A comparative study of two discrete-time phase delay estimators

Two simple discrete-time methods for unbiased estimation of the phase-shift between two real sinusoidal signals in white noise are proposed. The first estimator removes the bias of the recently proposed quadrature delay estimator (QDE) by utilizing all in-phase and quadrature-phase components of the received signals. The phase estimate of the second method is given by the phase difference of the discrete-time Fourier transforms (DTFTs) of two complex sinusoids derived from the real signals. In particular, we have derived the mean square phase-shift error of the DTFT-based estimator as well as the minimum achievable variance for phase-shift estimation, which are identical. Computer simulations show that the two proposed estimators are superior to the biased QDE and can attain optimum performance, although the second estimator has a larger signal-to-noise ratio operation range.