Optimized null-subcarrier selection for CFO estimation in OFDM over frequency-selective fading channels

We address the problem of frequency synchronization in OFDM-based communications systems in the context of frequency-selective fading channels. Frequency offsets are estimated by inserting null sub-carriers into a single OFDM block. The paper clarifies issues related to acquisition range and identifiability of carrier frequency offset (CFO), and performance of estimators. A deterministic maximum likelihood estimation approach is adopted. We derive necessary and sufficient conditions on the number of null-subcarriers and their placement in order to ensure identifiability. The Cramér-Rao bound (CRB) for the CFO is derived; for a given number of null sub-carriers, the optimal placement which minimizes the CRB is derived. We show that if the number of null sub-carriers is less than half the total number of sub-carriers, performance is optimal when the null sub-carriers are equispaced.