Abstract.1 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.
The concept of fractional biorthogonal partners has been introduced recently by the authors. They arise in many different contexts, one of them being channel equalization with fractionally spaced equalizers. If the amount of oversampling at the receiver is not an integer, but a rational number, the problem of fractionally spaced equalization can be treated using the fractional biorthogonal partner setting. This approach is adopted here. We consider fractionally spaced equalizers with a rational amount of oversampling, show that the FIR solution (if it exists) is not unique and can be chosen to minimize the noise power at the receiver. These findings are demonstrated by examples where we compare the performance of fractionally spaced zero forcing equalizers to that of the corresponding minimum mean-squared error solution.
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