In view of the problem of high complexity of the shaped-offset quadrature phase-shift keying (SOQPSK) symbol timing algorithm under high-precision conditions

an optimized maximum likelihood (ML)-based SOQPSK joint symbol timing and phase recovery algorithm was proposed. The SOQPSK-MIL signal model and the phase changing regulation of the signal were presented. The principle and estimation results of the ML-based algorithm for SOQPSK signal were given. The energy difference between different h functions in the algorithm was analyzed in detail

and the performance of the algorithm under different simplification degrees was discussed. The effectiveness of the algorithm when it only used Z+1 and Z+－1 parameters for estimation was analyzed. Considering the problem of the large amount of calculation during the convolution process in the implementation of the algorithm

an optimized processing method of h function was proposed. On the premise of ensuring that the energy of the h function remained unchanged

an optimization method was proposed

which quantizes the h function to make it a simple three-valued function with only three amplitudes of 0

A

and -A

thereby effectively reducing the calculation amount of the convolution process and reducing the computational complexity of the convolution part from O(N2L0) to O(NL0). Simulation results show that the algorithm had the characteristics of high estimation accuracy and low computational complexity. The implementation complexity of the algorithm was greatly reduced

and the previous high estimation accuracy was maintained. The minimum mean square errors of the timing error and phase error estimation results of the improved algorithm were almost the same as those before the improvement.