For the purpose of equalisation of rapidly time variant multipath channels, we derive a novel adaptive algorithm, the amplitude banded LMS (ABLMS), which implements a non-linear adaptation based on a coefficient matrix. Then we develop the ABLMS algorithm as the adaptation procedure for a linear transversal equaliser (LTE) and a decision feedback equaliser (DFE) where a parallel adaptation scheme is deployed. Computer simulations demonstrate that with a small increase of computational complexity, the ABLMS based parallel equalisers provide a significant improvement related to the conventional LMS DFE and the LMS LTE in the case of a second order Markov communication channel model.

It is well known that based on the structure of a transversal filter, the RLS equaliser provides the fastest convergence in stationary environments. This paper addresses an adaptive transversal equaliser which has the potential to provide more faster convergence than the RLS equaliser. A comparison is made with respect to computational complexity required for each update of equaliser coefficients, and computer simulations are demonstrated to show the superiority of the proposed equaliser.