A simple timing recovery scheme for SOQPSK

We consider symbol timing recovery for shaped-offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient and popular constant-envelope modulation scheme. The proposed timing recovery method makes use of a recent continuous phase modulation (CPM) interpretation of SOQPSK, where SOQPSK is viewed as a CPM with a constrained (correlated) ternary data alphabet. We derive a timing error detector (TED) that is an extended version of a non-data-aided (blind) TED for CPM, where the proposed extensions take the data correlation of SOQPSK explicitly into account. The merits of the modified TED are demonstrated by comparing its performance with and without taking the data correlation into account. As a further modification, we show that a quantization scheme can be used to yield an extremely low-complexity version of the system with only negligible performance losses. The S-curve of the proposed quantized TED is given, which rules out the existence of false lock points. Numerical performance results are given for the most popular SOQPSK variant: MIL-STD SOQPSK. These results show that the proposed scheme has great promise in a wide range of applications due to its low complexity, its lack of false lock points, and its blind nature; such applications include timing recovery in noncoherent detection schemes and false lock detectors.