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