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

326 Additional Techniques for Capacity and Flexibility Enhancement6.4.3 Equal Gain Transmission (EGT)EGT is a pre-coding scheme that requires knowledge about the phase of the channels H n(1)and H n(2) . The signals at the antennas are transmitted with a relative phase shift such thatthey superimpose constructively at the receiver antenna with α n = 0. Thus the pre-codingvector isc n = (1, e jα n) T , (6.27)where α n is the relative phase difference between H n (1) and H n(2) . The transmit power isequally split between both antennas, i.e.w n = √ 1 . (6.28)2The phase of the channels H n (1) and H n(2) has to be estimated at the receiver and therelative phase difference between both channels has to be fed back to the transmitter.EGT is a lower bound for SPC.6.4.4 Maximum Ratio Transmission (MRT)The optimum pre-coding scheme is MRT. The pre-coding coefficient of MRT isc n = (H n(1)∗ ,H n (2)∗ ) T . (6.29)Compared to the previous schemes, MRT allows for an unequal distribution of the transmitpower between both antennas. The power normalization factor results inw n =1√ . (6.30)∑2 (m)m=1 |H n | 2The full channel information about H n (1) and H n(2) has to be estimated at the receiver.Thus, MRT requires the most complex channel estimation with the highest overhead comparedto the previous schemes. Moreover, MRT requires full feedback of the amplitudeand phase of each channel, which exceeds the feedback required by the previous schemes.6.4.5 Performance AnalysisAn OFDM system with two transmit antennas and one receive antenna is investigated. Thetransmission bandwidth is 2 MHz and the carrier frequency is 2 GHz. The multi-carriermodulation is realized by OFDM occupying N c = 512 sub-carriers. An OFDM frameconsists of 24 OFDM symbols. The guard interval duration is 5 µs. Results are presentedfor a rate 1/2 and 2/3 coded transmission using convolutional codes with memory 6 as wellas uncoded transmission. QPSK is chosen for symbol mapping. In order to compare theperformance differences between pre-coding schemes without side effects, disturbancesdue to synchronization and feedback errors are omitted by assuming that these componentsare perfect. The channels from different transmit antennas to the receive antenna areassumed to be uncorrelated. The SNR given in the following results always refers toE t /N 0 ,whereE t is the total energy per bit at the transmitter and N 0 is the one-sidednoise power spectral density.