1. An apparatus compatible with a closed-loop loop multiple-input multiple-output (MIMO) system, the apparatus comprising: a plurality of antennas used to send and receive signals; and a transmitter configured to utilize a first group of matrices for processing signals when a total number of the plurality of antennas is two and to utilize a second group of matrices for processing the signals when the total number of the plurality of antennas is four or more, wherein the transmitter processes the first group of matrices and the second group of matrices, and wherein matrices of the second group are selected from at least one of the matrices of the first group, wherein a form of the first group of matrices comprises at least one of: [ 1 0 0 1 ] , [ 1 0 0 i ] , [ 1 1 1 - 1 ] , [ 1 i i 1 ] , [ 1 i 1 - i ] , and ⁢ [ 1 1 i - i ] where i denotes a variable, wherein a form of the second group of matrices comprises at least one of: [ A 0 0 A ] , [ A A A - A ] , [ A A B - B ] , and ⁢ [ A B A - B ] where A and B are matrices selected from the first group of matrices, wherein the transmitter is further configured to receive feedback information containing a corresponding index of one or more matrices of the second group selected from the matrices of the first group, and wherein selection of matrices from the first group is based upon an orthogonalization of a radio channel for the closed-loop MIMO system.