Steady-State Mean-Square Performance Analysis of the Affine Projection Sign Algorithm

Due to the robustness against impulsive noises and colored inputs, the affine projection sign algorithm (APSA) is widely used in practice. However, the steady-state mean-square performance of the algorithm has not been analyzed. In this brief, we perform the steady-state mean-square analysis of the APSA by using the energy conservation arguments, the Price’s theorem and some reasonable assumptions. The range of the step size is provided to guarantee the stability of the algorithm. The expression of the steady-state excess mean-square error (EMSE) is also presented. Simulation results confirm the accuracy of the proposed expressions under different operating scenarios.