On Performance Bounds for Timing Estimation under Fading Channels

In timing synchronization, the Cramer Rao Bound has been used as performance bounds for timing estimation in AWGN channel. However, the instantaneous CRB for timing estimation in fading channels depends on the channel realizations and may fail to bound the mean square error (MSE) of the estimator because the equivalent signal-to-noise ratio (SNR) is too low. In this paper, we demonstrate that the conventional CRB for timing estimation is no longer valid in fading channels. Furthermore, a new performance bound called Weighted Bayesian CRB (WBCRB) is proposed for the estimation of both single and multiple timing offsets under fading channels. The relationship between the conventional CRB and WBCRB are discussed in details, where numerical results show that the WBCRB is a valid bound for all SNR even under fading channels.