Praise for Fundamentals of WiMAX

5.3 Transmit Diversity 163where I iis the interference from the ith transmit antenna due to transmitting two simultaneousdata streams. The detection process of DSTTD should attempt to suppress the interferencebetween the two STBC encoders and for this purpose can turn to any of the spatial-multiplexingreceivers (see Section 5.5.1). In contrast to OSTBCs (Alamouti codes), the ML receiver forstacked STBCs is not linear.5.3.2.3 Transmit Diversity versus Receive DiversityThe three example space/time block codes showed that transmit and receive diversity are capableof providing an enhanced diversity that increases the robustness of communication overwireless fading channels. The manner in which this improvement is achieved is quite different,however.Receive diversity: For MRC with N rantennas and only one transmit antenna, the receivedSNR continuously grows as antennas are added, and the growth is linear:γMRCεN r∑x2= | hi| = γi.2σi=1N r∑i=1(5.28)The expected value, or average combined SNR, can thus be found asγMRC= γ,Nr(5.29)where γ is the average SNR on each branch. In other words, the SNR growth is linear with thenumber of receive antennas. Thus, from Shannon’s capacity formula, it can be observed thatsince C = B log (1 + SNR), the throughput growth due to receive diversity is logarithmic with thenumber of receive antennas, since receive diversity serves to increase the SNR.Transmit diversity: Due to the transmit-power penalty inherent to transmit diversity techniques,the received SNR does not always grow as transmit antennas are added. Instead, if thereis a single receive antenna, the received combined SNR in an orthogonal STBC scheme is generallyof the formεγ = xΣσ| | 2h .2 iNtN t∑i=1(5.30)As the number of transmit antennas grows large, this expression becomesε2γ = | h1| + | h2| + … + | h |xN tΣ 2σN2 2tε→σ2E[| h | ],x2 1(5.31)by the law of large numbers. Thus, open-loop transmit diversity causes the received SNR to“harden” to the average SNR. In other words, it eliminates the effects of fading but does notincrease the average amount of useful received signal-to-noise ratio.