Finite-length vs. infinite-length MMSE-DFE: the connection

The paper extends a number of results on the infinite-length minimum mean-square-error decision feedback equalizer (MMSE-DFE) reported in Cioffi et al. to the finite-length case. Cholesky factorization and displacement structure theory are demonstrated to be two powerful analytical tools for analyzing the finite-length MMSE-DFE. The objective throughout the paper is to establish finite-length analogs of the well known infinite-length MMSE-DFE results. Similarities and differences between the two cases are examined and delineated. Moreover, convergence of the derived finite-length results to their well-established infinite-length counterparts is shown. Several special cases and variations on the FIR MMSE-DFE structure are also analyzed and discussed