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# The complex LMS algorithm

@article{Widrow1975TheCL, title={The complex LMS algorithm}, author={Bernard Widrow and J. M. McCool and Michael Ball}, journal={Proceedings of the IEEE}, year={1975}, volume={63}, pages={719-720} }

- Published 1975 in Proceedings of the IEEE

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<sup>-</sup><inf>j</inf>, where the boldfaced terms represent complex (phasor) signals and the bar above X<inf>j</inf>designates complex conjugate.

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