Performance analysis of the time-delay phase-shifter in additive Gaussian noise: a statistical comparison with Hilbert transformer

It is shown that, in the presence of additive Gaussian noise, the performance of the time-delay phase-shifter, which produces a signal-dependent phase shift, is comparable to the performance of a Hilbert transformer which produces a signal-independent 90-degree phase shift, especially for high signal-to-noise ratios (SNR) and the proper choice of the delay. As SNR increases, the expected value of the time-delay phase estimator approaches the true value of the phase and its variance substantially decreases and converges to the Cramer-Rao bound for all ranges of the effective parameters