A parallel fast algorithm of Volterra adaptive filters

The recursive least squares (RLS) algorithm for Volterra adaptive filters has good convergence characteristics. However, this algorithm has prohibitively a lot of computational complexity. Several researchers have proposed various fast RLS, for quadratic Volterra adaptive filters, to reduce the computational complexity. Especially, fast transversal filters (FTF) in fast RLS algorithms using the idea of multichannel filters, have good convergence characteristics for quadratic Volterra adaptive filters. However, we require more reduction in computational complexity. In this paper, we present a method in which the Volterra filter is divided into each order of the Volterra kernels, and discuss the fast version algorithms in parallel. The proposed method leads to the reduction in the computational complexity. Finally, we show that the estimation accuracy of the proposed method is almost equal to that of the conventional method (FTF), using the computer simulation.