Cramer-Rao Lower Bound for Non-data Aided Carrier and Symbol Synchronization over Flat Rayleigh Fading Channel

Abstract

In this contribution, reliable analytical method to derive true Cramer-Rao lower bound (CRLB) for non-data aided (NDA) joint carrier phase, carrier frequency offset and time delay estimation is introduced. We consider a transmission over a flat Rayleigh fading channel (FRFC) with non-constant fading gain during the observation window. Analytical expressions of Fisher information matrix (FIM) entries are derived to jointly estimate the synchronization parameters from general linear modulated signals over FRFC corrupted with complex additive white Gaussian noise (CAWGN). The noise power and the signal amplitude are assumed completely unknown. The efficiency of the proposed method is made obvious through the assessment of the true and the modified CRLB (MCRB) using Monte Carlo (MC) integration method. Simulation results for joint carrier phase and carrier frequency offset estimation are drawn for different square QAM orders and are compared to the bounds derived for independent phase and frequency estimations. CRLB to MCRB ratio for carrier phase, carrier frequency offset and time delay estimation is also presented. It is shown that this ratio converges to 1 for high SNR range regardless the modulation order. Otherwise, analytical results show that time delay is not coupled to carrier phase and frequency, i.e. time delay does no impact the carrier synchronization and vice versa.