Adaptive Volterra filters using orthogonal structures

The paper presents an adaptive Volterra filter that employs an 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 N 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