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

Abstract

Abstract-In this work, we consider a second-order detection problem where rank-p signals are structured by an unknown, but common, p-dimensional random vector and then received through unknown M ⇥ p matrices at each of two M -element arrays. The noises in each channel are independent with identical variances. We derive generalized likelihood ratio (GLR) tests for this problem when the noise variance is either known or unknown. The resulting detection problems may be phrased as two-channel factor analysis problems.

Two-Channel Passive Detection of Cyclostationary Signals

“…Now we plug the ML estimates (65) and (73) into the likelihood ratio (17) to obtain (74) as shown at the top of this page, where D and C are given by (20) and (21), respectively. In this expression, we exploited the fact that the determinant of a block-diagonal matrix is equal to the product of the determinants of the single blocks, and the expression for the determinant of a 2 × 2 block matrix with invertible blocks.…”

“…These detectors assume that the noise has an arbitrary spatial correlation. The GLRT for spatially white noise with the same variance at SC and RC was derived in [17]. Finally, [18] extended the results to the detection of a rank-p signal in white noise with different variances at SC and RC and spatially uncorrelated noise with arbitrary variances.…”

An Augmented Generalized Likelihood Ratio Test Detector for Signal Detection in Clutter and Noise

“…However, few research considers the detection problem of correlated subspace signals [35]- [38]. Santamaria et al [35], [36] formulated a unified framework of the correlated case, which derived the GLRTs for different correlated noise models. But they make an ideal assumption that the clutter has been canceled, which is not suitable in practice.…”