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Orthogonal sets of idempotents are used to design sets of unitary matrices,known as constellations, such that the modulus of the determinant of thedifference of any two distinct elements is greater than $0$. It is shown thatunitary matrices in general are derived from orthogonal sets of idempotentsreducing the design problem to a construction problem of unitary matrices fromsuch sets. The quality of the constellations constructed in this way and theactual differences between the unitary matrices can be determined algebraicallyfrom the idempotents used.  This has applications to the design of unitary space time constellations.

Full diversity sets of unitary matrices from orthogonal sets of idempotents