Passive Radar Detection With Noisy Reference Channel Using Principal Subspace Similarity

Traditional passive radar detectors compute cross correlation of the raw data in the reference and surveillance channels. However, there is no optimality guarantee for this detector in the presence of a noisy reference. Here, we develop a new detector that utilizes a test statistic based on the cross correlation of the principal left singular vectors of the reference and surveillance signal-plus-noise matrices. This detector offers better performance by exploiting the inherent low-rank structure when the transmitted signals are a weighted periodic summation of several identical waveforms (amplitude and phase modulation), as is the case with commercial digital illuminators as well as noncooperative radar. We consider a scintillating target. We provide analytical detection performance guarantees establishing signal-to-noise ratio thresholds above which the proposed detection statistic reliably discriminates, in an asymptotic sense, the signal versus no-signal hypothesis. We validate these results using extensive numerical simulations. We demonstrate the “near constant false alarm rate (CFAR)” behavior of the proposed detector with respect to a fixed, SNR-independent threshold and contrast that with the need to adjust the detection threshold in an SNR-dependent manner to maintain CFAR for other detectors found in the literature. Extensions of the proposed detector for settings applicable to orthogonal frequency division multiplexing (OFDM), adaptive radar are discussed.