Diversity order in ISI channels with single-carrier frequency-domain equalizers

This paper analyzes the diversity gain achieved by single-carrier frequency-domain equalizers (SC-FDE) in frequency selective channels, and uncovers the interplay between diversity gain d, channel memory length ¿, transmission block length L, and the spectral efficiency R. We specifically show that for the class of minimum mean-square error (MMSE) SCFDE receivers, for rates R ¿ log L/¿ full diversity of d = ¿+ 1 is achievable, while for higher rates the diversity is given by d = [2^-R L + 1. In other words, the achievable diversity gain depends not only on the channel memory length, but also on the desired spectral efficiency and the transmission block length. A similar analysis reveals that for zero forcing SC-FDE, the diversity order is always one irrespective of channel memory length and spectral efficiency. These results are supported by simulations.