MMSE estimation of basis expansion model for rapidly time-varying channels

In this paper, we propose an estimation technique for rapidly time-varying channels. We approximate the time-varying channel using the basis expansion model (BEM). The BEM coefficients of the channel are needed to design channel equal-izers. We rely on pilot symbol assisted modulation (PSAM) to estimate the channel (or the BEM coefficients of the chan-nel). We first derive the optimal minimummean-square error (MMSE) interpolation based channel estimation technique. We then derive the BEM channel estimation, where only the BEM coefficients are estimated. We consider a BEM with a critically sampled Doppler spectrum, as well as a BEM with an oversampled Doppler spectrum. It has been shown that, while the first suffers from an error floor due to a model-ing error, the latter is sensitive to noise. A robust channel estimation can then be obtained by combining the MMSE in-terpolation based channel estimation and the BEM channel estimation technique. Through computer simulations, it is shown that the resulting algorithm provides a significant gain when an oversampled Doppler spectrum is used (an oversam-pling rate equal to 2 appears to be sufficient), while only a slight improvement is obtained when the critically sampled Doppler spectrum is used. 1