Low Cost Variable Step-Size LMS With Maximum Similarity to the Affine Projection Algorithm

The LMS algorithm is widely employed in adaptive systems due to its robustness, simplicity, and reasonable performance. However, it is well known that this algorithm suffers from a slow convergence speed when dealing with colored reference signals. Numerous variants and alternative algorithms have been proposed to address this issue, though all of them entail an increase in computational cost. Among the proposed alternatives, the affine projection algorithm stands out. This algorithm has the peculiarity of starting from
$N$
data vectors of the reference signal. It transforms these vectors into as many data vectors suitably normalized in energy and mutually orthogonal. In this work, we propose a version of the LMS algorithm that, similar to the affine projection algorithm, starts from
$N$
data vectors of the reference signal but corrects them by using only a scalar factor that functions as a convergence step. Our goal is to align the behavior of this algorithm with the behavior of the affine projection algorithm without significantly increasing the computational cost of the LMS.