How does the clipped LMS outperform the LMS?

The clipped input LMS (known as CLMS) is a common adaptive algorithm that has a lower complexity than the conventional LMS. Furthermore, the CLMS is appreciated in real-time audio embedded systems as it uses an implicit input normalization, which is necessary for non stationary audio/speech inputs. In this paper -through an exact convergence analysis- done without the common classical assumption, we show that, the CLMS algorithm can outperform the LMS in some situations at the optimal conditions. We stress the invalid common result that LMS is faster than CLMS. This is done for finite alphabet inputs where the lower the input cardinality is, the lower is CLMS/LMS complexity.