Performance bound for blind CFO estimation in OFDM with real-valued constellations

In this paper, we investigate the performance of the blind carrier frequency offset (CFO) estimation method for OFDM with real-valued constellations introduced in (T. Roman et al, ICASSP, vol.4, p.IV 369-IV 372, 2004). The method is based on minimizing the total off-diagonal power of the received pseudo-covariance matrix and the resulting solution has a simple closed-form expression. To assess the large sample performance, we derive the Cramer-Rao bound (CRB) for the blind CFO estimation problem. When deriving the CRB, the transmitted OFDM modulated signal is assumed to be a Gaussian process. Since real-valued constellations are used, the received signal is non-circular. As a result, the CRB has to be derived for a non-circular Gaussian model. Simulation results highlight significant differences in performance between the complex circular and non-circular cases.