Fast projection algorithm and its step size control

Of the many adaptive filtering algorithms, the normalized LMS (NLMS) algorithm is generally used in practice because of its simplicity. The computational complexity of the NLMS algorithm is low, however, convergence is very slow and tracking is poor for a colored input signal such as speech. The projection algorithm was proposed as a generalization of the NLMS algorithm. This paper provides a fast projection algorithm and a step size control to obtain the same steady-state excess mean squared error (MSE) for various projection orders. Computer simulations for colored noise and speech input signal confirm the effectiveness of the projection algorithm and the step size control