Techniques for rotating and transmitting multidimensional constellations are disclosed. A method for rotating a multidimensional constellation may include constructing a first rotation matrix, constructing a second rotation matrix, applying orthogonality constraints to the first and second rotation matrices; selecting an optimizing rotation matrix from the first and second rotation matrices; and rotating the multidimensional constellation using the optimizing rotation matrix. Constructing the first rotation matrix and second rotation matrices may include constructing a first column that includes first matrix elements based on the number of axes in the multidimensional constellation, and additional columns that include permutations of the first matrix elements.