Dispersion of phase-shift keyed systems with fixed number of blocks

An exact formula is derived for the dispersion of signal systems with a fixed number of blocks; it is proven that signal systems with M* blocks have the least dispersion. It is also proven that the dispersion of signal systems with least number of blocks becomes smaller as the quantity M-M sub 0 decreases, where M sub zero = (N+1)/2 and N = number of elements in signal. The results of calculating the dispersions for several signals systems are presented. It is concluded that the dispersion of signal systems increases near-expotentially as the figure M-M sub 0 increases.