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

Spatial Pre-Coding for Multi-Carrier Transmission 32510with SPCoriginal|Hn|10.10 100 200 300 400 500Sub-carrier nFigure 6-28COST 207 typical urban channel with and without spatial phase codingExemplarily the effects of SPC on the channel transfer function for an OFDM systemwith 512 sub-carriers and two transmit antennas applying the COST 207 typical urban(TU) channel are shown in Figure 6-28. A snapshot of the absolute value of the superimposedchannel coefficient |H n | is plotted over the 512 sub-carriers. It has to be mentionedthat the channel |H n | without SPC (original) is normalized to E{|H n | 2 }=1. The thindashed line shows the original channel coefficients while the thick solid line shows |H n |after SPC. The threshold is chosen equal to 0.9. It can be observed that in cases wherethe original channel is in a deep fade, the channel after SPC often is even enhancing thetransmitted signal.6.4.2 Selection Diversity (SD)With SD the signal is transmitted over the antenna where the absolute value of theindividual channel is largest, i.e.{(1, 0) T if |H n (1) |≥|H n (2) |c n =(0, 1) T , (6.26)otherwiseand the power normalization factor w n is equal to 1. With SD the receiver has to estimateboth channels in order to determine which channel has a larger absolute value and hasto indicate this back to the transmitter via a feedback channel. As with SPC, 1 bit issufficient for the feedback. However, SD needs twice the overhead for channel estimationthan SPC since SD needs the estimation of |H n (1) | and |H n(2) | instead of |H n | only.