Efficient Computation of the Feedback Filter for the Hybrid Decision Feedback Equalizer in Highly Dispersive Channels

The hybrid decision feedback equalizer (DFE) is a combined time-frequency domain implementation of the conventional time-domain DFE that is able to provide a good trade-off between performance and computational complexity in single carrier transmission over severely frequency-selective channels. In the hybrid DFE the implementation of the feedforward filter is done in the frequency domain, while the feedback filter (FBF) is implemented in the time-domain. The computation of the coefficients for the two filters is usually done in the same domain where they are implemented. A method for frequency-domain computation of the FBF is proposed in the paper. As is known, the key operation in the computation of the FBF is the spectral factorization. In the paper it is proposed to adopt the (cepstral) method for spectral factorization due to Kolmogoroff, which can be efficiently implemented by using the fast Fourier transform (FFT). The application of the method is considered for highly dispersive channels. By using simulations we show that for this type 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 approach is that the efficient FFT gives a substantial reduction of complexity compared to time-domain methods.