Diversity Order in ISI Channels with Single-Carrier Frequency-Domain Equalizers

Details Diversity Order in ISI Channels with Single-Carrier Frequency-Domain Equalizers Diversity Order in ISI Channels with Single-Carrier Frequency-Domain Equalizers

2009-11-25

arxiv.org/abs/0911.4896v1

Computer Science

Information Theory

30 pages, 6 figures, to appear in the IEEE Transactions on Wireless Communications

Scientific paper

This paper analyzes the diversity gain achieved by single-carrier frequency-domain equalizer (SC-FDE) in frequency selective channels, and uncovers the interplay between diversity gain $d$, channel memory length $\nu$, transmission block length $L$, and the spectral efficiency $R$. We specifically show that for the class of minimum means-square error (MMSE) SC-FDE receivers, for rates $R\leq\log\frac{L}{\nu}$ full diversity of $d=\nu+1$ is achievable, while for higher rates the diversity is given by $d=\lfloor2^{-R}L\rfloor+1$. 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.

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