Unified linear precoding for minimum SER

New unified linear preceding and decoding techniques are presented in this paper, which are suitable for block transmission systems such as orthogonal frequency division multiplexing (OFDM) systems, synchronous code division multiple access (CDMA) systems, single carrier systems and multiple-input-multiple-output (MIMO) systems. First, a linear precoder that achieves minimum symbol-error-rate (MSER) is proposed and analyzed. Motivated by the fact that the conventional and the MSER precoders achieve a diversity order of one, a new method of applying linear preceding over subchannels, named multichannel precoding (MP), is developed to exploit the diversity gain. It is shown that even if a suboptimal linear decoder is used, MP improves the SER performance significantly. Given the block and linear nature of the linearly preceded system, lattice decoding is a suitable and efficient method for optimally detecting data symbols. Some analytical results are presented for the linearly preceded system with lattice decoding. The SER performance of different linearly preceded systems are also compared numerically.