Title: Minimum BER Linear Precoder for Zero-forcing Equalization

In this paper we determine the linear precoder which minimizes the bit error rate (BER) at moderate-to-high signal-to-noise ratios for block transmission systems with zero-forcing 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 the schemes of discrete multitone (DMT) modulation with water-filling power loading and orthogonal frequency division multiplexing (OFDM). The corresponding SNR gains can be of 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 DMT scheme in which the diagonalwater-filling power loading is replaced by a full matrix which consists of a diagonal minimum mean square error power loading matrix post multiplied by a discrete Fourier transform matrix.