1. A method for using a numerical method to design reference signals for multiple input: multiple output (MIMO) systems, the method comprising: determining an input multiple input multiple output signal; obtaining a nearest tight frame to one or more given structured vectors; obtaining one or more structured vectors from the nearest tight frame; computing orthogonal subsets for a plurality of sequences, wherein each of the subsets is replaced with a matrix that comprises a function of one or more elements in each of the plurality of sequences and an identity matrix associated with the one or more elements; projecting the one or more structured vectors onto the space of circulant matrices; and outputting one or more classes of matrices associated with reference signals.