A high order composite automatic frequency control Costas loop for synchronization

Synchronization plays an important role in wireless communication systems when tracking a phase-shift keying (PSK) signal, especially when the initial frequency error is comparable to the loop bandwidth. In order to improve frequency acquisition, an automatic frequency control (AFC) augmentation is used. This paper presents a composite AFC/Costas loop by combining both the AFC loop with a phase-locked loop (PLL) Costas loop for carrier frequency recovery. Therefore, pull-in from both frequency and phase errors is feasible using the composite AFC/Costas loop. The AFC/Costas loop combination filter coefficient setting is evaluated by a theoretic analysis. Improved frequency and phase acquisition can be realized by changing the first order AFC/Costas loop to the second order. First, the structure of the composite AFC/Costas loop is shown. This structure makes use of phase detectors to obtain the phase differences between the received signal and reference signal, where the phase differences can be used to generate the phase and frequency control signals. Difference equations are proposed to describe the composite AFC/Costas loop. Then, the theoretic analysis for both frequency and phase control are derived in a linearized model of the composite loop. The phase error variance is simulated to show the performance of the composite AFC/Costas loop. Moreover, the frequency and phase synchronization performance for different signal to noise ratio (SNR) and loop filter bandwidth are shown to demonstrate the effectiveness of the composite AFC/Costas loop. Finally, the Quadrature Phase Shift Keying (QPSK) data is demodulated and decoded through the composite AFC/Costas loop. Extensive simulations are implemented to show that the demodulated data matches the transmitted data, which proves that differential QPSK can effectively reduce the phase ambiguity and increase frequency pull-in range, especially for the low SNR region (E
_b
/N
₀
<; 3 dB). The proposed composite AFC/Costas loop sheds insights on the design of frequency and phase synchronization in wireless communication systems.