Augmented Affine Projection Algorithm Based on Error Nonlinearity and Its Simplified Version

The augmented affine projection algorithm (AAPA) has a faster convergence rate than the augmented complex-valued LMS (ACLMS) algorithm for correlated inputs. However, they are both not robust against impulsive interference. This work proposes an improved AAPA based on error nonlinearity, which is implemented with the derivative of the logistic distance metric. To reduce its computational complexity, this work also proposes a simplified version of the improved AAPA using the first-order Taylor approximation of the exponential function that is included in the derivative of logistic distance metric. To study the stochastic behaviors of the improved AAPA and its simplified version, their stability conditions and transient and steady-state performance are analyzed. Simulations are performed in the context of system identification and stereo acoustic echo cancellation to show the merits of the two proposed algorithms and to verify the accuracy of the theory on stability conditions and transient and steady-state performance.