Asymptotically minimum bit error rate block precoders for minimum mean square error equalization

We determine linear block precoders which asymptotically minimize the bit error rate (BER) of block-based communication systems employing minimum mean square error (MMSE) equalization and threshold detection. The problem is solved by a two-stage optimization procedure in which a lower bound on the BER over its convex region is first minimized, followed by showing that this lower bound is actually achieved by the solution obtained in the first stage. Simulation results show that at moderate to-high signal-to-noise ratios (SNRs), the SNR gain for the proposed design over the standard MMSE precoder, and several other conventional systems such as orthogonal frequency division multiplexing (OFDM) and discrete multitone (DMT) modulation can be several decibels (dB).