Frequency Domain Computation of the Feedback Filter of the Hybrid Decision Feedback Equalizer

The hybrid decision feedback equalizer is a combined time-frequency domain implementation of the classical decision feedback equalizer. In the original hybrid decision feedback equalizer, independently proposed by Falconer et al. and by Benvenuto and Tomasin, the computation of the feedforward filter is done in the frequency-domain, while the impulse response of the feedback filter is computed in the time-domain. In this paper we focus on the frequency-domain approach for computing the coefficients of the feedback filter. The proposed approach is based on the Kolmogoroff (cepstral) method of spectral factorization. We consider the application of the method to highly dispersive channels. By using simulations we show that for these types of channels the performance of the proposed method is virtually the same as that obtained by using time-domain approaches. The advantage of the proposed method is that the efficient fast Fourier transform gives a substantial reduction of complexity compared to time-domain methods.