Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

306 Additional Techniques for Capacity and Flexibility EnhancementThe delay diversity can be viewed as a rate 1/M repetition code. The detector couldbe a standard equalizer. Replacing the repetition code by a more powerful code, additionalcoding gain on top of the diversity advantage can be obtained [23]. However,there is no general rule of how to obtain good space–time trellis codes for arbitrarynumbers of transmit antennas and modulation methods. Powerful STTCs are given inReference [25] and obtained from an exhaustive search. However, the problem of STTCsis that the detection complexity measured in the number of states grows exponentiallywith m M .In Figure 6-5, an example of an STTC for two transmit antennas M = 2inthecaseof QPSK m = 2 is given. This code has four states with spectral efficiency of 2 bit/s/Hz.Assuming ideal channel estimation, the decoding of this code at the receive antenna jcan be performed by minimizing the following metric:L−1∑D =∣ r j −j=0M−1∑i=0h i,j x i∣ ∣∣∣∣2, (6.3)where r j is the received signal at receive antenna j and x i is the branch metric in thetransition of the encoder trellis. Here, the Viterbi algorithm can be used to choose thebest path with the lowest accumulated metric. The results in Reference [25] show thecoding advantages obtained by increasing the number of states as the number of receivedantennas is increased.State 00100State 0210State 1101213020311State 13State 220212223State 230 31State 33233State 3Figure 6-5Space–time trellis code with four states