Praise for Fundamentals of WiMAX

5.3 Transmit Diversity 161The resulting signals at times 0 andTon antennas 1 and 2 can be represented asUsing the following combining schemeyields the following decision statistics:and results in the following SNR:r(0) = h s + h s + n (0),1 11 1 21 2 1* *r( T) = − h s + h s + n ( T),1 11 2r (0) =2h*2 12 221 1s + h s + n (0),12 1 22 2 2r ( T) = − h s + h s + n ( T).*22 1** **y = h r(0) + h r ( T) + h r (0) + h r ( T),1 11 1 21 1*y = h r(0)h*2 21 1−1 111212 2 22 2r ( T) + h r (0) −h r ( T),**22 2 21 22222y =(| h | + | h | + | h | + | h | ) s + 4 noise terms,y1 11=(| h |2 112122122222+ | h12| + | h21| + | h22| ) s 2+ 4 noise terms,1(5.23)(5.23)(5.23)⎛ ⎞2 22⎜∑∑| hij| ⎟ ∑∑ | hij|γ = ⎝ j i ⎠Σσ | | 2 = j=1i=12 22hσ∑∑jiij22εx2 .(5.24)This SNR is like MRC with four receive antennas, where again there is a 3 dB penalty dueto transmitting each symbol twice. An orthogonal, full-rate, full-diversity STBC over anN channel will provide a diversity gain equivalent to that of an MRC system witht× NrNN t rantennas, with a 10log dB transmit power penalty owing to the transmit antennas. In10N tN tother words, in theory, it is generally beneficial to have somewhat evenly balanced antennaarrays, as this will maximize the diversity order for a fixed number of antenna elements. In practice,it is important to note that full-diversity, orthogonal STBCs exist only for certain combinationsof and .N tN r5.3.2.2 4 × 2 Stacked STBCsThe 2×2 Alamouti code achieves full diversity gain. In some cases, it may be possible to affordfour transmit antennas at the base station. In this case, two data streams can be sent, using a doublespace/time transmit diversity (DSTTD) scheme that consists of operating two 2×1 Alamouticode systems in parallel [46, 61]. DSTTD, also called stacked STBCs, combines transmit diversityand MRC techniques, along with a form of spatial multiplexing, as shown in Figure 5.6.