Methods that precisely compensate for propagation distortion using pilot symbols are widely used in mobile communications. We describe such a pilot-symbol-assisted technique for precise compensation of flat fading and frequency offset. This technique provides a wide range of offset compensation. Conventional methods using fast Fourier transform (FFT) compensate for both slow and fast fading, but their tolerable range of frequency offset is very limited. By composing a system with an approximate frequency estimator, we can estimate and compensate for fading and a large frequency offset at the same time. The estimation and compensation are carried out by periodic pilot symbols and no other index sequences are needed. This method enables high-data-rate transmission. We describe the method and provide a theoretical analysis for the compensable range of fading and frequency offset for a transmission frame structure with pilot symbols. Then, we evaluate the method by computer simulation.