A general construction of space-time trellis codes for PSK signal sets

The diversity order and coding gain are crucial for the performance of a multiple antenna communication system. It is known that Space-Time Trellis Codes (STTC) can be used to achieve the above objectives. In particular we can use STTCs to obtain large coding gains. Many attempts have been made to construct STTCs which achieve full-diversity and good coding gains, though a general method of construction does not exist. Delay diversity code (rate-1), introduced in [8] [9], is known to achieve full-diversity, for any number of transmit antennas and any signal set, but does not give a good coding gain. In [1], a product distance code based delay diversity scheme is given which enables one to improve the coding gain and constructing STTCs for any given number of states using coding in conjunction with delay diversity it was stated as an open problem. In this work we achieve such a construction. We assume a shift register based model to construct a STTC for any state complexity. We derive a sufficient condition for this STTC to achieve full-diversity, based on the delay diversity scheme. This condition provides a framework to do coding in conjunction with delay diversity for any signal constellation. Using this condition we provide a formal rate-1 STTC construction scheme for PSK signal sets, for any number of transmit antennas and any given number of states, which achieves full-diversity and gives a good coding gain.