An improved affine projection algorithm for network echo cancellation with its fast version is proposed to increase the convergence speed.On the basis of the sparse structure characteristic of network echo path

each coefficient of adaptive filter in the new algorithm obtains different step-size in proportion to its current absolute value

which leads to high overall convergence speed.Statistical analysis of the new algorithm provides theoretical basis for its outstanding capacity in converging to the objective system.The simulation result verifies that the new algorithm achieves faster convergence speed and lower final misalignment.In addition its low computational complexity satisfies the requirement of real-time system.