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 updating the coefficients. The main application emphasis is oriented towards echo cancellation applications but other areas of adaptive signal processing such as postcursor filters in decision feedback equalization can be included. The particular realization proposed is based on a generalized orthonormal family of functions that has the Laguerre functions and the Kautz functions as special cases. Except for the lattice realization, that is based on the 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 has several advantages relating mainly to suitable internal (coefficients and variables) normalization and robust numerical conditioning. The Steiglitz-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.