A derivation of the excess mean square error for affine projection algorithms using the condition number

This paper presents a numerical expression for the excess mean-square error (EMSE) of affine projection(AP) algorithms, and the expression is proportional to the data reuse factor and the condition number of the input data. For the condition number, a recently reported technique developed by using E-norm is adopted instead of L₂-norm. The proposed expression offers an insight into the mechanics of the AP algorithm by including the condition number in the EMSE. Our simulation results show a relatively good match between the proposed expression and the practice.