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

MIMO Overview 3076.2.2.2 Space–Time Block Code (STBC)A simple transmit diversity scheme for two transmit antennas using STBCs was introducedby Alamouti in Reference [2] and generalized to an arbitrary number of antennas byTarokh et al. [24]. Basically, STBCs are designed as pure diversity schemes and provideno additional coding gain as with STTCs. In the simplest Alamouti scheme with M = 2antennas, the transmitted symbols x i are mapped to the transmit antenna with the mapping[ ]xB = 0 x 1−x1 ∗ , (6.4)x∗ 0where the row corresponds to the time index and the column to the transmit antenna index.In the first symbol time interval x 0 is transmitted from antenna 0 and x 1 is transmitted fromantenna 1 simultaneously, while in the second symbol time interval antenna 0 transmits−x ∗ 1 and simultaneously antenna 1 transmits x∗ 0 .The coding rate of this STBC is one, meaning that no bandwidth expansion takes place(see Figure 6-6). Due to the orthogonality of the space–time block codes, the symbolscan be separated at the receiver by a simple linear combining (see Figure 6-7). The spatialdiversity combining with block codes applied for multi-carrier transmission is describedin more detail in Section 6.3.4.6.2.3 Achievable CapacityFor STBCs of rate R the channel capacity is given by [3]⎡⎛⎞⎤C = R log 2⎣⎝1 + E M−1s/N o∑L−1∑|h i,j | 2 ⎠⎦ . (6.5)MFor R = 1andL = 1, this is equivalent to the channel capacity of a MISO scheme.However, for L>1, the capacity curve is only shifted, but the asymptotic slope is noti=0j=0SinglestreamSpace–timemapper, B(STBC)OptionalDetectionSinglestreamFigure 6-6Space–time block code transceiver