Analysis of conjugate gradient algorithms for adaptive filtering

The paper presents and analyzes two approaches to the implementation of the conjugate gradient (CG) algorithm for filtering where several modifications to the original CG method are proposed. The convergence rates and 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-length computation are described, and dynamic range considerations are discussed. It is shown that in finite word-length computation and close to steady state, the algorithms' behaviors are similar to the steepest descent algorithm, where the stalling phenomenon is observed. Using 16-bit fixed-point number representation, our simulations show that the algorithms are numerically stable.