An Adaptive Algorithm for Stable Decision-Feedback Filtering

A new method of decision-feedback filtering is introduced in this paper. The new method is shown to be particularly well suited for data that have undergone spectral nulling. The lack of spectral content causes a large eigenvalue spread of the data correlation matrix. This condition has deleterious effects on the performance of conventional adaptive algorithms, primarily numerical instability and noise amplification. This paper presents an adaptive decision-feedback equalizer update algorithm that does not have these undesirable properties. The algorithm calculates an iterative regularized inverse solution for the decision-feedback equalizer coefficients and applies appropriate attenuation (regularization) at frequencies lacking signal energy. This automatic estimation of the significant signal components is an improvement over other methods that use matrix arithmetic to perform the same task. The other features of the algorithm are linear computational complexity and fast tracking capability. Simulation results are presented that compare the algorithm to the conventional LMS and RLS algorithms for fractionally spaced decision-feedback filtering of a time-varying multipath communication channel.