Kalman Optimal GMSK Signal Timing Synchronization Algorithm Based on SNR Matching

This paper proposes a GMSK signal timing synchronization algorithm with strong noise immunity under Doppler frequency offset and small BT parameter conditions. In air-to-air communication missions, small BT GMSK signals are usually used as the wireless communication system. Although the conventional joint frequency and timing parameters estimation algorithm can adapt to the Doppler frequency offset generated by the aircraft and the inter-code interference caused by the reduced BT parameter of GMSK signals, the conventional algorithm has poor noise immunity and it cannot obtain good timing error estimation performance under the noise interference condition. In order to solve this problem, this paper proposes a Kalman optimal GMSK signal timing synchronization algorithm based on SNR matching. Proposed algorithm uses the conventional joint frequency and timing parameters estimation algorithm to obtain the initial observation of the timing parameter, and then uses Kalman filtering to optimally estimate the initial observation of the timing parameter. In the process, the blind SNR estimation algorithm is used to obtain the $\mathrm{E}_{\mathrm{b}} / \mathrm{N}_{0}$ of the current received signal, in order to update the measurement error of the conventional algorithm and realize the calculation of the Kalman gain. The proposed algorithm effectively enhances the timing error estimation performance of the conventional algorithm under the noise interference condition while possessing the Doppler frequency offset independence and the applicability of small BT parameter range. The parameters and performance of the proposed algorithm are simulated and verified by MATLAB.