Computation of a constrained decision feedback equalizer for reduced error propagation

It has been previously shown that the effects of error propagation in a decision feedback equalizer may be reduced by constraining the 2-norm of the feedback filter. This paper describes three algorithms for calculating the constrained equalizer based on a channel estimate. An iteration function is derived for the Karush-Kuhn-Tucker multiplier and the algorithms are designed to quickly find a fixed point of this function. The algorithms include a modified regula falsi algorithm known as the Pegasus iteration, a modified secant algorithm, and a nonlinear fit to the iteration function. At each iteration, the conjugate gradient algorithm is used to solve the resulting linear equations. The algorithms are demonstrated on the 8-VSB terrestrial broadcast digital TV system. While all three algorithms exhibit good convergence characteristics, the nonlinear fit converges the fastest.