Structured Covariance Matrix Estimation for Noise-Type Radars

Standard noise radars, as well as noise-type radars such as quantum two-mode squeezing (QTMS) radar, are characterized by a covariance matrix with a very specific structure. This matrix has four independent parameters: the amplitude of the received signal, the amplitude of the internal signal used for matched filtering, the correlation between the two signals, and the relative phase between them. In this article, we derive estimators for these four parameters using two techniques. The first is based on minimizing the Frobenius norm between the structured covariance matrix and the sample covariance matrix; the second is maximum likelihood (ML) parameter estimation. The two techniques yield the same estimators. We then give probability density functions (pdf's) for all four estimators. Because some of these pdf's are quite complicated, we also provide approximate pdf's. Finally, we apply our results to the problem of target detection and derive expressions for the receiver operating characteristic (ROC) curves of two different noise radar detectors. In summary, our work gives a broad overview of the basic statistical behavior of noise-type radars.