Low-complexity nonlinear least squares carrier offset estimator for OFDM: identifiability, diversity and performance

Orthogonal frequency division multiplexing (OFDM) transforms frequency-selective channels into multiple low-rate flat-fading subchannels. Carrier frequency offset between transmitter and receiver local oscillators must be estimated and compensated at the receiver to maintain orthogonality of these subchannels. In this paper, we derive the nonlinear least squares (NLS) estimator for carrier frequency synchronization that exploits receiver diversity and known OFDM signal subspace structure due to the placement of unmodulated (virtual) subcarriers. The resulting estimator benefits from the high-resolution subspace method without the computational overhead associated with subspace decomposition. Fundamental estimator performance relationships against parameters such as signal-to-noise ratio (SNR), frequency-selective fading, and diversity branch correlation are derived. In particular, we derive the Cramer-Rao bound (CRB) for the mean square error (MSE) of the carrier frequency offset estimator. Numerical studies are presented to verify the results.