The role of virtual noise in unconstrained frequency domain equalization

Decision feedback equalization is a popular method for signal detection that allows a good trade off between complexity and performance. The complexity of the decision feedback equalizer (DFE) is mainly concentrated in the feedforward filter, which is often realized in FIR form. When the number of taps of the FIR filter needed to obtain nearly optimal performance becomes large, one may take advantage of the efficiency of the FFT/IFFT algorithm realizing the feedforward filter in the discrete frequency domain. In this paper we consider the minimum mean square error (MMSE) DFE with feedforward filter in the discrete frequency domain, assuming perfect knowledge of a static channel. We move from the observation that the optimal MMSE-DFE feedforward filter is IIR, and point out that the classical scheme of unconstrained frequency domain filtering with overlap/save digital signal processing may induce substantial increase in the error rate when the approximation of the linear convolution between the received signal and the mentioned IIR, to a circular convolution is poor. Our main finding is that the error rate can be significantly improved by deliberately augmenting the power of the noise in the computation of the transfer function of the frequency domain feedforward filter.