Cyclic correlation based symbol rate estimation

In this paper, we consider the estimation problem of the modulation rate of an unknown emitter using a linear (unknown) modulation. We use the basic observation that the received signal is cyclostationary, and that the modulation rate is one of the cyclic frequencies. The classical estimator based on the maximization in the cyclic frequency domain of a sum of square modulus cyclic correlations sum has poor performance if the excess bandwidth used by the emitter is small. In this paper, we study in detail an estimator introduced by Dandawate and Giannakis (1994), which is based on an appropriate weighted version of the statistics used by Gardner (1988). The optimal weighting matrix depends on the unknown parameters, and has to be estimated in practice. In particular, the optimal matrix depends in general on the unknown cyclic frequencies, and is thus difficult to estimate. The main contribution of this paper is to show that, for low excess bandwidth signals, the optimal weighting matrix actually does not depend on the non zero cyclic frequencies to be estimated. It can be thus consistently estimated from the cyclic statistics of the observation at cyclic frequency 0. We evaluate the performance of the weighted approach, and show that it provide considerable improvement over the traditional estimator.