Cramer-Rao Bounds of key parameters estimation for Galileo SAR signal

Considering the uncertainty of message bit width, the Cramer-Rao Bounds (CRBs) for the estimation of message bit width, frequency of arrival (FOA) and time of arrival (TOA) from Galileo search and rescue (SAR) signal were researched. General formula for calculating the elements of Fisher information matrix was derived first. Then the calculation expressions for the Fisher matrix elements of Galileo SAR signal were acquired. 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. Then the closed-form analytical solutions of the CRBs for the estimation of message bit width, FOA and TOA were derived. Numerical calculation and Monte Carlo simulation results validate the effectiveness of the CRBs above which can be used to evaluate the performance of message bit width, FOA and TOA estimation algorithm.