Decision-Directed Symbol Timing Recovery for SOQPSK

Abstract

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 CPMs is that it has a constrained (correlated) ternary data alphabet. CPM-based detection models for SOQPSK have been developed only recently. While these detectors offer an appreciable performance gain over current detection schemes, one roadblock standing in the way of their being adopted is the lack of a CPM-based symbol timing recovery scheme that will work with SOQPSK. We show how an existing CPM-based timing error detector (TED) can be adapted to the unique characteristics of SOQPSK. The TED is formulated for a coherent detector but can be extended to the noncoherent case. We apply this timing recovery method 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 decision-directed TED (DD-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 (NDA-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.