An $\alpha$-Sigmoid Affine Projection Algorithm for In-Car Echo Cancellation and Channel Estimation

An $\alpha$-sigmoid affine-projection ($\alpha$SAP) algorithm is proposed based on an improved $\alpha$-sigmoid cost function. The algorithm optimizes the sigmoid function by introducing the $\alpha$ parameter and combines it with the $L_{2}$ constraint, which accelerates the convergence speed when color signals are input to the system, and enhances the robustness to impulse interference. Through theory analysis and simulation experiments, the superior performance for our constructed $\alpha$SAP in dealing with highly correlated input signals and impulse disturbances, as well as its advantages in ensuring stability and minimizing the steady-state excess-mean-square-error (EMSE) are demonstrated. Simulated results obtained from the in-car echo-cancellation and channel-estimation show that the $\alpha$SAP algorithm outperforms the commonly used AP algorithms under different impulse interferences and provides better tracking performance at the same time.