Theory of fractionally spaced cyclic-prefix equalizers

The cyclic prefix system is widely used for frequency domain equalization in discrete multitone channels. In this paper we show how the idea of fractionally spaced equalization (FSE) can be adapted to cyclic prefix systems. We derive the condition for a perfect FSE, and show that there is a certain freedom in the choice of the equalizer coefficients. This freedom is then exploited to minimize the effect of additive noise at the detector input. The theory is generally applicable to any deconvolution problem, though the setting used for our development uses the language of digital communication.