Bounds for estimation of multicomponent signals with random amplitude and deterministic phase

We study a class of nonstationary multicomponent signals, where each component has the form a(t) exp jφ(t), where a(t) is a random amplitude function, and φ(t) is a deterministic phase function. The amplitude function consists of a stationary Gaussian process and a time varying mean. The phase and the amplitude mean are characterized by a linear parametric model, while the covariance of the amplitude function is parameterized in some general manner. This model encompasses signals that are commonly used in communications, radar, sonar, and other engineering systems. We derive the Cramer-Rao bound (CRB) for the estimates of the amplitude and phase parameters, and of functions of these parameters, such as the instantaneous frequencies of the signal components