LMS adaptive algorithms for joint forward and decision feedback equalisation

The mean-square error is used as the performance measure to find the joint optimum tap settings of an equaliser, consisting of a forward filter and a decision feedback part. The paper provides two LMS adaptive algorithms to attain two different sets of tap settings and shows that one of these sets is suboptimum in the mean-square error sense. In practice the largest possible step size that ensures the algorithm stability must be approximated. Using these step sizes for the iterations, one algorithm converges faster than the other. Switching after initial convergence from the faster algorithm to the slower algorithm yields faster convergence to the minimum mean-square error of the complete equaliser. The results of realised simulations are in good agreement with the calculations