Learning Characteristics of Transpose-Form LMS Adaptive Filters

Transpose-form filter structures have several advantages over direct-form structures for high-speed, parallel implementation of FIR filters. Transpose-form LMS adaptive filter architectures are often used in parallel implementations [1]-[5]; however, the behavior of these filters differs from the standard LMS algorithm and has not been adequately studied. This paper develops a method for determining the maximum convergence factor yielding convergence of the mean of the transpose-form LMS adaptive filter taps. The analysis reveals the great similarity of transpose-form LMS adaptive filters to delayed-update LMS adaptive filters, which have been much more fully characterized.