On Bias-Variance Trade-Off in Superimposed Training-Based Doubly Selective Channel Estimation

Channel estimation for single-user frequency-selective time-varying channels is considered using superimposed training. The time-varying channel is assumed to be well-approximated by a complex exponential basis expansion model (CE-BEM). A periodic (non-random) training sequence is arithmetically added (superimposed) at a low power to the information sequence at the transmitter before modulation and transmission. First we present a performance analysis of a first-order statistics-based channel estimator for time-varying random channels, accounting for modeling errors. Using these results we address the issue of selection of the number of bases from an equalization viewpoint where we optimize a signal-to-noise ratio for data detection. An illustrative computer simulation example is presented.