A short proof of the equivalence of LCMV and GSC beamforming

Charles Jim (1977) showed the conditions under which a linearly constrained minimum-variance (LCMV) beamformer produces outputs equivalent to a generalized sidelobe canceller (GSC). Buckley (1986) has stated that the proof of equivalence extends to general multilinear constraints. In this article a short proof based on complementary subspaces is presented.