To　minimize　speech　distortion　and　residual　noise,　an　optimal　tradeoff　between　noise　reduction　and　speech　distortion　needs　to　be　considered.　An　optimal　tradeoff　method　for　single　channel　speech　enhancement　was　presented　by　solving　a　real-valued　constrained　optimization　model　in　a　recent　literature.　This　paper　proposes　a　new　optimal　tradeoff　method　for　multichannel　speech　enhancement　by　solving　a　complex-valued　optimization　problem　subject　to　a　residual　noise　constraint　with　the　masking　threshold　of　the　clean　speech.　An　effective　complex-valued　multichannel　learning　algorithm　is　developed　and　its　convergence　analysis　is　established　completely　in　a　complex　domain.　Experiment　results　confirm　that　the　proposed　multichannel　speech　enhancement　algorithm　outperforms　several　conventional　algorithms　in　terms　of　both　objective　measures　and　subjective　measures.　(C)　2017　Elsevier　B.V.　All　rights　reserved.