A MIMO pre-coding system for a delta quantizer for MIMO pre-coders with finite rate channel state information feedback may include quantizing a change in channel state information in a MIMO pre-coding system onto a codebook, which comprises one or more unitary matrices, using a cost function. The codebook may be generated based on at least the channel state information. The channel state information may comprise a matrix V and the cost function f(A) may be defined by the following relationship: f ⁡ ( A ) = ( 1 N ⁢ ∑ j = 1 N ⁢  a jj  2 ) where A is a matrix of size N by N and aij is element (i,j) of matrix A. One or more unitary matrices may be generated from at least a first set of matrices and a second set of matrices, where the first set of matrices may comprise one or more Givens matrices. A dynamic range and a resolution of the codebook may be modified.