Decision Directed Timing Recovery for SOQPSK

Shaped offset quadrature phase shift keying (SOQPSK) is a highly bandwidth efficient modulation technique used widely in military and aeronautical telemetry standards. It can be classified as a form of continuous phase modulation (CPM), but its major distinction from other CPM schemes is that it has a constrained (correlated) ternary data alphabet. CPM-based detection models for SOQPSK have been developed only recently. One roadblock standing in the way of these detectors being adopted is that existing symbol timing recovery techniques for CPM are not always applicable since the data symbols are correlated. We investigate the performance of one CPM-based timing error detector (TED) that can be used with SOQPSK, and apply it to the versions of SOQPSK used in military (MIL-STD SOQPSK) and telemetry group (SOQPSK-TG) standards. We derive the theoretical performance limits on the accuracy of timing recovery for SOQPSK, as given by the modified Cramer-Rao bound (MCRB), and show that the proposed TED performs close to these bounds in computer simulations and is free of false-lock points. We also show that the proposed scheme outperforms a non-data aided TED that was recently developed for SOQPSK. These results show that the proposed scheme has great promise in a wide range of applications due to its low complexity, strong performance, and lack of false-lock points.