Lattice Reduction Aided MMSE Decision Feedback Equalizers

The LLL algorithm developed by Lenstra, Lenstra, and Lovász has been widely studied to improve the conditioning of linear systems of equations that arise in multi-input multi-output (MIMO) antenna systems. In the first part of this correspondence, we show how a certain class of matrices can be transformed so that the LLL algorithm can be carried out efficiently, without compromising its performance. Then, the proposed transformation is applied to the matrix with block lower triangular Toeplitz matrices that arises in the decision feedback equalizer (DFE) to improve the bit error rate (BER) performance with a slight computational overhead.