The present invention describes a method and a system for executing preamble detection, symbol timing recovery, and frequency offset estimation that are applied to a PHS system for executing the preamble symbol detection and timing recovery. The system includes a first absolute value circuit, an average circuit, a multiplier, a sample and accumulate circuit coupled to the multiplier, a second absolute value circuit, a first compare circuit, and a second compare circuit, such that the system with the foregoing structure can detect a preamble symbol by less symbols while performing a timing recovery. The invention also describes a frequency offset computation method and its circuit.