on equivalence of channel estimation with transform and without transform for multicarrier signals

Accurate channel estimation is necessary for coherent detection and adaptive control techniques, e.g., adaptive modulation and channel coding, of multicarrier signals. In this paper, we study frequency-(or time)-domain channel estimation with transform and without transform, using frequency (or time)-multiplexed pilot. It is shown that the frequency (or time)-domain channel estimation is equivalent to windowing of the delay time-domain impulse response (or Doppler frequency-domain spectrum) obtained by discrete transform as discrete Fourier transform (DFT)