A synchronization of a pilot assisted channel estimation orthogonal frequency
division
multiplexing can be achieved by receiving a signal containing pilot symbols, providing
an initial time and frequency synchronization to the signal, phase rotating the
signal across time, transforming the signal with a fast Fourier transformation,
phase rotating the signal across frequency, extracting the pilot symbols and generating
a channel estimator. The phase rotating across time and the phase rotating across
frequency are controlled by a phase rotation controller in accordance with the
channel estimator. The initial time and frequency synchronization synchronizes
the signal such that intercarrier interference effects and intersymbol interference
effects are negligible. The signal may include plural carrier frequencies each
having an arrival timing offset and a frequency offset. The signal may also include
delay spread or Doppler spread. The phase rotation controller measures a phase
different between the channel estimator at times k and k+k, where k is time
and k is a symbol period and measures a phase difference between the channel
estimator at frequencies n and n+n, where n is tone frequency and n
is a frequency spacing between adjacent tones.