An optimized basis expansion model for time-varying channel estimation

We address the problem of estimating time-varying channels using the complex exponential (CE) basis expansion model (BEM). The frequencies of the CE-BEM are uniformly distributed over [-f_max, f_max] where f_max is the maximum Doppler spread. The coefficients of the BEM are estimated using equispaced and equipowered pilots that are time-division multiplexed with the data. For a fixed number of pilot symbols, we analytically derive the optimum number of CE basis functions in the sense of minimizing the mean-square error (MSE) on the estimation of the actual channel. This optimum value depends on the statistics of the channel, the spacing between the pilot symbols and the signal to-noise ratio (SNR). Further, semi-blind channel estimation, based on an iterative approach that makes use of the detected data, is also investigated. Simulation results confirm that for a wide range of SNR and Doppler spread values, this optimization greatly reduces both the channel estimation MSE and the bit-error rate.