Transform domain adaptive Volterra filter algorithm based on constrained optimization

In this paper, a transform domain normalised partially decoupled LMS (TP-LMS) algorithm is proposed based on the partially decoupled transform domain Volterra filter. It is formulated by applying an orthogonal transform to the first order of the partially decoupled Volterra filter, in which the filter weights of a given order are optimised independently of those in the higher order. This approach results in solving the minimum mean square error (MSE) filtering problem as a series of constrained optimisation problems and the modular structure order by order. Simulation of a system identification application indicates TP-LMS algorithms provide a trade-off between convergence speed and computational complexity