Multiantenna GLR Detection of Rank-One Signals With Known Power Spectral Shape Under Spatially Uncorrelated Noise

Abstract

Abstract-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.

Improving Detection of Unknown Signal with Unknown Duration using an Information Criterion

“…The statistical distribution of test ( 12) is, to our knowledge, unknown (as mentionned in [7], it is already unknown without considering different time support, although the distributions of the two eigenvalues involved taken separately are known [10]). To have some insight on how a misknowledge of the true signal duration may affect the detection capacities, we propose to study what happens first for the classical Matched Filter case where the signal used for compression is the true signal, but on the wrong time support, and second for the detection test provided by (11) considering only one single channel and an unknown signal.…”

On the Detection of Low-Rank Signal in the Presence of Spatially Uncorrelated Noise: A Frequency Domain Approach

“…Moreover, when the receive antennas are not calibrated, it is reasonable to assume that the spectral densities of the components of the noise may not coincide, see e.g. [2], [3], [4], [5]. This will be the context of the present paper.…”

“…[6], [7], [8], [9], [10], [11]. Also relevant are the approaches in [2] and [3], where the possible useful signal is supposed to be the output of a filter driven by a low-dimensional white noise sequence. Our focus here is on another type of formulation, referred to as frequency domain approach, which consists in rewriting problem (2) as H 0 : S y (ν) = dg (S y (ν)) for all ν ∈ [0, 1] H 1 : S y (ν) = dg (S y (ν)) for some ν ∈ [0, 1]…”

On the detection of low-rank signal in the presence of spatially uncorrelated noise: a frequency domain approach

“…[6], [7], [8], [9], [10], [11]. Also relevant are the approaches in [2] and [3], where the possible useful signal is supposed to be the output of a filter driven by a low-dimensional white noise sequence.…”