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

318 Additional Techniques for Capacity and Flexibility EnhancementΠS n , S n + 1OFDMx 0, vspace/freq.mapperOFDMx 1, vFigure 6-20Space–frequency block coding in an OFDM transmittersub-carriers in multi-carrier systems. The feature of OFDM can be exploited, that twoadjacent narrowband sub-channels are affected by almost the same channel coefficients.Thus, a space–frequency block code (SFBC) requires only the reception of one OFDMsymbol for detection, avoids problems with coherence time restrictions, and reduces delayin the detection process.Figure 6-20 shows an OFDM transmitter with space–frequency block coding. Sequencesof N c interleaved data symbols S n are transmitted in one OFDM symbol. The datasymbols are interleaved by the block before space–frequency block coding such thatthe data symbols combined with space–frequency mapping and, thus, affected by thesame fading coefficient are not subsequent data symbols in the original data stream. Theinterleaver with size I performs frequency interleaving for I ≤ N c and time and frequencyinterleaving for I>N c .The mapping scheme of the data symbols S n for SFBC with two transmit antennas andcode rate 1 is shown in Table 6-1. The mapping scheme for SFBC is chosen such thaton the first antenna the original data are transmitted without any modification. Thus, themapping of the data symbols on the sub-carriers for the first antenna corresponds to theclassical inverse discrete Fourier transform withx 0,v = 1 N∑c −1N cn=0S n e j2πnv/N c, (6.15)where n is the sub-carrier index and ν is the sample index of the time signal. Only thedata symbol mapping on the second antenna has to be modified according to the mappingscheme for space–frequency block coding given in Table 6-1. The data symbols of thesecond transmit antenna are mapped on the sub-carriers as follows:x 1,v = 1 N c /2−1∑(S2n ∗ N ej2π(2n+1)v/N c− S2n+1 ∗ ej2π2nv/N c). (6.16)cn=0Table 6-1 Mapping with space–frequencyblock codes and two transmit antennasSub-carrier number Antenna 1 Antenna 2n S n −Sn+1∗n + 1 S n+1 Sn∗