Large System Analysis of a GLRT for Detection With Large Sensor Arrays in Temporally White Noise

Abstract : — This paper addresses the behaviour of a classical multi-antenna GLRT test that allows to detect the presence of a known signal corrupted by a multi-path propagation channel and by an additive temporally white Gaussian noise with unknown spatial covariance matrix. The paper is focused on the case where the number of sensors M is large, and of the same order of magnitude as the sample size N , a context which is modeled by the large system asymptotic regime M → +∞, N → +∞ in such a way that M/N → c for c ∈ (0, +∞). The purpose of this paper is to study the behaviour of a GLRT statistics in this regime, and to show that the corresponding theoretical analysis allows to accurately predict the performance of the test when M and N are of the same order of magnitude.
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IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2015, 63 (20), pp.5409 - 5423. 〈10.1109/TSP.2015.2452220〉
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Sonja Hiltunen, Philippe Loubaton, Pascal Chevalier. Large System Analysis of a GLRT for Detection With Large Sensor Arrays in Temporally White Noise. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2015, 63 (20), pp.5409 - 5423. 〈10.1109/TSP.2015.2452220〉. 〈hal-01579062〉

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