Training design for doubly-selective channel estimation

We address the problem of estimating time-varying channels using two different basis expansion models (BEMs): the complex exponential (CE)-BEM, and the discrete prolate spheroidal (DPS)-BEM. The frequencies of both of these BEMs are limited to [-f_max,f_max], where f_max is the maximum Doppler spread. The coefficients of the BEM are estimated using pilot clusters that are time-division multiplexed with the data. For a fixed number of pilot symbols, we attempt to optimize the power and placement of the pilot symbols used in transmission, and then optimize the BEM parameters used in channel estimation, in the sense of minimizing the mean-square estimation error (MSE) at the receiver. These optimum values depend on the statistics of the channel, the signal-to-noise ratio (SNR), and other system parameters. 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.