Performance of non-data aided carrier offset estimation for non-circular transmissions through frequency-selective channels

We consider blind estimation of the carrier frequency offset of a linearly modulated non-circular transmission through an unknown frequency selective channel. A frequency estimator is developed based on the unique conjugate cyclic frequency of the received signal that equals twice the frequency offset. We establish consistency and asymptotic normality of the frequency estimator, and calculate its asymptotic variance in closed form. This expression enables performance analysis of the proposed frequency offset estimator as a function of the number of estimated cyclic correlation coefficients used. Numerical simulations show that estimation and compensation of the carrier frequency offset in the presence of an unknown frequency selective channel can be performed with no loss in performance relative to methods where the channel is pre-equalized first and the frequency offset is compensated afterwards