Analysis of conjugate gradient algorithms for adaptive filtering. (Q2734295)

The authors present several approaches to the implementation of the conjugate gradient (CG) algorithm in adaptive filtering. Two of the proposed approaches are analyzed. The first one assumes a variable autocorrelation matrix \(R\) and cross-correlation vector \(b\), which are updated for each input data sample, and only one iteration of the algorithm is performed per time instant. The second approach assumes constant \(R\) and \(b\) within the internal iterations, and a number \(N\) of fewer internal iterations are performed per input data sample. Here \(N\) is the dimension of \(R\). The convergence rates and misadjustments for the two approaches are compared. A so-called \(z\)-domain approach was used to find the asymptotic performance, and also stability bounds for some system characteristics are established. Finally, 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 has also been observed. Simulation results demonstrate that the algorithms are numerically stable.