Joint phase and timing recovery for SOQPSK based on phase trajectory

Shaped-offset quadrature phase shift keying (SO-QPSK) is a special case of continuous phase modulation (CPM) and is widely employed on SATCOM links. We analyze the phase trajectory of SOQPSK and find that the phase change in a bit period is zero for a zero symbol and ±π/2 for a non-zero symbol. Based on this, we propose a new timing recovery scheme that uses the fourth-power nonlinearity to eliminate the self-noise caused by the symbol information. Through the nonlinear operation, the modulated SOQPSK signal is converted into a direct current (DC) signal for the zero symbol and a tone for the non-zero symbol. The phase drift is estimated from the DC signal and the timing offset is estimated from the initial phase of the tone. The lower bounds of the estimation errors for the phase and timing estimations are reduced in high signal-to-noise ratio (SNR). The lower bound for the phase error is 4 times of the MCRB(θ) and the lower bound for the timing error is also 4 times of the MCRB(τ). Simulation results indicate that the proposed scheme is effective and the estimation errors agree with the derived bounds.