Patent ID: 7961587

Claim:
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, wherein each tight frame meets or approaches a Welch Bound; 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 a product of an identity matrix associated with the one or more elements and a value, the value being greater than or equal to zero and less than or equal to one, wherein one less the value is added to the product; projecting the one or more structured vectors onto a space of circulant matrices; and outputting one or more classes of matrices associated with reference signals, wherein the method is performed by a communications device.