Optimum timing estimation without channel information over frequency-selective slowly fading channels

Applying the composite hypothesis testing procedure, we introduce the maximum a posteriori probability symbol synchronization in the point-to-point communications systems without channel information over frequency-selective slowly fading channels. This proposed estimation does not ignore the presence of interference due to frequency-selective channels and efficiently utilizes the inherited frequency-diversity to combat the channel fading impairment. By mathematical analysis, we prove the fundamental condition to have a consistent symbol synchronizer over frequency-selective slowly fading channels when the channel impulse response is unknown. We further conduct simulations to justify its performance considering the practical implementation with a finite number of timing candidates. This proposed approach considers more generalized scenarios with feasible complexity and therefore could be extensively applied in many practical communications systems.