On the optimality of the null subcarrier placement for blind carrier offset estimation in OFDM systems

Liu and Tureli proposed a blind carrier frequency offset (CFO) estimation method for orthogonal frequency-division multiplexing (OFDM) systems, making use of null subcarriers. The optimal subcarrier placement that minimizes the Cramer-Rao bound (CRB) of the CFO estimation was reported by Ghogho. In this paper, we study the optimality of the null subcarrier placement from another perspective. We first show that the SNR of the CFO estimation using null subcarriers is a function of the null subcarrier placement. We then formulate the CFO-SNR optimization for the null subcarrier placement as a convex optimization problem for small CFO values and derive the optimal placement when the number of subcarriers is a multiple of the number of null subcarriers. In addition, we show that the SNR-optimal null subcarrier placement also minimizes the theoretical mean square error in the high SNR region. When the number of subcarriers is not a multiple of the number of null subcarriers, we propose a heuristic method for the null subcarrier placement that still achieves good performance in the CFO estimation. We also discuss the optimality of the null subcarrier placement in practical OFDM systems, where guard bands are required at both ends of the spectrum.