On the performance of the cross-correlation detector for passive radar applications

For passive radar target detection, the cross-correlation (CC) based detector is a popular method, which cross-correlates the signal received in a reference channel (RC) and the signal in a surveillance channel (SC). The CC is simple to implement and resembles the clairvoyant matched filter (MF) in idealistic conditions. However, there is limited understanding on its performance in passive sensing environments with non-negligible noise in the RC and direct-path interference in the SC. This paper examines such effects on the detection performance of the CC detector. Closed-form expressions for the probabilities of false alarm and detection of the CC detector are derived, which are employed to quantify to what extent the noise in the RC and the direct-path interference in the SC should be suppressed in order to achieve a targeted performance loss of the CC detector relative to the MF. These results are useful in designing practical CC solutions for passive radar sensing.