Doppler shift cancellation using phasor and split phasor LMS algorithms

Two adaptive algorithms for estimating and correcting Doppler shift in coherent M-ary phase shift keying (MPSK) receiver are discussed. By compensating the error in the phase domain a 1-tap phasor least mean square (LMS) algorithm and a 1-tap split phasor LMS algorithm are developed. The structures of the algorithms are very simple. The algorithms operate in a decision directed mode. Monte Carlo simulations results show that the proposed algorithms converge in a few symbols and are very attractive for real time signal processing and hardware implementation. It is shown that the 1-tap split phasor LMS algorithm is an unbiased estimator. On the other hand, the 1-tap phasor LMS is a biased estimator; its steady state and tracking misadjustment is also discussed.