On the existence of FIR zero-forcing equalizers for nonredundantly precoded transmissions through FIR channels

We consider in this letter the problem of perfectly equalizing finite-impulse response (FIR) channels in digital communication systems employing nonredundant precoding at the transmitter. In this case, as it is well known, there is no linear FIR zero-forcing (ZF) block equalizer that is capable of perfectly recovering information symbols in the absence of noise. We show that, when the symbol constellation is improper, it is possible to design widely linear FIR-ZF block equalizers that, unlike their linear counterparts, process both the received signal and its complex-conjugate version. In addition, we propose a simple procedure to synthesize universal modulation-induced cyclostationary (MIC) precoders that assures perfect symbol recovery, regardless of the channel-zero locations.