Acceleration of normalized adaptive filtering data-reusing methods using the Tchebyshev and conjugate gradient methods

New normalized data reusing can significantly improve convergence rates over traditional LMS adaptive filtering methods. However, these methods can still be slow to converge for highly-correlated input data. The convergence rate of this normalized adaptive algorithm can be significantly improved by accelerating these methods using the conjugate gradient and Tchebyshev algorithms. Use of these acceleration techniques can be shown to be approximately equivalent to the popular methods of affine projection albeit at a lower overall computational complexity. Simulation examples illustrate that significant performance improvement may be obtained using these methods of acceleration. Theoretically optimal performance bounds for this method of data reusing are illustrated by proof and simulation.