Performance of a frequency detector based on the maximum likelihood principle

The noise performance of a maximum-likelihood- (ML-)based frequency difference detector (FDD) proposed by F.M. Gardner (ESA Final Report, 1990) is investigated. In particular, it is shown that the S-curve of this FDD is not affected by thermal noise (when the noise is wideband). The tracking performance of the algorithm is assessed, and simple formulas are provided to compute the frequency noise variance in an automatic frequency control (AFC) loop at the equilibrium. Computer simulations were run to validate the theory and to help understand the complex interactions between frequency recovery, and clock recovery during acquisition. A clock recovery method proposed by F.M. Gardner (1986) makes the AFC loop operation very close to that of one with an ideal clock