Lower Rao–Cramer Boundary of Variances for Parameter Joint Estimates of Narrowband and Broadband Signals Mixture with White Noise

Abstract

In this paper, we determine the joint estimates variance minimum of the signal parameters, a mixture of narrowband and wideband signals and white Gaussian noise that are presented as a complex total signal. An expression is obtained for calculating the Fisher matrix elements to establish the lower Rao–Cramer boundary. The dependences of the standard deviations (RMS) of the estimates on the signal-to-noise ratio, sample length, and on the initial signal parameters, such as the central frequencies of the signal components and the width of the broadband component, are presented. A comparison with the minimal standard deviations obtained for a signal model that includes only the broadband component is performed. Analysis of the results allows assessing the requirements that may be imposed on the developed algorithms for joint estimation of the mixture parameters of the considered signals depending on the set values of the sampling frequency and the sample size.