Robust Signal Detection Under Model Uncertainty

In detecting a deterministic signal in the presence of Gaussian noise, the receiver operating characteristic (ROC) curve determined by a linear detector with slope maximizing the signal-to-noise ratio (SNR) and with varying threshold characterizes limits of detection performance. In this note, we consider the problem of detecting a signal in the presence of uncertainty in the signal itself and the noise covariance. We show that the classical result can be generalized to robust signal detection with a convex uncertainty model: the ROC curve determined by a linear detector with slope maximizing the worst-case SNR gives limits of detection performance in the worst-case sense. The worst-case SNR maximization problem can be solved using convex optimization, so robust ROC analysis is tractable.