The Cramér-Rao bound for data-aided synchronization of SOQPSK

In this paper, we derive the Cramer-Rao bound (CRB) for shaped offset quadrature phase keying (SOQPSK) signals. We consider a situation where the carrier phase, frequency offset and symbol timing have to be estimated based on a known training sequence. The goal is to find the optimum training sequence for which the joint CRBs are minimized. It is shown that the proposed training sequence minimizes the CRBs for all three estimation parameters simultaneously. The presented results can be used in designing preambles for burst-mode SOQPSK transmissions.