On The Time Constant Under General Error Criterion

Time constant along with misadjustment offers a manner of analyzing the convergence behavior of adaptive algorithms. In particular, there are some advantages of using nonlinear functions of the error instead of linear ones to have enhanced convergence behavior. However, some equations for the time constant suggested in the literature are noise dependent, yielding an infinite value for the noiseless case, which is obviously wrong. This problem may explain the fact that no works compared the time constants theoretically found to those derived in practice. In this letter, we derive a new time constant which depends on both the inputs and the noise. The results show that the found equation conforms to practical results.