Comparison ofM-ary Modulation Systems

Consideration of large alphabet digital communication systems is of both theoretical and practical interest. Although performance bounds on optimum systems for the Gaussian channel are available, constructive methods for approaching these bounds are unknown, except in a few very special cases. Specific systems have been proposed and evaluated relative to these bounds, but exact evaluation of error probability is generally a difficult numerical task. It is of interest to consider simpler performance criteria which permit comparison of various systems without extensive computation. An easily evaluated criterion (based on the alphabet size and minimum distance between signal vectors) is shown to yield a simple sufficient condition for one system to be better than another (smaller error probability for the same energy-per-bit). The criterion is applied to orthogonal, biorthogonal, simplex, and more general permutation modulation systems. In addition to comparing the various systems, we consider ways of obtaining good special cases of permutation modulation. Finally, we assess a recently proposed system (“N-orthogonal phase modulation”) and show that it is generally inferior to more conventional techniques.