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In this paper we propose a zero forcing (ZF) time-varying (TV) finite-impulse response (FIR) equalizer for doubly-selective (time- and frequency-selective) channels. We use the basis expansion model (BEM) to approximate the doubly-selective channel and to design the TV FIR equalizer. This allows us to turn a large TV problem into an equivalent small-time invariant (TIV) problem, containing only the BEM coefficients of the doubly-selective channel and the TV FIR equalizer. It is shown that a ZF TV FIR equalizer only exists if there is more than one receive antenna. The ZF TV FIR equalizer approach we propose here unifies and extends many previously proposed serial equalization approaches. Through computer simulations we show that the performance of the ZF TV FIR equalizer approaches the one of the ZF block equalizer, while the equalization as well as the design complexity is much lower.