Selecting the length of an adaptive transversal filter

Optimum in the mean-square error sense, the Wiener filter is the best linear filter which can be derived given known input statistics. Excellent results have been achieved for the filtering problem with the LMS adaptive filter when these same statistics are unknown. The gradient descent algorithm introduces an excess mean-square error which is proportional to the adaptive filter's length. In an adaptive array processor, the LMS filter can be configured as a noise canceller to partially remove a sidelobe interference source from a given receive beam. This paper derives the optimum length of the adaptive transversal filter such that the residual interference signal energy plus the excess mean-square error contributed by the LMS algorithm is minimized. Both narrowband and wideband interference signals are considered.