Estimating correlation coefficients for quantum radar and noise radar: A simulation study

For target detection, quantum two-mode squeezing (QTMS) radars and noise radars require estimation of a covariance matrix. A scalar function of the covariance matrix is then used for deciding the presence or absence of a target. In this paper, estimation of the covariance matrix is carried out by minimizing the Frobenius norm between the sample covariance matrix and the theoretically expected form of the matrix. Two scalars, a normalized correlation coefficient and an unnormalized cross-correlation, are used for detecting the target. Their performances are compared and found to be the same. Probability distributions are then fit to the histograms of these estimated correlations. Using these fitted distributions, expressions are obtained for receiver operating characteristic (ROC) curves that predict the performance of these functions in the task of deciding whether a target is present or not. This work is a first step toward understanding and modeling target detection performance of a QTMS radar or noise radar when using correlation-related measures as detector functions