Precursor inter-symbol interference removal by block transmission-based time-reversed equalization

Single-carrier transmission is considered in the general finite impulse response inter-symbol interference (ISI) channel. In an ISI channel with a matched filter, the folded spectrum of the received pulse can be factored into a minimum phase causal part and a maximum phase anticausal part corresponding to the postcursor and precursor ISI, respectively. In this paper, zero-forcing ISI cancellation is considered. In a direct implementation, the precursor equalization is carried out based on truncating and delaying the ideal anticausal precursor equalizer impulse response. In the proposed scheme, a block transmission is adopted, and the precursor equalization is carried out by a time reversal within each block and using a practical minimum phase filter. We show that the ISI can be removed perfectly using the proposed scheme. By means of a numerical example, it is shown that the proposed scheme achieves improved performance compared to the truncateand delay-based equalizer in terms of transmission rate, delay, and implementation complexity.