Optimal precoder for block transmission over frequency-selective fading channels

The authors consider the design of a precoder for block transmission over a frequency-selective fading channel that minimises the worst-case averaged pairwise error probability (PEP) of the maximum likelihood detector. In applications in which the transmitter does not know the channel, the scaled identity matrix is shown to be an optimal precoder for the general uncorrelated frequency-selective Rayleigh fading channel. Such precoded communication systems automatically guarantee that the maximum likelihood detector extracts full diversity and that the optimal coding gain is achieved. A comparison of the error performance of the optimal precoded system with that of other systems with unitary precoders shows that the optimal system obtains a significant SNR gain (2-4 dB).