The complex LMS algorithm

A least-mean-square (LMS) adaptive algorithm for complex signals is derived. The original Widrow-Hoff LMS algorithm is W<inf>j+l</inf>= W<inf>j</inf>+ 2µεjX<inf>j</inf>. The complex form is shown to be W<inf>j+1</inf>= W<inf>j</inf>+ 2µεjX^-<inf>j</inf>, where the boldfaced terms represent complex (phasor) signals and the bar above X<inf>j</inf>designates complex conjugate.