Optimized training and basis expansion model parameters for doubly-selective channel estimation

We address the problem of estimating doubly-selective channels using pilot clusters that are time-division multiplexed with the data. The pilot clusters consist of zero-padded pilot symbols in order to decouple channel estimation from data detection. Channel estimation is carried out using the basis expansion model (BEM-)based method, where different BEMs are investigated, and the exact MMSE method which requires full knowledge of the channel statistics. For a fixed number of pilot symbols, we attempt to optimize the power and placement of the pilot symbols at the transmitter side used in transmission, and the number of BEM coefficients used in channel estimation, in the sense of minimizing the total mean-square estimation error (MSE) that includes modelling error. Simulation results confirm that for a wide range of SNR and Doppler spread values, this optimization greatly reduces the MSE and the bit-error rate, and that modelling error, which was ignored in existing work on training design, should be taken into account. The effects of uncertainty in the channel statistics are also studied.