Analysis of conjugate gradient algorithms for adaptive filtering

We describe and analyze two approaches to the implementation of the Conjugate Gradient algorithm for adaptive filtering. In particular their convergence rate and misadjustment are compared. A new analysis approach in the z-domain is used in order to find the asymptotic performance, and stability bounds are established. The behavior of the algorithms in finite word-length computation are described and dynamic range considerations are discussed. It is shown that, close to steady-state, the algorithms´ behaviors are similar to the Steepest Descent algorithm, where the stalling phenomenon is also observed. Using 16-bit fixed-point number representation, our simulations show that the algorithms are numerically stable