Doppler and frequency-offset synchronization in wideband OFDM

When the orthogonal frequency-division multiplexing (OFDM) signal is appreciably wideband, as in underwater communications, a single Doppler-shift parameter is inadequate to model the Doppler effect, and a rate parameter is required as well. Such a model also accommodates nonsynchronized sampling of the received signal. We establish conditions for the identifiability of the Doppler parameters, and show how they affect the placement of subcarriers (NSC). We derive the maximum-likelihood (ML) estimator and the corresponding conditional Crame´r-Rao lower bound. We show that the vector formulation is amenable to estimation of signal parameters via rotational invariance techniques (ESPRIT) analysis, leading to a suboptimal but closed-form estimator. If the rate parameter is left uncompensated, we establish that the effective SNR is drastically reduced, which further leads to an increased bit error rate (BER). The ML estimator is demonstrated by numerical simulations that show that the performance of the estimator approaches the Crame´r-Rao lower bound in the moderate-to-high SNR regions.