Minimum variance mean square methods with linear systems are widely us
ed in many areas of signal processing such as spectral estimation, bea
mforming or detection. However there is no reason to restrict these me
thods to the case of linear systems. The problem is then stated and so
lved in the most general context. The results are applied to some nonl
inear systems and it is especially shown that for complex inputs widel
y linear systems always have better performance than classical linear
systems. Some extensions are also presented for detection with quadrat
ic systems.