A complex algorithm for linearly constrained adaptive arrays

A linearly constrained least mean squares (lms) algorithm for complex signals is derived to minimize noise power in the array output. The original algorithm for real signals is
W(k + 1) = P[W(k) - \mu y(k)X(k)] + F
. The complex form is shown to be
W(k + 1) = P[W(k) - \mu y(k)\bar{X}(k)] + F
, where the bar above
\bar{X}
denotes complex conjugate.
W, y, X
, and
F
are complex.
P
and
\mu
are real.