A variable step size affine projection algorithm based on the principle of orthogonality

The orthogonality principle states that as an adaptive filter approaches to the Weiner solution and error approaches to its minimum value, the correlation between error and input signal approaches to zero. This fact has been exploited in the proposed scheme for the minimizing mean square deviation (MSD) for the tap weights and its estimated value at each iteration. Essentially, this paper proposes a variable step-size (VSS) affine projection algorithm (APA) where step-size is varied on the basis of instantaneous cross correlation of error and input signal along with the error power and estimated noise variance. The main advantage of the proposed method is that it does not need an initial tuning parameter of fixed step-size to kick-off VSS calculations unlike most VSS APAs. The simulation results show that the proposed algorithm has fast convergence and small steady state error than the existing VSS APAs.