BER optimized channel independent precoder for OFDM system

We consider the minimization of bit error rate (BER) for OFDM systems with orthogonal precoders. For low SNR, we show that the conventional OFDM system is the optimal solution and the optimal precoder is the identity matrix. For high SNR, corresponding to a relatively practical range of BER, there are channel independent solutions for optimal precoders. One such solution is the DFT matrix and the resulting optimal transceiver becomes the single carrier transmission system. Furthermore, in this case the conventional OFDM system has the largest BER among all OFDM systems with orthogonal precoders.