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