Asymptotic analysis of blind cyclic correlation based symbol rate estimation

We consider symbol rate estimation of an unknown signal linearly modulated by a sequence of symbols. We rely on the received signal is cyclostationarity, and consider an existing estimator obtained by maximizing in the cyclic domain a (possibly weighted) sum of modulus squares of cyclic correlation estimates. Although widely used, this estimate seems not to have been studied rigorously when the number of samples N is large. In this paper, we study rigorously the asymptotic behavior of this estimate. We establish consistency and asymptotic normality of the estimate, prove that its convergence rate is N³'², and calculate in closed form its asymptotic variance. The obtained formula allows us to discuss in relevant way on the influence of the number of estimated cyclic correlation coefficients to take into account in the cost function to maximize.