Analysis of conjugate gradient algorithms for adaptive filtering

This paper presents and analyzes two approaches to the implementation of th e conjugate gradient (CG) algorithm for adaptive filtering where several mo difications to the original CG method are proposed. The convergence rates a nd misadjustments for the two approaches are compared. An analysis 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-lengt h computation are described, and dynamic range considerations are discussed . It is shown that in finite word-length computation and close to steady st ate, the algorithms' behaviors are similar to the steepest descent algorith m, where the stalling phenomenon is observed. Using 16-bit fixed-point numb er representation, our simulations show that the algorithms are numerically stable.