The design of 2-Space-Time Trellis code by asymmetric constellation expansion

Analytically, we have designed some optimal 2-Space-Time Trellis codes (2-STTCs) by M-psk constellation expansion, and the constellations can be asymmetric to reach their optimal coding gain. The resultant codes are geometrically non-uniform. We show that when the constellation is symmetric and the size equals to the number of states, our design reduces to Tarokh´s uniform code. Simulations are done to compare our design to the known codes. It is proved that constellation expansion design outperforms state expansion design in both Frame Error Rate (FER) and decoding complexity. Our 4 states asymmetric 8-PSK 2-STTC can achieve the similar performance of Tarokh´s 32 states 4-PSK 2-STTC.