Cramer-Rao bounds for parameters estimation from actual Galileo search and rescue signal

Considering the asymmetry degree of modulation and the uncertainty of message bit width, the Cramer-Rao bounds (CRBs) of estimation for message bit width, frequency of arrival (FOA) and time of arrival (TOA) from actual Galileo search and rescue (SAR) signal were researched. Expressions to calculate the elements of Fisher information matrix of Galileo SAR signal were derived. When calculating the sum of the square of Dirac delta function, the properties of Dirac delta function and Parseval's theorem were used to transform the computation from time-domain to frequency-domain, and the closed-form analytical solution of CRBs were obtained. Numerical calculation and Monte Carlo simulation results validate the effectiveness of the CRBs above which can be used to evaluate the performance of estimation algorithm for the parameters of message bit width, frequency of arrival and time of arrival.