Parameter Estimation Bounds and Preamble Designs for SOQPSK Waveforms

In this paper, we derive joint parameter estimation bounds for the symbol timing offset, carrier phase, and carrier frequency offset for any shaped offset quadrature phase shift keying (SOQPSK) waveform. Specifically, we calculate the conditional Cramer-Rao bound (CCRB) for a known given data sequence and compare this to the modifued Cramer-Rao bound (MCRB) for the case in which the data pattern is unknown and random. This allows us to assess the performance of candidate preamble waveforms for parameter acquisition. We show how to simplify the CCRB when the preamble waveform is periodic and compare the CCRB performance of several candidate preambles to the MCRB. For the Telemetry Group (TG) variant of SOQPSK (i.e., SOQPSK-TG), we specifically show that certain candidate preambles can offer substantial improvements over the MCRB in terms of symbol timing offset estimation with negligible adverse impact on the estimation of the carrier phase and carrier frequency offset.