Journals: Multiantenna GLR Detection of Rank-One Signals with known Power Spectral Shape under Spatially Uncorrelated Noise
J. Sala Alvarez, Vazquez Vilar, López Valcarce, Sedighi and Taherpour


Digital Object Identifier (DOI): 10.1109/TSP.2012.2189767

We establish the generalized likelihood ratio (GLR) test for a Gaussian signal of known power spectral shape and
unknown rank-one spatial signature in additive white Gaussian noise with an unknown diagonal spatial correlation
matrix. This is motivated by spectrum sensing problems in dynamic spectrum access (DSA), in which the temporal
correlation of the primary signal can be assumed known up to a scaling, and where the noise is due to an uncalibrated
receive array. For spatially independent identically distributed (i.i.d.) noise, the corresponding GLR test reduces to a
scalar optimization problem, whereas the GLR detector in the general non-i.i.d. case yields a more involved expression,
which can be computed via alternating optimization methods. Low signal-to-noise ratio (SNR) approximations to the
detectors are given, together with an asymptotic analysis showing the influence on detection performance of the signal
power spectrum and SNR distribution across antennas. Under spatial rank-P conditions, we show that the rank-one
GLR detectors are consistent with a statistical criterion that maximizes the output energy of a beamformer operating
on filtered data. Simulation results support our theoretical findings in that exploiting prior knowledge on the signal
power spectrum can result in significant performance improvement.

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