  The LMS algorithm is one of the most widely used techniques in adaptive
filtering. Accurate modeling of the algorithm in various circumstances is
paramount to achieving an efficient adaptive Wiener filter design process. In
the recent decades, concerns have been raised on studying improper signals and
providing an accurate model of the LMS algorithm for both proper and improper
signals. Other models for the LMS algorithm for improper signals available in
the scientific literature either make use of the independence assumptions
regarding the desired signal and the input signal vector, or are exclusive to
proper signals; it is shown that by not considering these assumptions a more
general model can be derived. In the presented simulations it is possible to
verify that the model introduced in this paper outperforms the other available
models.
