The general order, multichannel FTF algorithm is a generalization of the multichannel FTF algorithm in which the orders of the input channels can be independently specified. The algorithm is applied to a special case of a two-input-channel, joint process estimator. One of the input channels is defined as the unit-delayed joint process signal; the configuration is an 'equation error' form for least squares (LS) pole-zero ARMA (autoregressive moving-average) system identification. This form is also used in decision-directed equalization and echo cancellation. For this special two-channel case, a computational savings of 2N+1 operations per recursive update is identified, where N is the total number of filter taps. The saving is proven using the concepts of projection onto a vector space. The reduction is available with any of the order-N 'fast' LS algorithms including the fast Kalman (FK) and FAEST algorithms; this had not been recognized for similar application of the FK algorithm to decision-directed equalization. A summary of the modified algorithm is given, with an operations count for each step.>

A new architecture for a single instruction stream, multiple data stream (SIMD) implementation of the LMS adaptive algorithm is investigated. This is denoted as a ring architecture, due to its physical configuration, and it effectively solves the latency problem often associated with prediction error feedback in adaptive filters. The multiprocessor ring efficiently updates the filter input vector by operating as a pipeline structure, while behaving as a parallel structure in computing the filter output and applying the weight adaptation algorithm. Last, individual processor timing and capacity considerations are examined.