Optimal basis for banded channel equalizers in OFDM system over doubly selective channels

We prove that discrete Fourier basis channel model is optimal for least squares estimation of channel coefficients used for low-complexity equalization of OFDM transmission over doubly selective channels. We show that regardless of channel statistics, the channel model order is determined by the number of coefficients used in the equalization. Our theoretical findings are numerically validated by using linear zero forcing equalizers and non-linear maximum likelihood equalizer with pilot-aided channel estimation.