Adaptive Volterra filters using orthogonal structures

This paper presents an adaptive Volterra filter that employs a recently developed orthogonalization procedure of Gaussian signals for Volterra system identification. The algorithm is capable of handling arbitrary orders of nonlinearity P as well as arbitrary lengths of memory M for the system model. The adaptive filter consists of a linear lattice predictor of order N, a set of Gram-Schmidt orthogonalizers for N vectors of size P+1 elements each, and a joint process estimator in which each coefficient is adapted individually. The complexity of implementing this adaptive filter is comparable to the complexity of the system model when N is much larger than P, a condition that is true in many practical situations. Experimental results demonstrating the capabilities of the algorithm are also presented in the paper.