a method and apparatus for multiple - input multiple - output signal decoding using complex lattice reduction in a multiple antenna system is provided . the method provides mimo signal decoding with increased operating speed using a transformation of reducing the lattice basis directly to a complex channel matrix that has a smaller size in comparison with a conventional matrix , which decreases the computational complexity of the lr transformation , as well as using a procedure of permutating columns of the channel matrix only twice without binding to the procedure of reducing off - diagonal elements of the matrix r , namely prior and after the procedure of reducing . moreover , the new method for mimo signal decoding has its output soft decisions .