Minimum BER block precoders for zero-forcing equalization

We determine the linear precoder that minimizes the bit error rate (BER) at moderate-to-high signal-to-noise ratios (SNRs) for block transmission systems with zero-forcing (ZF) equalization and threshold detection. The design is developed for the two standard schemes for eliminating inter-block interference, viz, zero padding (ZP) and cyclic prefix (CP). We show that both the ZP minimum BER precoder and the CP minimum BER precoder provide substantially lower error rates than standard block transmission schemes, such as orthogonal frequency division multiplexing (OFDM). The corresponding SNR gains can be on the order of several decibels. We also show that the CP minimum BER precoder can be obtained by a two-stage modification of the water-filling discrete multitone modulation (DMT) scheme in which the diagonal water-filling power loading is replaced by a full matrix consisting of a diagonal minimum mean square error power loading matrix post multiplied by a discrete Fourier transform (DFT) matrix.