Efficient echo cancellation based on an orthogonal adaptive IIR realization

Adaptive IIR filters have not been widely used in many areas because the updating algorithms and suitable representations (realizations) known in the literature do not cover different particularities of each application. We discuss both the utilization of a particular realization for the adaptive IIR filter and a special structural interpretation of the Steiglitz-McBride method for the updating of the coefficients. The main application emphasis is oriented to echo cancellation application but other area of adaptive signal processing can be included, as for example the postcursor filter in decision feedback equalization. The particular realization proposed is based on a generalized 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. The chosen realization as several advantages related mainly to suitable internal (coefficients and variables) normalization and robust numerical conditioning. The Steitglitz-McBride method is discussed mainly because it can avoid the local minima problem related to direct mean squared output error minimization. In this paper, we present some theoretical results related to the properties of a special orthonormal realization, suitable for echo cancellation, when used to minimize the mean square output error with the Steiglitz-McBride algorithm.