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

We consider blind estimation of the carrier frequency o set 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 o set. 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 o set estimator as a function of the number of estimated cyclic correlation coe cients used. Numerical simulations show that estimation and compensation of the carrier frequency o set 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 rst and the frequency o set is compensated afterwards.