Coefficient bias in constant modulus adaptive filters

The MMSE criterion introduces a bias of the coefficients in adaptive filtering. For constant modulus signals, an estimation of this bias is derived. Constant modulus (CM) criteria lead to different values of this bias. A simple approach is presented to derive estimations for the two criteria of practical interest, namely CM(1,2) and CM(2,2), and it is shown that the bias with CM(1,2) is smaller than the bias with MMSE, while the bias with CM(2,2) is larger. The case of non constant modulus signals is also considered. The results presented are likely to make the performance of CM algorithms better understood and they should contribute to stimulate their introduction in practical systems