Canonical correlations for target detection in a passive radar network

Abstract

In this work, we consider a two-channel multiple-input multiple-output (MIMO) passive detection problem, in which there is a surveillance array and a reference array. The reference array is known to carry a linear combination of broadband noise and a subspace signal of known dimension but unknown basis. The question is whether the surveillance channel carries a linear combination of broadband noise and a subspace signal of unknown basis, which is correlated with the subspace signal in the reference channel. We consider a second-order detection problem where these subspace signals are structured by an unknown, but common, p-dimensional random vector of symbols transmitted from sources of opportunity, and then received through unknown M × p matrices at each of the M-element arrays. The noises in each channel have arbitrary spatial correlation. We derive the generalized likelihood ratio test (GLRT) statistic and show it is a monotone function of canonical correlations between the reference and surveillance channels.

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

“…3 shows the results obtained for different SNR values. Not surprisingly, the GLRT in [19] provides the best results for both noise models (it is matched to Model 4). In general, the GLRT with assumed unknown noise variance is more robust against mismatched noise models than is the GLRT with assumed known noise variance.…”

“…) to a threshold, where the k i 's are squared canonical coordinates of the two channel sample covariance matrix [19], [20]. For the GLRT with known noise variance we use…”

“…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].…”

Robust estimation of the magnitude squared coherence based on kernel signal processing

“…with C = Σ −1 1 Σ 1,2 Σ −1 2 Σ 2,1 being the squared coherence matrix ( [13], [4]). If we denote λ i as the eigenvalues of C, which correspond to the canonical variables of the CCA, we can express the GC as follows:…”