Optimal design for decision-feedback equalizer

In this paper, an optimal precoder/decoder pair that maximized the information rate is proposed. We solve the problem by using the Lagrangian optimizing method to make the eigenvectors of precoder matrix match to the eigenvectors of the circulant channel matrix. We compare the performance of information rate between zero-forcing design and our design. In addition, on the basis of the first design, we further present a precoder/decoder pair to minimize the bit error rate by adopting the minimum mean-squared error criterion and using the discrete Fourier transform matrix. Therefore, bit error rates are minimized and information rates are maximized at the same time. The SNR gain for our purposed design over zero-forcing design can be several decibels. Simulation results highlights the improvements of our two designs.