An approximative maximum likelihood frequency detector for DS/SS systems

An approximative maximum likelihood frequency detector is derived. It is based on the first order Taylor series expansion of the frequency domain Doppler shifted signal. Besides the direct frequency detector and joint code phase and frequency detector, also a closed loop frequency detector form is given. The closed loop detector is equivalent to Gardner's (1990) maximum likelihood frequency detector. Alternative derivation of Gardner's maximum likelihood frequency detector loop is therefore given. Simulations show that the direct form estimator is biased and outperformed by an other, even simpler, direct form estimator presented in the literature.