Fast converging adaptive IIR LMS filter in direct form using the suboptimal step-size

The concept of adaptive noise cancelling is investigated by employing an adaptive IIR (infinite impulse response) digital filter in direct form with a simplified coefficient-updating algorithm. One of the drawbacks of this adaptive IIR LMS (least mean square) filter in direct form was the difficulty in choosing the step-size for fast coefficient updating. Initially, the optimal step-size is derived by using the output-equation-error technique. Simulations show that the adaptive IIR filter in direct form with the suboptimal step-size outperforms the output-equation-error technique. In connection with the problem of stability of the adaptive IIR filter considered, it is shown that with the suboptimal step-size the coefficient updating algorithm is very robust. In particular, a commonly used stability test prior to new coefficient adjustment is basically no longer required