This paper deals with the problem of designing linear time-varying (LTV) finite-impulse response zero-forcing (ZF) equalizers for time- and frequency-selective (so-called doubly selective) single-input multiple-output (SIMO) channels. Specifically, relying on a basis expansion model (BEM) of the rapidly time-varying channel impulse response, we derive the canonical frequency-domain representation of the minimal norm LTV-ZF equalizer, which allows one to implement it as a parallel bank of linear time-invariant filters having, as input signals, different frequency-shift (FRESH) versions of the received data. Moreover, on the basis of this FRESH representation, we propose a simple and effective low-complexity version of the minimal norm LTV-ZF equalizer and we discuss the relationships between the devised FRESH equalizers and a LTV-ZF equalizer recently proposed in the literature. The performance analysis, carried out by means of computer simulations, shows that the proposed FRESH-LTV-ZF equalizers significantly outperform their competitive alternative.
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