An Expansion for Simplex Signaling

A set of M simplex signals is built from a set of M orthogonal signals by removal of the average signal from each of the members of the set. It is known that the dimension of the space spanned by the simplex signals is M-1 . In this article, a set of M-1 orthonormal basis functions is found for the simplex signals. The basis functions are formed by projection of the orthogonal signals in the space that is perpendicular to the average vector. The projected vectors are then orthogonalized by Gram-Schmidt technique and the outputs of Gram-Schmidt algorithm are the basis functions.