Simplex (transorthogonal) signals are equally likely highly-correlated signals with the most negative correlation that can be achieved with a set of M orthogonal signals. That is, the correlation coefficient between any pair of signals in the set is defined by
One method of constructing simplex signals is to start with a set of M orthogonal signals each with energy E and then apply the minimum energy translate. Consider a set of three equally likely symbols whose signal constellation consists of the vertices of an equilateral triangle. Show that these three symbols constitute a simplex code.