Motivation

STBCs provide full diversity and small decoding complexity. STBCs can be considered as modulation schemes for multiple transmit antennas and as such do not provide coding gains. As we discussed earlier in Chapters 4 and 5, full rate STBCs do not exist for every possible number of transmit antennas. On the other hand, STTCs are designed to achieve full diversity and high coding gains while requiring a higher decoding complexity. The STTCs presented in Chapter 6 are designed either manually or by computer search. In this chapter, we provide a systematic method to design space-time trellis codes.

Another way of achieving high coding gains is to concatenate an outer trellis code that has been designed for the AWGN channel with a STBC. Let us view each of the possible orthogonal matrices generated by a STBC as a point in a high dimensional space. The outer trellis code's task is to select one of these high dimensional signal points to be transmitted based on the current state and the input bits. In [5], it is shown that for the slow fading channel, the trellis code should be based on the set partitioning concepts of “Ungerboeck codes” for the AWGN channel.

The main idea behind super-orthogonal space-time trellis codes (SOSTTCs) is to consider STBCs as modulation schemes for multiple transmit antennas. We assign a STBC with specific constellation symbols to transitions originating from a state.