BER minimized OFDM systems with channel independent precoders

We consider the minimization of uncoded bit error rate (BER) for the orthogonal frequency division multiplexing (OFDM) system with an orthogonal precoder. We analyze the BER performance of precoded OFDM systems with zero forcing and minimum mean squared error (MMSE) receivers. In the case of MMSE receivers, we show that for quadrature phase shift keying (QPSK), there exists a class of optimal precoders that are channel independent. Examples of this class include the discrete Fourier transform (DFT) matrix and the Hadamard matrix. When the precoder is the DFT matrix, the resulting optimal transceiver becomes the single carrier system with cyclic prefix (SC-CP) system. We also show that the worst solution corresponds to the conventional OFDM system; the conventional OFDM system has the largest BER. In the case of zero forcing receivers, the design of optimal transceiver depends on the signal-to-noise ratio (SNR). For higher SNR, solutions of optimal precoders are the same as those of MMSE receivers.