW - Hadamard ratio
KW - multiple-channel signal detection
JF - IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
CY - Dallas, TX
ER -