Low-complexity equalization of time-varying channels with precoding

This correspondence deals with time-varying (TV) single-input multiple-output (SIMO) channels, which are both frequency selective (due to high data rate) and time selective (due to mobility). A complex exponential basis expansion model (CE-BEM) is used to model the channel. We consider a block transmission system, where on the transmit side a precoder is employed to enable the maximum available diversity for a CE-BEM channel. After direct decoding on the receive side, the resulting channel resembles a finite-impulse-response (FIR) filter on both block and symbol level. We therefore propose an equalizer that bears a structure analogous to the effective channel. In comparison with a standard block minimum mean-square error decision-feedback equalizer (BMMSE-DFE) that involves the inversion of a large-size matrix, the proposed parametric equalizer renders a similar performance but at a lower computational cost if there are multiple outputs present. Another contribution of this correspondence is a semiblind algorithm to estimate this equalizer when the channel state information is not available: the equalizer taps and the information symbol estimates are refined recursively by means of normalized least-mean-squares (NLMS) adaptation.