Circular trellis-coded modulation with multidimensional simplex signal for power-limited applications

This paper proposes a systematic way to build an optimum signal constellation for 4-ary circular trellis-coded modulation system for power-limited channels. It is applicable to any size 4-ary circular trellis with permuted state structure. Algebraic representation of a simplex signal is introduced. A multi-dimensional matrix representation of a high dimensional simplex signal constellation is developed. The symbol assignment procedure is described.