Passive detection of rank-one signals with a multiantenna reference channel

Abstract

In this work we consider a two-channel passive detection problem, in which there is a surveillance array where the presence/absence of a target signal is to be detected, and a reference array that provides a noise-contaminated version of the target signal. We assume that the transmitted signal is an unknown rank-one signal, and that the noises are uncorrelated between the two channels, but each one having an unknown and arbitrary spatial covariance matrix. We show that the generalized likelihood ratio test (GLRT) for this problem rejects the null hypothesis when the largest canonical correlation of the sample coherence matrix between the surveillance and the reference channels exceeds a threshold. Further, based on recent results from random matrix theory, we provide an approximation for the null distribution of the test statistic.

A GLRT approach for detecting correlated signals in white noise in two MIMO channels

“…Noises with arbitrary spatial correlation: ⌃ ss and ⌃ rr are arbitrary full-rank positive definite (psd) matrices. Model 4 was considered in our previous works [3] and [19], for rank-one and rank-p signal models, respectively. The rankp detector for Model 4 was also reported in [20] for a different problem.…”

“…The conventional approach for passive detection uses the cross-correlation (CC) between the data received in the reference and surveillance channels as the test statistic [2]. However, the noise in the reference signal renders the CC detection scheme suboptimal, especially in multiple-input multiple-output (MIMO) scenarios for which the inherent subspace structure of the received signals can be exploited [3], [4].…”

Canonical correlations for target detection in a passive radar network

“…Under the alternative, the ML estimate has been derived for p = 1 in [2].To present the result for general p, let C = S ss −1/2 S sr S rr −H/2 be the sample coherence matrix between the surveillance and reference channels, and let C = FKG H be its singular value decomposition (SVD), where the matrix…”

“…The conventional approach for passive detection uses the cross-correlation (CC) between the data received in the reference and surveillance channels as the test statistic [1]. However, the noise in the reference signal renders the CC detection scheme suboptimal, especially in MIMO scenarios for which the inherent low-dimensional subspace structure of the transmitted signal can be exploited [2]. Passive MIMO target detection with a noisy reference channel has recently been considered in [3], where the transmitted waveform is considered as a deterministic unknown.…”

Two-Channel Passive Detection of Cyclostationary Signals

“…Although this resembles the matched filter, it is suboptimal due to noise at the RC [14]. In [15]- [18] generalized likelihood ratio tests (GLRT) were derived for the case of unknown stochastic waveforms and for various assumptions on the signal and noise models. Reference [15] considered the detection of a rankone signal received by a multiantenna array, whereas [16] generalized these results to a rank-p signal.…”