Comparison of orthonormal adaptive FIR and IIR filter realizations

We discuss both the utilization of a particular realization for an adaptive IIR filter and a related special structural interpretation of the Steiglitz-McBride method for the updating of the coefficients. The main application emphasis is oriented to echo cancellation but other areas of adaptive signal processing can be included, as for example postcursor filter in decision feedback equalization. The particular realization proposed is based on an orthonormal family of functions, that has as special cases the Laguerre functions and the Kautz functions. Except for the lattice realization, that is based on the nice properties of Szego orthonormal polynomials, no other adaptive IIR filter realization using orthonormal characteristics seems to be extensively studied in the literature. In spite of the fact that the proposed realization has manifolds, it is demonstrated that they are not an important drawback for convergence speed as for example in the parallel or cascade adaptive IIR realizations. A set of computer simulations to illustrate the comparison between the IIR adaptive filter structure proposed and an adaptive FIR filter structure based on a truncated Laguerre orthonormal realization is presented. In this comparison the relevant aspects studied were computational complexity, modeling capability and reduced order performance.